Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,5,Mod(687,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.687");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.d (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: | \(81.0420510577\) |
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: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 687.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.687 |
Dual form | 784.5.d.a.687.2 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 13.8564i | − 1.53960i | −0.638285 | − | 0.769800i | \(-0.720356\pi\) | ||||
0.638285 | − | 0.769800i | \(-0.279644\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −18.0000 | −0.720000 | −0.360000 | − | 0.932952i | \(-0.617223\pi\) | ||||
−0.360000 | + | 0.932952i | \(0.617223\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 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 | \(-0.676544\pi\) | ||||
−0.526627 | + | 0.850096i | \(0.676544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 249.415i | 1.10851i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 126.000 | 0.435986 | 0.217993 | − | 0.975950i | \(-0.430049\pi\) | ||||
0.217993 | + | 0.975950i | \(0.430049\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 401.836i | − 1.11312i | −0.830808 | − | 0.556559i | \(-0.812121\pi\) | ||||
0.830808 | − | 0.556559i | \(-0.187879\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 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 | \(-0.944646\pi\) | ||||
0.984917 | − | 0.173025i | \(-0.0553541\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1728.00 | −1.58678 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 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 | \(-0.515344\pi\) | ||||
−0.0481856 | + | 0.998838i | \(0.515344\pi\) | |||||||
\(42\) | 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 | \(0.290107\pi\) | ||||
−0.612642 | + | 0.790361i | \(0.709893\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 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 | \(-0.889458\pi\) | ||||
0.940303 | − | 0.340340i | \(-0.110542\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −626.000 | −0.168234 | −0.0841172 | − | 0.996456i | \(-0.526807\pi\) | ||||
−0.0841172 | + | 0.996456i | \(0.526807\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 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 | \(-0.284151\pi\) | ||||
0.627322 | + | 0.778760i | \(0.284151\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4170.78i | 0.741472i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 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 | \(-0.891299\pi\) | ||||
0.942255 | − | 0.334895i | \(-0.108701\pi\) | |||||||
\(84\) | 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 | \(-0.673790\pi\) | ||||
−0.519253 | + | 0.854621i | \(0.673790\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 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 | \(-0.472937\pi\) | ||||
0.0849187 | + | 0.996388i | \(0.472937\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13842.6i | 1.41236i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4590.00 | 0.449956 | 0.224978 | − | 0.974364i | \(-0.427769\pi\) | ||||
0.224978 | + | 0.974364i | \(0.427769\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 8951.24i | − 0.843740i | −0.906656 | − | 0.421870i | \(-0.861374\pi\) | ||||
0.906656 | − | 0.421870i | \(-0.138626\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 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 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 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 | \(0.207542\pi\) | ||||
−0.794864 | + | 0.606788i | \(0.792458\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 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 | \(-0.733579\pi\) | ||||
0.669705 | − | 0.742628i | \(-0.266421\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 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 | \(-0.703601\pi\) | ||||
−0.596900 | + | 0.802315i | \(0.703601\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 8230.71i | − 0.325569i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 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 | \(0.0879384\pi\) | ||||
−0.962080 | + | 0.272766i | \(0.912062\pi\) | |||||||
\(168\) | 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 | \(-0.389130\pi\) | ||||
0.341308 | + | 0.939952i | \(0.389130\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 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 | \(-0.303462\pi\) | ||||
0.578951 | + | 0.815363i | \(0.303462\pi\) | |||||||
\(182\) | 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 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | \(0.440999\pi\) | ||||
−0.184299 | + | 0.982870i | \(0.559001\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15168.0 | −0.375436 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 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 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 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 | \(0.0961814\pi\) | ||||
−0.954695 | + | 0.297586i | \(0.903819\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 33411.0 | 0.659970 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 8106.00i | − 0.157309i | −0.996902 | − | 0.0786547i | \(-0.974938\pi\) | ||||
0.996902 | − | 0.0786547i | \(-0.0250625\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26770.0 | −0.510478 | −0.255239 | − | 0.966878i | \(-0.582154\pi\) | ||||
−0.255239 | + | 0.966878i | \(0.582154\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 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 | \(-0.331619\pi\) | ||||
0.504657 | + | 0.863320i | \(0.331619\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 78441.1i | 1.32841i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 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 | \(-0.738863\pi\) | ||||
0.681939 | − | 0.731409i | \(-0.261137\pi\) | |||||||
\(252\) | 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 | \(-0.616064\pi\) | ||||
−0.356599 | + | 0.934258i | \(0.616064\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 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 | \(-0.598522\pi\) | ||||
−0.304598 | + | 0.952481i | \(0.598522\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 79203.2i | 1.07846i | 0.842158 | + | 0.539230i | \(0.181285\pi\) | ||||
−0.842158 | + | 0.539230i | \(0.818715\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 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 | \(-0.940087\pi\) | ||||
0.982338 | − | 0.187113i | \(-0.0599131\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 100224. | 1.23391 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 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 | \(-0.698446\pi\) | ||||
−0.583827 | + | 0.811878i | \(0.698446\pi\) | |||||||
\(294\) | 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 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 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 | \(0.282108\pi\) | ||||
−0.632308 | + | 0.774717i | \(0.717892\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −124032. | −1.29902 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 53624.3i | 0.554422i | 0.960809 | + | 0.277211i | \(0.0894102\pi\) | ||||
−0.960809 | + | 0.277211i | \(0.910590\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −145634. | −1.48653 | −0.743266 | − | 0.668996i | \(-0.766724\pi\) | ||||
−0.743266 | + | 0.668996i | \(0.766724\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 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 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 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 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 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 | \(-0.500818\pi\) | ||||
−0.00256977 | + | 0.999997i | \(0.500818\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 73993.2i | − 0.600589i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25218.0 | −0.202377 | −0.101189 | − | 0.994867i | \(-0.532265\pi\) | ||||
−0.101189 | + | 0.994867i | \(0.532265\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 139174.i | − 1.10433i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 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 | \(-0.983423\pi\) | ||||
0.998644 | − | 0.0520558i | \(-0.0165774\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17982.0 | 0.132064 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 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 | \(-0.851823\pi\) | ||||
0.893592 | − | 0.448879i | \(-0.148177\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 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 | \(-0.536581\pi\) | ||||
−0.114670 | + | 0.993404i | \(0.536581\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 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 | \(-0.774483\pi\) | ||||
−0.759351 | + | 0.650681i | \(0.774483\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 113983.i | − 0.674770i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 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 | \(-0.839407\pi\) | ||||
0.875408 | − | 0.483385i | \(-0.160593\pi\) | |||||||
\(420\) | 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 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 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 | \(-0.354131\pi\) | ||||
0.442389 | + | 0.896823i | \(0.354131\pi\) | |||||||
\(434\) | 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 | \(0.144800\pi\) | ||||
−0.898304 | + | 0.439373i | \(0.855200\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 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 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 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 | \(-0.409283\pi\) | ||||
0.281153 | + | 0.959663i | \(0.409283\pi\) | |||||||
\(462\) | 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 | \(-0.929065\pi\) | ||||
0.975272 | − | 0.221008i | \(-0.0709348\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 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 | \(-0.780169\pi\) | ||||
0.770851 | − | 0.637015i | \(-0.219831\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −94340.0 | −0.407761 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 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 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 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 | \(-0.744988\pi\) | ||||
0.695886 | − | 0.718153i | \(-0.255012\pi\) | |||||||
\(504\) | 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 | \(-0.333057\pi\) | ||||
0.500751 | + | 0.865592i | \(0.333057\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 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 | \(-0.510229\pi\) | ||||
−0.0321285 | + | 0.999484i | \(0.510229\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 6969.77i | − 0.0254809i | −0.999919 | − | 0.0127405i | \(-0.995944\pi\) | ||||
0.999919 | − | 0.0127405i | \(-0.00405553\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 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 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 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 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 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 | \(-0.948872\pi\) | ||||
0.987128 | − | 0.159933i | \(-0.0511277\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −339876. | −1.06469 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 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 | \(-0.585466\pi\) | ||||
−0.265285 | + | 0.964170i | \(0.585466\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 486886.i | − 1.45235i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 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 | \(0.0983880\pi\) | ||||
−0.952609 | + | 0.304197i | \(0.901612\pi\) | |||||||
\(588\) | 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 | \(-0.879661\pi\) | ||||
−0.929384 | + | 0.369114i | \(0.879661\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 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 | \(-0.534373\pi\) | ||||
−0.107777 | + | 0.994175i | \(0.534373\pi\) | |||||||
\(602\) | 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 | \(-0.933192\pi\) | ||||
0.978055 | − | 0.208345i | \(-0.0668077\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | \(0.111097\pi\) | ||||
−0.939708 | + | 0.341979i | \(0.888903\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 311040. | 0.806553 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 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 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 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 | \(0.238684\pi\) | ||||
−0.731792 | + | 0.681528i | \(0.761316\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −383616. | −0.922098 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 161871.i | 0.386687i | 0.981131 | + | 0.193343i | \(0.0619331\pi\) | ||||
−0.981131 | + | 0.193343i | \(0.938067\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −295488. | −0.701537 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 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 | \(-0.493968\pi\) | ||||
0.0189485 | + | 0.999820i | \(0.493968\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 310771.i | 0.706991i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 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 | \(-0.348769\pi\) | ||||
0.457433 | + | 0.889244i | \(0.348769\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 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 | \(0.00566738\pi\) | ||||
−0.999842 | + | 0.0178037i | \(0.994333\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 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 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 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 | \(0.0632264\pi\) | ||||
−0.980338 | + | 0.197328i | \(0.936774\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 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 | \(-0.956226\pi\) | ||||
0.990559 | − | 0.137088i | \(-0.0437744\pi\) | |||||||
\(728\) | 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 | \(-0.191502\pi\) | ||||
0.824419 | + | 0.565981i | \(0.191502\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 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 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 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 | \(-0.585439\pi\) | ||||
−0.265204 | + | 0.964192i | \(0.585439\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 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 | \(-0.470349\pi\) | ||||
0.0930176 | + | 0.995664i | \(0.470349\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 652720.i | 1.09804i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −685458. | −1.14715 | −0.573577 | − | 0.819152i | \(-0.694445\pi\) | ||||
−0.573577 | + | 0.819152i | \(0.694445\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 100099.i | 0.166658i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | \(0.0999754\pi\) | ||||
−0.951080 | + | 0.308944i | \(0.900025\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 798336. | 1.28242 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 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 | \(-0.677565\pi\) | ||||
−0.529352 | + | 0.848402i | \(0.677565\pi\) | |||||||
\(798\) | 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 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 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 | \(-0.703735\pi\) | ||||
0.597238 | − | 0.802064i | \(-0.296265\pi\) | |||||||
\(812\) | 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 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 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 | \(-0.601017\pi\) | ||||
−0.312055 | + | 0.950064i | \(0.601017\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 559827.i | − 0.810684i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 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 | \(-0.799358\pi\) | ||||
0.807830 | − | 0.589416i | \(-0.200642\pi\) | |||||||
\(840\) | 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 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 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 | \(-0.488732\pi\) | ||||
0.0353913 | + | 0.999374i | \(0.488732\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 802868.i | − 1.09828i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 574110. | 0.781688 | 0.390844 | − | 0.920457i | \(-0.372183\pi\) | ||||
0.390844 | + | 0.920457i | \(0.372183\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 173330.i | 0.234902i | 0.993079 | + | 0.117451i | \(0.0374723\pi\) | ||||
−0.993079 | + | 0.117451i | \(0.962528\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 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 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 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 | \(-0.350568\pi\) | ||||
0.452400 | + | 0.891815i | \(0.350568\pi\) | |||||||
\(882\) | 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 | \(0.0782322\pi\) | ||||
−0.969949 | + | 0.243307i | \(0.921768\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 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 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 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 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 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 | \(-0.390436\pi\) | ||||
0.337447 | + | 0.941344i | \(0.390436\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 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 | \(-0.668589\pi\) | ||||
−0.505222 | + | 0.862990i | \(0.668589\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.01796e6i | 2.28866i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 777294. | 0.877821 | 0.438911 | − | 0.898531i | \(-0.355364\pi\) | ||||
0.438911 | + | 0.898531i | \(0.355364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 121216.i | 0.136313i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 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 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 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 | \(0.216806\pi\) | ||||
−0.776870 | + | 0.629662i | \(0.783194\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 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 | \(-0.987961\pi\) | ||||
0.999285 | − | 0.0378141i | \(-0.0120395\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −829764. | −0.855228 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | \(-0.664033\pi\) | ||||
−0.492817 | + | 0.870133i | \(0.664033\pi\) | |||||||
\(998\) | 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 | 784.5.d.a.687.1 | 2 | ||
4.3 | odd | 2 | inner | 784.5.d.a.687.2 | 2 | ||
7.6 | odd | 2 | 16.5.c.a.15.2 | yes | 2 | ||
21.20 | even | 2 | 144.5.g.c.127.1 | 2 | |||
28.27 | even | 2 | 16.5.c.a.15.1 | ✓ | 2 | ||
35.13 | even | 4 | 400.5.h.b.399.1 | 4 | |||
35.27 | even | 4 | 400.5.h.b.399.3 | 4 | |||
35.34 | odd | 2 | 400.5.b.d.351.1 | 2 | |||
56.13 | odd | 2 | 64.5.c.c.63.1 | 2 | |||
56.27 | even | 2 | 64.5.c.c.63.2 | 2 | |||
84.83 | odd | 2 | 144.5.g.c.127.2 | 2 | |||
112.13 | odd | 4 | 256.5.d.f.127.1 | 4 | |||
112.27 | even | 4 | 256.5.d.f.127.2 | 4 | |||
112.69 | odd | 4 | 256.5.d.f.127.4 | 4 | |||
112.83 | even | 4 | 256.5.d.f.127.3 | 4 | |||
140.27 | odd | 4 | 400.5.h.b.399.2 | 4 | |||
140.83 | odd | 4 | 400.5.h.b.399.4 | 4 | |||
140.139 | even | 2 | 400.5.b.d.351.2 | 2 | |||
168.83 | odd | 2 | 576.5.g.h.127.2 | 2 | |||
168.125 | even | 2 | 576.5.g.h.127.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.5.c.a.15.1 | ✓ | 2 | 28.27 | even | 2 | ||
16.5.c.a.15.2 | yes | 2 | 7.6 | odd | 2 | ||
64.5.c.c.63.1 | 2 | 56.13 | odd | 2 | |||
64.5.c.c.63.2 | 2 | 56.27 | even | 2 | |||
144.5.g.c.127.1 | 2 | 21.20 | even | 2 | |||
144.5.g.c.127.2 | 2 | 84.83 | odd | 2 | |||
256.5.d.f.127.1 | 4 | 112.13 | odd | 4 | |||
256.5.d.f.127.2 | 4 | 112.27 | even | 4 | |||
256.5.d.f.127.3 | 4 | 112.83 | even | 4 | |||
256.5.d.f.127.4 | 4 | 112.69 | odd | 4 | |||
400.5.b.d.351.1 | 2 | 35.34 | odd | 2 | |||
400.5.b.d.351.2 | 2 | 140.139 | even | 2 | |||
400.5.h.b.399.1 | 4 | 35.13 | even | 4 | |||
400.5.h.b.399.2 | 4 | 140.27 | odd | 4 | |||
400.5.h.b.399.3 | 4 | 35.27 | even | 4 | |||
400.5.h.b.399.4 | 4 | 140.83 | odd | 4 | |||
576.5.g.h.127.1 | 2 | 168.125 | even | 2 | |||
576.5.g.h.127.2 | 2 | 168.83 | odd | 2 | |||
784.5.d.a.687.1 | 2 | 1.1 | even | 1 | trivial | ||
784.5.d.a.687.2 | 2 | 4.3 | odd | 2 | inner |