Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(289,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.289");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.f (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: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 39122x^{12} + 391243971x^{8} + 75462898750x^{4} + 18538406640625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{42}\cdot 5^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 289.7 | ||
Root | \(1.86808 - 3.34569i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.289 |
Dual form | 320.6.f.c.289.8 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −10.4275 | −0.668926 | −0.334463 | − | 0.942409i | \(-0.608555\pi\) | ||||
−0.334463 | + | 0.942409i | \(0.608555\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 17.9907 | − | 52.9276i | 0.321828 | − | 0.946798i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 86.7391i | − | 0.669067i | −0.942384 | − | 0.334534i | \(-0.891421\pi\) | ||
0.942384 | − | 0.334534i | \(-0.108579\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −134.267 | −0.552538 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 258.633i | 0.644470i | 0.946660 | + | 0.322235i | \(0.104434\pi\) | ||||
−0.946660 | + | 0.322235i | \(0.895566\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −465.165 | −0.763394 | −0.381697 | − | 0.924287i | \(-0.624660\pi\) | ||||
−0.381697 | + | 0.924287i | \(0.624660\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −187.599 | + | 551.904i | −0.215279 | + | 0.633338i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2029.54i | 1.70324i | 0.524158 | + | 0.851621i | \(0.324380\pi\) | ||||
−0.524158 | + | 0.851621i | \(0.675620\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1050.43i | 0.667551i | 0.942653 | + | 0.333776i | \(0.108323\pi\) | ||||
−0.942653 | + | 0.333776i | \(0.891677\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 904.474i | 0.447557i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3994.40i | − | 1.57446i | −0.616659 | − | 0.787230i | \(-0.711514\pi\) | ||
0.616659 | − | 0.787230i | \(-0.288486\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2477.67 | − | 1904.41i | −0.792853 | − | 0.609413i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3933.96 | 1.03853 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3242.70i | 0.715998i | 0.933722 | + | 0.357999i | \(0.116541\pi\) | ||||
−0.933722 | + | 0.357999i | \(0.883459\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 991.511 | 0.185308 | 0.0926538 | − | 0.995698i | \(-0.470465\pi\) | ||||
0.0926538 | + | 0.995698i | \(0.470465\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2696.91i | − | 0.431103i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4590.89 | − | 1560.50i | −0.633471 | − | 0.215325i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8820.20 | −1.05919 | −0.529596 | − | 0.848250i | \(-0.677656\pi\) | ||||
−0.529596 | + | 0.848250i | \(0.677656\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4850.52 | 0.510654 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5631.53 | 0.523199 | 0.261600 | − | 0.965177i | \(-0.415750\pi\) | ||||
0.261600 | + | 0.965177i | \(0.415750\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1775.46 | −0.146433 | −0.0732166 | − | 0.997316i | \(-0.523326\pi\) | ||||
−0.0732166 | + | 0.997316i | \(0.523326\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2415.56 | + | 7106.42i | −0.177822 | + | 0.523142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 17777.7i | − | 1.17390i | −0.809624 | − | 0.586949i | \(-0.800329\pi\) | ||
0.809624 | − | 0.586949i | \(-0.199671\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9283.33 | 0.552349 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 21163.1i | − | 1.13934i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 25903.3 | 1.26668 | 0.633338 | − | 0.773876i | \(-0.281684\pi\) | ||||
0.633338 | + | 0.773876i | \(0.281684\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13688.8 | + | 4653.00i | 0.610183 | + | 0.207409i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 10953.4i | − | 0.446542i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 18166.8i | 0.679437i | 0.940527 | + | 0.339718i | \(0.110332\pi\) | ||||
−0.940527 | + | 0.339718i | \(0.889668\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 35461.5i | 1.22020i | 0.792323 | + | 0.610102i | \(0.208872\pi\) | ||||
−0.792323 | + | 0.610102i | \(0.791128\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11646.2i | 0.369685i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8368.67 | + | 24620.1i | −0.245682 | + | 0.722780i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −42068.8 | −1.14492 | −0.572458 | − | 0.819934i | \(-0.694010\pi\) | ||||
−0.572458 | + | 0.819934i | \(0.694010\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 41651.7i | 1.05320i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 71392.3 | 1.68076 | 0.840380 | − | 0.541998i | \(-0.182332\pi\) | ||||
0.840380 | + | 0.541998i | \(0.182332\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3256.52i | − | 0.0715231i | −0.999360 | − | 0.0357615i | \(-0.988614\pi\) | ||
0.999360 | − | 0.0357615i | \(-0.0113857\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 25835.9 | + | 19858.3i | 0.530360 | + | 0.407652i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22433.6 | 0.431194 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 84229.0 | 1.51843 | 0.759214 | − | 0.650841i | \(-0.225584\pi\) | ||||
0.759214 | + | 0.650841i | \(0.225584\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8394.67 | −0.142164 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 79029.5 | 1.25920 | 0.629599 | − | 0.776920i | \(-0.283219\pi\) | ||||
0.629599 | + | 0.776920i | \(0.283219\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 107419. | + | 36513.0i | 1.61263 | + | 0.548151i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 33813.3i | − | 0.478950i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −65176.4 | −0.872199 | −0.436099 | − | 0.899899i | \(-0.643640\pi\) | ||||
−0.436099 | + | 0.899899i | \(0.643640\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 40348.0i | 0.510762i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10339.0 | −0.123957 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 55596.9 | + | 18898.1i | 0.632036 | + | 0.214837i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 33977.4i | 0.366658i | 0.983052 | + | 0.183329i | \(0.0586873\pi\) | ||||
−0.983052 | + | 0.183329i | \(0.941313\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 34725.8i | − | 0.356094i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 107891.i | 1.05240i | 0.850360 | + | 0.526202i | \(0.176384\pi\) | ||||
−0.850360 | + | 0.526202i | \(0.823616\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 23048.1i | − | 0.214063i | −0.994256 | − | 0.107032i | \(-0.965865\pi\) | ||
0.994256 | − | 0.107032i | \(-0.0341346\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 47871.7 | + | 16272.2i | 0.423746 | + | 0.144036i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 72095.2 | 0.608761 | 0.304381 | − | 0.952550i | \(-0.401551\pi\) | ||||
0.304381 | + | 0.952550i | \(0.401551\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 177590.i | 1.43170i | 0.698254 | + | 0.715850i | \(0.253960\pi\) | ||||
−0.698254 | + | 0.715850i | \(0.746040\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 91972.9 | 0.708521 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 147312.i | − | 1.08528i | −0.839966 | − | 0.542639i | \(-0.817425\pi\) | ||
0.839966 | − | 0.542639i | \(-0.182575\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −211414. | − | 71862.2i | −1.49070 | − | 0.506706i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 62456.2 | 0.421804 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 176041. | 1.13958 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 94159.8 | 0.584658 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −58723.0 | −0.349982 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −145371. | + | 96875.2i | −0.832153 | + | 0.554546i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 139884.i | − | 0.769588i | −0.923003 | − | 0.384794i | \(-0.874273\pi\) | ||
0.923003 | − | 0.384794i | \(-0.125727\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 18513.7 | 0.0979531 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 41603.5i | 0.211813i | 0.994376 | + | 0.105906i | \(0.0337743\pi\) | ||||
−0.994376 | + | 0.105906i | \(0.966226\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 91113.6 | 0.446636 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 70774.8 | − | 208215.i | 0.334229 | − | 0.983281i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 196186.i | 0.893029i | 0.894776 | + | 0.446515i | \(0.147335\pi\) | ||||
−0.894776 | + | 0.446515i | \(0.852665\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 79188.4i | − | 0.347636i | −0.984778 | − | 0.173818i | \(-0.944390\pi\) | ||
0.984778 | − | 0.173818i | \(-0.0556104\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 185377.i | 0.785251i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 120307.i | − | 0.491985i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 171628. | + | 58338.5i | 0.677905 | + | 0.230428i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −96802.2 | −0.369481 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3422.66i | 0.0126299i | 0.999980 | + | 0.00631493i | \(0.00201012\pi\) | ||||
−0.999980 | + | 0.00631493i | \(0.997990\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 166179. | 0.593107 | 0.296553 | − | 0.955016i | \(-0.404163\pi\) | ||||
0.296553 | + | 0.955016i | \(0.404163\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 272500.i | − | 0.941105i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17838.0 | − | 52478.3i | 0.0596372 | − | 0.175449i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −170561. | −0.552244 | −0.276122 | − | 0.961123i | \(-0.589049\pi\) | ||||
−0.276122 | + | 0.961123i | \(0.589049\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −270107. | −0.847312 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −346470. | −1.05342 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 604504. | 1.78209 | 0.891046 | − | 0.453913i | \(-0.149972\pi\) | ||||
0.891046 | + | 0.453913i | \(0.149972\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −142741. | − | 48519.3i | −0.408167 | − | 0.138741i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 395572.i | 1.09758i | 0.835962 | + | 0.548788i | \(0.184911\pi\) | ||||
−0.835962 | + | 0.548788i | \(0.815089\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −154914. | −0.417229 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 141038.i | − | 0.368847i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10014.5 | −0.0254397 | −0.0127199 | − | 0.999919i | \(-0.504049\pi\) | ||||
−0.0127199 | + | 0.999919i | \(0.504049\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −165187. | + | 214911.i | −0.407738 | + | 0.530472i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 189435.i | − | 0.454493i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 830246.i | 1.93675i | 0.249496 | + | 0.968376i | \(0.419735\pi\) | ||||
−0.249496 | + | 0.968376i | \(0.580265\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 324055.i | − | 0.735228i | −0.929979 | − | 0.367614i | \(-0.880175\pi\) | ||
0.929979 | − | 0.367614i | \(-0.119825\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 369776.i | − | 0.816227i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −158682. | + | 466832.i | −0.340877 | + | 1.00284i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −524908. | −1.09769 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 341228.i | − | 0.694848i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −658765. | −1.30661 | −0.653307 | − | 0.757093i | \(-0.726619\pi\) | ||||
−0.653307 | + | 0.757093i | \(0.726619\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 107546.i | 0.207827i | 0.994586 | + | 0.103914i | \(0.0331366\pi\) | ||||
−0.994586 | + | 0.103914i | \(0.966863\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 87264.5 | − | 256727.i | 0.164343 | − | 0.483487i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 834075. | 1.53123 | 0.765613 | − | 0.643301i | \(-0.222436\pi\) | ||||
0.765613 | + | 0.643301i | \(0.222436\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 168087. | 0.300886 | 0.150443 | − | 0.988619i | \(-0.451930\pi\) | ||||
0.150443 | + | 0.988619i | \(0.451930\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 438674. | 0.765864 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 281269. | 0.479050 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 101315. | − | 298064.i | 0.168380 | − | 0.495364i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 536314.i | 0.869949i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −271677. | −0.430217 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 344841.i | − | 0.533228i | −0.963803 | − | 0.266614i | \(-0.914095\pi\) | ||
0.963803 | − | 0.266614i | \(-0.0859049\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −744445. | −1.12430 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −31941.8 | + | 93970.9i | −0.0471264 | + | 0.138643i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 86002.8i | − | 0.123983i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 33957.4i | 0.0478437i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 944073.i | − | 1.30024i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.19367e6i | 1.60739i | 0.595040 | + | 0.803696i | \(0.297136\pi\) | ||||
−0.595040 | + | 0.803696i | \(0.702864\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 332668. | + | 255699.i | 0.438081 | + | 0.336723i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 308573. | 0.397460 | 0.198730 | − | 0.980054i | \(-0.436318\pi\) | ||||
0.198730 | + | 0.980054i | \(0.436318\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 659870.i | − | 0.831514i | −0.909476 | − | 0.415757i | \(-0.863517\pi\) | ||
0.909476 | − | 0.415757i | \(-0.136483\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −233927. | −0.288437 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 724262.i | − | 0.873988i | −0.899464 | − | 0.436994i | \(-0.856043\pi\) | ||
0.899464 | − | 0.436994i | \(-0.143957\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −940930. | − | 319834.i | −1.11144 | − | 0.377793i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −878300. | −1.01572 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.56003e6 | −1.76661 | −0.883303 | − | 0.468803i | \(-0.844685\pi\) | ||||
−0.883303 | + | 0.468803i | \(0.844685\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.12357e6 | 1.24612 | 0.623058 | − | 0.782176i | \(-0.285890\pi\) | ||||
0.623058 | + | 0.782176i | \(0.285890\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −868416. | −0.943436 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 167014. | − | 491345.i | 0.177762 | − | 0.522963i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 488625.i | − | 0.509605i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −824083. | −0.842311 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 525339.i | − | 0.526327i | −0.964751 | − | 0.263163i | \(-0.915234\pi\) | ||
0.964751 | − | 0.263163i | \(-0.0847659\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.03308e6 | 1.01469 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.12011e6 | − | 380740.i | −1.07873 | − | 0.366673i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 788671.i | 0.744840i | 0.928064 | + | 0.372420i | \(0.121472\pi\) | ||||
−0.928064 | + | 0.372420i | \(0.878528\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 765056.i | 0.708670i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 435386.i | − | 0.395616i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 776592.i | 0.692315i | 0.938176 | + | 0.346157i | \(0.112514\pi\) | ||||
−0.938176 | + | 0.346157i | \(0.887486\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 466019. | − | 1.37100e6i | 0.407652 | − | 1.19929i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 679629. | 0.583436 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.08192e6i | − | 0.911620i | −0.890077 | − | 0.455810i | \(-0.849350\pi\) | ||
0.890077 | − | 0.455810i | \(-0.150650\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.47594e6 | −1.22081 | −0.610403 | − | 0.792091i | \(-0.708992\pi\) | ||||
−0.610403 | + | 0.792091i | \(0.708992\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 420730.i | − | 0.341662i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 492545. | − | 640807.i | 0.392748 | − | 0.510970i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.51985e6 | −1.19015 | −0.595076 | − | 0.803670i | \(-0.702878\pi\) | ||||
−0.595076 | + | 0.803670i | \(0.702878\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −133127. | −0.102389 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26579.0 | 0.0200804 | 0.0100402 | − | 0.999950i | \(-0.496804\pi\) | ||||
0.0100402 | + | 0.999950i | \(0.496804\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.44903e6 | 1.07551 | 0.537753 | − | 0.843102i | \(-0.319273\pi\) | ||||
0.537753 | + | 0.843102i | \(0.319273\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −579739. | − | 197060.i | −0.422786 | − | 0.143710i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 488474.i | − | 0.350055i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.69919e6 | −1.90103 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 354300.i | − | 0.245267i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.00717e6 | −1.36589 | −0.682944 | − | 0.730470i | \(-0.739301\pi\) | ||||
−0.682944 | + | 0.730470i | \(0.739301\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 961527. | + | 326835.i | 0.643290 | + | 0.218662i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.01745e6i | 0.669304i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.85805e6i | 1.20193i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 154002.i | 0.0979737i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 1.12504e6i | − | 0.703981i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.87689e6 | + | 637979.i | 1.15529 | + | 0.392696i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −115077. | −0.0696854 | −0.0348427 | − | 0.999393i | \(-0.511093\pi\) | ||||
−0.0348427 | + | 0.999393i | \(0.511093\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 240335.i | 0.143192i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.24273e6 | 0.728580 | 0.364290 | − | 0.931286i | \(-0.381312\pi\) | ||||
0.364290 | + | 0.931286i | \(0.381312\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.22445e6i | 1.28340i | 0.766956 | + | 0.641700i | \(0.221770\pi\) | ||||
−0.766956 | + | 0.641700i | \(0.778230\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 616404. | + | 209523.i | 0.350017 | + | 0.118975i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 745432. | 0.416639 | 0.208319 | − | 0.978061i | \(-0.433201\pi\) | ||||
0.208319 | + | 0.978061i | \(0.433201\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −838670. | −0.461439 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −751775. | −0.407216 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.13190e6 | −1.13700 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.15252e6 | + | 885867.i | 0.605260 | + | 0.465222i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 1.85182e6i | − | 0.957701i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.54202e6 | −0.785416 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 547701.i | 0.274773i | 0.990518 | + | 0.137386i | \(0.0438702\pi\) | ||||
−0.990518 | + | 0.137386i | \(0.956130\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.18426e6 | 0.585243 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −756849. | + | 2.22660e6i | −0.368466 | + | 1.08400i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.59535e6i | − | 1.72451i | −0.506472 | − | 0.862257i | \(-0.669051\pi\) | ||
0.506472 | − | 0.862257i | \(-0.330949\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.53610e6i | 0.725972i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 256438.i | 0.119425i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.26305e6i | − | 1.03863i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.20452e6 | + | 749345.i | 0.997166 | + | 0.338949i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.14196e6 | −0.509130 | −0.254565 | − | 0.967056i | \(-0.581932\pi\) | ||||
−0.254565 | + | 0.967056i | \(0.581932\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.98347e6i | 0.871690i | 0.900022 | + | 0.435845i | \(0.143550\pi\) | ||||
−0.900022 | + | 0.435845i | \(0.856450\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.82994e6 | −0.792810 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.33021e6i | 0.568177i | 0.958798 | + | 0.284088i | \(0.0916909\pi\) | ||||
−0.958798 | + | 0.284088i | \(0.908309\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.28440e6 | − | 3.77862e6i | 0.540916 | − | 1.59134i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.83567e6 | −0.762297 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.28909e6 | 1.75642 | 0.878212 | − | 0.478272i | \(-0.158737\pi\) | ||||
0.878212 | + | 0.478272i | \(0.158737\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.37269e6 | 0.554376 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −981854. | −0.391093 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −172360. | − | 58587.2i | −0.0677179 | − | 0.0230181i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.61572e6i | 1.40130i | 0.713507 | + | 0.700648i | \(0.247106\pi\) | ||||
−0.713507 | + | 0.700648i | \(0.752894\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −756127. | −0.289087 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 2.24683e6i | − | 0.847491i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.58778e6 | 0.963064 | 0.481532 | − | 0.876428i | \(-0.340080\pi\) | ||||
0.481532 | + | 0.876428i | \(0.340080\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.51586e6 | − | 1.01017e6i | 0.556649 | − | 0.370950i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.50839e6i | − | 0.546588i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.70716e6i | 1.32570i | 0.748754 | + | 0.662848i | \(0.230652\pi\) | ||||
−0.748754 | + | 0.662848i | \(0.769348\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.45864e6i | 0.514797i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.49277e6i | 0.519990i | 0.965610 | + | 0.259995i | \(0.0837209\pi\) | ||||
−0.965610 | + | 0.259995i | \(0.916279\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 403597. | − | 1.18736e6i | 0.138770 | − | 0.408253i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 238385. | 0.0809099 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.73759e6i | 0.582200i | 0.956693 | + | 0.291100i | \(0.0940213\pi\) | ||||
−0.956693 | + | 0.291100i | \(0.905979\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.10681e6 | 2.68169 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 433822.i | − | 0.141687i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.51534e6 | − | 4.45804e6i | 0.488673 | − | 1.43764i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.65675e6 | 1.48288 | 0.741441 | − | 0.671018i | \(-0.234143\pi\) | ||||
0.741441 | + | 0.671018i | \(0.234143\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −950090. | −0.298767 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.42492e6 | 1.06363 | 0.531814 | − | 0.846861i | \(-0.321511\pi\) | ||||
0.531814 | + | 0.846861i | \(0.321511\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −461217. | −0.141463 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −151026. | + | 444310.i | −0.0457525 | + | 0.134601i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.28120e6i | − | 0.682617i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.66454e6 | −1.37880 | −0.689399 | − | 0.724382i | \(-0.742125\pi\) | ||||
−0.689399 | + | 0.724382i | \(0.742125\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 2.04573e6i | − | 0.597371i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.57577e6 | 0.454589 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.42180e6 | − | 4.18285e6i | 0.405246 | − | 1.19221i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 825740.i | 0.232543i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.50348e6i | 1.25318i | 0.779349 | + | 0.626590i | \(0.215550\pi\) | ||||
−0.779349 | + | 0.626590i | \(0.784450\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.44553e6i | 1.49739i | 0.662915 | + | 0.748694i | \(0.269319\pi\) | ||||
−0.662915 | + | 0.748694i | \(0.730681\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.38695e6i | 0.648623i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.86509e6 | − | 5.02853e6i | 1.03798 | − | 1.35042i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.07590e6 | 0.816399 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.25451e6i | 0.329101i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.34161e6 | −0.347884 | −0.173942 | − | 0.984756i | \(-0.555650\pi\) | ||||
−0.173942 | + | 0.984756i | \(0.555650\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.17119e6i | 0.812834i | 0.913688 | + | 0.406417i | \(0.133222\pi\) | ||||
−0.913688 | + | 0.406417i | \(0.866778\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.78966e6 | − | 608327.i | −0.453469 | − | 0.154139i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.19585e6 | 1.05103 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.68194e6 | 1.90243 | 0.951217 | − | 0.308524i | \(-0.0998350\pi\) | ||||
0.951217 | + | 0.308524i | \(0.0998350\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.24644e6 | −0.305194 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.10003e6 | −1.23471 | −0.617353 | − | 0.786686i | \(-0.711795\pi\) | ||||
−0.617353 | + | 0.786686i | \(0.711795\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.17257e6 | + | 3.44963e6i | −0.280698 | + | 0.825796i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 35689.9i | − | 0.00844844i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.82882e6 | −1.36447 | −0.682237 | − | 0.731131i | \(-0.738993\pi\) | ||||
−0.682237 | + | 0.731131i | \(0.738993\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.45650e6i | 0.337186i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.73283e6 | −0.396745 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.13552e6 | + | 725890.i | 0.483588 | + | 0.164378i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.68037e6i | 1.94423i | 0.234505 | + | 0.972115i | \(0.424653\pi\) | ||||
−0.234505 | + | 0.972115i | \(0.575347\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.98414e6i | 1.76887i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 591360.i | 0.129598i | 0.997898 | + | 0.0647992i | \(0.0206407\pi\) | ||||
−0.997898 | + | 0.0647992i | \(0.979359\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.01246e6i | − | 0.219496i | −0.993959 | − | 0.109748i | \(-0.964996\pi\) | ||
0.993959 | − | 0.109748i | \(-0.0350044\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −186006. | + | 547219.i | −0.0398929 | + | 0.117362i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.51182e6 | 0.532962 | 0.266481 | − | 0.963840i | \(-0.414139\pi\) | ||||
0.266481 | + | 0.963840i | \(0.414139\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.64901e6i | 0.766025i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.77853e6 | 0.369411 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 459193.i | − | 0.0943719i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00046e6 | − | 2.60262e6i | 0.406814 | − | 0.529270i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.47795e6 | −0.699886 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.99715e6 | −0.995139 | −0.497569 | − | 0.867424i | \(-0.665774\pi\) | ||||
−0.497569 | + | 0.867424i | \(0.665774\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.10285e6 | 0.808580 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.61283e6 | 0.704660 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.79834e6 | + | 611279.i | 0.347151 | + | 0.118001i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 173192.i | 0.0330907i | 0.999863 | + | 0.0165454i | \(0.00526679\pi\) | ||||
−0.999863 | + | 0.0165454i | \(0.994733\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.30348e6 | −1.19209 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 9.01553e6i | − | 1.68767i | −0.536603 | − | 0.843835i | \(-0.680293\pi\) | ||
0.536603 | − | 0.843835i | \(-0.319707\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.58120e6 | −1.21952 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.83796e6 | − | 624743.i | −0.337149 | − | 0.114601i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 6.19250e6i | − | 1.12454i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.77675e6i | 1.21834i | 0.793038 | + | 0.609172i | \(0.208498\pi\) | ||||
−0.793038 | + | 0.609172i | \(0.791502\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 4.12484e6i | − | 0.734197i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.01435e7i | − | 1.78758i | −0.448482 | − | 0.893792i | \(-0.648035\pi\) | ||
0.448482 | − | 0.893792i | \(-0.351965\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.71042e6 | + | 1.94104e6i | 0.996414 | + | 0.338693i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.61537e6 | 0.279096 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 530805.i | − | 0.0908114i | −0.998969 | − | 0.0454057i | \(-0.985542\pi\) | ||
0.998969 | − | 0.0454057i | \(-0.0144580\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −282467. | −0.0478537 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.13236e6i | 0.693274i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.21988e6 | − | 414652.i | −0.202675 | − | 0.0688916i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.59790e6 | 0.756542 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 104426. | 0.0170173 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.22572e6 | 0.682034 | 0.341017 | − | 0.940057i | \(-0.389229\pi\) | ||||
0.341017 | + | 0.940057i | \(0.389229\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.69056e6 | −1.06957 | −0.534784 | − | 0.844989i | \(-0.679607\pi\) | ||||
−0.534784 | + | 0.844989i | \(0.679607\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.72249e6 | − | 2.24099e6i | 0.272747 | − | 0.354847i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.01232e6i | 0.315624i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.51887e6 | −1.47892 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 2.43920e6i | − | 0.375415i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.61959e6 | −0.399407 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.29705e6 | − | 3.81583e6i | 0.195917 | − | 0.576374i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 8.65741e6i | − | 1.29554i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.40098e6i | 0.355973i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.30697e6i | 0.779567i | 0.920906 | + | 0.389784i | \(0.127450\pi\) | ||||
−0.920906 | + | 0.389784i | \(0.872550\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.37909e6i | 0.491813i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.39941e6 | + | 3.19497e6i | 1.35553 | + | 0.460761i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.16772e6 | −1.02427 | −0.512133 | − | 0.858906i | \(-0.671145\pi\) | ||||
−0.512133 | + | 0.858906i | \(0.671145\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 4.76130e6i | − | 0.674209i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.40624e6 | −0.477965 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 7.30595e6i | − | 1.01593i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.65466e6 | − | 4.86791e6i | 0.228022 | − | 0.670826i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.38525e6 | −1.28176 | −0.640881 | − | 0.767640i | \(-0.721431\pi\) | ||||
−0.640881 | + | 0.767640i | \(0.721431\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 825882. | 0.111786 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.47349e6 | 0.734273 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.01789e7 | 1.35342 | 0.676708 | − | 0.736252i | \(-0.263406\pi\) | ||||
0.676708 | + | 0.736252i | \(0.263406\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.79686e6 | − | 2.65025e6i | −1.02754 | − | 0.349273i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 728146.i | 0.0951175i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.24155e6 | −1.06716 | −0.533578 | − | 0.845751i | \(-0.679153\pi\) | ||||
−0.533578 | + | 0.845751i | \(0.679153\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 4.37997e6i | − | 0.562187i | −0.959680 | − | 0.281094i | \(-0.909303\pi\) | ||
0.959680 | − | 0.281094i | \(-0.0906972\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.86930e6 | 0.874029 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.60699e6 | + | 9.89678e6i | −0.959496 | + | 1.24832i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 3.21889e6i | − | 0.402501i | −0.979540 | − | 0.201250i | \(-0.935499\pi\) | ||
0.979540 | − | 0.201250i | \(-0.0645005\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 1.12144e6i | − | 0.139021i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 6.85495e6i | − | 0.842488i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.69945e6i | 0.816334i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.12363e6 | − | 3.30566e6i | 0.135748 | − | 0.399363i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.75640e6 | −1.16868 | −0.584338 | − | 0.811510i | \(-0.698646\pi\) | ||||
−0.584338 | + | 0.811510i | \(0.698646\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.04152e6i | 0.123702i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.69734e6 | −1.02428 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 299475.i | 0.0349723i | 0.999847 | + | 0.0174861i | \(0.00556630\pi\) | ||||
−0.999847 | + | 0.0174861i | \(0.994434\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.16710e6 | − | 9.31742e6i | 0.366750 | − | 1.07895i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.75274e6 | −0.201271 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.03103e7 | −1.17410 | −0.587051 | − | 0.809550i | \(-0.699711\pi\) | ||||
−0.587051 | + | 0.809550i | \(0.699711\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.99550e6 | 0.564148 | 0.282074 | − | 0.959393i | \(-0.408978\pi\) | ||||
0.282074 | + | 0.959393i | \(0.408978\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.64844e6 | 0.632609 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.69400e6 | − | 4.98365e6i | 0.188159 | − | 0.553553i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 9.01015e6i | − | 0.992568i | −0.868160 | − | 0.496284i | \(-0.834698\pi\) | ||
0.868160 | − | 0.496284i | \(-0.165302\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.93294e6 | −0.320449 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.26956e6i | 0.896147i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.84050e7 | 1.97827 | 0.989133 | − | 0.147022i | \(-0.0469687\pi\) | ||||
0.989133 | + | 0.147022i | \(0.0469687\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.05647e6 | + | 3.10807e6i | −0.112634 | + | 0.331362i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.78493e7i | 1.88759i | 0.330534 | + | 0.943794i | \(0.392771\pi\) | ||||
−0.330534 | + | 0.943794i | \(0.607229\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.63628e7i | 1.71645i | 0.513271 | + | 0.858226i | \(0.328433\pi\) | ||||
−0.513271 | + | 0.858226i | \(0.671567\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 1.57138e7i | − | 1.63513i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.65334e6i | 0.583559i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.51204e6 | + | 9.43701e6i | 0.257233 | + | 0.966349i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.83292e6 | 0.287783 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.79010e7i | − | 1.80406i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 102581. | 0.0102564 | 0.00512819 | − | 0.999987i | \(-0.498368\pi\) | ||||
0.00512819 | + | 0.999987i | \(0.498368\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.59584e6i | 0.356690i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.40372e6 | − | 2.51661e6i | −0.728644 | − | 0.247675i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.31828e6 | −0.421660 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.58561e6 | −0.928683 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.56255e6 | −0.726981 | −0.363490 | − | 0.931598i | \(-0.618415\pi\) | ||||
−0.363490 | + | 0.931598i | \(0.618415\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.63176e6 | −0.823326 | −0.411663 | − | 0.911336i | \(-0.635052\pi\) | ||||
−0.411663 | + | 0.911336i | \(0.635052\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 333074. | − | 979884.i | 0.0315241 | − | 0.0927418i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.19255e7i | 1.11999i | 0.828495 | + | 0.559996i | \(0.189197\pi\) | ||||
−0.828495 | + | 0.559996i | \(0.810803\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.69855e6 | −0.437877 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 896796.i | 0.0829357i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.84123e7 | −1.68976 | −0.844881 | − | 0.534954i | \(-0.820329\pi\) | ||||
−0.844881 | + | 0.534954i | \(0.820329\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.20197e6 | + | 748478.i | 0.200544 | + | 0.0681672i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 437242.i | 0.0395192i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.96887e6i | 0.894196i | 0.894485 | + | 0.447098i | \(0.147542\pi\) | ||||
−0.894485 | + | 0.447098i | \(0.852458\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.71610e6i | − | 0.152771i | −0.997078 | − | 0.0763853i | \(-0.975662\pi\) | ||
0.997078 | − | 0.0763853i | \(-0.0243379\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.84435e6i | 0.869768i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.63920e6 | − | 4.82243e6i | 0.143740 | − | 0.422875i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.29526e7 | 1.12731 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 1.24470e7i | − | 1.07523i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.17153e6 | −0.786385 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 2.09946e7i | − | 1.78678i | −0.449286 | − | 0.893388i | \(-0.648321\pi\) | ||
0.449286 | − | 0.893388i | \(-0.351679\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.74704e6 | − | 7.49189e6i | −0.823404 | − | 0.632895i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.74843e6 | −0.565889 | −0.282944 | − | 0.959136i | \(-0.591311\pi\) | ||||
−0.282944 | + | 0.959136i | \(0.591311\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.94717e6 | 0.245319 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.21766e6 | −0.265872 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.05079e7 | 1.68217 | 0.841085 | − | 0.540902i | \(-0.181917\pi\) | ||||
0.841085 | + | 0.540902i | \(0.181917\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.03836e7 | + | 3.52952e6i | 0.845518 | + | 0.287402i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.88081e6i | 0.556222i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.20493e7 | −0.966972 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 7.55462e6i | − | 0.601891i | −0.953641 | − | 0.300945i | \(-0.902698\pi\) | ||
0.953641 | − | 0.300945i | \(-0.0973022\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.01209e6 | −0.238251 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.19126e6 | − | 1.42466e6i | −0.329141 | − | 0.111879i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.14294e7i | 0.891135i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.55226e6i | 0.584634i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 4.32288e6i | − | 0.332260i | −0.986104 | − | 0.166130i | \(-0.946873\pi\) | ||
0.986104 | − | 0.166130i | \(-0.0531272\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 9.26504e6i | − | 0.707064i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.81157e6 | + | 3.33507e6i | 0.743474 | + | 0.252716i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.35838e6 | 0.704129 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.01901e7i | 1.50843i | 0.656630 | + | 0.754213i | \(0.271981\pi\) | ||||
−0.656630 | + | 0.754213i | \(0.728019\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.13091e7 | −0.838988 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 3.96049e6i | − | 0.291760i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.36758e6 | − | 2.16442e6i | −0.465810 | − | 0.158335i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.62673e7 | 1.18173 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.05198e6 | −0.364451 | −0.182226 | − | 0.983257i | \(-0.558330\pi\) | ||||
−0.182226 | + | 0.983257i | \(0.558330\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.99917e6 | −0.143223 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.17161e7 | −0.833560 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.17544e6 | − | 8.03433e6i | 0.436338 | − | 0.567681i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.58378e7i | − | 1.11137i | −0.831393 | − | 0.555685i | \(-0.812456\pi\) | ||
0.831393 | − | 0.555685i | \(-0.187544\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.10953e7 | 0.773253 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 3.60338e6i | − | 0.249411i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.41498e6 | −0.578487 | −0.289243 | − | 0.957256i | \(-0.593404\pi\) | ||||
−0.289243 | + | 0.957256i | \(0.593404\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.74154e6 | + | 5.12351e6i | −0.118909 | + | 0.349824i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.08804e7i | − | 0.737864i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 5.98826e6i | − | 0.403357i | −0.979452 | − | 0.201679i | \(-0.935360\pi\) | ||
0.979452 | − | 0.201679i | \(-0.0646397\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.09515e6i | 0.340888i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.00035e7i | − | 0.664783i | −0.943141 | − | 0.332392i | \(-0.892144\pi\) | ||
0.943141 | − | 0.332392i | \(-0.107856\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 181153. | + | 61576.2i | 0.0119579 | + | 0.00406464i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.06110e7 | −0.695755 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 6.25347e6i | − | 0.407302i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.35108e7 | 1.52114 | 0.760568 | − | 0.649259i | \(-0.224921\pi\) | ||||
0.760568 | + | 0.649259i | \(0.224921\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.47799e6i | 0.352074i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.98968e6 | − | 8.79544e6i | 0.190878 | − | 0.561552i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.80703e7 | −1.14611 | −0.573055 | − | 0.819517i | \(-0.694242\pi\) | ||||
−0.573055 | + | 0.819517i | \(0.694242\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.07725e7 | −0.678754 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.53987e6 | 0.409362 | 0.204681 | − | 0.978829i | \(-0.434384\pi\) | ||||
0.204681 | + | 0.978829i | \(0.434384\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.54040e7 | 0.957903 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.44228e7 | − | 4.90248e6i | −0.891037 | − | 0.302874i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 8.45058e6i | − | 0.518678i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.15910e7 | 0.706814 | 0.353407 | − | 0.935470i | \(-0.385023\pi\) | ||||
0.353407 | + | 0.935470i | \(0.385023\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 8.22389e6i | − | 0.498243i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.50928e7 | −0.908490 | −0.454245 | − | 0.890877i | \(-0.650091\pi\) | ||||
−0.454245 | + | 0.890877i | \(0.650091\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.45663e6 | − | 1.88825e6i | −0.146922 | − | 0.112929i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 7.97765e6i | − | 0.474048i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.91555e6i | 0.349262i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.84644e7i | 1.08320i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.27566e7i | 0.743587i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.06852e6 | + | 9.02740e6i | −0.177728 | + | 0.522864i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.71625e7 | −1.56327 | −0.781633 | − | 0.623739i | \(-0.785613\pi\) | ||||
−0.781633 | + | 0.623739i | \(0.785613\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 8.09794e6i | − | 0.463107i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.27777e7 | −0.726124 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1.64955e7i | − | 0.931497i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.85943e6 | + | 1.42961e7i | −0.272689 | + | 0.802234i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.46344e7 | 0.816073 | 0.408036 | − | 0.912966i | \(-0.366214\pi\) | ||||
0.408036 | + | 0.912966i | \(0.366214\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.60806e7 | 1.99943 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.75102e6 | 0.481923 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 842244. | 0.0460945 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.23326e6 | + | 1.83379e7i | −0.339020 | + | 0.997376i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.12817e7i | 0.609806i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.40972e7 | −0.757290 | −0.378645 | − | 0.925542i | \(-0.623610\pi\) | ||||
−0.378645 | + | 0.925542i | \(0.623610\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.16831e7i | − | 0.623743i | −0.950124 | − | 0.311872i | \(-0.899044\pi\) | ||
0.950124 | − | 0.311872i | \(-0.100956\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.53904e7 | 0.816629 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.08755e7 | − | 3.19950e7i | 0.573527 | − | 1.68728i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.86500e6i | − | 0.0977517i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 5.41739e6i | − | 0.282215i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 8.26838e6i | − | 0.428117i | −0.976821 | − | 0.214058i | \(-0.931332\pi\) | ||
0.976821 | − | 0.214058i | \(-0.0686683\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.90582e6i | − | 0.0980802i | −0.998797 | − | 0.0490401i | \(-0.984384\pi\) | ||
0.998797 | − | 0.0490401i | \(-0.0156162\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.13603e6 | + | 6.68203e6i | −0.262720 | + | 0.341801i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.12708e7 | −1.08148 | −0.540741 | − | 0.841189i | \(-0.681856\pi\) | ||||
−0.540741 | + | 0.841189i | \(0.681856\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.62216e7i | 1.83055i | 0.402833 | + | 0.915274i | \(0.368026\pi\) | ||||
−0.402833 | + | 0.915274i | \(0.631974\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.58483e7 | 0.796123 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.88409e7i | 0.940784i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.09367e7 | + | 7.11663e6i | 1.03918 | + | 0.353231i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.90056e6 | 0.192448 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.16167e6 | −0.302199 | −0.151100 | − | 0.988519i | \(-0.548281\pi\) | ||||
−0.151100 | + | 0.988519i | \(0.548281\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.99605e6 | 0.487347 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −277153. | −0.0134323 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.78702e6 | + | 8.19925e6i | −0.134276 | + | 0.395032i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 8.16733e6i | − | 0.391176i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.51099e7 | −0.719434 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.52314e7i | 1.66765i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.45727e7 | 1.15633 | 0.578164 | − | 0.815921i | \(-0.303770\pi\) | ||||
0.578164 | + | 0.815921i | \(0.303770\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.46482e6 | − | 2.53738e6i | −0.349224 | − | 0.118705i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.77534e7i | 0.825712i | 0.910796 | + | 0.412856i | \(0.135469\pi\) | ||||
−0.910796 | + | 0.412856i | \(0.864531\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.96018e7i | − | 0.906386i | −0.891412 | − | 0.453193i | \(-0.850285\pi\) | ||
0.891412 | − | 0.453193i | \(-0.149715\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.09358e6i | 0.234161i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.32690e7i | − | 1.06353i | −0.846891 | − | 0.531766i | \(-0.821529\pi\) | ||
0.846891 | − | 0.531766i | \(-0.178471\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −180167. | + | 530041.i | −0.00818721 | + | 0.0240863i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.81459e7 | 1.27165 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.17844e7i | 0.978581i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.95690e7 | 0.874022 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 4.56203e6i | − | 0.202592i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.40286e6 | + | 1.26094e7i | 0.371028 | + | 0.556766i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.68047e7 | 0.737787 | 0.368894 | − | 0.929472i | \(-0.379737\pi\) | ||||
0.368894 | + | 0.929472i | \(0.379737\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.09298e7 | 0.913679 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.66214e6 | −0.332591 | −0.166295 | − | 0.986076i | \(-0.553181\pi\) | ||||
−0.166295 | + | 0.986076i | \(0.553181\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.71621e7 | 0.740743 | 0.370371 | − | 0.928884i | \(-0.379230\pi\) | ||||
0.370371 | + | 0.928884i | \(0.379230\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.00264e7 | − | 3.40808e6i | −0.430313 | − | 0.146269i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.29331e7i | 1.40548i | 0.711449 | + | 0.702738i | \(0.248039\pi\) | ||||
−0.711449 | + | 0.702738i | \(0.751961\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.21334e7 | −0.514906 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 2.17114e6i | − | 0.0916207i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.86743e7 | 0.783637 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.39429e7 | + | 1.49367e7i | 1.83371 | + | 0.623301i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 1.93749e7i | − | 0.804005i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.21517e6i | 0.132680i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.25719e7i | 2.15745i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 1.60586e6i | − | 0.0655372i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.71514e7 | − | 5.82998e6i | −0.696112 | − | 0.236617i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.57744e7 | 1.04033 | 0.520165 | − | 0.854066i | \(-0.325871\pi\) | ||||
0.520165 | + | 0.854066i | \(0.325871\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 1.44862e7i | − | 0.581493i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.92562e7 | 0.768732 | 0.384366 | − | 0.923181i | \(-0.374420\pi\) | ||||
0.384366 | + | 0.923181i | \(0.374420\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.04397e7i | 0.811516i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.95714e7 | − | 6.65254e6i | −0.772802 | − | 0.262685i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.60865e6 | 0.141717 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.33241e7 | 0.520415 | 0.260207 | − | 0.965553i | \(-0.416209\pi\) | ||||
0.260207 | + | 0.965553i | \(0.416209\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.19997e6 | 0.0466144 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.32092e7 | −1.28308 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.18535e7 | + | 1.67973e7i | 0.839783 | + | 0.645484i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.09459e6i | 0.118278i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.49178e7 | 1.70757 | 0.853786 | − | 0.520625i | \(-0.174301\pi\) | ||||
0.853786 | + | 0.520625i | \(0.174301\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.75152e6i | 0.368721i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.29586e7 | −0.487366 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.44348e6 | + | 2.77821e7i | −0.353267 | + | 1.03929i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.83880e6i | − | 0.142839i | −0.997446 | − | 0.0714194i | \(-0.977247\pi\) | ||
0.997446 | − | 0.0714194i | \(-0.0227529\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 2.31955e7i | − | 0.858499i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.00828e7i | − | 0.371198i | −0.982626 | − | 0.185599i | \(-0.940578\pi\) | ||
0.982626 | − | 0.185599i | \(-0.0594225\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.24946e7i | − | 0.823756i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.80604e7 | − | 6.13894e6i | −0.657881 | − | 0.223622i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.28132e7 | 0.464283 | 0.232141 | − | 0.972682i | \(-0.425427\pi\) | ||||
0.232141 | + | 0.972682i | \(0.425427\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.51482e6i | 0.0546003i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.77301e6 | −0.278701 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.37190e7i | − | 0.489318i | −0.969609 | − | 0.244659i | \(-0.921324\pi\) | ||
0.969609 | − | 0.244659i | \(-0.0786760\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.18517e7 | + | 3.48669e7i | −0.420505 | + | 1.23710i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.74525e6 | 0.308669 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.70170e7 | 0.597497 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.76461e7 | −0.965661 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.67999e6 | −0.336364 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.69217e6 | + | 1.93484e6i | 0.196770 | + | 0.0668847i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4.00339e7i | − | 1.37677i | −0.725344 | − | 0.688386i | \(-0.758319\pi\) | ||
0.725344 | − | 0.688386i | \(-0.241681\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.22305e7 | 0.760570 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 3.43712e7i | − | 1.16989i | −0.811071 | − | 0.584947i | \(-0.801115\pi\) | ||
0.811071 | − | 0.584947i | \(-0.198885\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.86873e6 | −0.232592 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.20180e7 | − | 9.23741e6i | −0.404874 | − | 0.311199i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.82576e7i | 0.611939i | 0.952041 | + | 0.305970i | \(0.0989806\pi\) | ||||
−0.952041 | + | 0.305970i | \(0.901019\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.68568e7i | − | 0.562106i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 2.38444e7i | − | 0.791068i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.19646e7i | 0.725001i | 0.931984 | + | 0.362500i | \(0.118077\pi\) | ||||
−0.931984 | + | 0.362500i | \(0.881923\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.50056e7 | − | 4.41456e7i | 0.492792 | − | 1.44976i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.60794e7 | 0.525386 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.09189e6i | 0.230553i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.76391e7 | 1.54092 | 0.770458 | − | 0.637490i | \(-0.220027\pi\) | ||||
0.770458 | + | 0.637490i | \(0.220027\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 5.71117e6i | − | 0.183803i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.02402e6 | − | 8.89647e6i | 0.0968337 | − | 0.284879i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.58049e7 | 1.45940 | 0.729700 | − | 0.683768i | \(-0.239660\pi\) | ||||
0.729700 | + | 0.683768i | \(0.239660\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.46983e7 | −1.10001 |
(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 | 320.6.f.c.289.7 | yes | 16 | |
4.3 | odd | 2 | inner | 320.6.f.c.289.11 | yes | 16 | |
5.4 | even | 2 | inner | 320.6.f.c.289.9 | yes | 16 | |
8.3 | odd | 2 | inner | 320.6.f.c.289.6 | yes | 16 | |
8.5 | even | 2 | inner | 320.6.f.c.289.10 | yes | 16 | |
20.19 | odd | 2 | inner | 320.6.f.c.289.5 | ✓ | 16 | |
40.19 | odd | 2 | inner | 320.6.f.c.289.12 | yes | 16 | |
40.29 | even | 2 | inner | 320.6.f.c.289.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.6.f.c.289.5 | ✓ | 16 | 20.19 | odd | 2 | inner | |
320.6.f.c.289.6 | yes | 16 | 8.3 | odd | 2 | inner | |
320.6.f.c.289.7 | yes | 16 | 1.1 | even | 1 | trivial | |
320.6.f.c.289.8 | yes | 16 | 40.29 | even | 2 | inner | |
320.6.f.c.289.9 | yes | 16 | 5.4 | even | 2 | inner | |
320.6.f.c.289.10 | yes | 16 | 8.5 | even | 2 | inner | |
320.6.f.c.289.11 | yes | 16 | 4.3 | odd | 2 | inner | |
320.6.f.c.289.12 | yes | 16 | 40.19 | odd | 2 | inner |