Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,5,Mod(685,882)]
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([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.685");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(91.1723074400\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.2048.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 98) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 685.3 | ||
Root | \(0.765367i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.685 |
Dual form | 882.5.c.c.685.4 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 8.00000 | 0.500000 | ||||||||
\(5\) | − 27.8477i | − 1.11391i | −0.830543 | − | 0.556954i | \(-0.811970\pi\) | ||||
0.830543 | − | 0.556954i | \(-0.188030\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 22.6274 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 78.7652i | − 0.787652i | ||||||||
\(11\) | 139.664 | 1.15425 | 0.577124 | − | 0.816657i | \(-0.304175\pi\) | ||||
0.577124 | + | 0.816657i | \(0.304175\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 101.931i | 0.603140i | 0.953444 | + | 0.301570i | \(0.0975106\pi\) | ||||
−0.953444 | + | 0.301570i | \(0.902489\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | − 542.887i | − 1.87850i | −0.343232 | − | 0.939251i | \(-0.611522\pi\) | ||||
0.343232 | − | 0.939251i | \(-0.388478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 139.953i | − 0.387682i | −0.981033 | − | 0.193841i | \(-0.937905\pi\) | ||||
0.981033 | − | 0.193841i | \(-0.0620947\pi\) | |||||||
\(20\) | − 222.782i | − 0.556954i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 395.029 | 0.816177 | ||||||||
\(23\) | −229.647 | −0.434115 | −0.217057 | − | 0.976159i | \(-0.569646\pi\) | ||||
−0.217057 | + | 0.976159i | \(0.569646\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −150.495 | −0.240791 | ||||||||
\(26\) | 288.303i | 0.426484i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 383.113 | 0.455544 | 0.227772 | − | 0.973714i | \(-0.426856\pi\) | ||||
0.227772 | + | 0.973714i | \(0.426856\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 397.492i | 0.413623i | 0.978381 | + | 0.206812i | \(0.0663087\pi\) | ||||
−0.978381 | + | 0.206812i | \(0.933691\pi\) | |||||||
\(32\) | 181.019 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 1535.52i | − 1.32830i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −898.912 | −0.656619 | −0.328310 | − | 0.944570i | \(-0.606479\pi\) | ||||
−0.328310 | + | 0.944570i | \(0.606479\pi\) | |||||||
\(38\) | − 395.848i | − 0.274133i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − 630.122i | − 0.393826i | ||||||||
\(41\) | − 657.862i | − 0.391352i | −0.980669 | − | 0.195676i | \(-0.937310\pi\) | ||||
0.980669 | − | 0.195676i | \(-0.0626900\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1155.70 | 0.625041 | 0.312521 | − | 0.949911i | \(-0.398827\pi\) | ||||
0.312521 | + | 0.949911i | \(0.398827\pi\) | |||||||
\(44\) | 1117.31 | 0.577124 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −649.539 | −0.306966 | ||||||||
\(47\) | 1294.51i | 0.586015i | 0.956110 | + | 0.293007i | \(0.0946561\pi\) | ||||
−0.956110 | + | 0.293007i | \(0.905344\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −425.663 | −0.170265 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 815.445i | 0.301570i | ||||||||
\(53\) | 5168.43 | 1.83996 | 0.919978 | − | 0.391971i | \(-0.128207\pi\) | ||||
0.919978 | + | 0.391971i | \(0.128207\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 3889.32i | − 1.28573i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1083.61 | 0.322118 | ||||||||
\(59\) | − 4155.24i | − 1.19369i | −0.802356 | − | 0.596846i | \(-0.796420\pi\) | ||||
0.802356 | − | 0.596846i | \(-0.203580\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1840.09i | 0.494514i | 0.968950 | + | 0.247257i | \(0.0795292\pi\) | ||||
−0.968950 | + | 0.247257i | \(0.920471\pi\) | |||||||
\(62\) | 1124.28i | 0.292476i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 512.000 | 0.125000 | ||||||||
\(65\) | 2838.53 | 0.671842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6315.57 | −1.40690 | −0.703450 | − | 0.710745i | \(-0.748358\pi\) | ||||
−0.703450 | + | 0.710745i | \(0.748358\pi\) | |||||||
\(68\) | − 4343.09i | − 0.939251i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1263.28 | −0.250601 | −0.125301 | − | 0.992119i | \(-0.539990\pi\) | ||||
−0.125301 | + | 0.992119i | \(0.539990\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 3995.44i | − 0.749753i | −0.927075 | − | 0.374877i | \(-0.877685\pi\) | ||||
0.927075 | − | 0.374877i | \(-0.122315\pi\) | |||||||
\(74\) | −2542.51 | −0.464300 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 1119.63i | − 0.193841i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10614.3 | −1.70073 | −0.850366 | − | 0.526192i | \(-0.823619\pi\) | ||||
−0.850366 | + | 0.526192i | \(0.823619\pi\) | |||||||
\(80\) | − 1782.25i | − 0.278477i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 1860.71i | − 0.276727i | ||||||||
\(83\) | − 5750.31i | − 0.834709i | −0.908744 | − | 0.417355i | \(-0.862957\pi\) | ||||
0.908744 | − | 0.417355i | \(-0.137043\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15118.2 | −2.09248 | ||||||||
\(86\) | 3268.82 | 0.441971 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3160.24 | 0.408088 | ||||||||
\(89\) | − 4187.05i | − 0.528601i | −0.964440 | − | 0.264301i | \(-0.914859\pi\) | ||||
0.964440 | − | 0.264301i | \(-0.0851411\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1837.17 | −0.217057 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3661.42i | 0.414375i | ||||||||
\(95\) | −3897.38 | −0.431843 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 3814.28i | − 0.405386i | −0.979242 | − | 0.202693i | \(-0.935031\pi\) | ||||
0.979242 | − | 0.202693i | \(-0.0649694\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1203.96 | −0.120396 | ||||||||
\(101\) | − 4925.41i | − 0.482836i | −0.970421 | − | 0.241418i | \(-0.922387\pi\) | ||||
0.970421 | − | 0.241418i | \(-0.0776126\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 18892.6i | − 1.78081i | −0.455166 | − | 0.890407i | \(-0.650420\pi\) | ||||
0.455166 | − | 0.890407i | \(-0.349580\pi\) | |||||||
\(104\) | 2306.43i | 0.213242i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14618.5 | 1.30104 | ||||||||
\(107\) | 8479.39 | 0.740623 | 0.370311 | − | 0.928908i | \(-0.379251\pi\) | ||||
0.370311 | + | 0.928908i | \(0.379251\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11678.0 | 0.982911 | 0.491455 | − | 0.870903i | \(-0.336465\pi\) | ||||
0.491455 | + | 0.870903i | \(0.336465\pi\) | |||||||
\(110\) | − 11000.7i | − 0.909146i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19683.8 | −1.54153 | −0.770763 | − | 0.637121i | \(-0.780125\pi\) | ||||
−0.770763 | + | 0.637121i | \(0.780125\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6395.13i | 0.483564i | ||||||||
\(116\) | 3064.90 | 0.227772 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 11752.8i | − 0.844067i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4865.03 | 0.332288 | ||||||||
\(122\) | 5204.55i | 0.349674i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3179.94i | 0.206812i | ||||||||
\(125\) | − 13213.9i | − 0.845689i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −27965.5 | −1.73386 | −0.866931 | − | 0.498428i | \(-0.833911\pi\) | ||||
−0.866931 | + | 0.498428i | \(0.833911\pi\) | |||||||
\(128\) | 1448.15 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8028.58 | 0.475064 | ||||||||
\(131\) | − 1169.73i | − 0.0681622i | −0.999419 | − | 0.0340811i | \(-0.989150\pi\) | ||||
0.999419 | − | 0.0340811i | \(-0.0108505\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −17863.1 | −0.994828 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 12284.1i | − 0.664150i | ||||||||
\(137\) | 20884.6 | 1.11272 | 0.556359 | − | 0.830942i | \(-0.312198\pi\) | ||||
0.556359 | + | 0.830942i | \(0.312198\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 3499.87i | − 0.181143i | −0.995890 | − | 0.0905716i | \(-0.971131\pi\) | ||||
0.995890 | − | 0.0905716i | \(-0.0288694\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3573.10 | −0.177202 | ||||||||
\(143\) | 14236.0i | 0.696173i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 10668.8i | − 0.507434i | ||||||||
\(146\) | − 11300.8i | − 0.530156i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7191.29 | −0.328310 | ||||||||
\(149\) | −29533.8 | −1.33029 | −0.665146 | − | 0.746713i | \(-0.731631\pi\) | ||||
−0.665146 | + | 0.746713i | \(0.731631\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 25780.8 | 1.13069 | 0.565344 | − | 0.824856i | \(-0.308744\pi\) | ||||
0.565344 | + | 0.824856i | \(0.308744\pi\) | |||||||
\(152\) | − 3166.78i | − 0.137066i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11069.2 | 0.460738 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 25629.4i | 1.03977i | 0.854235 | + | 0.519887i | \(0.174026\pi\) | ||||
−0.854235 | + | 0.519887i | \(0.825974\pi\) | |||||||
\(158\) | −30021.7 | −1.20260 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 5040.97i | − 0.196913i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6182.78 | −0.232707 | −0.116353 | − | 0.993208i | \(-0.537120\pi\) | ||||
−0.116353 | + | 0.993208i | \(0.537120\pi\) | |||||||
\(164\) | − 5262.90i | − 0.195676i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 16264.3i | − 0.590229i | ||||||||
\(167\) | − 39270.9i | − 1.40811i | −0.710144 | − | 0.704056i | \(-0.751370\pi\) | ||||
0.710144 | − | 0.704056i | \(-0.248630\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18171.2 | 0.636223 | ||||||||
\(170\) | −42760.6 | −1.47961 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9245.61 | 0.312521 | ||||||||
\(173\) | 32905.9i | 1.09946i | 0.835341 | + | 0.549732i | \(0.185270\pi\) | ||||
−0.835341 | + | 0.549732i | \(0.814730\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8938.50 | 0.288562 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 11842.8i | − 0.373777i | ||||||||
\(179\) | 4767.88 | 0.148806 | 0.0744029 | − | 0.997228i | \(-0.476295\pi\) | ||||
0.0744029 | + | 0.997228i | \(0.476295\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 35195.4i | − 1.07431i | −0.843484 | − | 0.537154i | \(-0.819499\pi\) | ||||
0.843484 | − | 0.537154i | \(-0.180501\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5196.31 | −0.153483 | ||||||||
\(185\) | 25032.6i | 0.731413i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 75821.7i | − 2.16826i | ||||||||
\(188\) | 10356.1i | 0.293007i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11023.5 | −0.305359 | ||||||||
\(191\) | −23315.1 | −0.639101 | −0.319551 | − | 0.947569i | \(-0.603532\pi\) | ||||
−0.319551 | + | 0.947569i | \(0.603532\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 59183.8 | 1.58887 | 0.794434 | − | 0.607350i | \(-0.207768\pi\) | ||||
0.794434 | + | 0.607350i | \(0.207768\pi\) | |||||||
\(194\) | − 10788.4i | − 0.286651i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 60902.2 | 1.56928 | 0.784640 | − | 0.619952i | \(-0.212848\pi\) | ||||
0.784640 | + | 0.619952i | \(0.212848\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 40116.7i | − 1.01302i | −0.862233 | − | 0.506512i | \(-0.830935\pi\) | ||||
0.862233 | − | 0.506512i | \(-0.169065\pi\) | |||||||
\(200\) | −3405.30 | −0.0851326 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 13931.2i | − 0.341417i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18319.9 | −0.435930 | ||||||||
\(206\) | − 53436.5i | − 1.25923i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6523.56i | 0.150785i | ||||||||
\(209\) | − 19546.4i | − 0.447482i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21929.0 | 0.492554 | 0.246277 | − | 0.969200i | \(-0.420793\pi\) | ||||
0.246277 | + | 0.969200i | \(0.420793\pi\) | |||||||
\(212\) | 41347.5 | 0.919978 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 23983.3 | 0.523699 | ||||||||
\(215\) | − 32183.6i | − 0.696238i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 33030.3 | 0.695023 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 31114.6i | − 0.642863i | ||||||||
\(221\) | 55336.8 | 1.13300 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 64358.0i | 1.29418i | 0.762416 | + | 0.647088i | \(0.224013\pi\) | ||||
−0.762416 | + | 0.647088i | \(0.775987\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −55674.1 | −1.09002 | ||||||||
\(227\) | 43774.8i | 0.849517i | 0.905307 | + | 0.424759i | \(0.139641\pi\) | ||||
−0.905307 | + | 0.424759i | \(0.860359\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 28506.4i | − 0.543590i | −0.962355 | − | 0.271795i | \(-0.912383\pi\) | ||||
0.962355 | − | 0.271795i | \(-0.0876173\pi\) | |||||||
\(230\) | 18088.2i | 0.341931i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8668.85 | 0.161059 | ||||||||
\(233\) | 2194.89 | 0.0404298 | 0.0202149 | − | 0.999796i | \(-0.493565\pi\) | ||||
0.0202149 | + | 0.999796i | \(0.493565\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 36049.0 | 0.652767 | ||||||||
\(236\) | − 33241.9i | − 0.596846i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −80942.6 | −1.41704 | −0.708519 | − | 0.705692i | \(-0.750636\pi\) | ||||
−0.708519 | + | 0.705692i | \(0.750636\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 43016.6i | 0.740631i | 0.928906 | + | 0.370316i | \(0.120751\pi\) | ||||
−0.928906 | + | 0.370316i | \(0.879249\pi\) | |||||||
\(242\) | 13760.4 | 0.234963 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14720.7i | 0.247257i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14265.5 | 0.233827 | ||||||||
\(248\) | 8994.21i | 0.146238i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 37374.5i | − 0.597992i | ||||||||
\(251\) | 31568.5i | 0.501080i | 0.968106 | + | 0.250540i | \(0.0806082\pi\) | ||||
−0.968106 | + | 0.250540i | \(0.919392\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32073.4 | −0.501076 | ||||||||
\(254\) | −79098.3 | −1.22603 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | − 68105.9i | − 1.03114i | −0.856847 | − | 0.515571i | \(-0.827580\pi\) | ||||
0.856847 | − | 0.515571i | \(-0.172420\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 22708.3 | 0.335921 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 3308.50i | − 0.0481980i | ||||||||
\(263\) | 8347.56 | 0.120684 | 0.0603418 | − | 0.998178i | \(-0.480781\pi\) | ||||
0.0603418 | + | 0.998178i | \(0.480781\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 143929.i | − 2.04954i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −50524.6 | −0.703450 | ||||||||
\(269\) | 91921.0i | 1.27031i | 0.772384 | + | 0.635156i | \(0.219064\pi\) | ||||
−0.772384 | + | 0.635156i | \(0.780936\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5134.36i | 0.0699114i | 0.999389 | + | 0.0349557i | \(0.0111290\pi\) | ||||
−0.999389 | + | 0.0349557i | \(0.988871\pi\) | |||||||
\(272\) | − 34744.8i | − 0.469625i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 59070.5 | 0.786810 | ||||||||
\(275\) | −21018.7 | −0.277933 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −66254.2 | −0.863483 | −0.431741 | − | 0.901997i | \(-0.642101\pi\) | ||||
−0.431741 | + | 0.901997i | \(0.642101\pi\) | |||||||
\(278\) | − 9899.12i | − 0.128088i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −38156.4 | −0.483230 | −0.241615 | − | 0.970372i | \(-0.577677\pi\) | ||||
−0.241615 | + | 0.970372i | \(0.577677\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 110233.i | 1.37638i | 0.725528 | + | 0.688192i | \(0.241595\pi\) | ||||
−0.725528 | + | 0.688192i | \(0.758405\pi\) | |||||||
\(284\) | −10106.3 | −0.125301 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 40265.6i | 0.492268i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −211205. | −2.52877 | ||||||||
\(290\) | − 30175.9i | − 0.358810i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 31963.5i | − 0.374877i | ||||||||
\(293\) | 79011.7i | 0.920357i | 0.887826 | + | 0.460179i | \(0.152215\pi\) | ||||
−0.887826 | + | 0.460179i | \(0.847785\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −115714. | −1.32966 | ||||||||
\(296\) | −20340.0 | −0.232150 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −83534.2 | −0.940659 | ||||||||
\(299\) | − 23408.0i | − 0.261832i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 72919.1 | 0.799517 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 8957.01i | − 0.0969206i | ||||||||
\(305\) | 51242.2 | 0.550843 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2801.57i | 0.0297252i | 0.999890 | + | 0.0148626i | \(0.00473109\pi\) | ||||
−0.999890 | + | 0.0148626i | \(0.995269\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 31308.5 | 0.325791 | ||||||||
\(311\) | 20659.3i | 0.213597i | 0.994281 | + | 0.106799i | \(0.0340600\pi\) | ||||
−0.994281 | + | 0.106799i | \(0.965940\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 37376.1i | 0.381509i | 0.981638 | + | 0.190755i | \(0.0610935\pi\) | ||||
−0.981638 | + | 0.190755i | \(0.938907\pi\) | |||||||
\(314\) | 72490.8i | 0.735231i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −84914.1 | −0.850366 | ||||||||
\(317\) | 106666. | 1.06147 | 0.530735 | − | 0.847538i | \(-0.321916\pi\) | ||||
0.530735 | + | 0.847538i | \(0.321916\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 53507.1 | 0.525811 | ||||||||
\(320\) | − 14258.0i | − 0.139239i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −75978.8 | −0.728262 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 15340.0i | − 0.145231i | ||||||||
\(326\) | −17487.5 | −0.164548 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 14885.7i | − 0.138364i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 108363. | 0.989063 | 0.494532 | − | 0.869160i | \(-0.335340\pi\) | ||||
0.494532 | + | 0.869160i | \(0.335340\pi\) | |||||||
\(332\) | − 46002.5i | − 0.417355i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 111075.i | − 0.995686i | ||||||||
\(335\) | 175874.i | 1.56716i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 186946. | 1.64610 | 0.823050 | − | 0.567968i | \(-0.192270\pi\) | ||||
0.823050 | + | 0.567968i | \(0.192270\pi\) | |||||||
\(338\) | 51395.8 | 0.449877 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −120945. | −1.04624 | ||||||||
\(341\) | 55515.3i | 0.477424i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 26150.5 | 0.220985 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 93071.9i | 0.777439i | ||||||||
\(347\) | 63227.3 | 0.525105 | 0.262552 | − | 0.964918i | \(-0.415436\pi\) | ||||
0.262552 | + | 0.964918i | \(0.415436\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 93605.0i | − 0.768508i | −0.923227 | − | 0.384254i | \(-0.874459\pi\) | ||||
0.923227 | − | 0.384254i | \(-0.125541\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 25281.9 | 0.204044 | ||||||||
\(353\) | − 143251.i | − 1.14960i | −0.818294 | − | 0.574800i | \(-0.805080\pi\) | ||||
0.818294 | − | 0.574800i | \(-0.194920\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 35179.5i | 0.279147i | ||||||||
\(356\) | − 33496.4i | − 0.264301i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13485.6 | 0.105222 | ||||||||
\(359\) | −102340. | −0.794065 | −0.397032 | − | 0.917805i | \(-0.629960\pi\) | ||||
−0.397032 | + | 0.917805i | \(0.629960\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 110734. | 0.849702 | ||||||||
\(362\) | − 99547.7i | − 0.759651i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −111264. | −0.835156 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15366.4i | 0.114088i | 0.998372 | + | 0.0570442i | \(0.0181676\pi\) | ||||
−0.998372 | + | 0.0570442i | \(0.981832\pi\) | |||||||
\(368\) | −14697.4 | −0.108529 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 70803.0i | 0.517187i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 97490.8 | 0.700722 | 0.350361 | − | 0.936615i | \(-0.386059\pi\) | ||||
0.350361 | + | 0.936615i | \(0.386059\pi\) | |||||||
\(374\) | − 214456.i | − 1.53319i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 29291.3i | 0.207188i | ||||||||
\(377\) | 39050.9i | 0.274757i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −66090.7 | −0.460110 | −0.230055 | − | 0.973178i | \(-0.573891\pi\) | ||||
−0.230055 | + | 0.973178i | \(0.573891\pi\) | |||||||
\(380\) | −31179.0 | −0.215921 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −65944.9 | −0.451913 | ||||||||
\(383\) | 208901.i | 1.42411i | 0.702126 | + | 0.712053i | \(0.252234\pi\) | ||||
−0.702126 | + | 0.712053i | \(0.747766\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 167397. | 1.12350 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 30514.2i | − 0.202693i | ||||||||
\(389\) | 143999. | 0.951614 | 0.475807 | − | 0.879550i | \(-0.342156\pi\) | ||||
0.475807 | + | 0.879550i | \(0.342156\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 124672.i | 0.815485i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 172257. | 1.10965 | ||||||||
\(395\) | 295583.i | 1.89446i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 284577.i | 1.80559i | 0.430070 | + | 0.902796i | \(0.358489\pi\) | ||||
−0.430070 | + | 0.902796i | \(0.641511\pi\) | |||||||
\(398\) | − 113467.i | − 0.716316i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9631.65 | −0.0601978 | ||||||||
\(401\) | 107846. | 0.670680 | 0.335340 | − | 0.942097i | \(-0.391149\pi\) | ||||
0.335340 | + | 0.942097i | \(0.391149\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −40516.6 | −0.249472 | ||||||||
\(404\) | − 39403.3i | − 0.241418i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −125546. | −0.757901 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 84932.2i | 0.507722i | 0.967241 | + | 0.253861i | \(0.0817005\pi\) | ||||
−0.967241 | + | 0.253861i | \(0.918299\pi\) | |||||||
\(410\) | −51816.6 | −0.308249 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 151141.i | − 0.890407i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −160133. | −0.929789 | ||||||||
\(416\) | 18451.4i | 0.106621i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 55285.7i | − 0.316417i | ||||||||
\(419\) | − 331905.i | − 1.89054i | −0.326292 | − | 0.945269i | \(-0.605799\pi\) | ||||
0.326292 | − | 0.945269i | \(-0.394201\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 101490. | 0.572609 | 0.286304 | − | 0.958139i | \(-0.407573\pi\) | ||||
0.286304 | + | 0.958139i | \(0.407573\pi\) | |||||||
\(422\) | 62024.5 | 0.348288 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 116948. | 0.650522 | ||||||||
\(425\) | 81701.5i | 0.452327i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 67835.1 | 0.370311 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − 91029.0i | − 0.492315i | ||||||||
\(431\) | −229798. | −1.23706 | −0.618530 | − | 0.785761i | \(-0.712272\pi\) | ||||
−0.618530 | + | 0.785761i | \(0.712272\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 114264.i | 0.609442i | 0.952442 | + | 0.304721i | \(0.0985632\pi\) | ||||
−0.952442 | + | 0.304721i | \(0.901437\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 93423.7 | 0.491455 | ||||||||
\(437\) | 32139.8i | 0.168299i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 352339.i | 1.82823i | 0.405453 | + | 0.914116i | \(0.367114\pi\) | ||||
−0.405453 | + | 0.914116i | \(0.632886\pi\) | |||||||
\(440\) | − 88005.3i | − 0.454573i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 156516. | 0.801151 | ||||||||
\(443\) | 196316. | 1.00034 | 0.500172 | − | 0.865926i | \(-0.333270\pi\) | ||||
0.500172 | + | 0.865926i | \(0.333270\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −116600. | −0.588813 | ||||||||
\(446\) | 182032.i | 0.915120i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −77520.3 | −0.384523 | −0.192262 | − | 0.981344i | \(-0.561582\pi\) | ||||
−0.192262 | + | 0.981344i | \(0.561582\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 91879.6i | − 0.451717i | ||||||||
\(452\) | −157470. | −0.770763 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 123814.i | 0.600699i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 189872. | 0.909137 | 0.454568 | − | 0.890712i | \(-0.349794\pi\) | ||||
0.454568 | + | 0.890712i | \(0.349794\pi\) | |||||||
\(458\) | − 80628.3i | − 0.384376i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 51161.1i | 0.241782i | ||||||||
\(461\) | − 52599.9i | − 0.247505i | −0.992313 | − | 0.123752i | \(-0.960507\pi\) | ||||
0.992313 | − | 0.123752i | \(-0.0394928\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −244268. | −1.13947 | −0.569736 | − | 0.821828i | \(-0.692955\pi\) | ||||
−0.569736 | + | 0.821828i | \(0.692955\pi\) | |||||||
\(464\) | 24519.2 | 0.113886 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6208.09 | 0.0285882 | ||||||||
\(467\) | 297615.i | 1.36465i | 0.731050 | + | 0.682324i | \(0.239031\pi\) | ||||
−0.731050 | + | 0.682324i | \(0.760969\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 101962. | 0.461576 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 94022.3i | − 0.422034i | ||||||||
\(473\) | 161410. | 0.721452 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21062.2i | 0.0933505i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −228940. | −1.00200 | ||||||||
\(479\) | 46870.8i | 0.204283i | 0.994770 | + | 0.102141i | \(0.0325694\pi\) | ||||
−0.994770 | + | 0.102141i | \(0.967431\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 91626.6i | − 0.396033i | ||||||||
\(482\) | 121669.i | 0.523706i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 38920.3 | 0.166144 | ||||||||
\(485\) | −106219. | −0.451563 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 107184. | 0.451930 | 0.225965 | − | 0.974135i | \(-0.427446\pi\) | ||||
0.225965 | + | 0.974135i | \(0.427446\pi\) | |||||||
\(488\) | 41636.4i | 0.174837i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 116367. | 0.482687 | 0.241344 | − | 0.970440i | \(-0.422412\pi\) | ||||
0.241344 | + | 0.970440i | \(0.422412\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 207987.i | − 0.855740i | ||||||||
\(494\) | 40349.0 | 0.165340 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 25439.5i | 0.103406i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 442908. | 1.77874 | 0.889369 | − | 0.457190i | \(-0.151144\pi\) | ||||
0.889369 | + | 0.457190i | \(0.151144\pi\) | |||||||
\(500\) | − 105711.i | − 0.422844i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 89289.3i | 0.354317i | ||||||||
\(503\) | − 68955.1i | − 0.272540i | −0.990672 | − | 0.136270i | \(-0.956489\pi\) | ||||
0.990672 | − | 0.136270i | \(-0.0435115\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −137161. | −0.537835 | ||||||||
\(506\) | −90717.2 | −0.354314 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −223724. | −0.866931 | ||||||||
\(509\) | − 92773.5i | − 0.358087i | −0.983841 | − | 0.179044i | \(-0.942700\pi\) | ||||
0.983841 | − | 0.179044i | \(-0.0573003\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11585.2 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 192632.i | − 0.729127i | ||||||||
\(515\) | −526117. | −1.98366 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 180796.i | 0.676406i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 64228.7 | 0.237532 | ||||||||
\(521\) | − 142912.i | − 0.526495i | −0.964728 | − | 0.263248i | \(-0.915206\pi\) | ||||
0.964728 | − | 0.263248i | \(-0.0847936\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 22203.5i | − 0.0811742i | −0.999176 | − | 0.0405871i | \(-0.987077\pi\) | ||||
0.999176 | − | 0.0405871i | \(-0.0129228\pi\) | |||||||
\(524\) | − 9357.85i | − 0.0340811i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23610.5 | 0.0853361 | ||||||||
\(527\) | 215793. | 0.776992 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −227103. | −0.811544 | ||||||||
\(530\) | − 407093.i | − 1.44924i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 67056.3 | 0.236040 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 236132.i | − 0.824986i | ||||||||
\(536\) | −142905. | −0.497414 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 259992.i | 0.898246i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 211209. | 0.721636 | 0.360818 | − | 0.932636i | \(-0.382498\pi\) | ||||
0.360818 | + | 0.932636i | \(0.382498\pi\) | |||||||
\(542\) | 14522.2i | 0.0494348i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 98273.0i | − 0.332075i | ||||||||
\(545\) | − 325204.i | − 1.09487i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 254227. | 0.849664 | 0.424832 | − | 0.905272i | \(-0.360333\pi\) | ||||
0.424832 | + | 0.905272i | \(0.360333\pi\) | |||||||
\(548\) | 167077. | 0.556359 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −59449.8 | −0.196528 | ||||||||
\(551\) | − 53617.9i | − 0.176606i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −187395. | −0.610575 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 27998.9i | − 0.0905716i | ||||||||
\(557\) | −46139.2 | −0.148717 | −0.0743584 | − | 0.997232i | \(-0.523691\pi\) | ||||
−0.0743584 | + | 0.997232i | \(0.523691\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 117801.i | 0.376987i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −107922. | −0.341695 | ||||||||
\(563\) | 349629.i | 1.10304i | 0.834162 | + | 0.551519i | \(0.185952\pi\) | ||||
−0.834162 | + | 0.551519i | \(0.814048\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 548147.i | 1.71712i | ||||||||
\(566\) | 311787.i | 0.973251i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −28584.8 | −0.0886010 | ||||||||
\(569\) | 176196. | 0.544217 | 0.272109 | − | 0.962267i | \(-0.412279\pi\) | ||||
0.272109 | + | 0.962267i | \(0.412279\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −176527. | −0.541426 | −0.270713 | − | 0.962660i | \(-0.587259\pi\) | ||||
−0.270713 | + | 0.962660i | \(0.587259\pi\) | |||||||
\(572\) | 113888.i | 0.348086i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34560.6 | 0.104531 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 226863.i | 0.681416i | 0.940169 | + | 0.340708i | \(0.110667\pi\) | ||||
−0.940169 | + | 0.340708i | \(0.889333\pi\) | |||||||
\(578\) | −597378. | −1.78811 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 85350.5i | − 0.253717i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 721844. | 2.12376 | ||||||||
\(584\) | − 90406.4i | − 0.265078i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 223479.i | 0.650791i | ||||||||
\(587\) | 349659.i | 1.01477i | 0.861719 | + | 0.507386i | \(0.169388\pi\) | ||||
−0.861719 | + | 0.507386i | \(0.830612\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 55630.3 | 0.160354 | ||||||||
\(590\) | −327288. | −0.940213 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −57530.3 | −0.164155 | ||||||||
\(593\) | 137755.i | 0.391739i | 0.980630 | + | 0.195870i | \(0.0627529\pi\) | ||||
−0.980630 | + | 0.195870i | \(0.937247\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −236271. | −0.665146 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 66207.9i | − 0.185143i | ||||||||
\(599\) | −80877.2 | −0.225410 | −0.112705 | − | 0.993629i | \(-0.535951\pi\) | ||||
−0.112705 | + | 0.993629i | \(0.535951\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 228798.i | 0.633438i | 0.948519 | + | 0.316719i | \(0.102581\pi\) | ||||
−0.948519 | + | 0.316719i | \(0.897419\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 206246. | 0.565344 | ||||||||
\(605\) | − 135480.i | − 0.370139i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 265951.i | − 0.721812i | −0.932602 | − | 0.360906i | \(-0.882468\pi\) | ||||
0.932602 | − | 0.360906i | \(-0.117532\pi\) | |||||||
\(608\) | − 25334.3i | − 0.0685332i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 144935. | 0.389505 | ||||||||
\(611\) | −131950. | −0.353449 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −306522. | −0.815718 | −0.407859 | − | 0.913045i | \(-0.633725\pi\) | ||||
−0.407859 | + | 0.913045i | \(0.633725\pi\) | |||||||
\(614\) | 7924.04i | 0.0210189i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −491906. | −1.29215 | −0.646074 | − | 0.763275i | \(-0.723590\pi\) | ||||
−0.646074 | + | 0.763275i | \(0.723590\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 115230.i | 0.300735i | 0.988630 | + | 0.150368i | \(0.0480457\pi\) | ||||
−0.988630 | + | 0.150368i | \(0.951954\pi\) | |||||||
\(620\) | 88553.9 | 0.230369 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 58433.5i | 0.151036i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −462035. | −1.18281 | ||||||||
\(626\) | 105716.i | 0.269768i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 205035.i | 0.519887i | ||||||||
\(629\) | 488007.i | 1.23346i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 72815.9 | 0.182880 | 0.0914402 | − | 0.995811i | \(-0.470853\pi\) | ||||
0.0914402 | + | 0.995811i | \(0.470853\pi\) | |||||||
\(632\) | −240173. | −0.601299 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 301697. | 0.750572 | ||||||||
\(635\) | 778774.i | 1.93136i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 151341. | 0.371805 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 40327.8i | − 0.0984565i | ||||||||
\(641\) | 757794. | 1.84431 | 0.922157 | − | 0.386815i | \(-0.126425\pi\) | ||||
0.922157 | + | 0.386815i | \(0.126425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 353082.i | 0.853992i | 0.904254 | + | 0.426996i | \(0.140428\pi\) | ||||
−0.904254 | + | 0.426996i | \(0.859572\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −214901. | −0.514959 | ||||||||
\(647\) | − 214561.i | − 0.512557i | −0.966603 | − | 0.256279i | \(-0.917504\pi\) | ||||
0.966603 | − | 0.256279i | \(-0.0824965\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 580337.i | − 1.37782i | ||||||||
\(650\) | − 43388.1i | − 0.102694i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −49462.3 | −0.116353 | ||||||||
\(653\) | 497591. | 1.16693 | 0.583467 | − | 0.812137i | \(-0.301696\pi\) | ||||
0.583467 | + | 0.812137i | \(0.301696\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −32574.3 | −0.0759264 | ||||||||
\(656\) | − 42103.2i | − 0.0978379i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 197464. | 0.454692 | 0.227346 | − | 0.973814i | \(-0.426995\pi\) | ||||
0.227346 | + | 0.973814i | \(0.426995\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 668423.i | 1.52985i | 0.644121 | + | 0.764924i | \(0.277223\pi\) | ||||
−0.644121 | + | 0.764924i | \(0.722777\pi\) | |||||||
\(662\) | 306496. | 0.699373 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − 130115.i | − 0.295114i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −87980.6 | −0.197759 | ||||||||
\(668\) | − 314167.i | − 0.704056i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 497447.i | 1.10815i | ||||||||
\(671\) | 256994.i | 0.570792i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −404534. | −0.893151 | −0.446575 | − | 0.894746i | \(-0.647357\pi\) | ||||
−0.446575 | + | 0.894746i | \(0.647357\pi\) | |||||||
\(674\) | 528763. | 1.16397 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 145369. | 0.318111 | ||||||||
\(677\) | − 211169.i | − 0.460737i | −0.973103 | − | 0.230369i | \(-0.926007\pi\) | ||||
0.973103 | − | 0.230369i | \(-0.0739932\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −342085. | −0.739803 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 157021.i | 0.337590i | ||||||||
\(683\) | 170109. | 0.364657 | 0.182329 | − | 0.983238i | \(-0.441637\pi\) | ||||
0.182329 | + | 0.983238i | \(0.441637\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 581588.i | − 1.23946i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 73964.9 | 0.156260 | ||||||||
\(689\) | 526822.i | 1.10975i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 168630.i | 0.353167i | 0.984286 | + | 0.176583i | \(0.0565045\pi\) | ||||
−0.984286 | + | 0.176583i | \(0.943496\pi\) | |||||||
\(692\) | 263247.i | 0.549732i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 178834. | 0.371305 | ||||||||
\(695\) | −97463.3 | −0.201777 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −357145. | −0.735154 | ||||||||
\(698\) | − 264755.i | − 0.543417i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 487646. | 0.992359 | 0.496179 | − | 0.868220i | \(-0.334736\pi\) | ||||
0.496179 | + | 0.868220i | \(0.334736\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 125806.i | 0.254560i | ||||||||
\(704\) | 71508.0 | 0.144281 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 405174.i | − 0.812890i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −386929. | −0.769731 | −0.384865 | − | 0.922973i | \(-0.625752\pi\) | ||||
−0.384865 | + | 0.922973i | \(0.625752\pi\) | |||||||
\(710\) | 99502.6i | 0.197387i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 94742.1i | − 0.186889i | ||||||||
\(713\) | − 91282.7i | − 0.179560i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 396441. | 0.775472 | ||||||||
\(716\) | 38143.1 | 0.0744029 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −289461. | −0.561489 | ||||||||
\(719\) | − 188374.i | − 0.364388i | −0.983263 | − | 0.182194i | \(-0.941680\pi\) | ||||
0.983263 | − | 0.182194i | \(-0.0583199\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 313203. | 0.600830 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 281563.i | − 0.537154i | ||||||||
\(725\) | −57656.4 | −0.109691 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 901538.i | 1.70575i | 0.522115 | + | 0.852875i | \(0.325143\pi\) | ||||
−0.522115 | + | 0.852875i | \(0.674857\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −314701. | −0.590545 | ||||||||
\(731\) | − 627415.i | − 1.17414i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 402482.i | 0.749098i | 0.927207 | + | 0.374549i | \(0.122202\pi\) | ||||
−0.927207 | + | 0.374549i | \(0.877798\pi\) | |||||||
\(734\) | 43462.9i | 0.0806726i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −41570.5 | −0.0767414 | ||||||||
\(737\) | −882058. | −1.62391 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37301.1 | −0.0683020 | −0.0341510 | − | 0.999417i | \(-0.510873\pi\) | ||||
−0.0341510 | + | 0.999417i | \(0.510873\pi\) | |||||||
\(740\) | 200261.i | 0.365707i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 831221. | 1.50570 | 0.752851 | − | 0.658191i | \(-0.228678\pi\) | ||||
0.752851 | + | 0.658191i | \(0.228678\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 822449.i | 1.48182i | ||||||||
\(746\) | 275746. | 0.495486 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 606574.i | − 1.08413i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −251098. | −0.445209 | −0.222605 | − | 0.974909i | \(-0.571456\pi\) | ||||
−0.222605 | + | 0.974909i | \(0.571456\pi\) | |||||||
\(752\) | 82848.4i | 0.146504i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 110453.i | 0.194282i | ||||||||
\(755\) | − 717936.i | − 1.25948i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −422399. | −0.737108 | −0.368554 | − | 0.929606i | \(-0.620147\pi\) | ||||
−0.368554 | + | 0.929606i | \(0.620147\pi\) | |||||||
\(758\) | −186933. | −0.325347 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −88187.6 | −0.152679 | ||||||||
\(761\) | − 247203.i | − 0.426859i | −0.976958 | − | 0.213430i | \(-0.931537\pi\) | ||||
0.976958 | − | 0.213430i | \(-0.0684634\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −186520. | −0.319551 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 590860.i | 1.00699i | ||||||||
\(767\) | 423546. | 0.719962 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 903767.i | − 1.52828i | −0.645049 | − | 0.764141i | \(-0.723163\pi\) | ||||
0.645049 | − | 0.764141i | \(-0.276837\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 473470. | 0.794434 | ||||||||
\(773\) | 244667.i | 0.409464i | 0.978818 | + | 0.204732i | \(0.0656323\pi\) | ||||
−0.978818 | + | 0.204732i | \(0.934368\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 59820.4i | − 0.0995968i | ||||||||
\(776\) | − 86307.3i | − 0.143326i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 407291. | 0.672893 | ||||||||
\(779\) | −92070.0 | −0.151720 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −176435. | −0.289256 | ||||||||
\(782\) | 352626.i | 0.576635i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 713719. | 1.15821 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 950431.i | − 1.53452i | −0.641339 | − | 0.767258i | \(-0.721621\pi\) | ||||
0.641339 | − | 0.767258i | \(-0.278379\pi\) | |||||||
\(788\) | 487218. | 0.784640 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 836035.i | 1.33958i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −187561. | −0.298261 | ||||||||
\(794\) | 804907.i | 1.27675i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 320934.i | − 0.506512i | ||||||||
\(797\) | 560412.i | 0.882248i | 0.897446 | + | 0.441124i | \(0.145420\pi\) | ||||
−0.897446 | + | 0.441124i | \(0.854580\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 702771. | 1.10083 | ||||||||
\(800\) | −27242.4 | −0.0425663 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 305035. | 0.474242 | ||||||||
\(803\) | − 558019.i | − 0.865401i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −114598. | −0.176404 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 111449.i | − 0.170708i | ||||||||
\(809\) | 51864.2 | 0.0792447 | 0.0396224 | − | 0.999215i | \(-0.487385\pi\) | ||||
0.0396224 | + | 0.999215i | \(0.487385\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 978879.i | − 1.48829i | −0.668019 | − | 0.744145i | \(-0.732857\pi\) | ||||
0.668019 | − | 0.744145i | \(-0.267143\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −355097. | −0.535917 | ||||||||
\(815\) | 172176.i | 0.259214i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 161744.i | − 0.242317i | ||||||||
\(818\) | 240224.i | 0.359013i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −146560. | −0.217965 | ||||||||
\(821\) | −148798. | −0.220755 | −0.110377 | − | 0.993890i | \(-0.535206\pi\) | ||||
−0.110377 | + | 0.993890i | \(0.535206\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.33907e6 | 1.97698 | 0.988490 | − | 0.151287i | \(-0.0483416\pi\) | ||||
0.988490 | + | 0.151287i | \(0.0483416\pi\) | |||||||
\(824\) | − 427492.i | − 0.629613i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 127284. | 0.186108 | 0.0930538 | − | 0.995661i | \(-0.470337\pi\) | ||||
0.0930538 | + | 0.995661i | \(0.470337\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 445598.i | − 0.648386i | −0.945991 | − | 0.324193i | \(-0.894907\pi\) | ||||
0.945991 | − | 0.324193i | \(-0.105093\pi\) | |||||||
\(830\) | −452924. | −0.657460 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 52188.5i | 0.0753924i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.09360e6 | −1.56851 | ||||||||
\(836\) | − 156372.i | − 0.223741i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 938768.i | − 1.33681i | ||||||||
\(839\) | 552232.i | 0.784509i | 0.919857 | + | 0.392254i | \(0.128305\pi\) | ||||
−0.919857 | + | 0.392254i | \(0.871695\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −560506. | −0.792479 | ||||||||
\(842\) | 287056. | 0.404896 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 175432. | 0.246277 | ||||||||
\(845\) | − 506025.i | − 0.708694i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 330780. | 0.459989 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 231087.i | 0.319843i | ||||||||
\(851\) | 206432. | 0.285048 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 753308.i | 1.03532i | 0.855586 | + | 0.517660i | \(0.173197\pi\) | ||||
−0.855586 | + | 0.517660i | \(0.826803\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 191867. | 0.261850 | ||||||||
\(857\) | − 1.30117e6i | − 1.77163i | −0.464037 | − | 0.885816i | \(-0.653600\pi\) | ||||
0.464037 | − | 0.885816i | \(-0.346400\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 982372.i | 1.33134i | 0.746245 | + | 0.665671i | \(0.231855\pi\) | ||||
−0.746245 | + | 0.665671i | \(0.768145\pi\) | |||||||
\(860\) | − 257469.i | − 0.348119i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −649966. | −0.874734 | ||||||||
\(863\) | 721435. | 0.968670 | 0.484335 | − | 0.874883i | \(-0.339062\pi\) | ||||
0.484335 | + | 0.874883i | \(0.339062\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 916353. | 1.22470 | ||||||||
\(866\) | 323186.i | 0.430940i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.48243e6 | −1.96307 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 643750.i | − 0.848557i | ||||||||
\(872\) | 264242. | 0.347511 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 90905.2i | 0.119005i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −717008. | −0.932234 | −0.466117 | − | 0.884723i | \(-0.654347\pi\) | ||||
−0.466117 | + | 0.884723i | \(0.654347\pi\) | |||||||
\(878\) | 996564.i | 1.29276i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − 248917.i | − 0.321432i | ||||||||
\(881\) | − 79128.9i | − 0.101949i | −0.998700 | − | 0.0509745i | \(-0.983767\pi\) | ||||
0.998700 | − | 0.0509745i | \(-0.0162327\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −286591. | −0.367571 | −0.183786 | − | 0.982966i | \(-0.558835\pi\) | ||||
−0.183786 | + | 0.982966i | \(0.558835\pi\) | |||||||
\(884\) | 442694. | 0.566499 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 555267. | 0.707350 | ||||||||
\(887\) | 837465.i | 1.06444i | 0.846607 | + | 0.532218i | \(0.178641\pi\) | ||||
−0.846607 | + | 0.532218i | \(0.821359\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −329794. | −0.416354 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 514864.i | 0.647088i | ||||||||
\(893\) | 181171. | 0.227188 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 132775.i | − 0.165756i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −219261. | −0.271899 | ||||||||
\(899\) | 152284.i | 0.188424i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 2.80588e6i | − 3.45636i | ||||||||
\(902\) | − 259875.i | − 0.319412i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −445393. | −0.545012 | ||||||||
\(905\) | −980112. | −1.19668 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −846569. | −1.02908 | −0.514538 | − | 0.857467i | \(-0.672037\pi\) | ||||
−0.514538 | + | 0.857467i | \(0.672037\pi\) | |||||||
\(908\) | 350198.i | 0.424759i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −167017. | −0.201244 | −0.100622 | − | 0.994925i | \(-0.532083\pi\) | ||||
−0.100622 | + | 0.994925i | \(0.532083\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 803112.i | − 0.963461i | ||||||||
\(914\) | 537040. | 0.642857 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 228051.i | − 0.271795i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.12203e6 | 1.32854 | 0.664268 | − | 0.747494i | \(-0.268743\pi\) | ||||
0.664268 | + | 0.747494i | \(0.268743\pi\) | |||||||
\(920\) | 144705.i | 0.170966i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 148775.i | − 0.175012i | ||||||||
\(923\) | − 128767.i | − 0.151148i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 135281. | 0.158108 | ||||||||
\(926\) | −690893. | −0.805729 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 69350.8 | 0.0805296 | ||||||||
\(929\) | − 1.42663e6i | − 1.65302i | −0.562921 | − | 0.826511i | \(-0.690323\pi\) | ||||
0.562921 | − | 0.826511i | \(-0.309677\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 17559.1 | 0.0202149 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 841781.i | 0.964952i | ||||||||
\(935\) | −2.11146e6 | −2.41524 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 265587.i | − 0.302502i | −0.988495 | − | 0.151251i | \(-0.951670\pi\) | ||||
0.988495 | − | 0.151251i | \(-0.0483301\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 288392. | 0.326383 | ||||||||
\(941\) | 598591.i | 0.676007i | 0.941145 | + | 0.338003i | \(0.109751\pi\) | ||||
−0.941145 | + | 0.338003i | \(0.890249\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 151076.i | 0.169892i | ||||||||
\(944\) | − 265935.i | − 0.298423i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 456536. | 0.510144 | ||||||||
\(947\) | −1.15085e6 | −1.28328 | −0.641639 | − | 0.767007i | \(-0.721745\pi\) | ||||
−0.641639 | + | 0.767007i | \(0.721745\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 407257. | 0.452206 | ||||||||
\(950\) | 59572.9i | 0.0660088i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −464604. | −0.511561 | −0.255781 | − | 0.966735i | \(-0.582332\pi\) | ||||
−0.255781 | + | 0.966735i | \(0.582332\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 649271.i | 0.711900i | ||||||||
\(956\) | −647541. | −0.708519 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 132571.i | 0.144450i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 765521. | 0.828916 | ||||||||
\(962\) | − 259159.i | − 0.280038i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 344133.i | 0.370316i | ||||||||
\(965\) | − 1.64813e6i | − 1.76985i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 101298. | 0.108330 | 0.0541648 | − | 0.998532i | \(-0.482750\pi\) | ||||
0.0541648 | + | 0.998532i | \(0.482750\pi\) | |||||||
\(968\) | 110083. | 0.117482 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −300432. | −0.319303 | ||||||||
\(971\) | − 326280.i | − 0.346060i | −0.984917 | − | 0.173030i | \(-0.944644\pi\) | ||||
0.984917 | − | 0.173030i | \(-0.0553558\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 303162. | 0.319563 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 117765.i | 0.123628i | ||||||||
\(977\) | −741928. | −0.777272 | −0.388636 | − | 0.921391i | \(-0.627054\pi\) | ||||
−0.388636 | + | 0.921391i | \(0.627054\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 584780.i | − 0.610137i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 329135. | 0.341311 | ||||||||
\(983\) | − 584497.i | − 0.604888i | −0.953167 | − | 0.302444i | \(-0.902197\pi\) | ||||
0.953167 | − | 0.302444i | \(-0.0978026\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 1.69599e6i | − 1.74803i | ||||||||
\(986\) | − 588276.i | − 0.605100i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 114124. | 0.116913 | ||||||||
\(989\) | −265403. | −0.271340 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 582343. | 0.592969 | 0.296484 | − | 0.955038i | \(-0.404186\pi\) | ||||
0.296484 | + | 0.955038i | \(0.404186\pi\) | |||||||
\(992\) | 71953.7i | 0.0731189i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.11716e6 | −1.12842 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.36934e6i | − 1.37759i | −0.724954 | − | 0.688797i | \(-0.758139\pi\) | ||||
0.724954 | − | 0.688797i | \(-0.241861\pi\) | |||||||
\(998\) | 1.25273e6 | 1.25776 | ||||||||
\(999\) | 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.c.c.685.3 | 4 | ||
3.2 | odd | 2 | 98.5.b.a.97.1 | ✓ | 4 | ||
7.6 | odd | 2 | inner | 882.5.c.c.685.4 | 4 | ||
12.11 | even | 2 | 784.5.c.a.97.4 | 4 | |||
21.2 | odd | 6 | 98.5.d.c.31.4 | 8 | |||
21.5 | even | 6 | 98.5.d.c.31.3 | 8 | |||
21.11 | odd | 6 | 98.5.d.c.19.3 | 8 | |||
21.17 | even | 6 | 98.5.d.c.19.4 | 8 | |||
21.20 | even | 2 | 98.5.b.a.97.2 | yes | 4 | ||
84.83 | odd | 2 | 784.5.c.a.97.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.5.b.a.97.1 | ✓ | 4 | 3.2 | odd | 2 | ||
98.5.b.a.97.2 | yes | 4 | 21.20 | even | 2 | ||
98.5.d.c.19.3 | 8 | 21.11 | odd | 6 | |||
98.5.d.c.19.4 | 8 | 21.17 | even | 6 | |||
98.5.d.c.31.3 | 8 | 21.5 | even | 6 | |||
98.5.d.c.31.4 | 8 | 21.2 | odd | 6 | |||
784.5.c.a.97.1 | 4 | 84.83 | odd | 2 | |||
784.5.c.a.97.4 | 4 | 12.11 | even | 2 | |||
882.5.c.c.685.3 | 4 | 1.1 | even | 1 | trivial | ||
882.5.c.c.685.4 | 4 | 7.6 | odd | 2 | inner |