Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,5,Mod(197,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.197");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(91.1723074400\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 32x^{4} - 7932x^{3} + 185683x^{2} + 6753864x + 64548144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.6 | ||
Root | \(21.9137 - 13.5986i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.197 |
Dual form | 882.5.b.g.197.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | 25.7831i | 1.03132i | 0.856792 | + | 0.515661i | \(0.172454\pi\) | ||||
−0.856792 | + | 0.515661i | \(0.827546\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 22.6274i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −72.9255 | −0.729255 | ||||||||
\(11\) | − 2.36859i | − 0.0195751i | −0.999952 | − | 0.00978756i | \(-0.996884\pi\) | ||||
0.999952 | − | 0.00978756i | \(-0.00311553\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 268.521 | 1.58888 | 0.794440 | − | 0.607343i | \(-0.207765\pi\) | ||||
0.794440 | + | 0.607343i | \(0.207765\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | − 258.563i | − 0.894682i | −0.894363 | − | 0.447341i | \(-0.852371\pi\) | ||||
0.894363 | − | 0.447341i | \(-0.147629\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −527.634 | −1.46159 | −0.730795 | − | 0.682597i | \(-0.760850\pi\) | ||||
−0.730795 | + | 0.682597i | \(0.760850\pi\) | |||||||
\(20\) | − 206.265i | − 0.515661i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.69938 | 0.0138417 | ||||||||
\(23\) | 128.190i | 0.242326i | 0.992633 | + | 0.121163i | \(0.0386623\pi\) | ||||
−0.992633 | + | 0.121163i | \(0.961338\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −39.7667 | −0.0636267 | ||||||||
\(26\) | 759.491i | 1.12351i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1457.13i | 1.73261i | 0.499514 | + | 0.866306i | \(0.333512\pi\) | ||||
−0.499514 | + | 0.866306i | \(0.666488\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 792.400 | 0.824558 | 0.412279 | − | 0.911058i | \(-0.364733\pi\) | ||||
0.412279 | + | 0.911058i | \(0.364733\pi\) | |||||||
\(32\) | 181.019i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 731.327 | 0.632636 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2004.12 | 1.46393 | 0.731966 | − | 0.681341i | \(-0.238603\pi\) | ||||
0.731966 | + | 0.681341i | \(0.238603\pi\) | |||||||
\(38\) | − 1492.37i | − 1.03350i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 583.404 | 0.364628 | ||||||||
\(41\) | 1014.13i | 0.603289i | 0.953420 | + | 0.301645i | \(0.0975356\pi\) | ||||
−0.953420 | + | 0.301645i | \(0.902464\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2491.96 | 1.34774 | 0.673868 | − | 0.738852i | \(-0.264632\pi\) | ||||
0.673868 | + | 0.738852i | \(0.264632\pi\) | |||||||
\(44\) | 18.9487i | 0.00978756i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −362.577 | −0.171350 | ||||||||
\(47\) | 655.817i | 0.296884i | 0.988921 | + | 0.148442i | \(0.0474258\pi\) | ||||
−0.988921 | + | 0.148442i | \(0.952574\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 112.477i | − 0.0449909i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2148.17 | −0.794440 | ||||||||
\(53\) | − 2820.60i | − 1.00413i | −0.864830 | − | 0.502065i | \(-0.832574\pi\) | ||||
0.864830 | − | 0.502065i | \(-0.167426\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 61.0695 | 0.0201883 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4121.38 | −1.22514 | ||||||||
\(59\) | 1915.65i | 0.550315i | 0.961399 | + | 0.275158i | \(0.0887300\pi\) | ||||
−0.961399 | + | 0.275158i | \(0.911270\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3243.35 | 0.871635 | 0.435818 | − | 0.900035i | \(-0.356459\pi\) | ||||
0.435818 | + | 0.900035i | \(0.356459\pi\) | |||||||
\(62\) | 2241.25i | 0.583051i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | 6923.29i | 1.63865i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2699.22 | −0.601295 | −0.300648 | − | 0.953735i | \(-0.597203\pi\) | ||||
−0.300648 | + | 0.953735i | \(0.597203\pi\) | |||||||
\(68\) | 2068.51i | 0.447341i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 4680.05i | − 0.928397i | −0.885731 | − | 0.464199i | \(-0.846342\pi\) | ||||
0.885731 | − | 0.464199i | \(-0.153658\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 939.107 | 0.176226 | 0.0881129 | − | 0.996110i | \(-0.471916\pi\) | ||||
0.0881129 | + | 0.996110i | \(0.471916\pi\) | |||||||
\(74\) | 5668.52i | 1.03516i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4221.07 | 0.730795 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5391.03 | −0.863808 | −0.431904 | − | 0.901920i | \(-0.642158\pi\) | ||||
−0.431904 | + | 0.901920i | \(0.642158\pi\) | |||||||
\(80\) | 1650.12i | 0.257831i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2868.39 | −0.426590 | ||||||||
\(83\) | 7991.44i | 1.16003i | 0.814606 | + | 0.580014i | \(0.196953\pi\) | ||||
−0.814606 | + | 0.580014i | \(0.803047\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6666.55 | 0.922706 | ||||||||
\(86\) | 7048.34i | 0.952993i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −53.5951 | −0.00692085 | ||||||||
\(89\) | 4128.97i | 0.521269i | 0.965438 | + | 0.260634i | \(0.0839317\pi\) | ||||
−0.965438 | + | 0.260634i | \(0.916068\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 1025.52i | − 0.121163i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1854.93 | −0.209929 | ||||||||
\(95\) | − 13604.0i | − 1.50737i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3972.54 | −0.422206 | −0.211103 | − | 0.977464i | \(-0.567706\pi\) | ||||
−0.211103 | + | 0.977464i | \(0.567706\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 318.134 | 0.0318134 | ||||||||
\(101\) | 13514.6i | 1.32483i | 0.749136 | + | 0.662416i | \(0.230469\pi\) | ||||
−0.749136 | + | 0.662416i | \(0.769531\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10215.6 | −0.962918 | −0.481459 | − | 0.876469i | \(-0.659893\pi\) | ||||
−0.481459 | + | 0.876469i | \(0.659893\pi\) | |||||||
\(104\) | − 6075.93i | − 0.561754i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7977.87 | 0.710027 | ||||||||
\(107\) | − 21890.2i | − 1.91197i | −0.293410 | − | 0.955987i | \(-0.594790\pi\) | ||||
0.293410 | − | 0.955987i | \(-0.405210\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8385.96 | −0.705830 | −0.352915 | − | 0.935655i | \(-0.614809\pi\) | ||||
−0.352915 | + | 0.935655i | \(0.614809\pi\) | |||||||
\(110\) | 172.731i | 0.0142753i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 8691.80i | − 0.680695i | −0.940300 | − | 0.340348i | \(-0.889455\pi\) | ||||
0.940300 | − | 0.340348i | \(-0.110545\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3305.14 | −0.249916 | ||||||||
\(116\) | − 11657.0i | − 0.866306i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5418.27 | −0.389132 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14635.4 | 0.999617 | ||||||||
\(122\) | 9173.59i | 0.616339i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6339.20 | −0.412279 | ||||||||
\(125\) | 15089.1i | 0.965703i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −238.060 | −0.0147598 | −0.00737989 | − | 0.999973i | \(-0.502349\pi\) | ||||
−0.00737989 | + | 0.999973i | \(0.502349\pi\) | |||||||
\(128\) | − 1448.15i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −19582.0 | −1.15870 | ||||||||
\(131\) | 32201.2i | 1.87642i | 0.346073 | + | 0.938208i | \(0.387515\pi\) | ||||
−0.346073 | + | 0.938208i | \(0.612485\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − 7634.53i | − 0.425180i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5850.62 | −0.316318 | ||||||||
\(137\) | 35602.4i | 1.89687i | 0.316970 | + | 0.948436i | \(0.397335\pi\) | ||||
−0.316970 | + | 0.948436i | \(0.602665\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11433.9 | 0.591786 | 0.295893 | − | 0.955221i | \(-0.404383\pi\) | ||||
0.295893 | + | 0.955221i | \(0.404383\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13237.2 | 0.656476 | ||||||||
\(143\) | − 636.015i | − 0.0311025i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −37569.2 | −1.78688 | ||||||||
\(146\) | 2656.20i | 0.124610i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −16033.0 | −0.731966 | ||||||||
\(149\) | 21519.8i | 0.969318i | 0.874703 | + | 0.484659i | \(0.161056\pi\) | ||||
−0.874703 | + | 0.484659i | \(0.838944\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9444.26 | −0.414204 | −0.207102 | − | 0.978319i | \(-0.566403\pi\) | ||||
−0.207102 | + | 0.978319i | \(0.566403\pi\) | |||||||
\(152\) | 11939.0i | 0.516750i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20430.5i | 0.850386i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −33876.2 | −1.37435 | −0.687173 | − | 0.726494i | \(-0.741148\pi\) | ||||
−0.687173 | + | 0.726494i | \(0.741148\pi\) | |||||||
\(158\) | − 15248.1i | − 0.610804i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4667.23 | −0.182314 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −40735.0 | −1.53318 | −0.766589 | − | 0.642138i | \(-0.778048\pi\) | ||||
−0.766589 | + | 0.642138i | \(0.778048\pi\) | |||||||
\(164\) | − 8113.03i | − 0.301645i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −22603.2 | −0.820264 | ||||||||
\(167\) | 8580.60i | 0.307670i | 0.988097 | + | 0.153835i | \(0.0491624\pi\) | ||||
−0.988097 | + | 0.153835i | \(0.950838\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 43542.4 | 1.52454 | ||||||||
\(170\) | 18855.9i | 0.652452i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −19935.7 | −0.673868 | ||||||||
\(173\) | 18416.1i | 0.615326i | 0.951495 | + | 0.307663i | \(0.0995469\pi\) | ||||
−0.951495 | + | 0.307663i | \(0.900453\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 151.590i | − 0.00489378i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11678.5 | −0.368593 | ||||||||
\(179\) | 53015.7i | 1.65462i | 0.561744 | + | 0.827311i | \(0.310130\pi\) | ||||
−0.561744 | + | 0.827311i | \(0.689870\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23866.0 | 0.728487 | 0.364243 | − | 0.931304i | \(-0.381328\pi\) | ||||
0.364243 | + | 0.931304i | \(0.381328\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2900.62 | 0.0856751 | ||||||||
\(185\) | 51672.5i | 1.50979i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −612.430 | −0.0175135 | ||||||||
\(188\) | − 5246.53i | − 0.148442i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 38478.0 | 1.06587 | ||||||||
\(191\) | 5915.71i | 0.162159i | 0.996708 | + | 0.0810793i | \(0.0258367\pi\) | ||||
−0.996708 | + | 0.0810793i | \(0.974163\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2029.50 | 0.0544847 | 0.0272424 | − | 0.999629i | \(-0.491327\pi\) | ||||
0.0272424 | + | 0.999629i | \(0.491327\pi\) | |||||||
\(194\) | − 11236.0i | − 0.298545i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 65625.9i | − 1.69100i | −0.533978 | − | 0.845499i | \(-0.679303\pi\) | ||||
0.533978 | − | 0.845499i | \(-0.320697\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −40607.3 | −1.02541 | −0.512705 | − | 0.858565i | \(-0.671357\pi\) | ||||
−0.512705 | + | 0.858565i | \(0.671357\pi\) | |||||||
\(200\) | 899.818i | 0.0224954i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −38225.1 | −0.936798 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −26147.4 | −0.622186 | ||||||||
\(206\) | − 28894.1i | − 0.680886i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 17185.3 | 0.397220 | ||||||||
\(209\) | 1249.75i | 0.0286108i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 79629.9 | 1.78859 | 0.894295 | − | 0.447477i | \(-0.147677\pi\) | ||||
0.894295 | + | 0.447477i | \(0.147677\pi\) | |||||||
\(212\) | 22564.8i | 0.502065i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 61914.8 | 1.35197 | ||||||||
\(215\) | 64250.5i | 1.38995i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 23719.1i | − 0.499097i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −488.556 | −0.0100941 | ||||||||
\(221\) | − 69429.6i | − 1.42154i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −76804.2 | −1.54446 | −0.772228 | − | 0.635346i | \(-0.780858\pi\) | ||||
−0.772228 | + | 0.635346i | \(0.780858\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 24584.1 | 0.481324 | ||||||||
\(227\) | − 21098.1i | − 0.409441i | −0.978820 | − | 0.204720i | \(-0.934371\pi\) | ||||
0.978820 | − | 0.204720i | \(-0.0656285\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −45785.6 | −0.873088 | −0.436544 | − | 0.899683i | \(-0.643798\pi\) | ||||
−0.436544 | + | 0.899683i | \(0.643798\pi\) | |||||||
\(230\) | − 9348.35i | − 0.176717i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 32971.0 | 0.612571 | ||||||||
\(233\) | 4191.34i | 0.0772042i | 0.999255 | + | 0.0386021i | \(0.0122905\pi\) | ||||
−0.999255 | + | 0.0386021i | \(0.987710\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16909.0 | −0.306183 | ||||||||
\(236\) | − 15325.2i | − 0.275158i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 30870.6i | 0.540442i | 0.962798 | + | 0.270221i | \(0.0870967\pi\) | ||||
−0.962798 | + | 0.270221i | \(0.912903\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 33963.1 | 0.584754 | 0.292377 | − | 0.956303i | \(-0.405554\pi\) | ||||
0.292377 | + | 0.956303i | \(0.405554\pi\) | |||||||
\(242\) | 41395.1i | 0.706836i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −25946.8 | −0.435818 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −141681. | −2.32229 | ||||||||
\(248\) | − 17930.0i | − 0.291525i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −42678.5 | −0.682855 | ||||||||
\(251\) | − 32972.4i | − 0.523364i | −0.965154 | − | 0.261682i | \(-0.915723\pi\) | ||||
0.965154 | − | 0.261682i | \(-0.0842771\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 303.630 | 0.00474356 | ||||||||
\(254\) | − 673.336i | − 0.0104367i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | − 84545.3i | − 1.28004i | −0.768359 | − | 0.640019i | \(-0.778926\pi\) | ||||
0.768359 | − | 0.640019i | \(-0.221074\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − 55386.3i | − 0.819324i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −91078.6 | −1.32683 | ||||||||
\(263\) | 103271.i | 1.49303i | 0.665371 | + | 0.746513i | \(0.268273\pi\) | ||||
−0.665371 | + | 0.746513i | \(0.731727\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 72723.8 | 1.03558 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 21593.7 | 0.300648 | ||||||||
\(269\) | 115242.i | 1.59259i | 0.604907 | + | 0.796296i | \(0.293210\pi\) | ||||
−0.604907 | + | 0.796296i | \(0.706790\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −119513. | −1.62734 | −0.813668 | − | 0.581330i | \(-0.802533\pi\) | ||||
−0.813668 | + | 0.581330i | \(0.802533\pi\) | |||||||
\(272\) | − 16548.0i | − 0.223671i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −100699. | −1.34129 | ||||||||
\(275\) | 94.1910i | 0.00124550i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −35918.2 | −0.468117 | −0.234059 | − | 0.972222i | \(-0.575201\pi\) | ||||
−0.234059 | + | 0.972222i | \(0.575201\pi\) | |||||||
\(278\) | 32339.9i | 0.418456i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 107567.i | − 1.36227i | −0.732156 | − | 0.681137i | \(-0.761486\pi\) | ||||
0.732156 | − | 0.681137i | \(-0.238514\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 74573.0 | 0.931127 | 0.465563 | − | 0.885015i | \(-0.345852\pi\) | ||||
0.465563 | + | 0.885015i | \(0.345852\pi\) | |||||||
\(284\) | 37440.4i | 0.464199i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1798.92 | 0.0219928 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16666.1 | 0.199544 | ||||||||
\(290\) | − 106262.i | − 1.26352i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7512.86 | −0.0881129 | ||||||||
\(293\) | − 31081.0i | − 0.362042i | −0.983479 | − | 0.181021i | \(-0.942060\pi\) | ||||
0.983479 | − | 0.181021i | \(-0.0579403\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −49391.3 | −0.567552 | ||||||||
\(296\) | − 45348.1i | − 0.517578i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −60867.3 | −0.685411 | ||||||||
\(299\) | 34421.7i | 0.385026i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 26712.4i | − 0.292886i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −33768.6 | −0.365397 | ||||||||
\(305\) | 83623.6i | 0.898937i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19922.2 | −0.211378 | −0.105689 | − | 0.994399i | \(-0.533705\pi\) | ||||
−0.105689 | + | 0.994399i | \(0.533705\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −57786.2 | −0.601314 | ||||||||
\(311\) | 174219.i | 1.80125i | 0.434596 | + | 0.900626i | \(0.356891\pi\) | ||||
−0.434596 | + | 0.900626i | \(0.643109\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −85378.5 | −0.871485 | −0.435743 | − | 0.900071i | \(-0.643514\pi\) | ||||
−0.435743 | + | 0.900071i | \(0.643514\pi\) | |||||||
\(314\) | − 95816.5i | − 0.971809i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 43128.2 | 0.431904 | ||||||||
\(317\) | − 177007.i | − 1.76146i | −0.473623 | − | 0.880728i | \(-0.657054\pi\) | ||||
0.473623 | − | 0.880728i | \(-0.342946\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3451.33 | 0.0339161 | ||||||||
\(320\) | − 13200.9i | − 0.128915i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 136427.i | 1.30766i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10678.2 | −0.101095 | ||||||||
\(326\) | − 115216.i | − 1.08412i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 22947.1 | 0.213295 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 137003. | 1.25047 | 0.625234 | − | 0.780437i | \(-0.285003\pi\) | ||||
0.625234 | + | 0.780437i | \(0.285003\pi\) | |||||||
\(332\) | − 63931.5i | − 0.580014i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −24269.6 | −0.217555 | ||||||||
\(335\) | − 69594.1i | − 0.620130i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 56842.6 | 0.500511 | 0.250256 | − | 0.968180i | \(-0.419485\pi\) | ||||
0.250256 | + | 0.968180i | \(0.419485\pi\) | |||||||
\(338\) | 123156.i | 1.07801i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −53332.4 | −0.461353 | ||||||||
\(341\) | − 1876.87i | − 0.0161408i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 56386.7i | − 0.476497i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −52088.6 | −0.435101 | ||||||||
\(347\) | − 51452.6i | − 0.427315i | −0.976909 | − | 0.213658i | \(-0.931462\pi\) | ||||
0.976909 | − | 0.213658i | \(-0.0685377\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −69068.5 | −0.567060 | −0.283530 | − | 0.958963i | \(-0.591506\pi\) | ||||
−0.283530 | + | 0.958963i | \(0.591506\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 428.761 | 0.00346043 | ||||||||
\(353\) | 20365.1i | 0.163432i | 0.996656 | + | 0.0817161i | \(0.0260401\pi\) | ||||
−0.996656 | + | 0.0817161i | \(0.973960\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 120666. | 0.957477 | ||||||||
\(356\) | − 33031.8i | − 0.260634i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −149951. | −1.16999 | ||||||||
\(359\) | − 134562.i | − 1.04408i | −0.852922 | − | 0.522039i | \(-0.825172\pi\) | ||||
0.852922 | − | 0.522039i | \(-0.174828\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 148076. | 1.13624 | ||||||||
\(362\) | 67503.1i | 0.515118i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24213.1i | 0.181746i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 199428. | 1.48066 | 0.740329 | − | 0.672244i | \(-0.234670\pi\) | ||||
0.740329 | + | 0.672244i | \(0.234670\pi\) | |||||||
\(368\) | 8204.18i | 0.0605814i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −146152. | −1.06758 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12186.3 | 0.0875898 | 0.0437949 | − | 0.999041i | \(-0.486055\pi\) | ||||
0.0437949 | + | 0.999041i | \(0.486055\pi\) | |||||||
\(374\) | − 1732.21i | − 0.0123839i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14839.4 | 0.104964 | ||||||||
\(377\) | 391269.i | 2.75291i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −47966.9 | −0.333936 | −0.166968 | − | 0.985962i | \(-0.553398\pi\) | ||||
−0.166968 | + | 0.985962i | \(0.553398\pi\) | |||||||
\(380\) | 108832.i | 0.753685i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16732.1 | −0.114663 | ||||||||
\(383\) | − 7540.04i | − 0.0514015i | −0.999670 | − | 0.0257008i | \(-0.991818\pi\) | ||||
0.999670 | − | 0.0257008i | \(-0.00818170\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5740.30i | 0.0385265i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 31780.3 | 0.211103 | ||||||||
\(389\) | − 30745.8i | − 0.203183i | −0.994826 | − | 0.101591i | \(-0.967607\pi\) | ||||
0.994826 | − | 0.101591i | \(-0.0323935\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33145.3 | 0.216804 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 185618. | 1.19572 | ||||||||
\(395\) | − 138997.i | − 0.890865i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 261023. | 1.65614 | 0.828070 | − | 0.560625i | \(-0.189439\pi\) | ||||
0.828070 | + | 0.560625i | \(0.189439\pi\) | |||||||
\(398\) | − 114855.i | − 0.725074i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2545.07 | −0.0159067 | ||||||||
\(401\) | − 10220.1i | − 0.0635574i | −0.999495 | − | 0.0317787i | \(-0.989883\pi\) | ||||
0.999495 | − | 0.0317787i | \(-0.0101172\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 212776. | 1.31012 | ||||||||
\(404\) | − 108117.i | − 0.662416i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 4746.95i | − 0.0286567i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −135962. | −0.812776 | −0.406388 | − | 0.913701i | \(-0.633212\pi\) | ||||
−0.406388 | + | 0.913701i | \(0.633212\pi\) | |||||||
\(410\) | − 73955.9i | − 0.439952i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 81724.8 | 0.481459 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −206044. | −1.19636 | ||||||||
\(416\) | 48607.4i | 0.280877i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3534.82 | −0.0202309 | ||||||||
\(419\) | 239307.i | 1.36310i | 0.731773 | + | 0.681549i | \(0.238693\pi\) | ||||
−0.731773 | + | 0.681549i | \(0.761307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 221785. | 1.25132 | 0.625659 | − | 0.780097i | \(-0.284830\pi\) | ||||
0.625659 | + | 0.780097i | \(0.284830\pi\) | |||||||
\(422\) | 225227.i | 1.26472i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −63822.9 | −0.355014 | ||||||||
\(425\) | 10282.2i | 0.0569257i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 175121.i | 0.955987i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −181728. | −0.982844 | ||||||||
\(431\) | − 25402.7i | − 0.136750i | −0.997660 | − | 0.0683748i | \(-0.978219\pi\) | ||||
0.997660 | − | 0.0683748i | \(-0.0217814\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 277393. | 1.47952 | 0.739759 | − | 0.672872i | \(-0.234939\pi\) | ||||
0.739759 | + | 0.672872i | \(0.234939\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 67087.7 | 0.352915 | ||||||||
\(437\) | − 67637.5i | − 0.354181i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 245813. | 1.27549 | 0.637743 | − | 0.770249i | \(-0.279868\pi\) | ||||
0.637743 | + | 0.770249i | \(0.279868\pi\) | |||||||
\(440\) | − 1381.85i | − 0.00713763i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 196376. | 1.00518 | ||||||||
\(443\) | 49514.3i | 0.252304i | 0.992011 | + | 0.126152i | \(0.0402626\pi\) | ||||
−0.992011 | + | 0.126152i | \(0.959737\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −106458. | −0.537596 | ||||||||
\(446\) | − 217235.i | − 1.09210i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 315550.i | 1.56522i | 0.622512 | + | 0.782610i | \(0.286112\pi\) | ||||
−0.622512 | + | 0.782610i | \(0.713888\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2402.06 | 0.0118095 | ||||||||
\(452\) | 69534.4i | 0.340348i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 59674.4 | 0.289518 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 47052.2 | 0.225293 | 0.112646 | − | 0.993635i | \(-0.464067\pi\) | ||||
0.112646 | + | 0.993635i | \(0.464067\pi\) | |||||||
\(458\) | − 129501.i | − 0.617367i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 26441.1 | 0.124958 | ||||||||
\(461\) | − 144717.i | − 0.680956i | −0.940252 | − | 0.340478i | \(-0.889411\pi\) | ||||
0.940252 | − | 0.340478i | \(-0.110589\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −314156. | −1.46549 | −0.732746 | − | 0.680502i | \(-0.761762\pi\) | ||||
−0.732746 | + | 0.680502i | \(0.761762\pi\) | |||||||
\(464\) | 93256.1i | 0.433153i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11854.9 | −0.0545916 | ||||||||
\(467\) | − 71579.3i | − 0.328211i | −0.986443 | − | 0.164106i | \(-0.947526\pi\) | ||||
0.986443 | − | 0.164106i | \(-0.0524738\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 47825.8i | − 0.216504i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 43346.1 | 0.194566 | ||||||||
\(473\) | − 5902.44i | − 0.0263821i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 20982.3 | 0.0929962 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −87315.2 | −0.382150 | ||||||||
\(479\) | − 31394.1i | − 0.136829i | −0.997657 | − | 0.0684144i | \(-0.978206\pi\) | ||||
0.997657 | − | 0.0684144i | \(-0.0217940\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 538149. | 2.32601 | ||||||||
\(482\) | 96062.2i | 0.413484i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −117083. | −0.499808 | ||||||||
\(485\) | − 102424.i | − 0.435431i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −162986. | −0.687214 | −0.343607 | − | 0.939114i | \(-0.611649\pi\) | ||||
−0.343607 | + | 0.939114i | \(0.611649\pi\) | |||||||
\(488\) | − 73388.7i | − 0.308170i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 213254.i | 0.884573i | 0.896874 | + | 0.442286i | \(0.145833\pi\) | ||||
−0.896874 | + | 0.442286i | \(0.854167\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 376759. | 1.55014 | ||||||||
\(494\) | − 400733.i | − 1.64211i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 50713.6 | 0.206140 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 170422. | 0.684421 | 0.342210 | − | 0.939623i | \(-0.388824\pi\) | ||||
0.342210 | + | 0.939623i | \(0.388824\pi\) | |||||||
\(500\) | − 120713.i | − 0.482852i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 93260.1 | 0.370074 | ||||||||
\(503\) | 144506.i | 0.571151i | 0.958356 | + | 0.285575i | \(0.0921847\pi\) | ||||
−0.958356 | + | 0.285575i | \(0.907815\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −348448. | −1.36633 | ||||||||
\(506\) | 858.796i | 0.00335420i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1904.48 | 0.00737989 | ||||||||
\(509\) | 423335.i | 1.63399i | 0.576647 | + | 0.816993i | \(0.304361\pi\) | ||||
−0.576647 | + | 0.816993i | \(0.695639\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11585.2i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 239130. | 0.905124 | ||||||||
\(515\) | − 263390.i | − 0.993080i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1553.36 | 0.00581154 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 156656. | 0.579350 | ||||||||
\(521\) | 221150.i | 0.814726i | 0.913266 | + | 0.407363i | \(0.133552\pi\) | ||||
−0.913266 | + | 0.407363i | \(0.866448\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −377707. | −1.38087 | −0.690434 | − | 0.723396i | \(-0.742580\pi\) | ||||
−0.690434 | + | 0.723396i | \(0.742580\pi\) | |||||||
\(524\) | − 257609.i | − 0.938208i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −292095. | −1.05573 | ||||||||
\(527\) | − 204886.i | − 0.737718i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 263408. | 0.941278 | ||||||||
\(530\) | 205694.i | 0.732267i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 272315.i | 0.958554i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 564396. | 1.97186 | ||||||||
\(536\) | 61076.3i | 0.212590i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −325952. | −1.12613 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 135542. | 0.463105 | 0.231553 | − | 0.972822i | \(-0.425619\pi\) | ||||
0.231553 | + | 0.972822i | \(0.425619\pi\) | |||||||
\(542\) | − 338034.i | − 1.15070i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 46804.9 | 0.158159 | ||||||||
\(545\) | − 216216.i | − 0.727938i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 314274. | 1.05035 | 0.525175 | − | 0.850994i | \(-0.324000\pi\) | ||||
0.525175 | + | 0.850994i | \(0.324000\pi\) | |||||||
\(548\) | − 284819.i | − 0.948436i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −266.412 | −0.000880702 0 | ||||||||
\(551\) | − 768829.i | − 2.53237i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 101592.i | − 0.331009i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −91471.2 | −0.295893 | ||||||||
\(557\) | 59258.7i | 0.191004i | 0.995429 | + | 0.0955019i | \(0.0304456\pi\) | ||||
−0.995429 | + | 0.0955019i | \(0.969554\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 669144. | 2.14139 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 304244. | 0.963273 | ||||||||
\(563\) | − 214575.i | − 0.676958i | −0.940974 | − | 0.338479i | \(-0.890088\pi\) | ||||
0.940974 | − | 0.338479i | \(-0.109912\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 224101. | 0.702016 | ||||||||
\(566\) | 210924.i | 0.658406i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −105897. | −0.328238 | ||||||||
\(569\) | − 123955.i | − 0.382861i | −0.981506 | − | 0.191430i | \(-0.938687\pi\) | ||||
0.981506 | − | 0.191430i | \(-0.0613126\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 169974. | 0.521327 | 0.260664 | − | 0.965430i | \(-0.416059\pi\) | ||||
0.260664 | + | 0.965430i | \(0.416059\pi\) | |||||||
\(572\) | 5088.12i | 0.0155513i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 5097.71i | − 0.0154184i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 336708. | 1.01135 | 0.505675 | − | 0.862724i | \(-0.331243\pi\) | ||||
0.505675 | + | 0.862724i | \(0.331243\pi\) | |||||||
\(578\) | 47138.8i | 0.141099i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 300554. | 0.893441 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6680.85 | −0.0196560 | ||||||||
\(584\) | − 21249.6i | − 0.0623052i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 87910.3 | 0.256003 | ||||||||
\(587\) | 216616.i | 0.628658i | 0.949314 | + | 0.314329i | \(0.101780\pi\) | ||||
−0.949314 | + | 0.314329i | \(0.898220\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −418097. | −1.20517 | ||||||||
\(590\) | − 139700.i | − 0.401320i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 128264. | 0.365983 | ||||||||
\(593\) | − 186592.i | − 0.530619i | −0.964163 | − | 0.265310i | \(-0.914526\pi\) | ||||
0.964163 | − | 0.265310i | \(-0.0854742\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 172159.i | − 0.484659i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −97359.4 | −0.272255 | ||||||||
\(599\) | − 239406.i | − 0.667238i | −0.942708 | − | 0.333619i | \(-0.891730\pi\) | ||||
0.942708 | − | 0.333619i | \(-0.108270\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 51508.8 | 0.142604 | 0.0713021 | − | 0.997455i | \(-0.477285\pi\) | ||||
0.0713021 | + | 0.997455i | \(0.477285\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 75554.1 | 0.207102 | ||||||||
\(605\) | 377345.i | 1.03093i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24554.5 | −0.0666429 | −0.0333214 | − | 0.999445i | \(-0.510609\pi\) | ||||
−0.0333214 | + | 0.999445i | \(0.510609\pi\) | |||||||
\(608\) | − 95511.9i | − 0.258375i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −236523. | −0.635645 | ||||||||
\(611\) | 176100.i | 0.471713i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 169561. | 0.451237 | 0.225618 | − | 0.974216i | \(-0.427560\pi\) | ||||
0.225618 | + | 0.974216i | \(0.427560\pi\) | |||||||
\(614\) | − 56348.5i | − 0.149467i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 624837.i | − 1.64133i | −0.571409 | − | 0.820665i | \(-0.693603\pi\) | ||||
0.571409 | − | 0.820665i | \(-0.306397\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −334855. | −0.873928 | −0.436964 | − | 0.899479i | \(-0.643946\pi\) | ||||
−0.436964 | + | 0.899479i | \(0.643946\pi\) | |||||||
\(620\) | − 163444.i | − 0.425193i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −492765. | −1.27368 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −413898. | −1.05958 | ||||||||
\(626\) | − 241487.i | − 0.616233i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 271010. | 0.687173 | ||||||||
\(629\) | − 518193.i | − 1.30975i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −154411. | −0.387809 | −0.193905 | − | 0.981020i | \(-0.562115\pi\) | ||||
−0.193905 | + | 0.981020i | \(0.562115\pi\) | |||||||
\(632\) | 121985.i | 0.305402i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 500651. | 1.24554 | ||||||||
\(635\) | − 6137.93i | − 0.0152221i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9761.85i | 0.0239823i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 37337.9 | 0.0911569 | ||||||||
\(641\) | 350351.i | 0.852682i | 0.904562 | + | 0.426341i | \(0.140198\pi\) | ||||
−0.904562 | + | 0.426341i | \(0.859802\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 79292.9 | 0.191784 | 0.0958920 | − | 0.995392i | \(-0.469430\pi\) | ||||
0.0958920 | + | 0.995392i | \(0.469430\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −385873. | −0.924654 | ||||||||
\(647\) | 711211.i | 1.69899i | 0.527600 | + | 0.849493i | \(0.323092\pi\) | ||||
−0.527600 | + | 0.849493i | \(0.676908\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4537.38 | 0.0107725 | ||||||||
\(650\) | − 30202.5i | − 0.0714851i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 325880. | 0.766589 | ||||||||
\(653\) | 33637.9i | 0.0788864i | 0.999222 | + | 0.0394432i | \(0.0125584\pi\) | ||||
−0.999222 | + | 0.0394432i | \(0.987442\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −830245. | −1.93519 | ||||||||
\(656\) | 64904.3i | 0.150822i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 358536.i | 0.825585i | 0.910825 | + | 0.412793i | \(0.135447\pi\) | ||||
−0.910825 | + | 0.412793i | \(0.864553\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 584224. | 1.33714 | 0.668569 | − | 0.743650i | \(-0.266907\pi\) | ||||
0.668569 | + | 0.743650i | \(0.266907\pi\) | |||||||
\(662\) | 387502.i | 0.884215i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 180826. | 0.410132 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −186789. | −0.419856 | ||||||||
\(668\) | − 68644.8i | − 0.153835i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 196842. | 0.438498 | ||||||||
\(671\) | − 7682.18i | − 0.0170624i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −175181. | −0.386773 | −0.193387 | − | 0.981123i | \(-0.561947\pi\) | ||||
−0.193387 | + | 0.981123i | \(0.561947\pi\) | |||||||
\(674\) | 160775.i | 0.353915i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −348339. | −0.762269 | ||||||||
\(677\) | − 61931.0i | − 0.135124i | −0.997715 | − | 0.0675618i | \(-0.978478\pi\) | ||||
0.997715 | − | 0.0675618i | \(-0.0215220\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − 150847.i | − 0.326226i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5308.60 | 0.0114133 | ||||||||
\(683\) | − 206583.i | − 0.442846i | −0.975178 | − | 0.221423i | \(-0.928930\pi\) | ||||
0.975178 | − | 0.221423i | \(-0.0710702\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −917939. | −1.95629 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 159486. | 0.336934 | ||||||||
\(689\) | − 757390.i | − 1.59544i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 140378. | 0.293997 | 0.146998 | − | 0.989137i | \(-0.453039\pi\) | ||||
0.146998 | + | 0.989137i | \(0.453039\pi\) | |||||||
\(692\) | − 147329.i | − 0.307663i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 145530. | 0.302157 | ||||||||
\(695\) | 294801.i | 0.610322i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 262216. | 0.539752 | ||||||||
\(698\) | − 195355.i | − 0.400972i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 798257.i | 1.62445i | 0.583343 | + | 0.812226i | \(0.301744\pi\) | ||||
−0.583343 | + | 0.812226i | \(0.698256\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.05744e6 | −2.13967 | ||||||||
\(704\) | 1212.72i | 0.00244689i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −57601.3 | −0.115564 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −409921. | −0.815470 | −0.407735 | − | 0.913100i | \(-0.633681\pi\) | ||||
−0.407735 | + | 0.913100i | \(0.633681\pi\) | |||||||
\(710\) | 341295.i | 0.677039i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 93427.9 | 0.184296 | ||||||||
\(713\) | 101578.i | 0.199812i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16398.4 | 0.0320767 | ||||||||
\(716\) | − 424126.i | − 0.827311i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 380598. | 0.738274 | ||||||||
\(719\) | − 721642.i | − 1.39593i | −0.716131 | − | 0.697966i | \(-0.754089\pi\) | ||||
0.716131 | − | 0.697966i | \(-0.245911\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 418823.i | 0.803445i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −190928. | −0.364243 | ||||||||
\(725\) | − 57945.1i | − 0.110240i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −695893. | −1.31666 | −0.658330 | − | 0.752729i | \(-0.728737\pi\) | ||||
−0.658330 | + | 0.752729i | \(0.728737\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −68484.9 | −0.128514 | ||||||||
\(731\) | − 644330.i | − 1.20580i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 344991. | 0.642096 | 0.321048 | − | 0.947063i | \(-0.395965\pi\) | ||||
0.321048 | + | 0.947063i | \(0.395965\pi\) | |||||||
\(734\) | 564069.i | 1.04698i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −23204.9 | −0.0428375 | ||||||||
\(737\) | 6393.33i | 0.0117704i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 553173. | 1.01291 | 0.506457 | − | 0.862266i | \(-0.330955\pi\) | ||||
0.506457 | + | 0.862266i | \(0.330955\pi\) | |||||||
\(740\) | − 413380.i | − 0.754893i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 331872.i | − 0.601163i | −0.953756 | − | 0.300582i | \(-0.902819\pi\) | ||||
0.953756 | − | 0.300582i | \(-0.0971808\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −554847. | −0.999680 | ||||||||
\(746\) | 34468.0i | 0.0619353i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4899.44 | 0.00875676 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 908007. | 1.60994 | 0.804969 | − | 0.593316i | \(-0.202182\pi\) | ||||
0.804969 | + | 0.593316i | \(0.202182\pi\) | |||||||
\(752\) | 41972.3i | 0.0742210i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.10667e6 | −1.94660 | ||||||||
\(755\) | − 243502.i | − 0.427178i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 906297. | 1.58153 | 0.790767 | − | 0.612117i | \(-0.209682\pi\) | ||||
0.790767 | + | 0.612117i | \(0.209682\pi\) | |||||||
\(758\) | − 135671.i | − 0.236129i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −307824. | −0.532936 | ||||||||
\(761\) | 972723.i | 1.67966i | 0.542853 | + | 0.839828i | \(0.317344\pi\) | ||||
−0.542853 | + | 0.839828i | \(0.682656\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − 47325.7i | − 0.0810793i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21326.4 | 0.0363464 | ||||||||
\(767\) | 514391.i | 0.874384i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −91810.6 | −0.155253 | −0.0776265 | − | 0.996983i | \(-0.524734\pi\) | ||||
−0.0776265 | + | 0.996983i | \(0.524734\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16236.0 | −0.0272424 | ||||||||
\(773\) | 493582.i | 0.826039i | 0.910722 | + | 0.413020i | \(0.135526\pi\) | ||||
−0.910722 | + | 0.413020i | \(0.864474\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31511.2 | −0.0524639 | ||||||||
\(776\) | 89888.3i | 0.149272i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 86962.4 | 0.143672 | ||||||||
\(779\) | − 535089.i | − 0.881761i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11085.1 | −0.0181735 | ||||||||
\(782\) | 93749.0i | 0.153304i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 873433.i | − 1.41739i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 172472. | 0.278465 | 0.139232 | − | 0.990260i | \(-0.455537\pi\) | ||||
0.139232 | + | 0.990260i | \(0.455537\pi\) | |||||||
\(788\) | 525007.i | 0.845499i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 393143. | 0.629937 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 870908. | 1.38492 | ||||||||
\(794\) | 738283.i | 1.17107i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 324858. | 0.512705 | ||||||||
\(797\) | − 48077.3i | − 0.0756873i | −0.999284 | − | 0.0378437i | \(-0.987951\pi\) | ||||
0.999284 | − | 0.0378437i | \(-0.0120489\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 169570. | 0.265617 | ||||||||
\(800\) | − 7198.54i | − 0.0112477i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28906.8 | 0.0449419 | ||||||||
\(803\) | − 2224.36i | − 0.00344964i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 601821.i | 0.926398i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 305801. | 0.468399 | ||||||||
\(809\) | 692003.i | 1.05733i | 0.848830 | + | 0.528666i | \(0.177307\pi\) | ||||
−0.848830 | + | 0.528666i | \(0.822693\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 327815. | 0.498410 | 0.249205 | − | 0.968451i | \(-0.419831\pi\) | ||||
0.249205 | + | 0.968451i | \(0.419831\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 13426.4 | 0.0202633 | ||||||||
\(815\) | − 1.05027e6i | − 1.58120i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.31484e6 | −1.96984 | ||||||||
\(818\) | − 384559.i | − 0.574720i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 209179. | 0.311093 | ||||||||
\(821\) | 327066.i | 0.485232i | 0.970122 | + | 0.242616i | \(0.0780055\pi\) | ||||
−0.970122 | + | 0.242616i | \(0.921995\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 378351. | 0.558593 | 0.279296 | − | 0.960205i | \(-0.409899\pi\) | ||||
0.279296 | + | 0.960205i | \(0.409899\pi\) | |||||||
\(824\) | 231153.i | 0.340443i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 555342.i | − 0.811988i | −0.913876 | − | 0.405994i | \(-0.866925\pi\) | ||||
0.913876 | − | 0.405994i | \(-0.133075\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −519799. | −0.756356 | −0.378178 | − | 0.925733i | \(-0.623449\pi\) | ||||
−0.378178 | + | 0.925733i | \(0.623449\pi\) | |||||||
\(830\) | − 582780.i | − 0.845957i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −137483. | −0.198610 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −221234. | −0.317307 | ||||||||
\(836\) | − 9997.98i | − 0.0143054i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −676862. | −0.963855 | ||||||||
\(839\) | − 836509.i | − 1.18836i | −0.804333 | − | 0.594178i | \(-0.797477\pi\) | ||||
0.804333 | − | 0.594178i | \(-0.202523\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.41594e6 | −2.00194 | ||||||||
\(842\) | 627302.i | 0.884816i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −637039. | −0.894295 | ||||||||
\(845\) | 1.12266e6i | 1.57229i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 180518.i | − 0.251033i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −29082.5 | −0.0402526 | ||||||||
\(851\) | 256909.i | 0.354748i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.03133e6 | 1.41742 | 0.708711 | − | 0.705499i | \(-0.249277\pi\) | ||||
0.708711 | + | 0.705499i | \(0.249277\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −495318. | −0.675985 | ||||||||
\(857\) | − 781985.i | − 1.06472i | −0.846517 | − | 0.532362i | \(-0.821305\pi\) | ||||
0.846517 | − | 0.532362i | \(-0.178695\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.06243e6 | −1.43984 | −0.719921 | − | 0.694056i | \(-0.755822\pi\) | ||||
−0.719921 | + | 0.694056i | \(0.755822\pi\) | |||||||
\(860\) | − 514004.i | − 0.694975i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 71849.8 | 0.0966966 | ||||||||
\(863\) | − 839858.i | − 1.12768i | −0.825886 | − | 0.563838i | \(-0.809324\pi\) | ||||
0.825886 | − | 0.563838i | \(-0.190676\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −474823. | −0.634600 | ||||||||
\(866\) | 784587.i | 1.04618i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12769.1i | 0.0169091i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −724795. | −0.955386 | ||||||||
\(872\) | 189753.i | 0.249548i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 191308. | 0.250444 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −532982. | −0.692968 | −0.346484 | − | 0.938056i | \(-0.612625\pi\) | ||||
−0.346484 | + | 0.938056i | \(0.612625\pi\) | |||||||
\(878\) | 695264.i | 0.901905i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3908.45 | 0.00504707 | ||||||||
\(881\) | 1.36059e6i | 1.75297i | 0.481430 | + | 0.876484i | \(0.340117\pi\) | ||||
−0.481430 | + | 0.876484i | \(0.659883\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.42318e6 | 1.82531 | 0.912657 | − | 0.408727i | \(-0.134027\pi\) | ||||
0.912657 | + | 0.408727i | \(0.134027\pi\) | |||||||
\(884\) | 555436.i | 0.710771i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −140048. | −0.178406 | ||||||||
\(887\) | − 158940.i | − 0.202016i | −0.994886 | − | 0.101008i | \(-0.967793\pi\) | ||||
0.994886 | − | 0.101008i | \(-0.0322068\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 301107.i | − 0.380138i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 614434. | 0.772228 | ||||||||
\(893\) | − 346031.i | − 0.433923i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.36691e6 | −1.70645 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −892510. | −1.10678 | ||||||||
\(899\) | 1.15463e6i | 1.42864i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −729304. | −0.898377 | ||||||||
\(902\) | 6794.04i | 0.00835055i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −196673. | −0.240662 | ||||||||
\(905\) | 615338.i | 0.751305i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −683535. | −0.830895 | −0.415447 | − | 0.909617i | \(-0.636375\pi\) | ||||
−0.415447 | + | 0.909617i | \(0.636375\pi\) | |||||||
\(908\) | 168785.i | 0.204720i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16125.4i | 0.0194300i | 0.999953 | + | 0.00971500i | \(0.00309243\pi\) | ||||
−0.999953 | + | 0.00971500i | \(0.996908\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18928.4 | 0.0227077 | ||||||||
\(914\) | 133084.i | 0.159306i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 366285. | 0.436544 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −418627. | −0.495674 | −0.247837 | − | 0.968802i | \(-0.579720\pi\) | ||||
−0.247837 | + | 0.968802i | \(0.579720\pi\) | |||||||
\(920\) | 74786.8i | 0.0883587i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 409323. | 0.481509 | ||||||||
\(923\) | − 1.25669e6i | − 1.47511i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −79697.4 | −0.0931452 | ||||||||
\(926\) | − 888567.i | − 1.03626i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −263768. | −0.306285 | ||||||||
\(929\) | 268591.i | 0.311214i | 0.987819 | + | 0.155607i | \(0.0497334\pi\) | ||||
−0.987819 | + | 0.155607i | \(0.950267\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 33530.7i | − 0.0386021i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 202457. | 0.232080 | ||||||||
\(935\) | − 15790.3i | − 0.0180621i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −543470. | −0.619008 | −0.309504 | − | 0.950898i | \(-0.600163\pi\) | ||||
−0.309504 | + | 0.950898i | \(0.600163\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 135272. | 0.153092 | ||||||||
\(941\) | 434266.i | 0.490430i | 0.969469 | + | 0.245215i | \(0.0788585\pi\) | ||||
−0.969469 | + | 0.245215i | \(0.921141\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −130002. | −0.146192 | ||||||||
\(944\) | 122601.i | 0.137579i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16694.6 | 0.0186550 | ||||||||
\(947\) | 873995.i | 0.974560i | 0.873246 | + | 0.487280i | \(0.162011\pi\) | ||||
−0.873246 | + | 0.487280i | \(0.837989\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 252170. | 0.280001 | ||||||||
\(950\) | 59346.8i | 0.0657582i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 1.51221e6i | − 1.66504i | −0.553994 | − | 0.832521i | \(-0.686897\pi\) | ||||
0.553994 | − | 0.832521i | \(-0.313103\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −152525. | −0.167238 | ||||||||
\(956\) | − 246965.i | − 0.270221i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 88796.1 | 0.0967526 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −295622. | −0.320104 | ||||||||
\(962\) | 1.52211e6i | 1.64474i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −271705. | −0.292377 | ||||||||
\(965\) | 52326.8i | 0.0561913i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.49916e6 | 1.60322 | 0.801612 | − | 0.597844i | \(-0.203976\pi\) | ||||
0.801612 | + | 0.597844i | \(0.203976\pi\) | |||||||
\(968\) | − 331161.i | − 0.353418i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 289699. | 0.307896 | ||||||||
\(971\) | − 470558.i | − 0.499085i | −0.968364 | − | 0.249543i | \(-0.919720\pi\) | ||||
0.968364 | − | 0.249543i | \(-0.0802803\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 460994.i | − 0.485934i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 207575. | 0.217909 | ||||||||
\(977\) | − 126944.i | − 0.132992i | −0.997787 | − | 0.0664959i | \(-0.978818\pi\) | ||||
0.997787 | − | 0.0664959i | \(-0.0211819\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9779.84 | 0.0102039 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −603173. | −0.625487 | ||||||||
\(983\) | − 218289.i | − 0.225904i | −0.993600 | − | 0.112952i | \(-0.963969\pi\) | ||||
0.993600 | − | 0.112952i | \(-0.0360306\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.69204e6 | 1.74396 | ||||||||
\(986\) | 1.06564e6i | 1.09611i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.13344e6 | 1.16114 | ||||||||
\(989\) | 319446.i | 0.326591i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −203403. | −0.207115 | −0.103557 | − | 0.994623i | \(-0.533023\pi\) | ||||
−0.103557 | + | 0.994623i | \(0.533023\pi\) | |||||||
\(992\) | 143440.i | 0.145763i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1.04698e6i | − 1.05753i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 461568. | 0.464350 | 0.232175 | − | 0.972674i | \(-0.425416\pi\) | ||||
0.232175 | + | 0.972674i | \(0.425416\pi\) | |||||||
\(998\) | 482025.i | 0.483959i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 882.5.b.g.197.6 | 6 | ||
3.2 | odd | 2 | inner | 882.5.b.g.197.1 | 6 | ||
7.3 | odd | 6 | 126.5.s.a.107.3 | yes | 12 | ||
7.5 | odd | 6 | 126.5.s.a.53.4 | yes | 12 | ||
7.6 | odd | 2 | 882.5.b.f.197.4 | 6 | |||
21.5 | even | 6 | 126.5.s.a.53.3 | ✓ | 12 | ||
21.17 | even | 6 | 126.5.s.a.107.4 | yes | 12 | ||
21.20 | even | 2 | 882.5.b.f.197.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.5.s.a.53.3 | ✓ | 12 | 21.5 | even | 6 | ||
126.5.s.a.53.4 | yes | 12 | 7.5 | odd | 6 | ||
126.5.s.a.107.3 | yes | 12 | 7.3 | odd | 6 | ||
126.5.s.a.107.4 | yes | 12 | 21.17 | even | 6 | ||
882.5.b.f.197.3 | 6 | 21.20 | even | 2 | |||
882.5.b.f.197.4 | 6 | 7.6 | odd | 2 | |||
882.5.b.g.197.1 | 6 | 3.2 | odd | 2 | inner | ||
882.5.b.g.197.6 | 6 | 1.1 | even | 1 | trivial |