Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,3,Mod(197,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.197");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.0327593166\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.1 | ||
Root | \(-1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.197 |
Dual form | 882.3.b.c.197.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.41421i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | − 1.41421i | − 0.282843i | −0.989949 | − | 0.141421i | \(-0.954833\pi\) | ||||
0.989949 | − | 0.141421i | \(-0.0451672\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.00000 | −0.200000 | ||||||||
\(11\) | − 7.07107i | − 0.642824i | −0.946939 | − | 0.321412i | \(-0.895843\pi\) | ||||
0.946939 | − | 0.321412i | \(-0.104157\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.0000 | 1.15385 | 0.576923 | − | 0.816798i | \(-0.304253\pi\) | ||||
0.576923 | + | 0.816798i | \(0.304253\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − 11.3137i | − 0.665512i | −0.943013 | − | 0.332756i | \(-0.892021\pi\) | ||||
0.943013 | − | 0.332756i | \(-0.107979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −13.0000 | −0.684211 | −0.342105 | − | 0.939662i | \(-0.611140\pi\) | ||||
−0.342105 | + | 0.939662i | \(0.611140\pi\) | |||||||
\(20\) | 2.82843i | 0.141421i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −10.0000 | −0.454545 | ||||||||
\(23\) | 22.6274i | 0.983801i | 0.870651 | + | 0.491900i | \(0.163698\pi\) | ||||
−0.870651 | + | 0.491900i | \(0.836302\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 23.0000 | 0.920000 | ||||||||
\(26\) | − 21.2132i | − 0.815892i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 22.6274i | − 0.780256i | −0.920761 | − | 0.390128i | \(-0.872431\pi\) | ||||
0.920761 | − | 0.390128i | \(-0.127569\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | 0.0967742 | 0.0483871 | − | 0.998829i | \(-0.484592\pi\) | ||||
0.0483871 | + | 0.998829i | \(0.484592\pi\) | |||||||
\(32\) | − 5.65685i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −16.0000 | −0.470588 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 17.0000 | 0.459459 | 0.229730 | − | 0.973254i | \(-0.426216\pi\) | ||||
0.229730 | + | 0.973254i | \(0.426216\pi\) | |||||||
\(38\) | 18.3848i | 0.483810i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.00000 | 0.100000 | ||||||||
\(41\) | − 80.6102i | − 1.96610i | −0.183333 | − | 0.983051i | \(-0.558689\pi\) | ||||
0.183333 | − | 0.983051i | \(-0.441311\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −85.0000 | −1.97674 | −0.988372 | − | 0.152055i | \(-0.951411\pi\) | ||||
−0.988372 | + | 0.152055i | \(0.951411\pi\) | |||||||
\(44\) | 14.1421i | 0.321412i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 32.0000 | 0.695652 | ||||||||
\(47\) | − 72.1249i | − 1.53457i | −0.641305 | − | 0.767286i | \(-0.721607\pi\) | ||||
0.641305 | − | 0.767286i | \(-0.278393\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 32.5269i | − 0.650538i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −30.0000 | −0.576923 | ||||||||
\(53\) | 33.9411i | 0.640399i | 0.947350 | + | 0.320199i | \(0.103750\pi\) | ||||
−0.947350 | + | 0.320199i | \(0.896250\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.0000 | −0.181818 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −32.0000 | −0.551724 | ||||||||
\(59\) | − 90.5097i | − 1.53406i | −0.641610 | − | 0.767031i | \(-0.721733\pi\) | ||||
0.641610 | − | 0.767031i | \(-0.278267\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −72.0000 | −1.18033 | −0.590164 | − | 0.807283i | \(-0.700937\pi\) | ||||
−0.590164 | + | 0.807283i | \(0.700937\pi\) | |||||||
\(62\) | − 4.24264i | − 0.0684297i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | − 21.2132i | − 0.326357i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 43.0000 | 0.641791 | 0.320896 | − | 0.947115i | \(-0.396016\pi\) | ||||
0.320896 | + | 0.947115i | \(0.396016\pi\) | |||||||
\(68\) | 22.6274i | 0.332756i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 52.3259i | 0.736985i | 0.929631 | + | 0.368492i | \(0.120126\pi\) | ||||
−0.929631 | + | 0.368492i | \(0.879874\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −95.0000 | −1.30137 | −0.650685 | − | 0.759348i | \(-0.725518\pi\) | ||||
−0.650685 | + | 0.759348i | \(0.725518\pi\) | |||||||
\(74\) | − 24.0416i | − 0.324887i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 26.0000 | 0.342105 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 69.0000 | 0.873418 | 0.436709 | − | 0.899603i | \(-0.356144\pi\) | ||||
0.436709 | + | 0.899603i | \(0.356144\pi\) | |||||||
\(80\) | − 5.65685i | − 0.0707107i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −114.000 | −1.39024 | ||||||||
\(83\) | 60.8112i | 0.732665i | 0.930484 | + | 0.366332i | \(0.119387\pi\) | ||||
−0.930484 | + | 0.366332i | \(0.880613\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.0000 | −0.188235 | ||||||||
\(86\) | 120.208i | 1.39777i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 20.0000 | 0.227273 | ||||||||
\(89\) | − 135.765i | − 1.52544i | −0.646727 | − | 0.762722i | \(-0.723863\pi\) | ||||
0.646727 | − | 0.762722i | \(-0.276137\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 45.2548i | − 0.491900i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −102.000 | −1.08511 | ||||||||
\(95\) | 18.3848i | 0.193524i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.0000 | 0.164948 | 0.0824742 | − | 0.996593i | \(-0.473718\pi\) | ||||
0.0824742 | + | 0.996593i | \(0.473718\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −46.0000 | −0.460000 | ||||||||
\(101\) | − 69.2965i | − 0.686104i | −0.939316 | − | 0.343052i | \(-0.888539\pi\) | ||||
0.939316 | − | 0.343052i | \(-0.111461\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −61.0000 | −0.592233 | −0.296117 | − | 0.955152i | \(-0.595692\pi\) | ||||
−0.296117 | + | 0.955152i | \(0.595692\pi\) | |||||||
\(104\) | 42.4264i | 0.407946i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 48.0000 | 0.452830 | ||||||||
\(107\) | − 169.706i | − 1.58603i | −0.609200 | − | 0.793017i | \(-0.708509\pi\) | ||||
0.609200 | − | 0.793017i | \(-0.291491\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −65.0000 | −0.596330 | −0.298165 | − | 0.954514i | \(-0.596375\pi\) | ||||
−0.298165 | + | 0.954514i | \(0.596375\pi\) | |||||||
\(110\) | 14.1421i | 0.128565i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 137.179i | − 1.21397i | −0.794713 | − | 0.606985i | \(-0.792379\pi\) | ||||
0.794713 | − | 0.606985i | \(-0.207621\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 32.0000 | 0.278261 | ||||||||
\(116\) | 45.2548i | 0.390128i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −128.000 | −1.08475 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 71.0000 | 0.586777 | ||||||||
\(122\) | 101.823i | 0.834618i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.00000 | −0.0483871 | ||||||||
\(125\) | − 67.8823i | − 0.543058i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −171.000 | −1.34646 | −0.673228 | − | 0.739435i | \(-0.735093\pi\) | ||||
−0.673228 | + | 0.739435i | \(0.735093\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −30.0000 | −0.230769 | ||||||||
\(131\) | 117.380i | 0.896028i | 0.894026 | + | 0.448014i | \(0.147869\pi\) | ||||
−0.894026 | + | 0.448014i | \(0.852131\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − 60.8112i | − 0.453815i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 32.0000 | 0.235294 | ||||||||
\(137\) | 214.960i | 1.56905i | 0.620094 | + | 0.784527i | \(0.287094\pi\) | ||||
−0.620094 | + | 0.784527i | \(0.712906\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −83.0000 | −0.597122 | −0.298561 | − | 0.954391i | \(-0.596507\pi\) | ||||
−0.298561 | + | 0.954391i | \(0.596507\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 74.0000 | 0.521127 | ||||||||
\(143\) | − 106.066i | − 0.741720i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −32.0000 | −0.220690 | ||||||||
\(146\) | 134.350i | 0.920207i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −34.0000 | −0.229730 | ||||||||
\(149\) | 101.823i | 0.683378i | 0.939813 | + | 0.341689i | \(0.110999\pi\) | ||||
−0.939813 | + | 0.341689i | \(0.889001\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 40.0000 | 0.264901 | 0.132450 | − | 0.991190i | \(-0.457715\pi\) | ||||
0.132450 | + | 0.991190i | \(0.457715\pi\) | |||||||
\(152\) | − 36.7696i | − 0.241905i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 4.24264i | − 0.0273719i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 296.000 | 1.88535 | 0.942675 | − | 0.333712i | \(-0.108301\pi\) | ||||
0.942675 | + | 0.333712i | \(0.108301\pi\) | |||||||
\(158\) | − 97.5807i | − 0.617600i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.00000 | −0.0500000 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 128.000 | 0.785276 | 0.392638 | − | 0.919693i | \(-0.371563\pi\) | ||||
0.392638 | + | 0.919693i | \(0.371563\pi\) | |||||||
\(164\) | 161.220i | 0.983051i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 86.0000 | 0.518072 | ||||||||
\(167\) | − 60.8112i | − 0.364139i | −0.983286 | − | 0.182069i | \(-0.941720\pi\) | ||||
0.983286 | − | 0.182069i | \(-0.0582796\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 56.0000 | 0.331361 | ||||||||
\(170\) | 22.6274i | 0.133102i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 170.000 | 0.988372 | ||||||||
\(173\) | 113.137i | 0.653972i | 0.945029 | + | 0.326986i | \(0.106033\pi\) | ||||
−0.945029 | + | 0.326986i | \(0.893967\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 28.2843i | − 0.160706i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −192.000 | −1.07865 | ||||||||
\(179\) | − 29.6985i | − 0.165913i | −0.996553 | − | 0.0829567i | \(-0.973564\pi\) | ||||
0.996553 | − | 0.0829567i | \(-0.0264363\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 81.0000 | 0.447514 | 0.223757 | − | 0.974645i | \(-0.428168\pi\) | ||||
0.223757 | + | 0.974645i | \(0.428168\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −64.0000 | −0.347826 | ||||||||
\(185\) | − 24.0416i | − 0.129955i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −80.0000 | −0.427807 | ||||||||
\(188\) | 144.250i | 0.767286i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 26.0000 | 0.136842 | ||||||||
\(191\) | − 63.6396i | − 0.333192i | −0.986025 | − | 0.166596i | \(-0.946722\pi\) | ||||
0.986025 | − | 0.166596i | \(-0.0532775\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −223.000 | −1.15544 | −0.577720 | − | 0.816235i | \(-0.696058\pi\) | ||||
−0.577720 | + | 0.816235i | \(0.696058\pi\) | |||||||
\(194\) | − 22.6274i | − 0.116636i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 158.392i | 0.804020i | 0.915635 | + | 0.402010i | \(0.131688\pi\) | ||||
−0.915635 | + | 0.402010i | \(0.868312\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −136.000 | −0.683417 | −0.341709 | − | 0.939806i | \(-0.611006\pi\) | ||||
−0.341709 | + | 0.939806i | \(0.611006\pi\) | |||||||
\(200\) | 65.0538i | 0.325269i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −98.0000 | −0.485149 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −114.000 | −0.556098 | ||||||||
\(206\) | 86.2670i | 0.418772i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 60.0000 | 0.288462 | ||||||||
\(209\) | 91.9239i | 0.439827i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 272.000 | 1.28910 | 0.644550 | − | 0.764562i | \(-0.277045\pi\) | ||||
0.644550 | + | 0.764562i | \(0.277045\pi\) | |||||||
\(212\) | − 67.8823i | − 0.320199i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −240.000 | −1.12150 | ||||||||
\(215\) | 120.208i | 0.559108i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 91.9239i | 0.421669i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 20.0000 | 0.0909091 | ||||||||
\(221\) | − 169.706i | − 0.767899i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 248.000 | 1.11211 | 0.556054 | − | 0.831146i | \(-0.312315\pi\) | ||||
0.556054 | + | 0.831146i | \(0.312315\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −194.000 | −0.858407 | ||||||||
\(227\) | 165.463i | 0.728912i | 0.931221 | + | 0.364456i | \(0.118745\pi\) | ||||
−0.931221 | + | 0.364456i | \(0.881255\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 433.000 | 1.89083 | 0.945415 | − | 0.325869i | \(-0.105657\pi\) | ||||
0.945415 | + | 0.325869i | \(0.105657\pi\) | |||||||
\(230\) | − 45.2548i | − 0.196760i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 64.0000 | 0.275862 | ||||||||
\(233\) | − 227.688i | − 0.977203i | −0.872507 | − | 0.488602i | \(-0.837507\pi\) | ||||
0.872507 | − | 0.488602i | \(-0.162493\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −102.000 | −0.434043 | ||||||||
\(236\) | 181.019i | 0.767031i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 343.654i | 1.43788i | 0.695071 | + | 0.718941i | \(0.255373\pi\) | ||||
−0.695071 | + | 0.718941i | \(0.744627\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 158.000 | 0.655602 | 0.327801 | − | 0.944747i | \(-0.393693\pi\) | ||||
0.327801 | + | 0.944747i | \(0.393693\pi\) | |||||||
\(242\) | − 100.409i | − 0.414914i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 144.000 | 0.590164 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −195.000 | −0.789474 | ||||||||
\(248\) | 8.48528i | 0.0342148i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −96.0000 | −0.384000 | ||||||||
\(251\) | − 237.588i | − 0.946565i | −0.880911 | − | 0.473283i | \(-0.843069\pi\) | ||||
0.880911 | − | 0.473283i | \(-0.156931\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 160.000 | 0.632411 | ||||||||
\(254\) | 241.831i | 0.952089i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − 318.198i | − 1.23812i | −0.785342 | − | 0.619062i | \(-0.787513\pi\) | ||||
0.785342 | − | 0.619062i | \(-0.212487\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 42.4264i | 0.163178i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 166.000 | 0.633588 | ||||||||
\(263\) | − 169.706i | − 0.645269i | −0.946524 | − | 0.322634i | \(-0.895432\pi\) | ||||
0.946524 | − | 0.322634i | \(-0.104568\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 48.0000 | 0.181132 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −86.0000 | −0.320896 | ||||||||
\(269\) | − 485.075i | − 1.80325i | −0.432515 | − | 0.901627i | \(-0.642374\pi\) | ||||
0.432515 | − | 0.901627i | \(-0.357626\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 216.000 | 0.797048 | 0.398524 | − | 0.917158i | \(-0.369523\pi\) | ||||
0.398524 | + | 0.917158i | \(0.369523\pi\) | |||||||
\(272\) | − 45.2548i | − 0.166378i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 304.000 | 1.10949 | ||||||||
\(275\) | − 162.635i | − 0.591398i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 305.000 | 1.10108 | 0.550542 | − | 0.834808i | \(-0.314421\pi\) | ||||
0.550542 | + | 0.834808i | \(0.314421\pi\) | |||||||
\(278\) | 117.380i | 0.422229i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.6274i | 0.0805246i | 0.999189 | + | 0.0402623i | \(0.0128194\pi\) | ||||
−0.999189 | + | 0.0402623i | \(0.987181\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 157.000 | 0.554770 | 0.277385 | − | 0.960759i | \(-0.410532\pi\) | ||||
0.277385 | + | 0.960759i | \(0.410532\pi\) | |||||||
\(284\) | − 104.652i | − 0.368492i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −150.000 | −0.524476 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 161.000 | 0.557093 | ||||||||
\(290\) | 45.2548i | 0.156051i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 190.000 | 0.650685 | ||||||||
\(293\) | 101.823i | 0.347520i | 0.984788 | + | 0.173760i | \(0.0555917\pi\) | ||||
−0.984788 | + | 0.173760i | \(0.944408\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −128.000 | −0.433898 | ||||||||
\(296\) | 48.0833i | 0.162443i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 144.000 | 0.483221 | ||||||||
\(299\) | 339.411i | 1.13515i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 56.5685i | − 0.187313i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −52.0000 | −0.171053 | ||||||||
\(305\) | 101.823i | 0.333847i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.0000 | −0.0358306 | −0.0179153 | − | 0.999840i | \(-0.505703\pi\) | ||||
−0.0179153 | + | 0.999840i | \(0.505703\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.00000 | −0.0193548 | ||||||||
\(311\) | 524.673i | 1.68705i | 0.537088 | + | 0.843526i | \(0.319524\pi\) | ||||
−0.537088 | + | 0.843526i | \(0.680476\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 553.000 | 1.76677 | 0.883387 | − | 0.468645i | \(-0.155258\pi\) | ||||
0.883387 | + | 0.468645i | \(0.155258\pi\) | |||||||
\(314\) | − 418.607i | − 1.33314i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −138.000 | −0.436709 | ||||||||
\(317\) | 135.765i | 0.428279i | 0.976803 | + | 0.214140i | \(0.0686947\pi\) | ||||
−0.976803 | + | 0.214140i | \(0.931305\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −160.000 | −0.501567 | ||||||||
\(320\) | 11.3137i | 0.0353553i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 147.078i | 0.455350i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 345.000 | 1.06154 | ||||||||
\(326\) | − 181.019i | − 0.555274i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 228.000 | 0.695122 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −61.0000 | −0.184290 | −0.0921450 | − | 0.995746i | \(-0.529372\pi\) | ||||
−0.0921450 | + | 0.995746i | \(0.529372\pi\) | |||||||
\(332\) | − 121.622i | − 0.366332i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −86.0000 | −0.257485 | ||||||||
\(335\) | − 60.8112i | − 0.181526i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 135.000 | 0.400593 | 0.200297 | − | 0.979735i | \(-0.435809\pi\) | ||||
0.200297 | + | 0.979735i | \(0.435809\pi\) | |||||||
\(338\) | − 79.1960i | − 0.234308i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 32.0000 | 0.0941176 | ||||||||
\(341\) | − 21.2132i | − 0.0622088i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 240.416i | − 0.698885i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 160.000 | 0.462428 | ||||||||
\(347\) | 101.823i | 0.293439i | 0.989178 | + | 0.146720i | \(0.0468715\pi\) | ||||
−0.989178 | + | 0.146720i | \(0.953129\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −152.000 | −0.435530 | −0.217765 | − | 0.976001i | \(-0.569877\pi\) | ||||
−0.217765 | + | 0.976001i | \(0.569877\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −40.0000 | −0.113636 | ||||||||
\(353\) | 386.080i | 1.09371i | 0.837227 | + | 0.546856i | \(0.184175\pi\) | ||||
−0.837227 | + | 0.546856i | \(0.815825\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 74.0000 | 0.208451 | ||||||||
\(356\) | 271.529i | 0.762722i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −42.0000 | −0.117318 | ||||||||
\(359\) | 45.2548i | 0.126058i | 0.998012 | + | 0.0630290i | \(0.0200761\pi\) | ||||
−0.998012 | + | 0.0630290i | \(0.979924\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −192.000 | −0.531856 | ||||||||
\(362\) | − 114.551i | − 0.316440i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 134.350i | 0.368083i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 101.000 | 0.275204 | 0.137602 | − | 0.990488i | \(-0.456060\pi\) | ||||
0.137602 | + | 0.990488i | \(0.456060\pi\) | |||||||
\(368\) | 90.5097i | 0.245950i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −34.0000 | −0.0918919 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −311.000 | −0.833780 | −0.416890 | − | 0.908957i | \(-0.636880\pi\) | ||||
−0.416890 | + | 0.908957i | \(0.636880\pi\) | |||||||
\(374\) | 113.137i | 0.302506i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 204.000 | 0.542553 | ||||||||
\(377\) | − 339.411i | − 0.900295i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 91.0000 | 0.240106 | 0.120053 | − | 0.992768i | \(-0.461694\pi\) | ||||
0.120053 | + | 0.992768i | \(0.461694\pi\) | |||||||
\(380\) | − 36.7696i | − 0.0967620i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −90.0000 | −0.235602 | ||||||||
\(383\) | 328.098i | 0.856652i | 0.903624 | + | 0.428326i | \(0.140896\pi\) | ||||
−0.903624 | + | 0.428326i | \(0.859104\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 315.370i | 0.817020i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −32.0000 | −0.0824742 | ||||||||
\(389\) | − 688.722i | − 1.77049i | −0.465122 | − | 0.885247i | \(-0.653989\pi\) | ||||
0.465122 | − | 0.885247i | \(-0.346011\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 256.000 | 0.654731 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 224.000 | 0.568528 | ||||||||
\(395\) | − 97.5807i | − 0.247040i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −279.000 | −0.702771 | −0.351385 | − | 0.936231i | \(-0.614289\pi\) | ||||
−0.351385 | + | 0.936231i | \(0.614289\pi\) | |||||||
\(398\) | 192.333i | 0.483249i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 92.0000 | 0.230000 | ||||||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 45.0000 | 0.111663 | ||||||||
\(404\) | 138.593i | 0.343052i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 120.208i | − 0.295352i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −223.000 | −0.545232 | −0.272616 | − | 0.962123i | \(-0.587889\pi\) | ||||
−0.272616 | + | 0.962123i | \(0.587889\pi\) | |||||||
\(410\) | 161.220i | 0.393220i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 122.000 | 0.296117 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 86.0000 | 0.207229 | ||||||||
\(416\) | − 84.8528i | − 0.203973i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 130.000 | 0.311005 | ||||||||
\(419\) | 581.242i | 1.38721i | 0.720355 | + | 0.693606i | \(0.243979\pi\) | ||||
−0.720355 | + | 0.693606i | \(0.756021\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 153.000 | 0.363420 | 0.181710 | − | 0.983352i | \(-0.441837\pi\) | ||||
0.181710 | + | 0.983352i | \(0.441837\pi\) | |||||||
\(422\) | − 384.666i | − 0.911531i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −96.0000 | −0.226415 | ||||||||
\(425\) | − 260.215i | − 0.612271i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 339.411i | 0.793017i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 170.000 | 0.395349 | ||||||||
\(431\) | − 140.007i | − 0.324843i | −0.986722 | − | 0.162421i | \(-0.948070\pi\) | ||||
0.986722 | − | 0.162421i | \(-0.0519304\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 137.000 | 0.316397 | 0.158199 | − | 0.987407i | \(-0.449431\pi\) | ||||
0.158199 | + | 0.987407i | \(0.449431\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 130.000 | 0.298165 | ||||||||
\(437\) | − 294.156i | − 0.673127i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −600.000 | −1.36674 | −0.683371 | − | 0.730071i | \(-0.739487\pi\) | ||||
−0.683371 | + | 0.730071i | \(0.739487\pi\) | |||||||
\(440\) | − 28.2843i | − 0.0642824i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −240.000 | −0.542986 | ||||||||
\(443\) | 633.568i | 1.43018i | 0.699035 | + | 0.715088i | \(0.253613\pi\) | ||||
−0.699035 | + | 0.715088i | \(0.746387\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −192.000 | −0.431461 | ||||||||
\(446\) | − 350.725i | − 0.786379i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 383.252i | − 0.853568i | −0.904354 | − | 0.426784i | \(-0.859647\pi\) | ||||
0.904354 | − | 0.426784i | \(-0.140353\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −570.000 | −1.26386 | ||||||||
\(452\) | 274.357i | 0.606985i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 234.000 | 0.515419 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −239.000 | −0.522976 | −0.261488 | − | 0.965207i | \(-0.584213\pi\) | ||||
−0.261488 | + | 0.965207i | \(0.584213\pi\) | |||||||
\(458\) | − 612.354i | − 1.33702i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −64.0000 | −0.139130 | ||||||||
\(461\) | 452.548i | 0.981667i | 0.871253 | + | 0.490833i | \(0.163308\pi\) | ||||
−0.871253 | + | 0.490833i | \(0.836692\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 211.000 | 0.455724 | 0.227862 | − | 0.973693i | \(-0.426827\pi\) | ||||
0.227862 | + | 0.973693i | \(0.426827\pi\) | |||||||
\(464\) | − 90.5097i | − 0.195064i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −322.000 | −0.690987 | ||||||||
\(467\) | 312.541i | 0.669253i | 0.942351 | + | 0.334627i | \(0.108610\pi\) | ||||
−0.942351 | + | 0.334627i | \(0.891390\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 144.250i | 0.306914i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 256.000 | 0.542373 | ||||||||
\(473\) | 601.041i | 1.27070i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −299.000 | −0.629474 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 486.000 | 1.01674 | ||||||||
\(479\) | 701.450i | 1.46440i | 0.681087 | + | 0.732202i | \(0.261508\pi\) | ||||
−0.681087 | + | 0.732202i | \(0.738492\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 255.000 | 0.530146 | ||||||||
\(482\) | − 223.446i | − 0.463580i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −142.000 | −0.293388 | ||||||||
\(485\) | − 22.6274i | − 0.0466545i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 419.000 | 0.860370 | 0.430185 | − | 0.902741i | \(-0.358448\pi\) | ||||
0.430185 | + | 0.902741i | \(0.358448\pi\) | |||||||
\(488\) | − 203.647i | − 0.417309i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 169.706i | − 0.345633i | −0.984954 | − | 0.172816i | \(-0.944713\pi\) | ||||
0.984954 | − | 0.172816i | \(-0.0552867\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −256.000 | −0.519270 | ||||||||
\(494\) | 275.772i | 0.558242i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.0000 | 0.0241935 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 187.000 | 0.374749 | 0.187375 | − | 0.982289i | \(-0.440002\pi\) | ||||
0.187375 | + | 0.982289i | \(0.440002\pi\) | |||||||
\(500\) | 135.765i | 0.271529i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −336.000 | −0.669323 | ||||||||
\(503\) | − 173.948i | − 0.345822i | −0.984937 | − | 0.172911i | \(-0.944683\pi\) | ||||
0.984937 | − | 0.172911i | \(-0.0553172\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −98.0000 | −0.194059 | ||||||||
\(506\) | − 226.274i | − 0.447182i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 342.000 | 0.673228 | ||||||||
\(509\) | − 258.801i | − 0.508450i | −0.967145 | − | 0.254225i | \(-0.918180\pi\) | ||||
0.967145 | − | 0.254225i | \(-0.0818204\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 22.6274i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −450.000 | −0.875486 | ||||||||
\(515\) | 86.2670i | 0.167509i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −510.000 | −0.986460 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 60.0000 | 0.115385 | ||||||||
\(521\) | − 407.294i | − 0.781753i | −0.920443 | − | 0.390877i | \(-0.872172\pi\) | ||||
0.920443 | − | 0.390877i | \(-0.127828\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −811.000 | −1.55067 | −0.775335 | − | 0.631551i | \(-0.782419\pi\) | ||||
−0.775335 | + | 0.631551i | \(0.782419\pi\) | |||||||
\(524\) | − 234.759i | − 0.448014i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −240.000 | −0.456274 | ||||||||
\(527\) | − 33.9411i | − 0.0644044i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.0000 | 0.0321361 | ||||||||
\(530\) | − 67.8823i | − 0.128080i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1209.15i | − 2.26858i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −240.000 | −0.448598 | ||||||||
\(536\) | 121.622i | 0.226907i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −686.000 | −1.27509 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −345.000 | −0.637708 | −0.318854 | − | 0.947804i | \(-0.603298\pi\) | ||||
−0.318854 | + | 0.947804i | \(0.603298\pi\) | |||||||
\(542\) | − 305.470i | − 0.563598i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −64.0000 | −0.117647 | ||||||||
\(545\) | 91.9239i | 0.168668i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −864.000 | −1.57952 | −0.789762 | − | 0.613413i | \(-0.789796\pi\) | ||||
−0.789762 | + | 0.613413i | \(0.789796\pi\) | |||||||
\(548\) | − 429.921i | − 0.784527i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −230.000 | −0.418182 | ||||||||
\(551\) | 294.156i | 0.533859i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 431.335i | − 0.778583i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 166.000 | 0.298561 | ||||||||
\(557\) | 948.937i | 1.70366i | 0.523820 | + | 0.851829i | \(0.324506\pi\) | ||||
−0.523820 | + | 0.851829i | \(0.675494\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1275.00 | −2.28086 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 32.0000 | 0.0569395 | ||||||||
\(563\) | 739.634i | 1.31374i | 0.754005 | + | 0.656868i | \(0.228119\pi\) | ||||
−0.754005 | + | 0.656868i | \(0.771881\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −194.000 | −0.343363 | ||||||||
\(566\) | − 222.032i | − 0.392282i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −148.000 | −0.260563 | ||||||||
\(569\) | 767.918i | 1.34959i | 0.738004 | + | 0.674796i | \(0.235768\pi\) | ||||
−0.738004 | + | 0.674796i | \(0.764232\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 477.000 | 0.835377 | 0.417688 | − | 0.908590i | \(-0.362840\pi\) | ||||
0.417688 | + | 0.908590i | \(0.362840\pi\) | |||||||
\(572\) | 212.132i | 0.370860i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 520.431i | 0.905097i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −263.000 | −0.455806 | −0.227903 | − | 0.973684i | \(-0.573187\pi\) | ||||
−0.227903 | + | 0.973684i | \(0.573187\pi\) | |||||||
\(578\) | − 227.688i | − 0.393925i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 64.0000 | 0.110345 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 240.000 | 0.411664 | ||||||||
\(584\) | − 268.701i | − 0.460104i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 144.000 | 0.245734 | ||||||||
\(587\) | 531.744i | 0.905868i | 0.891544 | + | 0.452934i | \(0.149623\pi\) | ||||
−0.891544 | + | 0.452934i | \(0.850377\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −39.0000 | −0.0662139 | ||||||||
\(590\) | 181.019i | 0.306812i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 68.0000 | 0.114865 | ||||||||
\(593\) | − 801.859i | − 1.35221i | −0.736806 | − | 0.676104i | \(-0.763667\pi\) | ||||
0.736806 | − | 0.676104i | \(-0.236333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 203.647i | − 0.341689i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 480.000 | 0.802676 | ||||||||
\(599\) | − 780.646i | − 1.30325i | −0.758542 | − | 0.651624i | \(-0.774088\pi\) | ||||
0.758542 | − | 0.651624i | \(-0.225912\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 383.000 | 0.637271 | 0.318636 | − | 0.947877i | \(-0.396775\pi\) | ||||
0.318636 | + | 0.947877i | \(0.396775\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −80.0000 | −0.132450 | ||||||||
\(605\) | − 100.409i | − 0.165966i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −765.000 | −1.26030 | −0.630148 | − | 0.776475i | \(-0.717006\pi\) | ||||
−0.630148 | + | 0.776475i | \(0.717006\pi\) | |||||||
\(608\) | 73.5391i | 0.120952i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 144.000 | 0.236066 | ||||||||
\(611\) | − 1081.87i | − 1.77066i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 408.000 | 0.665579 | 0.332790 | − | 0.943001i | \(-0.392010\pi\) | ||||
0.332790 | + | 0.943001i | \(0.392010\pi\) | |||||||
\(614\) | 15.5563i | 0.0253361i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 914.996i | − 1.48298i | −0.670966 | − | 0.741488i | \(-0.734120\pi\) | ||||
0.670966 | − | 0.741488i | \(-0.265880\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −947.000 | −1.52989 | −0.764943 | − | 0.644097i | \(-0.777233\pi\) | ||||
−0.764943 | + | 0.644097i | \(0.777233\pi\) | |||||||
\(620\) | 8.48528i | 0.0136859i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 742.000 | 1.19293 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 479.000 | 0.766400 | ||||||||
\(626\) | − 782.060i | − 1.24930i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −592.000 | −0.942675 | ||||||||
\(629\) | − 192.333i | − 0.305776i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −760.000 | −1.20444 | −0.602219 | − | 0.798331i | \(-0.705716\pi\) | ||||
−0.602219 | + | 0.798331i | \(0.705716\pi\) | |||||||
\(632\) | 195.161i | 0.308800i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 192.000 | 0.302839 | ||||||||
\(635\) | 241.831i | 0.380835i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 226.274i | 0.354662i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 16.0000 | 0.0250000 | ||||||||
\(641\) | 463.862i | 0.723654i | 0.932245 | + | 0.361827i | \(0.117847\pi\) | ||||
−0.932245 | + | 0.361827i | \(0.882153\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.0000 | −0.0295490 | −0.0147745 | − | 0.999891i | \(-0.504703\pi\) | ||||
−0.0147745 | + | 0.999891i | \(0.504703\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 208.000 | 0.321981 | ||||||||
\(647\) | − 1158.24i | − 1.79017i | −0.445894 | − | 0.895086i | \(-0.647114\pi\) | ||||
0.445894 | − | 0.895086i | \(-0.352886\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −640.000 | −0.986133 | ||||||||
\(650\) | − 487.904i | − 0.750621i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −256.000 | −0.392638 | ||||||||
\(653\) | 1030.96i | 1.57881i | 0.613874 | + | 0.789404i | \(0.289610\pi\) | ||||
−0.613874 | + | 0.789404i | \(0.710390\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 166.000 | 0.253435 | ||||||||
\(656\) | − 322.441i | − 0.491525i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 972.979i | 1.47645i | 0.674556 | + | 0.738224i | \(0.264335\pi\) | ||||
−0.674556 | + | 0.738224i | \(0.735665\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −401.000 | −0.606657 | −0.303328 | − | 0.952886i | \(-0.598098\pi\) | ||||
−0.303328 | + | 0.952886i | \(0.598098\pi\) | |||||||
\(662\) | 86.2670i | 0.130313i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −172.000 | −0.259036 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 512.000 | 0.767616 | ||||||||
\(668\) | 121.622i | 0.182069i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −86.0000 | −0.128358 | ||||||||
\(671\) | 509.117i | 0.758743i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 665.000 | 0.988113 | 0.494056 | − | 0.869430i | \(-0.335514\pi\) | ||||
0.494056 | + | 0.869430i | \(0.335514\pi\) | |||||||
\(674\) | − 190.919i | − 0.283262i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −112.000 | −0.165680 | ||||||||
\(677\) | − 916.410i | − 1.35363i | −0.736151 | − | 0.676817i | \(-0.763359\pi\) | ||||
0.736151 | − | 0.676817i | \(-0.236641\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − 45.2548i | − 0.0665512i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −30.0000 | −0.0439883 | ||||||||
\(683\) | 135.765i | 0.198777i | 0.995049 | + | 0.0993884i | \(0.0316886\pi\) | ||||
−0.995049 | + | 0.0993884i | \(0.968311\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 304.000 | 0.443796 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −340.000 | −0.494186 | ||||||||
\(689\) | 509.117i | 0.738921i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 221.000 | 0.319826 | 0.159913 | − | 0.987131i | \(-0.448879\pi\) | ||||
0.159913 | + | 0.987131i | \(0.448879\pi\) | |||||||
\(692\) | − 226.274i | − 0.326986i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 144.000 | 0.207493 | ||||||||
\(695\) | 117.380i | 0.168892i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −912.000 | −1.30846 | ||||||||
\(698\) | 214.960i | 0.307966i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 192.333i | − 0.274370i | −0.990545 | − | 0.137185i | \(-0.956195\pi\) | ||||
0.990545 | − | 0.137185i | \(-0.0438054\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −221.000 | −0.314367 | ||||||||
\(704\) | 56.5685i | 0.0803530i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 546.000 | 0.773371 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −328.000 | −0.462623 | −0.231312 | − | 0.972880i | \(-0.574302\pi\) | ||||
−0.231312 | + | 0.972880i | \(0.574302\pi\) | |||||||
\(710\) | − 104.652i | − 0.147397i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 384.000 | 0.539326 | ||||||||
\(713\) | 67.8823i | 0.0952065i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −150.000 | −0.209790 | ||||||||
\(716\) | 59.3970i | 0.0829567i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 64.0000 | 0.0891365 | ||||||||
\(719\) | − 1013.99i | − 1.41028i | −0.709068 | − | 0.705140i | \(-0.750884\pi\) | ||||
0.709068 | − | 0.705140i | \(-0.249116\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 271.529i | 0.376079i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −162.000 | −0.223757 | ||||||||
\(725\) | − 520.431i | − 0.717835i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1069.00 | 1.47043 | 0.735213 | − | 0.677836i | \(-0.237082\pi\) | ||||
0.735213 | + | 0.677836i | \(0.237082\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 190.000 | 0.260274 | ||||||||
\(731\) | 961.665i | 1.31555i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 495.000 | 0.675307 | 0.337653 | − | 0.941270i | \(-0.390367\pi\) | ||||
0.337653 | + | 0.941270i | \(0.390367\pi\) | |||||||
\(734\) | − 142.836i | − 0.194599i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 128.000 | 0.173913 | ||||||||
\(737\) | − 304.056i | − 0.412559i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 453.000 | 0.612991 | 0.306495 | − | 0.951872i | \(-0.400844\pi\) | ||||
0.306495 | + | 0.951872i | \(0.400844\pi\) | |||||||
\(740\) | 48.0833i | 0.0649774i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 538.815i | − 0.725189i | −0.931947 | − | 0.362594i | \(-0.881891\pi\) | ||||
0.931947 | − | 0.362594i | \(-0.118109\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 144.000 | 0.193289 | ||||||||
\(746\) | 439.820i | 0.589572i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 160.000 | 0.213904 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −339.000 | −0.451398 | −0.225699 | − | 0.974197i | \(-0.572467\pi\) | ||||
−0.225699 | + | 0.974197i | \(0.572467\pi\) | |||||||
\(752\) | − 288.500i | − 0.383643i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −480.000 | −0.636605 | ||||||||
\(755\) | − 56.5685i | − 0.0749252i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 198.000 | 0.261559 | 0.130779 | − | 0.991411i | \(-0.458252\pi\) | ||||
0.130779 | + | 0.991411i | \(0.458252\pi\) | |||||||
\(758\) | − 128.693i | − 0.169780i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −52.0000 | −0.0684211 | ||||||||
\(761\) | 362.039i | 0.475741i | 0.971297 | + | 0.237870i | \(0.0764493\pi\) | ||||
−0.971297 | + | 0.237870i | \(0.923551\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 127.279i | 0.166596i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 464.000 | 0.605744 | ||||||||
\(767\) | − 1357.65i | − 1.77007i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −929.000 | −1.20806 | −0.604031 | − | 0.796961i | \(-0.706440\pi\) | ||||
−0.604031 | + | 0.796961i | \(0.706440\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 446.000 | 0.577720 | ||||||||
\(773\) | − 171.120i | − 0.221371i | −0.993855 | − | 0.110686i | \(-0.964695\pi\) | ||||
0.993855 | − | 0.110686i | \(-0.0353046\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 69.0000 | 0.0890323 | ||||||||
\(776\) | 45.2548i | 0.0583181i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −974.000 | −1.25193 | ||||||||
\(779\) | 1047.93i | 1.34523i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 370.000 | 0.473752 | ||||||||
\(782\) | − 362.039i | − 0.462965i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 418.607i | − 0.533258i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 90.0000 | 0.114358 | 0.0571792 | − | 0.998364i | \(-0.481789\pi\) | ||||
0.0571792 | + | 0.998364i | \(0.481789\pi\) | |||||||
\(788\) | − 316.784i | − 0.402010i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −138.000 | −0.174684 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1080.00 | −1.36192 | ||||||||
\(794\) | 394.566i | 0.496934i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 272.000 | 0.341709 | ||||||||
\(797\) | − 1154.00i | − 1.44793i | −0.689838 | − | 0.723964i | \(-0.742318\pi\) | ||||
0.689838 | − | 0.723964i | \(-0.257682\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −816.000 | −1.02128 | ||||||||
\(800\) | − 130.108i | − 0.162635i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 671.751i | 0.836552i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 63.6396i | − 0.0789573i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 196.000 | 0.242574 | ||||||||
\(809\) | − 171.120i | − 0.211520i | −0.994392 | − | 0.105760i | \(-0.966272\pi\) | ||||
0.994392 | − | 0.105760i | \(-0.0337276\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −554.000 | −0.683107 | −0.341554 | − | 0.939862i | \(-0.610953\pi\) | ||||
−0.341554 | + | 0.939862i | \(0.610953\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −170.000 | −0.208845 | ||||||||
\(815\) | − 181.019i | − 0.222110i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1105.00 | 1.35251 | ||||||||
\(818\) | 315.370i | 0.385537i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 228.000 | 0.278049 | ||||||||
\(821\) | 1062.07i | 1.29364i | 0.762645 | + | 0.646818i | \(0.223900\pi\) | ||||
−0.762645 | + | 0.646818i | \(0.776100\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 856.000 | 1.04010 | 0.520049 | − | 0.854137i | \(-0.325914\pi\) | ||||
0.520049 | + | 0.854137i | \(0.325914\pi\) | |||||||
\(824\) | − 172.534i | − 0.209386i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1022.48i | 1.23637i | 0.786033 | + | 0.618184i | \(0.212131\pi\) | ||||
−0.786033 | + | 0.618184i | \(0.787869\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1039.00 | 1.25332 | 0.626659 | − | 0.779294i | \(-0.284422\pi\) | ||||
0.626659 | + | 0.779294i | \(0.284422\pi\) | |||||||
\(830\) | − 121.622i | − 0.146533i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −120.000 | −0.144231 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −86.0000 | −0.102994 | ||||||||
\(836\) | − 183.848i | − 0.219914i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 822.000 | 0.980907 | ||||||||
\(839\) | − 656.195i | − 0.782116i | −0.920366 | − | 0.391058i | \(-0.872109\pi\) | ||||
0.920366 | − | 0.391058i | \(-0.127891\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 329.000 | 0.391201 | ||||||||
\(842\) | − 216.375i | − 0.256977i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −544.000 | −0.644550 | ||||||||
\(845\) | − 79.1960i | − 0.0937230i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 135.765i | 0.160100i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −368.000 | −0.432941 | ||||||||
\(851\) | 384.666i | 0.452017i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1463.00 | 1.71512 | 0.857562 | − | 0.514381i | \(-0.171978\pi\) | ||||
0.857562 | + | 0.514381i | \(0.171978\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 480.000 | 0.560748 | ||||||||
\(857\) | − 67.8823i | − 0.0792092i | −0.999215 | − | 0.0396046i | \(-0.987390\pi\) | ||||
0.999215 | − | 0.0396046i | \(-0.0126098\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1462.00 | −1.70198 | −0.850990 | − | 0.525183i | \(-0.823997\pi\) | ||||
−0.850990 | + | 0.525183i | \(0.823997\pi\) | |||||||
\(860\) | − 240.416i | − 0.279554i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −198.000 | −0.229698 | ||||||||
\(863\) | − 807.516i | − 0.935708i | −0.883806 | − | 0.467854i | \(-0.845027\pi\) | ||||
0.883806 | − | 0.467854i | \(-0.154973\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 160.000 | 0.184971 | ||||||||
\(866\) | − 193.747i | − 0.223727i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 487.904i | − 0.561454i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 645.000 | 0.740528 | ||||||||
\(872\) | − 183.848i | − 0.210835i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −416.000 | −0.475973 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1480.00 | 1.68757 | 0.843786 | − | 0.536680i | \(-0.180322\pi\) | ||||
0.843786 | + | 0.536680i | \(0.180322\pi\) | |||||||
\(878\) | 848.528i | 0.966433i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −40.0000 | −0.0454545 | ||||||||
\(881\) | − 712.764i | − 0.809039i | −0.914529 | − | 0.404520i | \(-0.867439\pi\) | ||||
0.914529 | − | 0.404520i | \(-0.132561\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −115.000 | −0.130238 | −0.0651189 | − | 0.997878i | \(-0.520743\pi\) | ||||
−0.0651189 | + | 0.997878i | \(0.520743\pi\) | |||||||
\(884\) | 339.411i | 0.383949i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 896.000 | 1.01129 | ||||||||
\(887\) | 1192.18i | 1.34406i | 0.740524 | + | 0.672030i | \(0.234578\pi\) | ||||
−0.740524 | + | 0.672030i | \(0.765422\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 271.529i | 0.305089i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −496.000 | −0.556054 | ||||||||
\(893\) | 937.624i | 1.04997i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −42.0000 | −0.0469274 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −542.000 | −0.603563 | ||||||||
\(899\) | − 67.8823i | − 0.0755086i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 384.000 | 0.426193 | ||||||||
\(902\) | 806.102i | 0.893683i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 388.000 | 0.429204 | ||||||||
\(905\) | − 114.551i | − 0.126576i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −501.000 | −0.552370 | −0.276185 | − | 0.961104i | \(-0.589070\pi\) | ||||
−0.276185 | + | 0.961104i | \(0.589070\pi\) | |||||||
\(908\) | − 330.926i | − 0.364456i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 203.647i | 0.223542i | 0.993734 | + | 0.111771i | \(0.0356523\pi\) | ||||
−0.993734 | + | 0.111771i | \(0.964348\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 430.000 | 0.470975 | ||||||||
\(914\) | 337.997i | 0.369800i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −866.000 | −0.945415 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −653.000 | −0.710555 | −0.355277 | − | 0.934761i | \(-0.615614\pi\) | ||||
−0.355277 | + | 0.934761i | \(0.615614\pi\) | |||||||
\(920\) | 90.5097i | 0.0983801i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 640.000 | 0.694143 | ||||||||
\(923\) | 784.889i | 0.850367i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 391.000 | 0.422703 | ||||||||
\(926\) | − 298.399i | − 0.322245i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −128.000 | −0.137931 | ||||||||
\(929\) | 12.7279i | 0.0137007i | 0.999977 | + | 0.00685033i | \(0.00218055\pi\) | ||||
−0.999977 | + | 0.00685033i | \(0.997819\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 455.377i | 0.488602i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 442.000 | 0.473233 | ||||||||
\(935\) | 113.137i | 0.121002i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 761.000 | 0.812166 | 0.406083 | − | 0.913836i | \(-0.366894\pi\) | ||||
0.406083 | + | 0.913836i | \(0.366894\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 204.000 | 0.217021 | ||||||||
\(941\) | 282.843i | 0.300577i | 0.988642 | + | 0.150288i | \(0.0480202\pi\) | ||||
−0.988642 | + | 0.150288i | \(0.951980\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1824.00 | 1.93425 | ||||||||
\(944\) | − 362.039i | − 0.383516i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 850.000 | 0.898520 | ||||||||
\(947\) | − 1079.04i | − 1.13944i | −0.821841 | − | 0.569718i | \(-0.807053\pi\) | ||||
0.821841 | − | 0.569718i | \(-0.192947\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1425.00 | −1.50158 | ||||||||
\(950\) | 422.850i | 0.445105i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1074.80i | 1.12781i | 0.825840 | + | 0.563905i | \(0.190701\pi\) | ||||
−0.825840 | + | 0.563905i | \(0.809299\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −90.0000 | −0.0942408 | ||||||||
\(956\) | − 687.308i | − 0.718941i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 992.000 | 1.03549 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −952.000 | −0.990635 | ||||||||
\(962\) | − 360.624i | − 0.374869i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −316.000 | −0.327801 | ||||||||
\(965\) | 315.370i | 0.326808i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1163.00 | 1.20269 | 0.601344 | − | 0.798990i | \(-0.294632\pi\) | ||||
0.601344 | + | 0.798990i | \(0.294632\pi\) | |||||||
\(968\) | 200.818i | 0.207457i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −32.0000 | −0.0329897 | ||||||||
\(971\) | 1561.29i | 1.60792i | 0.594682 | + | 0.803961i | \(0.297278\pi\) | ||||
−0.594682 | + | 0.803961i | \(0.702722\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 592.555i | − 0.608373i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −288.000 | −0.295082 | ||||||||
\(977\) | − 1132.79i | − 1.15945i | −0.814811 | − | 0.579726i | \(-0.803160\pi\) | ||||
0.814811 | − | 0.579726i | \(-0.196840\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −960.000 | −0.980592 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −240.000 | −0.244399 | ||||||||
\(983\) | 305.470i | 0.310753i | 0.987855 | + | 0.155376i | \(0.0496591\pi\) | ||||
−0.987855 | + | 0.155376i | \(0.950341\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 224.000 | 0.227411 | ||||||||
\(986\) | 362.039i | 0.367179i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 390.000 | 0.394737 | ||||||||
\(989\) | − 1923.33i | − 1.94472i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −973.000 | −0.981837 | −0.490918 | − | 0.871206i | \(-0.663339\pi\) | ||||
−0.490918 | + | 0.871206i | \(0.663339\pi\) | |||||||
\(992\) | − 16.9706i | − 0.0171074i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 192.333i | 0.193300i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −79.0000 | −0.0792377 | −0.0396189 | − | 0.999215i | \(-0.512614\pi\) | ||||
−0.0396189 | + | 0.999215i | \(0.512614\pi\) | |||||||
\(998\) | − 264.458i | − 0.264988i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 882.3.b.c.197.1 | 2 | ||
3.2 | odd | 2 | inner | 882.3.b.c.197.2 | 2 | ||
7.2 | even | 3 | 126.3.s.b.53.1 | ✓ | 4 | ||
7.3 | odd | 6 | 882.3.s.c.863.2 | 4 | |||
7.4 | even | 3 | 126.3.s.b.107.2 | yes | 4 | ||
7.5 | odd | 6 | 882.3.s.c.557.1 | 4 | |||
7.6 | odd | 2 | 882.3.b.d.197.1 | 2 | |||
21.2 | odd | 6 | 126.3.s.b.53.2 | yes | 4 | ||
21.5 | even | 6 | 882.3.s.c.557.2 | 4 | |||
21.11 | odd | 6 | 126.3.s.b.107.1 | yes | 4 | ||
21.17 | even | 6 | 882.3.s.c.863.1 | 4 | |||
21.20 | even | 2 | 882.3.b.d.197.2 | 2 | |||
28.11 | odd | 6 | 1008.3.dc.a.737.2 | 4 | |||
28.23 | odd | 6 | 1008.3.dc.a.305.1 | 4 | |||
84.11 | even | 6 | 1008.3.dc.a.737.1 | 4 | |||
84.23 | even | 6 | 1008.3.dc.a.305.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.s.b.53.1 | ✓ | 4 | 7.2 | even | 3 | ||
126.3.s.b.53.2 | yes | 4 | 21.2 | odd | 6 | ||
126.3.s.b.107.1 | yes | 4 | 21.11 | odd | 6 | ||
126.3.s.b.107.2 | yes | 4 | 7.4 | even | 3 | ||
882.3.b.c.197.1 | 2 | 1.1 | even | 1 | trivial | ||
882.3.b.c.197.2 | 2 | 3.2 | odd | 2 | inner | ||
882.3.b.d.197.1 | 2 | 7.6 | odd | 2 | |||
882.3.b.d.197.2 | 2 | 21.20 | even | 2 | |||
882.3.s.c.557.1 | 4 | 7.5 | odd | 6 | |||
882.3.s.c.557.2 | 4 | 21.5 | even | 6 | |||
882.3.s.c.863.1 | 4 | 21.17 | even | 6 | |||
882.3.s.c.863.2 | 4 | 7.3 | odd | 6 | |||
1008.3.dc.a.305.1 | 4 | 28.23 | odd | 6 | |||
1008.3.dc.a.305.2 | 4 | 84.23 | even | 6 | |||
1008.3.dc.a.737.1 | 4 | 84.11 | even | 6 | |||
1008.3.dc.a.737.2 | 4 | 28.11 | odd | 6 |