Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(191,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.191");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.6567334422\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.4 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.191 |
Dual form | 384.4.f.c.191.3 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.24264 | + | 3.00000i | 0.816497 | + | 0.577350i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.65685 | −0.505964 | −0.252982 | − | 0.967471i | \(-0.581411\pi\) | ||||
−0.252982 | + | 0.967471i | \(0.581411\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.9706i | 0.916324i | 0.888869 | + | 0.458162i | \(0.151492\pi\) | ||||
−0.888869 | + | 0.458162i | \(0.848508\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | + | 25.4558i | 0.333333 | + | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 30.0000i | − | 0.822304i | −0.911567 | − | 0.411152i | \(-0.865127\pi\) | ||
0.911567 | − | 0.411152i | \(-0.134873\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 72.0000i | 1.53609i | 0.640394 | + | 0.768046i | \(0.278771\pi\) | ||||
−0.640394 | + | 0.768046i | \(0.721229\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −24.0000 | − | 16.9706i | −0.413118 | − | 0.292119i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 50.9117i | − | 0.726347i | −0.931722 | − | 0.363173i | \(-0.881693\pi\) | ||
0.931722 | − | 0.363173i | \(-0.118307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.4558 | 0.307367 | 0.153683 | − | 0.988120i | \(-0.450886\pi\) | ||||
0.153683 | + | 0.988120i | \(0.450886\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −50.9117 | + | 72.0000i | −0.529040 | + | 0.748176i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −144.000 | −1.30548 | −0.652741 | − | 0.757581i | \(-0.726381\pi\) | ||||
−0.652741 | + | 0.757581i | \(0.726381\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −93.0000 | −0.744000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −38.1838 | + | 135.000i | −0.272166 | + | 0.962250i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.65685 | −0.0362225 | −0.0181112 | − | 0.999836i | \(-0.505765\pi\) | ||||
−0.0181112 | + | 0.999836i | \(0.505765\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 220.617i | 1.27819i | 0.769126 | + | 0.639097i | \(0.220692\pi\) | ||||
−0.769126 | + | 0.639097i | \(0.779308\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 90.0000 | − | 127.279i | 0.474757 | − | 0.671408i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 96.0000i | − | 0.463627i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 72.0000i | − | 0.319912i | −0.987124 | − | 0.159956i | \(-0.948865\pi\) | ||
0.987124 | − | 0.159956i | \(-0.0511352\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −216.000 | + | 305.470i | −0.886864 | + | 1.25421i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 305.470i | 1.16357i | 0.813342 | + | 0.581786i | \(0.197646\pi\) | ||||
−0.813342 | + | 0.581786i | \(0.802354\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −229.103 | −0.812507 | −0.406254 | − | 0.913760i | \(-0.633165\pi\) | ||||
−0.406254 | + | 0.913760i | \(0.633165\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −50.9117 | − | 144.000i | −0.168655 | − | 0.477028i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −576.000 | −1.78762 | −0.893811 | − | 0.448444i | \(-0.851978\pi\) | ||||
−0.893811 | + | 0.448444i | \(0.851978\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 55.0000 | 0.160350 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 152.735 | − | 216.000i | 0.419357 | − | 0.593060i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 514.774 | 1.33414 | 0.667072 | − | 0.744993i | \(-0.267547\pi\) | ||||
0.667072 | + | 0.744993i | \(0.267547\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 169.706i | 0.416056i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 108.000 | + | 76.3675i | 0.250964 | + | 0.177458i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 414.000i | 0.913529i | 0.889588 | + | 0.456764i | \(0.150992\pi\) | ||||
−0.889588 | + | 0.456764i | \(0.849008\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 504.000i | − | 1.05788i | −0.848660 | − | 0.528939i | \(-0.822590\pi\) | ||
0.848660 | − | 0.528939i | \(-0.177410\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −432.000 | + | 152.735i | −0.863919 | + | 0.305441i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 407.294i | − | 0.777208i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 789.131 | 1.43892 | 0.719461 | − | 0.694533i | \(-0.244389\pi\) | ||||
0.719461 | + | 0.694533i | \(0.244389\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −610.940 | − | 432.000i | −1.06592 | − | 0.753720i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −720.000 | −1.20350 | −0.601748 | − | 0.798686i | \(-0.705529\pi\) | ||||
−0.601748 | + | 0.798686i | \(0.705529\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −178.000 | −0.285388 | −0.142694 | − | 0.989767i | \(-0.545576\pi\) | ||||
−0.142694 | + | 0.989767i | \(0.545576\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −394.566 | − | 279.000i | −0.607473 | − | 0.429549i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 509.117 | 0.753497 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 967.322i | 1.37762i | 0.724940 | + | 0.688812i | \(0.241867\pi\) | ||||
−0.724940 | + | 0.688812i | \(0.758133\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −567.000 | + | 458.205i | −0.777778 | + | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 438.000i | − | 0.579238i | −0.957142 | − | 0.289619i | \(-0.906471\pi\) | ||
0.957142 | − | 0.289619i | \(-0.0935286\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 288.000i | 0.367506i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −24.0000 | − | 16.9706i | −0.0295755 | − | 0.0209130i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 865.499i | − | 1.03082i | −0.856945 | − | 0.515408i | \(-0.827640\pi\) | ||
0.856945 | − | 0.515408i | \(-0.172360\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1221.88 | −1.40756 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −661.852 | + | 936.000i | −0.737966 | + | 1.04364i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −144.000 | −0.155517 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 650.000 | 0.680387 | 0.340193 | − | 0.940356i | \(-0.389507\pi\) | ||||
0.340193 | + | 0.940356i | \(0.389507\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 763.675 | − | 270.000i | 0.775275 | − | 0.274101i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 718.420 | 0.707777 | 0.353889 | − | 0.935288i | \(-0.384859\pi\) | ||||
0.353889 | + | 0.935288i | \(0.384859\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 356.382i | 0.340926i | 0.985364 | + | 0.170463i | \(0.0545263\pi\) | ||||
−0.985364 | + | 0.170463i | \(0.945474\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 288.000 | − | 407.294i | 0.267675 | − | 0.378550i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1662.00i | 1.50160i | 0.660527 | + | 0.750802i | \(0.270333\pi\) | ||||
−0.660527 | + | 0.750802i | \(0.729667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1224.00i | 1.07558i | 0.843080 | + | 0.537789i | \(0.180740\pi\) | ||||
−0.843080 | + | 0.537789i | \(0.819260\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 216.000 | − | 305.470i | 0.184701 | − | 0.261207i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2341.94i | 1.94965i | 0.222961 | + | 0.974827i | \(0.428428\pi\) | ||||
−0.222961 | + | 0.974827i | \(0.571572\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 814.587 | 0.660527 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1832.82 | + | 648.000i | −1.44824 | + | 0.512031i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 864.000 | 0.665569 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 431.000 | 0.323817 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −916.410 | + | 1296.00i | −0.671788 | + | 0.950052i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1233.19 | 0.882402 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2630.44i | − | 1.83790i | −0.394372 | − | 0.918951i | \(-0.629038\pi\) | ||
0.394372 | − | 0.918951i | \(-0.370962\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −972.000 | − | 687.308i | −0.663410 | − | 0.469101i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2634.00i | − | 1.75675i | −0.477976 | − | 0.878373i | \(-0.658630\pi\) | ||
0.477976 | − | 0.878373i | \(-0.341370\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 432.000i | 0.281648i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 216.000 | − | 763.675i | 0.137706 | − | 0.486864i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 203.647i | − | 0.126998i | −0.997982 | − | 0.0634990i | \(-0.979774\pi\) | ||
0.997982 | − | 0.0634990i | \(-0.0202260\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −992.778 | −0.605801 | −0.302900 | − | 0.953022i | \(-0.597955\pi\) | ||||
−0.302900 | + | 0.953022i | \(0.597955\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2443.76 | − | 1728.00i | −1.45959 | − | 1.03208i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2160.00 | 1.26313 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 32.0000 | 0.0183273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 233.345 | + | 165.000i | 0.130925 | + | 0.0925780i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2438.10 | 1.34052 | 0.670259 | − | 0.742127i | \(-0.266183\pi\) | ||||
0.670259 | + | 0.742127i | \(0.266183\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 729.734i | − | 0.393278i | −0.980476 | − | 0.196639i | \(-0.936997\pi\) | ||
0.980476 | − | 0.196639i | \(-0.0630026\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1296.00 | − | 458.205i | 0.684806 | − | 0.242116i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 1248.00i | − | 0.646721i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 792.000i | − | 0.402602i | −0.979529 | − | 0.201301i | \(-0.935483\pi\) | ||
0.979529 | − | 0.201301i | \(-0.0645169\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2184.00 | + | 1544.32i | 1.08932 | + | 0.770268i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2443.76i | − | 1.19624i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2774.69 | 1.33331 | 0.666657 | − | 0.745364i | \(-0.267724\pi\) | ||||
0.666657 | + | 0.745364i | \(0.267724\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −509.117 | + | 720.000i | −0.240210 | + | 0.339709i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2448.00 | 1.13432 | 0.567161 | − | 0.823607i | \(-0.308042\pi\) | ||||
0.567161 | + | 0.823607i | \(0.308042\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2987.00 | −1.35958 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 229.103 | + | 648.000i | 0.102456 | + | 0.289788i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3162.18 | 1.38969 | 0.694845 | − | 0.719160i | \(-0.255473\pi\) | ||||
0.694845 | + | 0.719160i | \(0.255473\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1578.26i | − | 0.681745i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1242.00 | + | 1756.45i | −0.527426 | + | 0.745893i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2454.00i | 1.02470i | 0.858778 | + | 0.512348i | \(0.171224\pi\) | ||||
−0.858778 | + | 0.512348i | \(0.828776\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3240.00i | − | 1.33054i | −0.746604 | − | 0.665269i | \(-0.768317\pi\) | ||
0.746604 | − | 0.665269i | \(-0.231683\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1512.00 | − | 2138.29i | 0.610766 | − | 0.863754i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 407.294i | 0.161864i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1527.35 | −0.597278 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2291.03 | − | 648.000i | −0.881733 | − | 0.249392i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2016.00 | 0.763731 | 0.381866 | − | 0.924218i | \(-0.375282\pi\) | ||||
0.381866 | + | 0.924218i | \(0.375282\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3382.00 | 1.26136 | 0.630678 | − | 0.776045i | \(-0.282777\pi\) | ||||
0.630678 | + | 0.776045i | \(0.282777\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1221.88 | − | 1728.00i | 0.448721 | − | 0.634588i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1736.65 | 0.628079 | 0.314039 | − | 0.949410i | \(-0.398318\pi\) | ||||
0.314039 | + | 0.949410i | \(0.398318\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2358.91i | − | 0.840294i | −0.907456 | − | 0.420147i | \(-0.861978\pi\) | ||
0.907456 | − | 0.420147i | \(-0.138022\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3348.00 | + | 2367.39i | 1.17487 | + | 0.830762i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 96.0000i | − | 0.0331915i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 1728.00i | − | 0.588726i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1296.00 | − | 3665.64i | −0.435161 | − | 1.23082i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 763.675i | − | 0.252749i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3589.27 | −1.17107 | −0.585535 | − | 0.810647i | \(-0.699116\pi\) | ||||
−0.585535 | + | 0.810647i | \(0.699116\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3054.70 | − | 2160.00i | −0.982651 | − | 0.694839i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1296.00 | 0.411100 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3744.00 | −1.17124 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −755.190 | − | 534.000i | −0.233018 | − | 0.164769i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3665.64 | 1.11574 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 967.322i | 0.290478i | 0.989397 | + | 0.145239i | \(0.0463952\pi\) | ||||
−0.989397 | + | 0.145239i | \(0.953605\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −837.000 | − | 2367.39i | −0.248000 | − | 0.701450i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 198.000i | − | 0.0578930i | −0.999581 | − | 0.0289465i | \(-0.990785\pi\) | ||
0.999581 | − | 0.0289465i | \(-0.00921525\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2232.00i | 0.644082i | 0.946726 | + | 0.322041i | \(0.104369\pi\) | ||||
−0.946726 | + | 0.322041i | \(0.895631\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2160.00 | + | 1527.35i | 0.615228 | + | 0.435032i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4022.02i | 1.13086i | 0.824795 | + | 0.565432i | \(0.191291\pi\) | ||||
−0.824795 | + | 0.565432i | \(0.808709\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3258.35 | 0.904473 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2901.97 | + | 4104.00i | −0.795371 | + | 1.12482i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −576.000 | −0.155893 | −0.0779463 | − | 0.996958i | \(-0.524836\pi\) | ||||
−0.0779463 | + | 0.996958i | \(0.524836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2342.00 | 0.625981 | 0.312991 | − | 0.949756i | \(-0.398669\pi\) | ||||
0.312991 | + | 0.949756i | \(0.398669\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3780.19 | + | 243.000i | −0.997940 | + | 0.0641500i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −311.127 | −0.0811313 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1832.82i | 0.472144i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1314.00 | − | 1858.28i | 0.334423 | − | 0.472946i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4482.00i | 1.12710i | 0.826083 | + | 0.563548i | \(0.190564\pi\) | ||||
−0.826083 | + | 0.563548i | \(0.809436\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4320.00i | 1.07350i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −864.000 | + | 1221.88i | −0.212180 | + | 0.300067i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1731.00i | − | 0.420143i | −0.977686 | − | 0.210071i | \(-0.932630\pi\) | ||
0.977686 | − | 0.210071i | \(-0.0673696\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1221.88 | 0.293143 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −50.9117 | − | 144.000i | −0.0120742 | − | 0.0341509i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1296.00 | −0.303858 | −0.151929 | − | 0.988391i | \(-0.548549\pi\) | ||||
−0.151929 | + | 0.988391i | \(0.548549\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2912.00 | −0.675029 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2596.50 | − | 3672.00i | 0.595142 | − | 0.841658i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 197.990 | 0.0448760 | 0.0224380 | − | 0.999748i | \(-0.492857\pi\) | ||||
0.0224380 | + | 0.999748i | \(0.492857\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4361.43i | 0.977632i | 0.872387 | + | 0.488816i | \(0.162571\pi\) | ||||
−0.872387 | + | 0.488816i | \(0.837429\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5184.00 | − | 3665.64i | −1.14927 | − | 0.812655i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2790.00i | 0.611794i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7128.00i | 1.54614i | 0.634322 | + | 0.773069i | \(0.281279\pi\) | ||||
−0.634322 | + | 0.773069i | \(0.718721\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5616.00 | + | 1985.56i | −1.20509 | + | 0.426065i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 254.558i | 0.0540416i | 0.999635 | + | 0.0270208i | \(0.00860203\pi\) | ||||
−0.999635 | + | 0.0270208i | \(0.991398\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2571.04 | 0.540044 | 0.270022 | − | 0.962854i | \(-0.412969\pi\) | ||||
0.270022 | + | 0.962854i | \(0.412969\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −610.940 | − | 432.000i | −0.126979 | − | 0.0897876i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5184.00 | −1.06621 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2321.00 | 0.472420 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2757.72 | + | 1950.00i | 0.555533 | + | 0.392821i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −707.107 | −0.140988 | −0.0704942 | − | 0.997512i | \(-0.522458\pi\) | ||||
−0.0704942 | + | 0.997512i | \(0.522458\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2341.94i | − | 0.462213i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4050.00 | + | 1145.51i | 0.791262 | + | 0.223803i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 10368.0i | − | 2.00534i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 3888.00i | − | 0.744520i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3048.00 | + | 2155.26i | 0.577898 | + | 0.408635i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2851.05i | 0.535249i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10207.8 | −1.89769 | −0.948843 | − | 0.315749i | \(-0.897744\pi\) | ||||
−0.948843 | + | 0.315749i | \(0.897744\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1069.15 | + | 1512.00i | −0.196834 | + | 0.278365i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7920.00 | −1.44406 | −0.722029 | − | 0.691863i | \(-0.756790\pi\) | ||||
−0.722029 | + | 0.691863i | \(0.756790\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −538.000 | −0.0971551 | −0.0485776 | − | 0.998819i | \(-0.515469\pi\) | ||||
−0.0485776 | + | 0.998819i | \(0.515469\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2443.76 | − | 864.000i | 0.437112 | − | 0.154542i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4689.53 | −0.830884 | −0.415442 | − | 0.909620i | \(-0.636373\pi\) | ||||
−0.415442 | + | 0.909620i | \(0.636373\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 169.706i | 0.0297859i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4986.00 | + | 7051.27i | −0.866951 | + | 1.22605i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1296.00i | − | 0.223255i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 6696.00i | − | 1.14285i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3672.00 | + | 5192.99i | −0.620985 | + | 0.878205i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 9775.04i | − | 1.63804i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7051.27 | 1.17091 | 0.585457 | − | 0.810703i | \(-0.300915\pi\) | ||||
0.585457 | + | 0.810703i | \(0.300915\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1832.82 | − | 648.000i | 0.301615 | − | 0.106637i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4464.00 | −0.728043 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11086.0 | 1.79197 | 0.895984 | − | 0.444087i | \(-0.146472\pi\) | ||||
0.895984 | + | 0.444087i | \(0.146472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7025.81 | + | 9936.00i | −1.12563 | + | 1.59189i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6618.52 | 1.05106 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6754.28i | 1.06326i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3456.00 | + | 2443.76i | 0.539318 | + | 0.381356i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 1086.00i | − | 0.168010i | −0.996465 | − | 0.0840051i | \(-0.973229\pi\) | ||
0.996465 | − | 0.0840051i | \(-0.0267712\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1080.00i | − | 0.165648i | −0.996564 | − | 0.0828239i | \(-0.973606\pi\) | ||
0.996564 | − | 0.0828239i | \(-0.0263939\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9720.00 | − | 2749.23i | −1.47811 | − | 0.418072i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6720.34i | 1.01328i | 0.862158 | + | 0.506640i | \(0.169113\pi\) | ||||
−0.862158 | + | 0.506640i | \(0.830887\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4072.94 | 0.608927 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3665.64 | + | 2592.00i | 0.543435 | + | 0.384267i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4176.00 | −0.613930 | −0.306965 | − | 0.951721i | \(-0.599313\pi\) | ||||
−0.306965 | + | 0.951721i | \(0.599313\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6211.00 | −0.905526 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1828.58 | + | 1293.00i | 0.264395 | + | 0.186956i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1006.92 | 0.144396 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6737.31i | 0.958269i | 0.877741 | + | 0.479135i | \(0.159049\pi\) | ||||
−0.877741 | + | 0.479135i | \(0.840951\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7776.00 | + | 2749.23i | −1.09703 | + | 0.387857i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8736.00i | 1.22251i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 5832.00i | − | 0.809570i | −0.914412 | − | 0.404785i | \(-0.867346\pi\) | ||
0.914412 | − | 0.404785i | \(-0.132654\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5232.00 | + | 3699.58i | 0.720478 | + | 0.509455i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 407.294i | − | 0.0556411i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −636.396 | −0.0862519 | −0.0431260 | − | 0.999070i | \(-0.513732\pi\) | ||||
−0.0431260 | + | 0.999070i | \(0.513732\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7891.31 | − | 11160.0i | 1.06111 | − | 1.50064i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 288.000 | 0.0384233 | 0.0192116 | − | 0.999815i | \(-0.493884\pi\) | ||||
0.0192116 | + | 0.999815i | \(0.493884\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2880.00 | −0.381243 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2061.92 | − | 5832.00i | −0.270836 | − | 0.766039i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10798.9 | −1.40753 | −0.703763 | − | 0.710435i | \(-0.748498\pi\) | ||||
−0.703763 | + | 0.710435i | \(0.748498\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7331.28i | 0.948233i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7902.00 | − | 11175.1i | 1.01426 | − | 1.43438i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 5472.00i | − | 0.697028i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2952.00i | 0.373191i | 0.982437 | + | 0.186595i | \(0.0597453\pi\) | ||||
−0.982437 | + | 0.186595i | \(0.940255\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1296.00 | + | 1832.82i | −0.162609 | + | 0.229964i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 8502.25i | − | 1.05881i | −0.848370 | − | 0.529404i | \(-0.822415\pi\) | ||
0.848370 | − | 0.529404i | \(-0.177585\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15884.4 | −1.96343 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3207.44 | − | 2592.00i | 0.393528 | − | 0.318019i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2160.00 | −0.263064 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −614.000 | −0.0742307 | −0.0371153 | − | 0.999311i | \(-0.511817\pi\) | ||||
−0.0371153 | + | 0.999311i | \(0.511817\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 610.940 | − | 864.000i | 0.0733223 | − | 0.103693i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7025.81 | −0.837089 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2477.70i | 0.293074i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4212.00 | − | 2978.33i | −0.494634 | − | 0.349759i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 4950.00i | − | 0.577144i | −0.957458 | − | 0.288572i | \(-0.906820\pi\) | ||
0.957458 | − | 0.288572i | \(-0.0931805\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 5256.00i | − | 0.608460i | −0.952599 | − | 0.304230i | \(-0.901601\pi\) | ||
0.952599 | − | 0.304230i | \(-0.0983992\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5184.00 | − | 14662.6i | −0.595874 | − | 1.68539i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4734.79i | 0.540402i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8553.16 | 0.969360 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9164.10 | + | 6480.00i | 1.03135 | + | 0.729271i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2880.00 | −0.321867 | −0.160934 | − | 0.986965i | \(-0.551450\pi\) | ||||
−0.160934 | + | 0.986965i | \(0.551450\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2554.00 | 0.283458 | 0.141729 | − | 0.989905i | \(-0.454734\pi\) | ||||
0.141729 | + | 0.989905i | \(0.454734\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 135.765 | + | 96.0000i | 0.0149642 | + | 0.0105813i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3665.64 | −0.401262 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 10504.8i | − | 1.14206i | −0.820928 | − | 0.571032i | \(-0.806543\pi\) | ||
0.820928 | − | 0.571032i | \(-0.193457\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 495.000 | + | 1400.07i | 0.0534500 | + | 0.151179i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3186.00i | 0.341696i | 0.985297 | + | 0.170848i | \(0.0546507\pi\) | ||||
−0.985297 | + | 0.170848i | \(0.945349\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4896.00i | 0.521557i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10344.0 | + | 7314.31i | 1.09453 | + | 0.773949i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12982.5i | 1.36455i | 0.731098 | + | 0.682273i | \(0.239008\pi\) | ||||
−0.731098 | + | 0.682273i | \(0.760992\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9164.10 | 0.956809 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2189.20 | − | 3096.00i | 0.227059 | − | 0.321110i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6912.00 | 0.712175 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8534.00 | −0.873531 | −0.436766 | − | 0.899575i | \(-0.643876\pi\) | ||||
−0.436766 | + | 0.899575i | \(0.643876\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6873.08 | + | 1944.00i | 0.698928 | + | 0.197687i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12722.3 | −1.28533 | −0.642663 | − | 0.766149i | \(-0.722170\pi\) | ||||
−0.642663 | + | 0.766149i | \(0.722170\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16614.2i | − | 1.66766i | −0.552021 | − | 0.833830i | \(-0.686143\pi\) | ||
0.552021 | − | 0.833830i | \(-0.313857\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3744.00 | − | 5294.82i | 0.373385 | − | 0.528046i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12378.0i | 1.22652i | 0.789881 | + | 0.613261i | \(0.210143\pi\) | ||||
−0.789881 | + | 0.613261i | \(0.789857\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13392.0i | 1.31852i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2376.00 | − | 3360.17i | 0.232442 | − | 0.328723i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6873.08i | 0.668128i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2367.39 | −0.228681 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4632.96 | + | 13104.0i | 0.444715 | + | 1.25784i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5184.00 | 0.494495 | 0.247247 | − | 0.968952i | \(-0.420474\pi\) | ||||
0.247247 | + | 0.968952i | \(0.420474\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5184.00 | 0.491414 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7331.28 | − | 10368.0i | 0.690652 | − | 0.976729i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3676.96 | −0.344251 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6262.14i | 0.582679i | 0.956620 | + | 0.291339i | \(0.0941009\pi\) | ||||
−0.956620 | + | 0.291339i | \(0.905899\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11772.0 | + | 8324.06i | 1.08865 | + | 0.769789i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 114.000i | − | 0.0104781i | −0.999986 | − | 0.00523905i | \(-0.998332\pi\) | ||
0.999986 | − | 0.00523905i | \(-0.00166765\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 288.000i | 0.0263101i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4320.00 | + | 1527.35i | −0.392262 | + | 0.138685i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 12218.8i | − | 1.10279i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4607.51 | −0.413347 | −0.206674 | − | 0.978410i | \(-0.566264\pi\) | ||||
−0.206674 | + | 0.978410i | \(0.566264\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10386.0 | + | 7344.00i | 0.926171 | + | 0.654902i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19728.0 | 1.74876 | 0.874382 | − | 0.485239i | \(-0.161267\pi\) | ||||
0.874382 | + | 0.485239i | \(0.161267\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4064.00 | −0.358110 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12672.8 | − | 8961.00i | −1.11009 | − | 0.784955i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6115.06 | −0.532505 | −0.266253 | − | 0.963903i | \(-0.585786\pi\) | ||||
−0.266253 | + | 0.963903i | \(0.585786\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 3020.76i | − | 0.261508i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −972.000 | + | 3436.54i | −0.0836547 | + | 0.295764i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 2016.00i | − | 0.172496i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17280.0i | 1.46997i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13416.0 | + | 9486.54i | 1.13468 | + | 0.802337i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7331.28i | − | 0.616486i | −0.951308 | − | 0.308243i | \(-0.900259\pi\) | ||
0.951308 | − | 0.308243i | \(-0.0997410\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −941.866 | −0.0787475 | −0.0393737 | − | 0.999225i | \(-0.512536\pi\) | ||||
−0.0393737 | + | 0.999225i | \(0.512536\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4734.79 | − | 6696.00i | 0.393606 | − | 0.556643i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11232.0 | 0.928413 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8569.00 | 0.704282 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10538.7 | + | 3726.00i | −0.861283 | + | 0.304510i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21993.8 | −1.78735 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 9401.69i | − | 0.759758i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7362.00 | + | 10411.4i | −0.591608 | + | 0.836661i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1650.00i | − | 0.131856i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 17208.0i | − | 1.36752i | −0.729706 | − | 0.683761i | \(-0.760343\pi\) | ||
0.729706 | − | 0.683761i | \(-0.239657\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9720.00 | − | 13746.2i | 0.768186 | − | 1.08638i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 6923.99i | − | 0.544204i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18353.7 | 1.43464 | 0.717318 | − | 0.696746i | \(-0.245369\pi\) | ||||
0.717318 | + | 0.696746i | \(0.245369\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12829.7 | − | 4536.00i | 0.997377 | − | 0.352626i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −144.000 | −0.0111336 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16416.0 | −1.26235 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1221.88 | + | 1728.00i | −0.0934521 | + | 0.132161i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11704.0 | −0.890333 | −0.445167 | − | 0.895448i | \(-0.646856\pi\) | ||||
−0.445167 | + | 0.895448i | \(0.646856\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 16495.4i | − | 1.24809i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6480.00 | − | 4582.05i | −0.487675 | − | 0.344838i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 102.000i | − | 0.00763550i | −0.999993 | − | 0.00381775i | \(-0.998785\pi\) | ||
0.999993 | − | 0.00381775i | \(-0.00121523\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 13248.0i | − | 0.986456i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7776.00 | − | 9622.31i | −0.575946 | − | 0.712697i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1018.23i | − | 0.0750204i | −0.999296 | − | 0.0375102i | \(-0.988057\pi\) | ||
0.999296 | − | 0.0375102i | \(-0.0119427\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22477.5 | −1.64738 | −0.823690 | − | 0.567040i | \(-0.808089\pi\) | ||||
−0.823690 | + | 0.567040i | \(0.808089\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8553.16 | + | 6048.00i | 0.623584 | + | 0.440940i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13392.0 | 0.971278 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3778.00 | −0.272583 | −0.136291 | − | 0.990669i | \(-0.543518\pi\) | ||||
−0.136291 | + | 0.990669i | \(0.543518\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14348.6 | + | 10146.0i | 1.02989 | + | 0.728244i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7433.11 | 0.530770 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 15443.2i | − | 1.09707i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10368.0 | − | 3665.64i | 0.732759 | − | 0.259069i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18366.0i | 1.29139i | 0.763595 | + | 0.645695i | \(0.223432\pi\) | ||||
−0.763595 | + | 0.645695i | \(0.776568\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5616.00i | 0.392875i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7368.00 | + | 5209.96i | 0.512824 | + | 0.362621i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 14255.3i | − | 0.987174i | −0.869697 | − | 0.493587i | \(-0.835686\pi\) | ||
0.869697 | − | 0.493587i | \(-0.164314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4887.52 | −0.336754 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7076.72 | − | 10008.0i | 0.485144 | − | 0.686097i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1584.00 | 0.108048 | 0.0540238 | − | 0.998540i | \(-0.482795\pi\) | ||||
0.0540238 | + | 0.998540i | \(0.482795\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11230.0 | 0.762198 | 0.381099 | − | 0.924534i | \(-0.375546\pi\) | ||||
0.381099 | + | 0.924534i | \(0.375546\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7102.18 | + | 20088.0i | 0.479640 | + | 1.35663i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2438.10 | −0.163840 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8094.96i | 0.541292i | 0.962679 | + | 0.270646i | \(0.0872373\pi\) | ||||
−0.962679 | + | 0.270646i | \(0.912763\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 288.000 | − | 407.294i | 0.0191631 | − | 0.0271008i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 41472.0i | − | 2.74595i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1512.00i | − | 0.0996233i | −0.998759 | − | 0.0498117i | \(-0.984138\pi\) | ||
0.998759 | − | 0.0498117i | \(-0.0158621\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5184.00 | − | 7331.28i | 0.339901 | − | 0.480692i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25710.4i | 1.67757i | 0.544461 | + | 0.838786i | \(0.316734\pi\) | ||||
−0.544461 | + | 0.838786i | \(0.683266\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4963.89 | −0.322319 | −0.161160 | − | 0.986928i | \(-0.551523\pi\) | ||||
−0.161160 | + | 0.986928i | \(0.551523\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5498.46 | − | 19440.0i | 0.355307 | − | 1.25620i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14688.0 | 0.944562 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4649.00 | 0.297536 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2291.03 | − | 3240.00i | 0.145925 | − | 0.206369i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3665.64 | −0.232367 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5311.79i | 0.335117i | 0.985862 | + | 0.167559i | \(0.0535883\pi\) | ||||
−0.985862 | + | 0.167559i | \(0.946412\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15228.0 | − | 10767.8i | −0.956175 | − | 0.676118i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14880.0i | 0.929913i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3960.00i | 0.246312i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6480.00 | − | 18328.2i | −0.401166 | − | 1.13467i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11658.8i | 0.718399i | 0.933261 | + | 0.359200i | \(0.116950\pi\) | ||||
−0.933261 | + | 0.359200i | \(0.883050\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15909.9 | 0.975778 | 0.487889 | − | 0.872906i | \(-0.337767\pi\) | ||||
0.487889 | + | 0.872906i | \(0.337767\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5498.46 | + | 3888.00i | 0.335662 | + | 0.237349i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10224.0 | −0.621247 | −0.310624 | − | 0.950533i | \(-0.600538\pi\) | ||||
−0.310624 | + | 0.950533i | \(0.600538\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12420.0 | 0.751198 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15884.4 | − | 11232.0i | −0.956314 | − | 0.676216i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18639.3 | 1.11702 | 0.558510 | − | 0.829498i | \(-0.311373\pi\) | ||||
0.558510 | + | 0.829498i | \(0.311373\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14900.2i | 0.888851i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1602.00 | − | 4531.14i | −0.0951293 | − | 0.269066i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 8490.00i | − | 0.501857i | −0.968006 | − | 0.250928i | \(-0.919264\pi\) | ||
0.968006 | − | 0.250928i | \(-0.0807358\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 32904.0i | − | 1.93618i | −0.250596 | − | 0.968092i | \(-0.580627\pi\) | ||
0.250596 | − | 0.968092i | \(-0.419373\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15552.0 | + | 10996.9i | 0.910995 | + | 0.644171i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 2443.76i | − | 0.142504i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 814.587 | 0.0472878 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2901.97 | + | 4104.00i | −0.167708 | + | 0.237175i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15120.0 | −0.869897 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4214.00 | −0.241364 | −0.120682 | − | 0.992691i | \(-0.538508\pi\) | ||||
−0.120682 | + | 0.992691i | \(0.538508\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3551.09 | − | 12555.0i | 0.202491 | − | 0.715914i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25665.1 | −1.45700 | −0.728502 | − | 0.685044i | \(-0.759783\pi\) | ||||
−0.728502 | + | 0.685044i | \(0.759783\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11030.9i | 0.623455i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 594.000 | − | 840.043i | 0.0334246 | − | 0.0472695i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 16110.0i | − | 0.902536i | −0.892389 | − | 0.451268i | \(-0.850972\pi\) | ||
0.892389 | − | 0.451268i | \(-0.149028\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1152.00i | 0.0642564i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6696.00 | + | 9469.57i | −0.371861 | + | 0.525891i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 37063.7i | 2.04937i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17844.5 | 0.982400 | 0.491200 | − | 0.871047i | \(-0.336558\pi\) | ||||
0.491200 | + | 0.871047i | \(0.336558\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4582.05 | + | 12960.0i | 0.251166 | + | 0.710404i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5616.00 | 0.306514 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15552.0 | 0.845156 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12066.1 | + | 17064.0i | −0.652905 | + | 0.923347i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3456.34 | 0.186226 | 0.0931128 | − | 0.995656i | \(-0.470318\pi\) | ||||
0.0931128 | + | 0.995656i | \(0.470318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1832.82i | − | 0.0983302i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13824.0 | + | 9775.04i | 0.738499 | + | 0.522198i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12192.0i | 0.648554i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1224.00i | − | 0.0648354i | −0.999474 | − | 0.0324177i | \(-0.989679\pi\) | ||
0.999474 | − | 0.0324177i | \(-0.0103207\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −24624.0 | + | 8705.90i | −1.29884 | + | 0.459208i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 31768.9i | − | 1.66866i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12218.8 | −0.639101 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2443.76 | − | 1728.00i | −0.127286 | − | 0.0900047i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19872.0 | −1.03074 | −0.515369 | − | 0.856968i | \(-0.672345\pi\) | ||||
−0.515369 | + | 0.856968i | \(0.672345\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6048.00 | −0.312398 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9936.26 | + | 7026.00i | 0.511112 | + | 0.361410i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 526.087 | 0.0269495 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2223.14i | − | 0.113414i | −0.998391 | − | 0.0567069i | \(-0.981940\pi\) | ||
0.998391 | − | 0.0567069i | \(-0.0180601\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16767.0 | − | 10309.6i | −0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11664.0i | 0.590162i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9288.00i | 0.468022i | 0.972234 | + | 0.234011i | \(0.0751852\pi\) | ||||
−0.972234 | + | 0.234011i | \(0.924815\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1320.00 | − | 933.381i | −0.0662434 | − | 0.0468412i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 23673.9i | − | 1.18323i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15349.9 | 0.764079 | 0.382039 | − | 0.924146i | \(-0.375222\pi\) | ||||
0.382039 | + | 0.924146i | \(0.375222\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5498.46 | + | 7776.00i | −0.272593 | + | 0.385504i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7632.00 | 0.376838 | 0.188419 | − | 0.982089i | \(-0.439664\pi\) | ||||
0.188419 | + | 0.982089i | \(0.439664\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13792.0 | −0.678255 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11149.7 | − | 3942.00i | 0.546111 | − | 0.193079i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −28205.1 | −1.37596 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10199.3i | 0.495577i | 0.968814 | + | 0.247788i | \(0.0797037\pi\) | ||||
−0.968814 | + | 0.247788i | \(0.920296\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13446.0 | + | 19015.5i | −0.650730 | + | 0.920271i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4128.00i | 0.198985i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38232.0i | 1.83562i | 0.397018 | + | 0.917811i | \(0.370045\pi\) | ||||
−0.397018 | + | 0.917811i | \(0.629955\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12960.0 | + | 18328.2i | −0.619787 | + | 0.876511i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 15171.7i | − | 0.722698i | −0.932431 | − | 0.361349i | \(-0.882316\pi\) | ||
0.932431 | − | 0.361349i | \(-0.117684\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20772.0 | −0.985578 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7331.28 | + | 2592.00i | −0.346488 | + | 0.122502i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −29808.0 | −1.40327 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20810.0 | −0.975849 | −0.487924 | − | 0.872886i | \(-0.662246\pi\) | ||||
−0.487924 | + | 0.872886i | \(0.662246\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5192.99 | − | 7344.00i | 0.242569 | − | 0.343045i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34931.1 | 1.62533 | 0.812667 | − | 0.582728i | \(-0.198015\pi\) | ||||
0.812667 | + | 0.582728i | \(0.198015\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 20517.4i | − | 0.950977i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5184.00 | + | 3665.64i | 0.239350 | + | 0.169246i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7776.00i | 0.357643i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21600.0i | 0.989640i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 216.000 | − | 763.675i | 0.00985851 | − | 0.0348551i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4480.23i | 0.203702i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13924.3 | −0.630685 | −0.315343 | − | 0.948978i | \(-0.602119\pi\) | ||||
−0.315343 | + | 0.948978i | \(0.602119\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5498.46 | − | 3888.00i | −0.248099 | − | 0.175433i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −39744.0 | −1.78652 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36288.0 | 1.62500 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12354.6 | − | 8736.00i | −0.551159 | − | 0.389728i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22915.9 | 1.01847 | 0.509237 | − | 0.860626i | \(-0.329928\pi\) | ||||
0.509237 | + | 0.860626i | \(0.329928\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29325.1i | 1.29843i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22032.0 | − | 7789.49i | 0.971863 | − | 0.343606i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5340.00i | 0.234676i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13824.0i | 0.605257i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 840.000 | + | 593.970i | 0.0366411 | + | 0.0259092i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 7229.46i | − | 0.314183i | −0.987584 | − | 0.157092i | \(-0.949788\pi\) | ||
0.987584 | − | 0.157092i | \(-0.0502118\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10106.0 | −0.437569 | −0.218785 | − | 0.975773i | \(-0.570209\pi\) | ||||
−0.218785 | + | 0.975773i | \(0.570209\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13084.3 | + | 18504.0i | −0.564436 | + | 0.798233i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15696.0 | −0.674610 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5832.00 | −0.249738 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10996.9 | − | 31104.0i | −0.469186 | − | 1.32706i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16795.2 | −0.713954 | −0.356977 | − | 0.934113i | \(-0.616193\pi\) | ||||
−0.356977 | + | 0.934113i | \(0.616193\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13321.9i | 0.564243i | 0.959379 | + | 0.282121i | \(0.0910381\pi\) | ||||
−0.959379 | + | 0.282121i | \(0.908962\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8370.00 | + | 11837.0i | −0.353219 | + | 0.499528i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2574.00i | 0.108231i | 0.998535 | + | 0.0541153i | \(0.0172339\pi\) | ||||
−0.998535 | + | 0.0541153i | \(0.982766\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 24408.0i | − | 1.02259i | −0.859406 | − | 0.511294i | \(-0.829166\pi\) | ||
0.859406 | − | 0.511294i | \(-0.170834\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21384.0 | + | 30241.5i | −0.892663 | + | 1.26242i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 2800.14i | − | 0.116470i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13848.0 | −0.573927 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −29783.3 | − | 8424.00i | −1.22994 | − | 0.347881i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8784.00 | −0.361451 | −0.180725 | − | 0.983534i | \(-0.557845\pi\) | ||||
−0.180725 | + | 0.983534i | \(0.557845\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24357.0 | −0.998688 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −763.675 | + | 1080.00i | −0.0312009 | + | 0.0441248i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16897.0 | 0.687900 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7314.31i | 0.296721i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10908.0 | + | 7713.12i | 0.440944 | + | 0.311795i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10368.0i | 0.417639i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11448.0i | 0.459522i | 0.973247 | + | 0.229761i | \(0.0737944\pi\) | ||||
−0.973247 | + | 0.229761i | \(0.926206\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1296.00 | − | 3665.64i | −0.0518389 | − | 0.146623i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21790.2i | 0.868540i | 0.900783 | + | 0.434270i | \(0.142994\pi\) | ||||
−0.900783 | + | 0.434270i | \(0.857006\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31132.5 | 1.23659 | 0.618293 | − | 0.785948i | \(-0.287825\pi\) | ||||
0.618293 | + | 0.785948i | \(0.287825\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21993.8 | − | 15552.0i | −0.870556 | − | 0.615576i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31392.0 | 1.23823 | 0.619117 | − | 0.785299i | \(-0.287491\pi\) | ||||
0.619117 | + | 0.785299i | \(0.287491\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17888.0 | −0.703133 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9847.17 | + | 6963.00i | 0.385729 | + | 0.272752i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29019.7 | 1.13282 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56817.4i | 2.21032i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5850.00 | + | 16546.3i | 0.226796 | + | 0.641475i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20928.0i | 0.808566i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 32472.0i | − | 1.25029i | −0.780510 | − | 0.625143i | \(-0.785040\pi\) | ||
0.780510 | − | 0.625143i | \(-0.214960\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3000.00 | − | 2121.32i | −0.115117 | − | 0.0813997i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33907.2i | 1.29667i | 0.761357 | + | 0.648333i | \(0.224533\pi\) | ||||
−0.761357 | + | 0.648333i | \(0.775467\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18557.3 | 0.707252 | 0.353626 | − | 0.935387i | \(-0.384949\pi\) | ||||
0.353626 | + | 0.935387i | \(0.384949\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7025.81 | − | 9936.00i | 0.266859 | − | 0.377395i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31536.0 | −1.19377 | −0.596886 | − | 0.802326i | \(-0.703595\pi\) | ||||
−0.596886 | + | 0.802326i | \(0.703595\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 44640.0 | 1.68411 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13746.2 | + | 17010.0i | 0.516850 | + | 0.639570i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14662.6 | −0.549456 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 13881.9i | − | 0.518460i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 31104.0 | − | 43987.7i | 1.15778 | − | 1.63735i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1248.00i | − | 0.0462994i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 26208.0i | − | 0.969051i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11664.0 | − | 16495.4i | 0.429849 | − | 0.607898i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18328.2i | 0.673205i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15451.7 | 0.565673 | 0.282836 | − | 0.959168i | \(-0.408725\pi\) | ||||
0.282836 | + | 0.959168i | \(0.408725\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6465.78 | + | 18288.0i | 0.235926 | + | 0.667299i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18432.0 | −0.670340 | −0.335170 | − | 0.942158i | \(-0.608794\pi\) | ||||
−0.335170 | + | 0.942158i | \(0.608794\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13140.0 | −0.476309 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8553.16 | + | 12096.0i | −0.309026 | + | 0.437029i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 44700.5 | 1.60975 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7619.78i | 0.273508i | 0.990605 | + | 0.136754i | \(0.0436669\pi\) | ||||
−0.990605 | + | 0.136754i | \(0.956333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −43308.0 | − | 30623.4i | −1.54945 | − | 1.09563i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 51840.0i | − | 1.84868i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6696.00i | 0.238014i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9072.00 | + | 3207.44i | −0.321428 | + | 0.113642i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 29070.6i | − | 1.02667i | −0.858189 | − | 0.513334i | \(-0.828410\pi\) | ||
0.858189 | − | 0.513334i | \(-0.171590\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1400.07 | 0.0492862 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −33601.7 | − | 23760.0i | −1.17907 | − | 0.833727i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8640.00 | 0.302201 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8462.00 | −0.295028 | −0.147514 | − | 0.989060i | \(-0.547127\pi\) | ||||
−0.147514 | + | 0.989060i | \(0.547127\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2282.54 | − | 1614.00i | −0.0793268 | − | 0.0560925i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50408.2 | 1.74629 | 0.873146 | − | 0.487458i | \(-0.162076\pi\) | ||||
0.873146 | + | 0.487458i | \(0.162076\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 43987.7i | − | 1.51902i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12960.0 | + | 3665.64i | 0.446126 | + | 0.126183i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 28794.0i | − | 0.988046i | −0.869449 | − | 0.494023i | \(-0.835526\pi\) | ||
0.869449 | − | 0.494023i | \(-0.164474\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 12816.0i | − | 0.438382i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19896.0 | − | 14068.6i | −0.678414 | − | 0.479711i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6516.70i | 0.221507i | 0.993848 | + | 0.110754i | \(0.0353265\pi\) | ||||
−0.993848 | + | 0.110754i | \(0.964674\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11404.2 | −0.386421 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −509.117 | + | 720.000i | −0.0171969 | + | 0.0243201i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3456.00 | 0.116371 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18881.0 | −0.633782 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −42307.6 | + | 14958.0i | −1.41573 | + | 0.500535i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19131.5 | −0.638201 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 10165.4i | − | 0.338052i | −0.985612 | − | 0.169026i | \(-0.945938\pi\) | ||
0.985612 | − | 0.169026i | \(-0.0540622\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3888.00 | − | 5498.46i | 0.128896 | − | 0.182287i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 3342.00i | − | 0.110453i | −0.998474 | − | 0.0552265i | \(-0.982412\pi\) | ||
0.998474 | − | 0.0552265i | \(-0.0175881\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 16848.0i | − | 0.555110i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20088.0 | − | 28408.7i | 0.659827 | − | 0.933136i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 30394.3i | − | 0.995291i | −0.867381 | − | 0.497645i | \(-0.834198\pi\) | ||
0.867381 | − | 0.497645i | \(-0.165802\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25965.0 | −0.847644 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −31158.0 | + | 11016.0i | −1.01406 | + | 0.358526i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39312.0 | 1.27554 | 0.637771 | − | 0.770226i | \(-0.279857\pi\) | ||||
0.637771 | + | 0.770226i | \(0.279857\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9824.00 | −0.317785 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 29325.1 | − | 41472.0i | 0.945724 | − | 1.33746i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32990.8 | 1.06071 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1747.97i | − | 0.0560303i | −0.999607 | − | 0.0280152i | \(-0.991081\pi\) | ||
0.999607 | − | 0.0280152i | \(-0.00891867\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29916.0 | + | 21153.8i | 0.956048 | + | 0.676028i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13344.0i | 0.425159i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 37512.0i | − | 1.19159i | −0.803136 | − | 0.595796i | \(-0.796837\pi\) | ||
0.803136 | − | 0.595796i | \(-0.203163\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9720.00 | + | 2749.23i | 0.307835 | + | 0.0870689i |
(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 | 384.4.f.c.191.4 | yes | 4 | |
3.2 | odd | 2 | 384.4.f.d.191.3 | yes | 4 | ||
4.3 | odd | 2 | 384.4.f.d.191.1 | yes | 4 | ||
8.3 | odd | 2 | 384.4.f.d.191.4 | yes | 4 | ||
8.5 | even | 2 | inner | 384.4.f.c.191.1 | ✓ | 4 | |
12.11 | even | 2 | inner | 384.4.f.c.191.2 | yes | 4 | |
16.3 | odd | 4 | 768.4.c.h.767.1 | 2 | |||
16.5 | even | 4 | 768.4.c.i.767.1 | 2 | |||
16.11 | odd | 4 | 768.4.c.c.767.2 | 2 | |||
16.13 | even | 4 | 768.4.c.b.767.2 | 2 | |||
24.5 | odd | 2 | 384.4.f.d.191.2 | yes | 4 | ||
24.11 | even | 2 | inner | 384.4.f.c.191.3 | yes | 4 | |
48.5 | odd | 4 | 768.4.c.c.767.1 | 2 | |||
48.11 | even | 4 | 768.4.c.i.767.2 | 2 | |||
48.29 | odd | 4 | 768.4.c.h.767.2 | 2 | |||
48.35 | even | 4 | 768.4.c.b.767.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.f.c.191.1 | ✓ | 4 | 8.5 | even | 2 | inner | |
384.4.f.c.191.2 | yes | 4 | 12.11 | even | 2 | inner | |
384.4.f.c.191.3 | yes | 4 | 24.11 | even | 2 | inner | |
384.4.f.c.191.4 | yes | 4 | 1.1 | even | 1 | trivial | |
384.4.f.d.191.1 | yes | 4 | 4.3 | odd | 2 | ||
384.4.f.d.191.2 | yes | 4 | 24.5 | odd | 2 | ||
384.4.f.d.191.3 | yes | 4 | 3.2 | odd | 2 | ||
384.4.f.d.191.4 | yes | 4 | 8.3 | odd | 2 | ||
768.4.c.b.767.1 | 2 | 48.35 | even | 4 | |||
768.4.c.b.767.2 | 2 | 16.13 | even | 4 | |||
768.4.c.c.767.1 | 2 | 48.5 | odd | 4 | |||
768.4.c.c.767.2 | 2 | 16.11 | odd | 4 | |||
768.4.c.h.767.1 | 2 | 16.3 | odd | 4 | |||
768.4.c.h.767.2 | 2 | 48.29 | odd | 4 | |||
768.4.c.i.767.1 | 2 | 16.5 | even | 4 | |||
768.4.c.i.767.2 | 2 | 48.11 | even | 4 |