Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(193,384)]
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([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.6567334422\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.4 | ||
Root | \(1.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.4.d.e.193.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 10.4222i | 0.932190i | 0.884735 | + | 0.466095i | \(0.154340\pi\) | ||||
−0.884735 | + | 0.466095i | \(0.845660\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.42221 | −0.346766 | −0.173383 | − | 0.984854i | \(-0.555470\pi\) | ||||
−0.173383 | + | 0.984854i | \(0.555470\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 61.6888i | − 1.69090i | −0.534056 | − | 0.845449i | \(-0.679333\pi\) | ||||
0.534056 | − | 0.845449i | \(-0.320667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 64.8444i | − 1.38343i | −0.722170 | − | 0.691716i | \(-0.756855\pi\) | ||||
0.722170 | − | 0.691716i | \(-0.243145\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −31.2666 | −0.538200 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −75.6888 | −1.07984 | −0.539919 | − | 0.841717i | \(-0.681545\pi\) | ||||
−0.539919 | + | 0.841717i | \(0.681545\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 10.3112i | − 0.124502i | −0.998061 | − | 0.0622512i | \(-0.980172\pi\) | ||||
0.998061 | − | 0.0622512i | \(-0.0198280\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 19.2666i | − 0.200206i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 156.844 | 1.42193 | 0.710963 | − | 0.703229i | \(-0.248259\pi\) | ||||
0.710963 | + | 0.703229i | \(0.248259\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 16.3776 | 0.131021 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 53.7998i | 0.344496i | 0.985054 | + | 0.172248i | \(0.0551030\pi\) | ||||
−0.985054 | + | 0.172248i | \(0.944897\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 227.489 | 1.31801 | 0.659003 | − | 0.752141i | \(-0.270979\pi\) | ||||
0.659003 | + | 0.752141i | \(0.270979\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 185.066 | 0.976240 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 66.9335i | − 0.323252i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.3112i | 0.0458148i | 0.999738 | + | 0.0229074i | \(0.00729229\pi\) | ||||
−0.999738 | + | 0.0229074i | \(0.992708\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 194.533 | 0.798724 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −70.4441 | −0.268330 | −0.134165 | − | 0.990959i | \(-0.542835\pi\) | ||||
−0.134165 | + | 0.990959i | \(0.542835\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 298.311i | − 1.05795i | −0.848636 | − | 0.528977i | \(-0.822576\pi\) | ||||
0.848636 | − | 0.528977i | \(-0.177424\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 93.7998i | − 0.310730i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −89.9109 | −0.279039 | −0.139520 | − | 0.990219i | \(-0.544556\pi\) | ||||
−0.139520 | + | 0.990219i | \(0.544556\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −301.755 | −0.879753 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 227.066i | − 0.623444i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 388.333i | 1.00645i | 0.864157 | + | 0.503223i | \(0.167853\pi\) | ||||
−0.864157 | + | 0.503223i | \(0.832147\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 642.934 | 1.57624 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 30.9335 | 0.0718815 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 324.000i | − 0.714936i | −0.933925 | − | 0.357468i | \(-0.883640\pi\) | ||||
0.933925 | − | 0.357468i | \(-0.116360\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 324.000i | − 0.680065i | −0.940414 | − | 0.340032i | \(-0.889562\pi\) | ||||
0.940414 | − | 0.340032i | \(-0.110438\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 57.7998 | 0.115589 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 675.822 | 1.28962 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 920.266i | − 1.67804i | −0.544104 | − | 0.839018i | \(-0.683130\pi\) | ||||
0.544104 | − | 0.839018i | \(-0.316870\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 470.533i | 0.820950i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 995.156 | 1.66343 | 0.831713 | − | 0.555206i | \(-0.187361\pi\) | ||||
0.831713 | + | 0.555206i | \(0.187361\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 362.266 | 0.580822 | 0.290411 | − | 0.956902i | \(-0.406208\pi\) | ||||
0.290411 | + | 0.956902i | \(0.406208\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 49.1329i | 0.0756451i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 396.178i | 0.586347i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1098.91 | −1.56503 | −0.782513 | − | 0.622634i | \(-0.786062\pi\) | ||||
−0.782513 | + | 0.622634i | \(0.786062\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 791.822i | − 1.04715i | −0.851979 | − | 0.523577i | \(-0.824597\pi\) | ||||
0.851979 | − | 0.523577i | \(-0.175403\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 788.844i | − 1.00661i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −161.400 | −0.198895 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −150.622 | −0.179393 | −0.0896963 | − | 0.995969i | \(-0.528590\pi\) | ||||
−0.0896963 | + | 0.995969i | \(0.528590\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 416.444i | 0.479728i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 682.466i | 0.760951i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 107.465 | 0.116060 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1879.15 | −1.96700 | −0.983501 | − | 0.180903i | \(-0.942098\pi\) | ||||
−0.983501 | + | 0.180903i | \(0.942098\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 555.199i | 0.563633i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1722.51i | − 1.69699i | −0.529202 | − | 0.848496i | \(-0.677509\pi\) | ||||
0.529202 | − | 0.848496i | \(-0.322491\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1908.82 | 1.82604 | 0.913018 | − | 0.407919i | \(-0.133745\pi\) | ||||
0.913018 | + | 0.407919i | \(0.133745\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 200.801 | 0.186630 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 128.622i | − 0.116209i | −0.998310 | − | 0.0581046i | \(-0.981494\pi\) | ||||
0.998310 | − | 0.0581046i | \(-0.0185057\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 758.267i | − 0.666320i | −0.942870 | − | 0.333160i | \(-0.891885\pi\) | ||||
0.942870 | − | 0.333160i | \(-0.108115\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −30.9335 | −0.0264512 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 921.643 | 0.767265 | 0.383632 | − | 0.923486i | \(-0.374673\pi\) | ||||
0.383632 | + | 0.923486i | \(0.374673\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1634.66i | 1.32551i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 583.600i | 0.461144i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 486.089 | 0.374451 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2474.51 | −1.85914 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 211.332i | − 0.154920i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1473.47i | 1.05433i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1647.22 | −1.15092 | −0.575462 | − | 0.817828i | \(-0.695178\pi\) | ||||
−0.575462 | + | 0.817828i | \(0.695178\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 894.934 | 0.610810 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2000.27i | 1.33408i | 0.745023 | + | 0.667038i | \(0.232438\pi\) | ||||
−0.745023 | + | 0.667038i | \(0.767562\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 66.2205i | 0.0431733i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 281.400 | 0.179400 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2574.71 | 1.60564 | 0.802819 | − | 0.596223i | \(-0.203333\pi\) | ||||
0.802819 | + | 0.596223i | \(0.203333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 1331.29i | − 0.812362i | −0.913793 | − | 0.406181i | \(-0.866860\pi\) | ||||
0.913793 | − | 0.406181i | \(-0.133140\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 269.733i | − 0.161103i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4000.18 | −2.33924 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −560.713 | −0.321136 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 905.266i | − 0.507926i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 552.377i | 0.303708i | 0.988403 | + | 0.151854i | \(0.0485243\pi\) | ||||
−0.988403 | + | 0.151854i | \(0.951476\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1307.13 | −0.704456 | −0.352228 | − | 0.935914i | \(-0.614576\pi\) | ||||
−0.352228 | + | 0.935914i | \(0.614576\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 681.199 | 0.359946 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2370.93i | 1.22863i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3527.11i | − 1.79295i | −0.443089 | − | 0.896477i | \(-0.646118\pi\) | ||||
0.443089 | − | 0.896477i | \(-0.353882\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1165.00 | −0.581072 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1007.29 | −0.493077 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 926.045i | 0.444991i | 0.974934 | + | 0.222495i | \(0.0714202\pi\) | ||||
−0.974934 | + | 0.222495i | \(0.928580\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1928.80i | 0.910042i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1393.33 | −0.645624 | −0.322812 | − | 0.946463i | \(-0.604628\pi\) | ||||
−0.322812 | + | 0.946463i | \(0.604628\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2007.80 | −0.913881 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 92.8006i | 0.0415008i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3311.71i | 1.45540i | 0.685894 | + | 0.727701i | \(0.259411\pi\) | ||||
−0.685894 | + | 0.727701i | \(0.740589\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −105.181 | −0.0454337 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 972.000 | 0.412768 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 323.287i | − 0.134992i | −0.997720 | − | 0.0674961i | \(-0.978499\pi\) | ||||
0.997720 | − | 0.0674961i | \(-0.0215010\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 3066.80i | − 1.25941i | −0.776834 | − | 0.629705i | \(-0.783176\pi\) | ||||
0.776834 | − | 0.629705i | \(-0.216824\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 972.000 | 0.392636 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −107.465 | −0.0427081 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4669.15i | 1.82589i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 173.400i | 0.0667352i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1856.44 | −0.703286 | −0.351643 | − | 0.936134i | \(-0.614377\pi\) | ||||
−0.351643 | + | 0.936134i | \(0.614377\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3008.84 | 1.12218 | 0.561091 | − | 0.827754i | \(-0.310382\pi\) | ||||
0.561091 | + | 0.827754i | \(0.310382\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2027.47i | 0.744563i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 909.309i | 0.328861i | 0.986389 | + | 0.164430i | \(0.0525786\pi\) | ||||
−0.986389 | + | 0.164430i | \(0.947421\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2780.24 | −0.990383 | −0.495191 | − | 0.868784i | \(-0.664902\pi\) | ||||
−0.495191 | + | 0.868784i | \(0.664902\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2760.80 | 0.968814 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 345.514i | − 0.119460i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 734.183i | − 0.250134i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1411.60 | −0.473976 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −636.085 | −0.210521 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 385.511i | − 0.125780i | −0.998020 | − | 0.0628901i | \(-0.979968\pi\) | ||||
0.998020 | − | 0.0628901i | \(-0.0200318\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2985.47i | 0.960379i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3109.06 | 0.986215 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1460.98 | −0.457040 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1086.80i | 0.335338i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4908.00i | 1.49388i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −601.975 | −0.180768 | −0.0903839 | − | 0.995907i | \(-0.528809\pi\) | ||||
−0.0903839 | + | 0.995907i | \(0.528809\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −147.399 | −0.0436737 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 185.779i | 0.0543199i | 0.999631 | + | 0.0271600i | \(0.00864634\pi\) | ||||
−0.999631 | + | 0.0271600i | \(0.991354\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1237.11i | 0.356989i | 0.983941 | + | 0.178495i | \(0.0571227\pi\) | ||||
−0.983941 | + | 0.178495i | \(0.942877\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1188.53 | −0.338527 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 217.378 | 0.0611197 | 0.0305598 | − | 0.999533i | \(-0.490271\pi\) | ||||
0.0305598 | + | 0.999533i | \(0.490271\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 937.070i | − 0.260118i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 3296.73i | − 0.903568i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6055.99 | 1.63904 | 0.819518 | − | 0.573053i | \(-0.194241\pi\) | ||||
0.819518 | + | 0.573053i | \(0.194241\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6815.69 | −1.82173 | −0.910865 | − | 0.412705i | \(-0.864584\pi\) | ||||
−0.910865 | + | 0.412705i | \(0.864584\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3144.96i | − 0.820097i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −668.622 | −0.172241 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2375.47 | 0.604574 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2448.53i | 0.615738i | 0.951429 | + | 0.307869i | \(0.0996158\pi\) | ||||
−0.951429 | + | 0.307869i | \(0.900384\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 9675.55i | − 2.40433i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2366.53 | 0.581169 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2949.55 | 0.715907 | 0.357953 | − | 0.933739i | \(-0.383475\pi\) | ||||
0.357953 | + | 0.933739i | \(0.383475\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 66.2205i | − 0.0158870i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 484.199i | − 0.114832i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4831.64 | −1.13282 | −0.566410 | − | 0.824124i | \(-0.691668\pi\) | ||||
−0.566410 | + | 0.824124i | \(0.691668\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4047.29 | −0.938199 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 451.867i | − 0.103572i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 1093.84i | − 0.247928i | −0.992287 | − | 0.123964i | \(-0.960439\pi\) | ||||
0.992287 | − | 0.123964i | \(-0.0395607\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3079.80 | 0.690349 | 0.345175 | − | 0.938539i | \(-0.387820\pi\) | ||||
0.345175 | + | 0.938539i | \(0.387820\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1249.33 | −0.276971 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1010.32i | − 0.221543i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5600.75i | 1.21486i | 0.794373 | + | 0.607430i | \(0.207800\pi\) | ||||
−0.794373 | + | 0.607430i | \(0.792200\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2047.40 | −0.439335 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −203.426 | −0.0431864 | −0.0215932 | − | 0.999767i | \(-0.506874\pi\) | ||||
−0.0215932 | + | 0.999767i | \(0.506874\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2214.84i | − 0.465225i | −0.972570 | − | 0.232612i | \(-0.925273\pi\) | ||||
0.972570 | − | 0.232612i | \(-0.0747273\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 322.396i | 0.0670073i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 452.406 | 0.0930478 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 815.798 | 0.166049 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 5637.46i | − 1.13565i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 5812.37i | − 1.15892i | −0.815002 | − | 0.579458i | \(-0.803264\pi\) | ||||
0.815002 | − | 0.579458i | \(-0.196736\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3376.79 | 0.666456 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1665.60 | −0.325413 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 10170.5i | − 1.96714i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1915.82i | 0.366863i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5167.53 | 0.979758 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3376.79 | 0.633950 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 7337.33i | − 1.36405i | −0.731329 | − | 0.682025i | \(-0.761099\pi\) | ||||
0.731329 | − | 0.682025i | \(-0.238901\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5726.46i | 1.05426i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6575.91 | −1.19899 | −0.599494 | − | 0.800379i | \(-0.704632\pi\) | ||||
−0.599494 | + | 0.800379i | \(0.704632\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1556.67 | 0.281113 | 0.140556 | − | 0.990073i | \(-0.455111\pi\) | ||||
0.140556 | + | 0.990073i | \(0.455111\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 602.402i | 0.107751i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9457.27i | 1.67562i | 0.545959 | + | 0.837812i | \(0.316166\pi\) | ||||
−0.545959 | + | 0.837812i | \(0.683834\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3318.85 | 0.582507 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 385.867 | 0.0670935 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 780.441i | 0.134442i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1062.00i | − 0.181259i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2274.80 | 0.384700 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 577.426 | 0.0967615 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 10907.6i | − 1.81129i | −0.424032 | − | 0.905647i | \(-0.639386\pi\) | ||||
0.424032 | − | 0.905647i | \(-0.360614\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 92.8006i | − 0.0152716i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9591.20 | 1.56425 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4256.22 | 0.687986 | 0.343993 | − | 0.938972i | \(-0.388220\pi\) | ||||
0.343993 | + | 0.938972i | \(0.388220\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2764.93i | 0.442981i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 14033.5i | − 2.22861i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4140.75 | 0.651835 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4903.99 | −0.765282 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4217.07i | 0.652403i | 0.945300 | + | 0.326202i | \(0.105769\pi\) | ||||
−0.945300 | + | 0.326202i | \(0.894231\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2986.57i | 0.458073i | 0.973418 | + | 0.229037i | \(0.0735576\pi\) | ||||
−0.973418 | + | 0.229037i | \(0.926442\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1750.80 | −0.266241 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8231.42 | −1.24112 | −0.620558 | − | 0.784160i | \(-0.713094\pi\) | ||||
−0.620558 | + | 0.784160i | \(0.713094\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10371.7i | 1.55063i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1458.27i | 0.216190i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5857.19 | 0.861088 | 0.430544 | − | 0.902569i | \(-0.358322\pi\) | ||||
0.430544 | + | 0.902569i | \(0.358322\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6752.68 | 0.984499 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 7423.53i | − 1.07337i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3775.61i | 0.541437i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10715.7 | 1.52412 | 0.762061 | − | 0.647505i | \(-0.224188\pi\) | ||||
0.762061 | + | 0.647505i | \(0.224188\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 633.997 | 0.0894433 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 2493.95i | − 0.349002i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1817.52i | 0.252299i | 0.992011 | + | 0.126149i | \(0.0402619\pi\) | ||||
−0.992011 | + | 0.126149i | \(0.959738\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4420.40 | −0.608716 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3488.62 | 0.476586 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9789.68i | 1.32681i | 0.748259 | + | 0.663407i | \(0.230890\pi\) | ||||
−0.748259 | + | 0.663407i | \(0.769110\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 4941.67i | − 0.664486i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11502.3 | 1.53457 | 0.767285 | − | 0.641306i | \(-0.221607\pi\) | ||||
0.767285 | + | 0.641306i | \(0.221607\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4129.05 | −0.546587 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2684.80i | 0.352651i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.06261i | 0 0.000790197i | 1.00000 | 0.000395098i | \(0.000125764\pi\) | |||||
−1.00000 | 0.000395098i | \(0.999874\pi\) | ||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11871.4 | −1.53545 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6000.80 | −0.770230 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 11453.1i | − 1.45890i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5982.31i | 0.756281i | 0.925748 | + | 0.378141i | \(0.123436\pi\) | ||||
−0.925748 | + | 0.378141i | \(0.876564\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −198.662 | −0.0249261 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10443.6 | 1.30057 | 0.650284 | − | 0.759691i | \(-0.274650\pi\) | ||||
0.650284 | + | 0.759691i | \(0.274650\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 14751.4i | − 1.82337i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 844.199i | 0.103577i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 636.085 | 0.0774682 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8141.01 | 0.984223 | 0.492112 | − | 0.870532i | \(-0.336225\pi\) | ||||
0.492112 | + | 0.870532i | \(0.336225\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7724.13i | 0.927015i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2080.79i | 0.247916i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8252.53 | 0.976146 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3993.86 | 0.469017 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 8716.96i | − 1.01635i | −0.861253 | − | 0.508176i | \(-0.830320\pi\) | ||||
0.861253 | − | 0.508176i | \(-0.169680\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13437.5i | 1.55560i | 0.628514 | + | 0.777798i | \(0.283663\pi\) | ||||
−0.628514 | + | 0.777798i | \(0.716337\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 809.198 | 0.0930131 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1239.60 | −0.141482 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2080.79i | 0.235824i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 12000.5i | − 1.35056i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7343.86 | −0.820745 | −0.410373 | − | 0.911918i | \(-0.634601\pi\) | ||||
−0.410373 | + | 0.911918i | \(0.634601\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4490.80 | 0.498416 | 0.249208 | − | 0.968450i | \(-0.419830\pi\) | ||||
0.249208 | + | 0.968450i | \(0.419830\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 1682.14i | − 0.185408i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1617.25i | − 0.177033i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9437.93 | −1.02608 | −0.513038 | − | 0.858366i | \(-0.671480\pi\) | ||||
−0.513038 | + | 0.858366i | \(0.671480\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2715.80 | 0.293251 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12668.3i | 1.35866i | 0.733832 | + | 0.679331i | \(0.237730\pi\) | ||||
−0.733832 | + | 0.679331i | \(0.762270\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1569.82i | − 0.167228i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1657.13 | −0.175346 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13052.0 | −1.37186 | −0.685929 | − | 0.727669i | \(-0.740604\pi\) | ||||
−0.685929 | + | 0.727669i | \(0.740604\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4345.61i | 0.453718i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 3921.40i | − 0.406718i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4340.27 | −0.447197 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1313.64 | 0.134463 | 0.0672316 | − | 0.997737i | \(-0.478583\pi\) | ||||
0.0672316 | + | 0.997737i | \(0.478583\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2043.60i | 0.207815i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 627.883i | 0.0634347i | 0.999497 | + | 0.0317174i | \(0.0100976\pi\) | ||||
−0.999497 | + | 0.0317174i | \(0.989902\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7315.03 | −0.734251 | −0.367126 | − | 0.930171i | \(-0.619658\pi\) | ||||
−0.367126 | + | 0.930171i | \(0.619658\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7112.80 | −0.709351 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 759.997i | − 0.0753072i | −0.999291 | − | 0.0376536i | \(-0.988012\pi\) | ||||
0.999291 | − | 0.0376536i | \(-0.0119883\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5910.14i | 0.581886i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10581.3 | 1.03516 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18402.5 | −1.78889 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 168.873i | − 0.0163125i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 3495.00i | − 0.335482i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7403.51 | −0.706211 | −0.353106 | − | 0.935583i | \(-0.614874\pi\) | ||||
−0.353106 | + | 0.935583i | \(0.614874\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 668.622 | 0.0633816 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 3021.86i | − 0.284678i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 19584.9i | − 1.83362i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3488.11 | −0.324561 | −0.162281 | − | 0.986745i | \(-0.551885\pi\) | ||||
−0.162281 | + | 0.986745i | \(0.551885\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2778.14 | −0.256915 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6575.73i | 0.604396i | 0.953245 | + | 0.302198i | \(0.0977204\pi\) | ||||
−0.953245 | + | 0.302198i | \(0.902280\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4072.05i | − 0.372000i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5786.40 | −0.525413 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6391.09 | −0.576820 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5187.82i | 0.465408i | 0.972548 | + | 0.232704i | \(0.0747574\pi\) | ||||
−0.972548 | + | 0.232704i | \(0.925243\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 4180.00i | − 0.372751i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7248.38 | −0.642524 | −0.321262 | − | 0.946990i | \(-0.604107\pi\) | ||||
−0.321262 | + | 0.946990i | \(0.604107\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17952.4 | 1.58192 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 6023.39i | − 0.527630i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6613.44i | 0.575905i | 0.957645 | + | 0.287952i | \(0.0929745\pi\) | ||||
−0.957645 | + | 0.287952i | \(0.907026\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2326.55 | −0.201410 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −278.402 | −0.0239605 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19894.1i | 1.70221i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5546.50i | 0.471827i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9935.13 | −0.840277 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20761.3 | −1.74581 | −0.872906 | − | 0.487888i | \(-0.837767\pi\) | ||||
−0.872906 | + | 0.487888i | \(0.837767\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 13494.2i | − 1.12822i | −0.825698 | − | 0.564112i | \(-0.809219\pi\) | ||||
0.825698 | − | 0.564112i | \(-0.190781\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 315.542i | − 0.0262312i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17218.3 | −1.42323 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12433.2 | 1.02188 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2916.00i | 0.238312i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4567.91i | 0.371216i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1340.53 | 0.108329 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 969.861 | 0.0779378 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18614.9i | 1.48757i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2708.58i | 0.215251i | 0.994191 | + | 0.107626i | \(0.0343248\pi\) | ||||
−0.994191 | + | 0.107626i | \(0.965675\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9200.39 | 0.727121 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7902.82 | 0.621137 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15783.5i | 1.23373i | 0.787068 | + | 0.616866i | \(0.211598\pi\) | ||||
−0.787068 | + | 0.616866i | \(0.788402\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2916.00i | 0.226688i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 554.740 | 0.0428906 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7057.43 | 0.542699 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 322.396i | − 0.0246575i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1892.77i | 0.143984i | 0.997405 | + | 0.0719922i | \(0.0229357\pi\) | ||||
−0.997405 | + | 0.0719922i | \(0.977064\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19343.8 | −1.46361 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14007.5 | −1.05418 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3876.26i | 0.290169i | 0.989419 | + | 0.145084i | \(0.0463454\pi\) | ||||
−0.989419 | + | 0.145084i | \(0.953655\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9605.56i | 0.715237i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −520.199 | −0.0385296 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14900.9 | 1.09785 | 0.548927 | − | 0.835870i | \(-0.315037\pi\) | ||||
0.548927 | + | 0.835870i | \(0.315037\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24926.0i | 1.82683i | 0.407032 | + | 0.913414i | \(0.366564\pi\) | ||||
−0.407032 | + | 0.913414i | \(0.633436\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 5569.33i | − 0.406042i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2568.74 | 0.186302 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21022.4 | 1.51677 | 0.758384 | − | 0.651808i | \(-0.225989\pi\) | ||||
0.758384 | + | 0.651808i | \(0.225989\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9026.52i | 0.647892i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5085.24i | 0.363118i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23955.8 | 1.70180 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6082.40 | −0.429874 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 13847.0i | − 0.973641i | −0.873502 | − | 0.486821i | \(-0.838157\pi\) | ||||
0.873502 | − | 0.486821i | \(-0.161843\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 2345.68i | − 0.164095i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2727.93 | −0.189868 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4113.01 | −0.284825 | −0.142413 | − | 0.989807i | \(-0.545486\pi\) | ||||
−0.142413 | + | 0.989807i | \(0.545486\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5066.12i | 0.349060i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 8340.73i | − 0.571798i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4863.60 | 0.331755 | 0.165878 | − | 0.986146i | \(-0.446954\pi\) | ||||
0.165878 | + | 0.986146i | \(0.446954\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6827.76 | −0.463411 | −0.231706 | − | 0.972786i | \(-0.574431\pi\) | ||||
−0.231706 | + | 0.972786i | \(0.574431\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8282.39i | 0.559345i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 25789.9i | − 1.73307i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18178.3 | −1.21554 | −0.607770 | − | 0.794113i | \(-0.707936\pi\) | ||||
−0.607770 | + | 0.794113i | \(0.707936\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1036.54 | 0.0689700 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5830.22i | 0.386032i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15687.2i | 1.03360i | 0.856105 | + | 0.516802i | \(0.172878\pi\) | ||||
−0.856105 | + | 0.516802i | \(0.827122\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2202.55 | 0.144415 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16420.2 | 1.07140 | 0.535700 | − | 0.844409i | \(-0.320048\pi\) | ||||
0.535700 | + | 0.844409i | \(0.320048\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5517.78i | 0.358285i | 0.983823 | + | 0.179142i | \(0.0573322\pi\) | ||||
−0.983823 | + | 0.179142i | \(0.942668\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 4234.80i | − 0.273650i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 967.328 | 0.0622073 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13309.6 | −0.851812 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 1908.25i | − 0.121544i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 780.441i | − 0.0494725i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1559.17 | 0.0983670 | 0.0491835 | − | 0.998790i | \(-0.484338\pi\) | ||||
0.0491835 | + | 0.998790i | \(0.484338\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1156.53 | 0.0726193 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 17167.7i | − 1.07288i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19567.1i | 1.21708i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8956.40 | −0.554475 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15188.6 | −0.935900 | −0.467950 | − | 0.883755i | \(-0.655007\pi\) | ||||
−0.467950 | + | 0.883755i | \(0.655007\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 16666.6i | − 1.02219i | −0.859524 | − | 0.511095i | \(-0.829240\pi\) | ||||
0.859524 | − | 0.511095i | \(-0.170760\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9327.18i | 0.569391i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3038.27 | 0.184616 | 0.0923081 | − | 0.995730i | \(-0.470576\pi\) | ||||
0.0923081 | + | 0.995730i | \(0.470576\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19987.2 | −1.20888 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 4382.94i | − 0.263872i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9078.99i | 0.544086i | 0.962285 | + | 0.272043i | \(0.0876994\pi\) | ||||
−0.962285 | + | 0.272043i | \(0.912301\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20847.2 | −1.24361 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3260.39 | −0.193607 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 16892.0i | − 0.998511i | −0.866455 | − | 0.499255i | \(-0.833607\pi\) | ||||
0.866455 | − | 0.499255i | \(-0.166393\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5064.16i | 0.297992i | 0.988838 | + | 0.148996i | \(0.0476042\pi\) | ||||
−0.988838 | + | 0.148996i | \(0.952396\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14724.0 | −0.862492 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −690.164 | −0.0402457 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8438.21i | 0.489848i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 1805.93i | − 0.104366i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19987.2 | −1.14992 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28625.9 | 1.63959 | 0.819797 | − | 0.572654i | \(-0.194086\pi\) | ||||
0.819797 | + | 0.572654i | \(0.194086\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 442.196i | − 0.0252150i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 16061.2i | − 0.911791i | −0.890033 | − | 0.455895i | \(-0.849319\pi\) | ||||
0.890033 | − | 0.455895i | \(-0.150681\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12068.3 | 0.682090 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −557.338 | −0.0313616 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 7868.09i | − 0.440796i | −0.975410 | − | 0.220398i | \(-0.929264\pi\) | ||||
0.975410 | − | 0.220398i | \(-0.0707357\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26834.2i | 1.49676i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3711.33 | −0.206108 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25181.2 | 1.39235 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16886.2i | 0.929641i | 0.885405 | + | 0.464820i | \(0.153881\pi\) | ||||
−0.885405 | + | 0.464820i | \(0.846119\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 3565.60i | − 0.195449i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13874.9 | 0.757276 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5331.83 | 0.289753 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 652.133i | 0.0352875i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 18293.6i | − 0.985647i | −0.870129 | − | 0.492824i | \(-0.835965\pi\) | ||||
0.870129 | − | 0.492824i | \(-0.164035\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 106.320 | 0.00570406 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2811.21 | 0.150179 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11062.3i | 0.588460i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 21555.6i | − 1.14180i | −0.821019 | − | 0.570900i | \(-0.806594\pi\) | ||||
0.821019 | − | 0.570900i | \(-0.193406\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9890.19 | 0.521675 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 35680.3 | 1.87411 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 41690.6i | − 2.18062i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18168.0i | 0.946298i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9059.31 | 0.469896 | 0.234948 | − | 0.972008i | \(-0.424508\pi\) | ||||
0.234948 | + | 0.972008i | \(0.424508\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12258.8 | −0.633208 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 20447.1i | − 1.05178i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 881.115i | 0.0451362i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7074.83 | 0.360923 | 0.180462 | − | 0.983582i | \(-0.442241\pi\) | ||||
0.180462 | + | 0.983582i | \(0.442241\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22578.8i | 1.14242i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17095.9i | 0.861459i | 0.902481 | + | 0.430730i | \(0.141744\pi\) | ||||
−0.902481 | + | 0.430730i | \(0.858256\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9434.87 | 0.473483 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −56770.1 | −2.83739 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 28157.4i | − 1.40161i | −0.713355 | − | 0.700803i | \(-0.752825\pi\) | ||||
0.713355 | − | 0.700803i | \(-0.247175\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 2005.87i | − 0.0994431i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34033.2 | 1.68043 | 0.840214 | − | 0.542255i | \(-0.182429\pi\) | ||||
0.840214 | + | 0.542255i | \(0.182429\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5756.99 | −0.283114 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7126.40i | 0.349051i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 826.039i | 0.0402975i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34356.8 | 1.66937 | 0.834685 | − | 0.550728i | \(-0.185650\pi\) | ||||
0.834685 | + | 0.550728i | \(0.185650\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7345.60 | −0.355496 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 13623.2i | − 0.656687i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 29464.6i | − 1.41467i | −0.706876 | − | 0.707337i | \(-0.749896\pi\) | ||||
0.706876 | − | 0.707337i | \(-0.250104\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 29026.6 | 1.38814 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27284.5 | −1.29969 | −0.649843 | − | 0.760069i | \(-0.725165\pi\) | ||||
−0.649843 | + | 0.760069i | \(0.725165\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4869.75i | 0.231057i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7099.60i | 0.335538i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21009.6 | −0.989064 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2320.13 | 0.108798 | 0.0543992 | − | 0.998519i | \(-0.482676\pi\) | ||||
0.0543992 | + | 0.998519i | \(0.482676\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8848.66i | 0.413329i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4217.83i | 0.196254i | 0.995174 | + | 0.0981272i | \(0.0312852\pi\) | ||||
−0.995174 | + | 0.0981272i | \(0.968715\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3725.73 | 0.172687 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 198.662 | 0.00917238 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 726.362i | 0.0334077i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 61390.0i | − 2.81268i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1452.60 | 0.0662983 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36760.3 | 1.67138 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 11436.3i | − 0.517991i | −0.965879 | − | 0.258995i | \(-0.916609\pi\) | ||||
0.965879 | − | 0.258995i | \(-0.0833914\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 14494.9i | − 0.654034i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5918.98 | −0.266062 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21009.6 | −0.940823 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 12141.9i | − 0.541670i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14102.3i | 0.626761i | 0.949628 | + | 0.313381i | \(0.101462\pi\) | ||||
−0.949628 | + | 0.313381i | \(0.898538\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6805.25 | 0.301317 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1355.60 | 0.0597975 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 22347.8i | − 0.982111i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 10498.2i | − 0.459641i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3281.52 | 0.143141 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18791.3 | −0.816647 | −0.408323 | − | 0.912837i | \(-0.633886\pi\) | ||||
−0.408323 | + | 0.912837i | \(0.633886\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14452.6i | 0.625771i | 0.949791 | + | 0.312886i | \(0.101296\pi\) | ||||
−0.949791 | + | 0.312886i | \(0.898704\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9239.40i | 0.398573i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9651.43 | −0.414816 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3075.94 | −0.131718 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 3748.00i | − 0.159909i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27786.1i | 1.18117i | 0.806975 | + | 0.590585i | \(0.201103\pi\) | ||||
−0.806975 | + | 0.590585i | \(0.798897\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39205.8 | 1.66055 | 0.830273 | − | 0.557357i | \(-0.188185\pi\) | ||||
0.830273 | + | 0.557357i | \(0.188185\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3030.95 | 0.127908 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 5929.15i | − 0.249307i | −0.992200 | − | 0.124653i | \(-0.960218\pi\) | ||||
0.992200 | − | 0.124653i | \(-0.0397819\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1269.44i | 0.0531840i | 0.999646 | + | 0.0265920i | \(0.00846550\pi\) | ||||
−0.999646 | + | 0.0265920i | \(0.991535\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16802.3 | −0.701400 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22839.5 | 0.949990 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 14521.6i | − 0.601845i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 6142.19i | − 0.253650i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17884.1 | 0.735910 | 0.367955 | − | 0.929844i | \(-0.380058\pi\) | ||||
0.367955 | + | 0.929844i | \(0.380058\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21494.6 | 0.881323 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 610.278i | − 0.0249337i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 20925.7i | − 0.851911i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15891.8 | 0.644686 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6644.52 | 0.268598 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1617.25i | 0.0651453i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16083.4i | 0.645585i | 0.946470 | + | 0.322793i | \(0.104622\pi\) | ||||
−0.946470 | + | 0.322793i | \(0.895378\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −967.187 | −0.0386867 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17203.6 | −0.685722 | −0.342861 | − | 0.939386i | \(-0.611396\pi\) | ||||
−0.342861 | + | 0.939386i | \(0.611396\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 24427.5i | − 0.970264i | −0.874441 | − | 0.485132i | \(-0.838772\pi\) | ||||
0.874441 | − | 0.485132i | \(-0.161228\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1357.22i | 0.0537212i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46584.1 | 1.83747 | 0.918737 | − | 0.394870i | \(-0.129210\pi\) | ||||
0.918737 | + | 0.394870i | \(0.129210\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34515.3 | −1.35671 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2447.39i | 0.0958683i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 67790.5i | 2.64630i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −59674.1 | −2.32145 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16912.4 | 0.655667 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 9462.91i | − 0.365605i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7402.05i | 0.285005i | 0.989794 | + | 0.142503i | \(0.0455149\pi\) | ||||
−0.989794 | + | 0.142503i | \(0.954485\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17437.1 | 0.669101 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12044.7 | 0.460608 | 0.230304 | − | 0.973119i | \(-0.426028\pi\) | ||||
0.230304 | + | 0.973119i | \(0.426028\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7150.02i | 0.272500i | 0.990674 | + | 0.136250i | \(0.0435050\pi\) | ||||
−0.990674 | + | 0.136250i | \(0.956495\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10130.4i | 0.384779i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21897.6 | 0.828916 | 0.414458 | − | 0.910068i | \(-0.363971\pi\) | ||||
0.414458 | + | 0.910068i | \(0.363971\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10578.8 | 0.399102 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 4996.79i | − 0.187878i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 927.087i | 0.0347411i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3369.36 | 0.125838 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 30511.4 | 1.13573 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12238.9i | 0.454047i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 29392.5i | − 1.08680i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5747.45 | −0.211808 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 31962.8 | 1.17401 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 800.885i | 0.0293197i | 0.999893 | + | 0.0146598i | \(0.00466654\pi\) | ||||
−0.999893 | + | 0.0146598i | \(0.995333\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15502.6i | 0.565664i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26742.9 | 0.972593 | 0.486296 | − | 0.873794i | \(-0.338348\pi\) | ||||
0.486296 | + | 0.873794i | \(0.338348\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −48846.5 | −1.77063 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10130.4i | 0.366011i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 12846.1i | − 0.462613i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3744.72 | −0.134414 | −0.0672072 | − | 0.997739i | \(-0.521409\pi\) | ||||
−0.0672072 | + | 0.997739i | \(0.521409\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22012.0 | 0.787535 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 64530.3i | − 2.30124i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 168.873i | 0.00600271i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17179.4 | −0.608679 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25667.3 | −0.906477 | −0.453238 | − | 0.891389i | \(-0.649731\pi\) | ||||
−0.453238 | + | 0.891389i | \(0.649731\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3111.45i | 0.109531i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 19727.7i | − 0.692236i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −48662.9 | −1.70208 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17978.7 | −0.626829 | −0.313414 | − | 0.949616i | \(-0.601473\pi\) | ||||
−0.313414 | + | 0.949616i | \(0.601473\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4670.01i | 0.162300i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 8120.01i | − 0.281302i | −0.990059 | − | 0.140651i | \(-0.955081\pi\) | ||||
0.990059 | − | 0.140651i | \(-0.0449195\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11048.8 | −0.381545 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1807.21 | −0.0622099 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7930.95i | 0.272145i | 0.990699 | + | 0.136072i | \(0.0434480\pi\) | ||||
−0.990699 | + | 0.136072i | \(0.956552\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 23490.9i | − 0.803527i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28371.8 | −0.967422 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29833.3 | −1.01406 | −0.507028 | − | 0.861930i | \(-0.669256\pi\) | ||||
−0.507028 | + | 0.861930i | \(0.669256\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 19348.2i | − 0.655596i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9956.55i | 0.336311i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16535.3 | −0.556781 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21960.1 | 0.737139 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1157.60i | 0.0387364i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 31358.7i | 1.04609i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7650.56 | 0.254421 | 0.127211 | − | 0.991876i | \(-0.459398\pi\) | ||||
0.127211 | + | 0.991876i | \(0.459398\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2341.32 | −0.0776204 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5634.51i | 0.186220i | 0.995656 | + | 0.0931102i | \(0.0296809\pi\) | ||||
−0.995656 | + | 0.0931102i | \(0.970319\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8549.80i | 0.281700i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3186.00 | 0.104650 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43983.5 | 1.44028 | 0.720142 | − | 0.693827i | \(-0.244077\pi\) | ||||
0.720142 | + | 0.693827i | \(0.244077\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9291.72i | 0.303335i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6824.41i | 0.222107i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7759.30 | −0.251763 | −0.125882 | − | 0.992045i | \(-0.540176\pi\) | ||||
−0.125882 | + | 0.992045i | \(0.540176\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9477.00 | −0.306561 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1732.28i | 0.0558653i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 46788.4i | − 1.50433i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10114.8 | −0.324226 | −0.162113 | − | 0.986772i | \(-0.551831\pi\) | ||||
−0.162113 | + | 0.986772i | \(0.551831\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32722.9 | 1.04575 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 28976.3i | − 0.923225i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 43842.2i | − 1.39267i | −0.717715 | − | 0.696337i | \(-0.754812\pi\) | ||||
0.717715 | − | 0.696337i | \(-0.245188\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 278.402 | 0.00881706 |
(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.d.e.193.4 | yes | 4 | |
3.2 | odd | 2 | 1152.4.d.o.577.2 | 4 | |||
4.3 | odd | 2 | 384.4.d.c.193.2 | ✓ | 4 | ||
8.3 | odd | 2 | 384.4.d.c.193.3 | yes | 4 | ||
8.5 | even | 2 | inner | 384.4.d.e.193.1 | yes | 4 | |
12.11 | even | 2 | 1152.4.d.i.577.2 | 4 | |||
16.3 | odd | 4 | 768.4.a.k.1.2 | 2 | |||
16.5 | even | 4 | 768.4.a.p.1.1 | 2 | |||
16.11 | odd | 4 | 768.4.a.j.1.1 | 2 | |||
16.13 | even | 4 | 768.4.a.e.1.2 | 2 | |||
24.5 | odd | 2 | 1152.4.d.o.577.3 | 4 | |||
24.11 | even | 2 | 1152.4.d.i.577.3 | 4 | |||
48.5 | odd | 4 | 2304.4.a.s.1.2 | 2 | |||
48.11 | even | 4 | 2304.4.a.t.1.2 | 2 | |||
48.29 | odd | 4 | 2304.4.a.bp.1.1 | 2 | |||
48.35 | even | 4 | 2304.4.a.bq.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.d.c.193.2 | ✓ | 4 | 4.3 | odd | 2 | ||
384.4.d.c.193.3 | yes | 4 | 8.3 | odd | 2 | ||
384.4.d.e.193.1 | yes | 4 | 8.5 | even | 2 | inner | |
384.4.d.e.193.4 | yes | 4 | 1.1 | even | 1 | trivial | |
768.4.a.e.1.2 | 2 | 16.13 | even | 4 | |||
768.4.a.j.1.1 | 2 | 16.11 | odd | 4 | |||
768.4.a.k.1.2 | 2 | 16.3 | odd | 4 | |||
768.4.a.p.1.1 | 2 | 16.5 | even | 4 | |||
1152.4.d.i.577.2 | 4 | 12.11 | even | 2 | |||
1152.4.d.i.577.3 | 4 | 24.11 | even | 2 | |||
1152.4.d.o.577.2 | 4 | 3.2 | odd | 2 | |||
1152.4.d.o.577.3 | 4 | 24.5 | odd | 2 | |||
2304.4.a.s.1.2 | 2 | 48.5 | odd | 4 | |||
2304.4.a.t.1.2 | 2 | 48.11 | even | 4 | |||
2304.4.a.bp.1.1 | 2 | 48.29 | odd | 4 | |||
2304.4.a.bq.1.1 | 2 | 48.35 | even | 4 |