Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,3,Mod(305,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.305");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.dc (of order \(6\), degree \(2\), not 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: | \(27.4660106475\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 305.1 | ||
Root | \(-1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.305 |
Dual form | 1008.3.dc.a.737.1 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.22474 | + | 0.707107i | −0.244949 | + | 0.141421i | −0.617449 | − | 0.786611i | \(-0.711834\pi\) |
0.372500 | + | 0.928032i | \(0.378501\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.12372 | − | 3.53553i | −0.556702 | − | 0.321412i | 0.195119 | − | 0.980780i | \(-0.437491\pi\) |
−0.751821 | + | 0.659367i | \(0.770824\pi\) | |||||||
\(12\) | 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 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 9.79796 | + | 5.65685i | 0.576351 | + | 0.332756i | 0.759682 | − | 0.650295i | \(-0.225355\pi\) |
−0.183331 | + | 0.983051i | \(0.558688\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.50000 | − | 11.2583i | −0.342105 | − | 0.592544i | 0.642718 | − | 0.766103i | \(-0.277807\pi\) |
−0.984823 | + | 0.173559i | \(0.944473\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −19.5959 | + | 11.3137i | −0.851996 | + | 0.491900i | −0.861324 | − | 0.508056i | \(-0.830364\pi\) |
0.00932753 | + | 0.999956i | \(0.497031\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.5000 | + | 19.9186i | −0.460000 | + | 0.796743i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 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 | ||||||||
\(31\) | 1.50000 | − | 2.59808i | 0.0483871 | − | 0.0838089i | −0.840817 | − | 0.541319i | \(-0.817925\pi\) |
0.889205 | + | 0.457510i | \(0.151259\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.12372 | − | 7.77817i | 0.174964 | − | 0.222234i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.50000 | − | 14.7224i | −0.229730 | − | 0.397904i | 0.727998 | − | 0.685579i | \(-0.240451\pi\) |
−0.957728 | + | 0.287675i | \(0.907118\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 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 | \(-0.0485890\pi\) | ||||
0.988372 | + | 0.152055i | \(0.0485890\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 62.4620 | − | 36.0624i | 1.32898 | − | 0.767286i | 0.343837 | − | 0.939029i | \(-0.388273\pi\) |
0.985142 | + | 0.171743i | \(0.0549400\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 35.5000 | − | 33.7750i | 0.724490 | − | 0.689286i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −29.3939 | − | 16.9706i | −0.554601 | − | 0.320199i | 0.196374 | − | 0.980529i | \(-0.437083\pi\) |
−0.750976 | + | 0.660330i | \(0.770417\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.0000 | 0.181818 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −78.3837 | − | 45.2548i | −1.32854 | − | 0.767031i | −0.343463 | − | 0.939166i | \(-0.611600\pi\) |
−0.985073 | + | 0.172135i | \(0.944933\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 36.0000 | + | 62.3538i | 0.590164 | + | 1.02219i | 0.994210 | + | 0.107455i | \(0.0342702\pi\) |
−0.404046 | + | 0.914739i | \(0.632396\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −18.3712 | + | 10.6066i | −0.282633 | + | 0.163178i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 21.5000 | − | 37.2391i | 0.320896 | − | 0.555807i | −0.659778 | − | 0.751461i | \(-0.729349\pi\) |
0.980673 | + | 0.195654i | \(0.0626828\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 52.3259i | − | 0.736985i | −0.929631 | − | 0.368492i | \(-0.879874\pi\) | ||
0.929631 | − | 0.368492i | \(-0.120126\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 47.5000 | − | 82.2724i | 0.650685 | − | 1.12702i | −0.332272 | − | 0.943184i | \(-0.607815\pi\) |
0.982957 | − | 0.183836i | \(-0.0588515\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 48.9898 | + | 7.07107i | 0.636231 | + | 0.0918320i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 34.5000 | + | 59.7558i | 0.436709 | + | 0.756402i | 0.997433 | − | 0.0716005i | \(-0.0228107\pi\) |
−0.560725 | + | 0.828002i | \(0.689477\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 60.8112i | − | 0.732665i | −0.930484 | − | 0.366332i | \(-0.880613\pi\) | ||
0.930484 | − | 0.366332i | \(-0.119387\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.0000 | −0.188235 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −117.576 | + | 67.8823i | −1.32107 | + | 0.762722i | −0.983900 | − | 0.178721i | \(-0.942804\pi\) |
−0.337173 | + | 0.941443i | \(0.609471\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −97.5000 | + | 38.9711i | −1.07143 | + | 0.428254i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.9217 | + | 9.19239i | 0.167597 | + | 0.0967620i | ||||
\(96\) | 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 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 60.0125 | + | 34.6482i | 0.594183 | + | 0.343052i | 0.766750 | − | 0.641946i | \(-0.221873\pi\) |
−0.172567 | + | 0.984998i | \(0.555206\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −30.5000 | − | 52.8275i | −0.296117 | − | 0.512889i | 0.679127 | − | 0.734020i | \(-0.262358\pi\) |
−0.975244 | + | 0.221131i | \(0.929025\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 146.969 | − | 84.8528i | 1.37355 | − | 0.793017i | 0.382173 | − | 0.924091i | \(-0.375176\pi\) |
0.991373 | + | 0.131074i | \(0.0418425\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 32.5000 | − | 56.2917i | 0.298165 | − | 0.516437i | −0.677551 | − | 0.735476i | \(-0.736959\pi\) |
0.975716 | + | 0.219039i | \(0.0702921\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 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 | ||||||||
\(115\) | 16.0000 | − | 27.7128i | 0.139130 | − | 0.240981i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −78.3837 | − | 11.3137i | −0.658686 | − | 0.0950732i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −35.5000 | − | 61.4878i | −0.293388 | − | 0.508164i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 67.8823i | − | 0.543058i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 171.000 | 1.34646 | 0.673228 | − | 0.739435i | \(-0.264907\pi\) | ||||
0.673228 | + | 0.739435i | \(0.264907\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −101.654 | + | 58.6899i | −0.775983 | + | 0.448014i | −0.835005 | − | 0.550242i | \(-0.814535\pi\) |
0.0590215 | + | 0.998257i | \(0.481202\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 71.5000 | + | 56.2917i | 0.537594 | + | 0.423245i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −186.161 | − | 107.480i | −1.35884 | − | 0.784527i | −0.369373 | − | 0.929281i | \(-0.620428\pi\) |
−0.989468 | + | 0.144754i | \(0.953761\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 83.0000 | 0.597122 | 0.298561 | − | 0.954391i | \(-0.403493\pi\) | ||||
0.298561 | + | 0.954391i | \(0.403493\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −91.8559 | − | 53.0330i | −0.642349 | − | 0.370860i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.0000 | + | 27.7128i | 0.110345 | + | 0.191123i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 88.1816 | − | 50.9117i | 0.591823 | − | 0.341689i | −0.173995 | − | 0.984747i | \(-0.555668\pi\) |
0.765818 | + | 0.643057i | \(0.222334\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0000 | − | 34.6410i | 0.132450 | − | 0.229411i | −0.792170 | − | 0.610300i | \(-0.791049\pi\) |
0.924621 | + | 0.380889i | \(0.124382\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.24264i | 0.0273719i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −148.000 | + | 256.344i | −0.942675 | + | 1.63276i | −0.182335 | + | 0.983237i | \(0.558365\pi\) |
−0.760340 | + | 0.649525i | \(0.774968\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 97.9796 | − | 124.451i | 0.608569 | − | 0.772986i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 64.0000 | + | 110.851i | 0.392638 | + | 0.680069i | 0.992797 | − | 0.119812i | \(-0.0382292\pi\) |
−0.600159 | + | 0.799881i | \(0.704896\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 60.8112i | 0.364139i | 0.983286 | + | 0.182069i | \(0.0582796\pi\) | ||||
−0.983286 | + | 0.182069i | \(0.941720\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 56.0000 | 0.331361 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 97.9796 | − | 56.5685i | 0.566356 | − | 0.326986i | −0.189337 | − | 0.981912i | \(-0.560634\pi\) |
0.755693 | + | 0.654926i | \(0.227300\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 23.0000 | − | 159.349i | 0.131429 | − | 0.910564i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25.7196 | − | 14.8492i | −0.143685 | − | 0.0829567i | 0.426434 | − | 0.904519i | \(-0.359770\pi\) |
−0.570119 | + | 0.821562i | \(0.693103\pi\) | |||||||
\(180\) | 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 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.8207 | + | 12.0208i | 0.112544 | + | 0.0649774i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −40.0000 | − | 69.2820i | −0.213904 | − | 0.370492i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 55.1135 | − | 31.8198i | 0.288552 | − | 0.166596i | −0.348736 | − | 0.937221i | \(-0.613389\pi\) |
0.637289 | + | 0.770625i | \(0.280056\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 111.500 | − | 193.124i | 0.577720 | − | 1.00064i | −0.418020 | − | 0.908438i | \(-0.637276\pi\) |
0.995740 | − | 0.0922029i | \(-0.0293909\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 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 | ||||||||
\(199\) | −68.0000 | + | 117.779i | −0.341709 | + | 0.591857i | −0.984750 | − | 0.173975i | \(-0.944339\pi\) |
0.643042 | + | 0.765831i | \(0.277672\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 58.7878 | + | 147.078i | 0.289595 | + | 0.724523i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 57.0000 | + | 98.7269i | 0.278049 | + | 0.481595i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 91.9239i | 0.439827i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −272.000 | −1.28910 | −0.644550 | − | 0.764562i | \(-0.722955\pi\) | ||||
−0.644550 | + | 0.764562i | \(0.722955\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −104.103 | + | 60.1041i | −0.484201 | + | 0.279554i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | + | 20.7846i | −0.0138249 | + | 0.0957816i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 146.969 | + | 84.8528i | 0.665020 | + | 0.383949i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −248.000 | −1.11211 | −0.556054 | − | 0.831146i | \(-0.687685\pi\) | ||||
−0.556054 | + | 0.831146i | \(0.687685\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 143.295 | + | 82.7315i | 0.631256 | + | 0.364456i | 0.781238 | − | 0.624233i | \(-0.214588\pi\) |
−0.149982 | + | 0.988689i | \(0.547922\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −216.500 | − | 374.989i | −0.945415 | − | 1.63751i | −0.754918 | − | 0.655819i | \(-0.772324\pi\) |
−0.190496 | − | 0.981688i | \(-0.561010\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −197.184 | + | 113.844i | −0.846283 | + | 0.488602i | −0.859395 | − | 0.511312i | \(-0.829160\pi\) |
0.0131120 | + | 0.999914i | \(0.495826\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −51.0000 | + | 88.3346i | −0.217021 | + | 0.375892i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 343.654i | − | 1.43788i | −0.695071 | − | 0.718941i | \(-0.744627\pi\) | ||
0.695071 | − | 0.718941i | \(-0.255373\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −79.0000 | + | 136.832i | −0.327801 | + | 0.567768i | −0.982075 | − | 0.188490i | \(-0.939641\pi\) |
0.654274 | + | 0.756257i | \(0.272974\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −19.5959 | + | 66.4680i | −0.0799833 | + | 0.271298i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −97.5000 | − | 168.875i | −0.394737 | − | 0.683704i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 237.588i | 0.946565i | 0.880911 | + | 0.473283i | \(0.156931\pi\) | ||||
−0.880911 | + | 0.473283i | \(0.843069\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 160.000 | 0.632411 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −275.568 | + | 159.099i | −1.07225 | + | 0.619062i | −0.928795 | − | 0.370595i | \(-0.879154\pi\) |
−0.143453 | + | 0.989657i | \(0.545821\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 93.5000 | + | 73.6122i | 0.361004 | + | 0.284217i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −146.969 | − | 84.8528i | −0.558819 | − | 0.322634i | 0.193852 | − | 0.981031i | \(-0.437902\pi\) |
−0.752671 | + | 0.658396i | \(0.771235\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 48.0000 | 0.181132 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 420.087 | + | 242.538i | 1.56166 | + | 0.901627i | 0.997089 | + | 0.0762447i | \(0.0242930\pi\) |
0.564574 | + | 0.825382i | \(0.309040\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 108.000 | + | 187.061i | 0.398524 | + | 0.690264i | 0.993544 | − | 0.113447i | \(-0.0361892\pi\) |
−0.595020 | + | 0.803711i | \(0.702856\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 140.846 | − | 81.3173i | 0.512166 | − | 0.295699i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −152.500 | + | 264.138i | −0.550542 | + | 0.953566i | 0.447694 | + | 0.894187i | \(0.352245\pi\) |
−0.998236 | + | 0.0593790i | \(0.981088\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 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 | ||||||||
\(283\) | 78.5000 | − | 135.966i | 0.277385 | − | 0.480445i | −0.693349 | − | 0.720602i | \(-0.743866\pi\) |
0.970734 | + | 0.240157i | \(0.0771989\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 209.431 | + | 523.966i | 0.729726 | + | 1.82567i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −80.5000 | − | 139.430i | −0.278547 | − | 0.482457i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 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 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −293.939 | + | 169.706i | −0.983073 | + | 0.567577i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −552.500 | + | 220.836i | −1.83555 | + | 0.733676i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −88.1816 | − | 50.9117i | −0.289120 | − | 0.166924i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.0000 | 0.0358306 | 0.0179153 | − | 0.999840i | \(-0.494297\pi\) | ||||
0.0179153 | + | 0.999840i | \(0.494297\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 454.380 | + | 262.337i | 1.46103 | + | 0.843526i | 0.999059 | − | 0.0433690i | \(-0.0138091\pi\) |
0.461971 | + | 0.886895i | \(0.347142\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −276.500 | − | 478.912i | −0.883387 | − | 1.53007i | −0.847552 | − | 0.530713i | \(-0.821924\pi\) |
−0.0358348 | − | 0.999358i | \(-0.511409\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 117.576 | − | 67.8823i | 0.370901 | − | 0.214140i | −0.302951 | − | 0.953006i | \(-0.597972\pi\) |
0.673852 | + | 0.738866i | \(0.264639\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −80.0000 | + | 138.564i | −0.250784 | + | 0.434370i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 147.078i | − | 0.455350i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −172.500 | + | 298.779i | −0.530769 | + | 0.919319i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −312.310 | + | 396.687i | −0.949270 | + | 1.20574i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.5000 | − | 52.8275i | −0.0921450 | − | 0.159600i | 0.816268 | − | 0.577673i | \(-0.196039\pi\) |
−0.908413 | + | 0.418073i | \(0.862706\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 60.8112i | 0.181526i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 135.000 | 0.400593 | 0.200297 | − | 0.979735i | \(-0.435809\pi\) | ||||
0.200297 | + | 0.979735i | \(0.435809\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.3712 | + | 10.6066i | −0.0538744 | + | 0.0311044i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −143.000 | + | 311.769i | −0.416910 | + | 0.908948i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 88.1816 | + | 50.9117i | 0.254126 | + | 0.146720i | 0.621652 | − | 0.783294i | \(-0.286462\pi\) |
−0.367526 | + | 0.930013i | \(0.619795\pi\) | |||||||
\(348\) | 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 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −334.355 | − | 193.040i | −0.947182 | − | 0.546856i | −0.0549778 | − | 0.998488i | \(-0.517509\pi\) |
−0.892205 | + | 0.451632i | \(0.850842\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 37.0000 | + | 64.0859i | 0.104225 | + | 0.180524i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −39.1918 | + | 22.6274i | −0.109169 | + | 0.0630290i | −0.553591 | − | 0.832789i | \(-0.686743\pi\) |
0.444421 | + | 0.895818i | \(0.353409\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 96.0000 | − | 166.277i | 0.265928 | − | 0.460601i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 134.350i | 0.368083i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 50.5000 | − | 87.4686i | 0.137602 | − | 0.238334i | −0.788986 | − | 0.614411i | \(-0.789394\pi\) |
0.926588 | + | 0.376077i | \(0.122727\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 235.151 | + | 33.9411i | 0.633830 | + | 0.0914855i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 155.500 | + | 269.334i | 0.416890 | + | 0.722075i | 0.995625 | − | 0.0934411i | \(-0.0297867\pi\) |
−0.578735 | + | 0.815516i | \(0.696453\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 339.411i | − | 0.900295i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −91.0000 | −0.240106 | −0.120053 | − | 0.992768i | \(-0.538306\pi\) | ||||
−0.120053 | + | 0.992768i | \(0.538306\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −284.141 | + | 164.049i | −0.741882 | + | 0.428326i | −0.822753 | − | 0.568399i | \(-0.807563\pi\) |
0.0808712 | + | 0.996725i | \(0.474230\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −65.0000 | + | 25.9808i | −0.168831 | + | 0.0674825i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 596.451 | + | 344.361i | 1.53329 | + | 0.885247i | 0.999207 | + | 0.0398163i | \(0.0126773\pi\) |
0.534085 | + | 0.845431i | \(0.320656\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −256.000 | −0.654731 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −84.5074 | − | 48.7904i | −0.213943 | − | 0.123520i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 139.500 | + | 241.621i | 0.351385 | + | 0.608617i | 0.986492 | − | 0.163807i | \(-0.0523774\pi\) |
−0.635107 | + | 0.772424i | \(0.719044\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.5000 | − | 38.9711i | 0.0558313 | − | 0.0967026i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 120.208i | 0.295352i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 111.500 | − | 193.124i | 0.272616 | − | 0.472185i | −0.696915 | − | 0.717154i | \(-0.745444\pi\) |
0.969531 | + | 0.244969i | \(0.0787778\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 627.069 | + | 90.5097i | 1.51833 | + | 0.219152i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 43.0000 | + | 74.4782i | 0.103614 | + | 0.179466i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 581.242i | − | 1.38721i | −0.720355 | − | 0.693606i | \(-0.756021\pi\) | ||
0.720355 | − | 0.693606i | \(-0.243979\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 153.000 | 0.363420 | 0.181710 | − | 0.983352i | \(-0.441837\pi\) | ||||
0.181710 | + | 0.983352i | \(0.441837\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −225.353 | + | 130.108i | −0.530242 | + | 0.306136i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −396.000 | − | 311.769i | −0.927400 | − | 0.730139i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −121.250 | − | 70.0036i | −0.281322 | − | 0.162421i | 0.352700 | − | 0.935737i | \(-0.385264\pi\) |
−0.634022 | + | 0.773315i | \(0.718597\pi\) | |||||||
\(432\) | 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 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 254.747 | + | 147.078i | 0.582945 | + | 0.336563i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −300.000 | − | 519.615i | −0.683371 | − | 1.18363i | −0.973946 | − | 0.226781i | \(-0.927180\pi\) |
0.290574 | − | 0.956852i | \(-0.406154\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −548.686 | + | 316.784i | −1.23857 | + | 0.715088i | −0.968801 | − | 0.247838i | \(-0.920280\pi\) |
−0.269767 | + | 0.962926i | \(0.586947\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 96.0000 | − | 166.277i | 0.215730 | − | 0.373656i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 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 | ||||||||
\(451\) | −285.000 | + | 493.634i | −0.631929 | + | 1.09453i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 91.8559 | − | 116.673i | 0.201881 | − | 0.256423i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 119.500 | + | 206.980i | 0.261488 | + | 0.452910i | 0.966638 | − | 0.256148i | \(-0.0824535\pi\) |
−0.705150 | + | 0.709059i | \(0.749120\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 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 | \(-0.573173\pi\) | ||||
−0.227862 | + | 0.973693i | \(0.573173\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −270.669 | + | 156.271i | −0.579590 | + | 0.334627i | −0.760971 | − | 0.648786i | \(-0.775277\pi\) |
0.181380 | + | 0.983413i | \(0.441944\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −43.0000 | + | 297.913i | −0.0916844 | + | 0.635208i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −520.517 | − | 300.520i | −1.10046 | − | 0.635350i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 299.000 | 0.629474 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 607.473 | + | 350.725i | 1.26821 | + | 0.732202i | 0.974649 | − | 0.223737i | \(-0.0718258\pi\) |
0.293562 | + | 0.955940i | \(0.405159\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −127.500 | − | 220.836i | −0.265073 | − | 0.459119i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.5959 | + | 11.3137i | −0.0404040 | + | 0.0233272i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 209.500 | − | 362.865i | 0.430185 | − | 0.745102i | −0.566704 | − | 0.823921i | \(-0.691782\pi\) |
0.996889 | + | 0.0788195i | \(0.0251151\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 169.706i | 0.345633i | 0.984954 | + | 0.172816i | \(0.0552867\pi\) | ||||
−0.984954 | + | 0.172816i | \(0.944713\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 128.000 | − | 221.703i | 0.259635 | − | 0.449701i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 135.947 | + | 340.118i | 0.273535 | + | 0.684343i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 93.5000 | + | 161.947i | 0.187375 | + | 0.324543i | 0.944374 | − | 0.328873i | \(-0.106669\pi\) |
−0.756999 | + | 0.653416i | \(0.773335\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 173.948i | 0.345822i | 0.984937 | + | 0.172911i | \(0.0553172\pi\) | ||||
−0.984937 | + | 0.172911i | \(0.944683\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −98.0000 | −0.194059 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −224.128 | + | 129.401i | −0.440331 | + | 0.254225i | −0.703738 | − | 0.710460i | \(-0.748487\pi\) |
0.263407 | + | 0.964685i | \(0.415154\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −95.0000 | + | 658.179i | −0.185910 | + | 1.28802i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 74.7094 | + | 43.1335i | 0.145067 | + | 0.0837544i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −510.000 | −0.986460 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 352.727 | + | 203.647i | 0.677018 | + | 0.390877i | 0.798731 | − | 0.601689i | \(-0.205505\pi\) |
−0.121712 | + | 0.992565i | \(0.538839\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −405.500 | − | 702.347i | −0.775335 | − | 1.34292i | −0.934606 | − | 0.355684i | \(-0.884248\pi\) |
0.159272 | − | 0.987235i | \(-0.449085\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 29.3939 | − | 16.9706i | 0.0557759 | − | 0.0322022i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.50000 | + | 14.7224i | −0.0160681 | + | 0.0278307i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1209.15i | − | 2.26858i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −120.000 | + | 207.846i | −0.224299 | + | 0.388497i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −336.805 | + | 81.3173i | −0.624870 | + | 0.150867i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 172.500 | + | 298.779i | 0.318854 | + | 0.552271i | 0.980249 | − | 0.197766i | \(-0.0633687\pi\) |
−0.661395 | + | 0.750038i | \(0.730035\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 91.9239i | 0.168668i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 864.000 | 1.57952 | 0.789762 | − | 0.613413i | \(-0.210204\pi\) | ||||
0.789762 | + | 0.613413i | \(0.210204\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −254.747 | + | 147.078i | −0.462336 | + | 0.266930i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −379.500 | − | 298.779i | −0.686257 | − | 0.540287i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −821.804 | − | 474.469i | −1.47541 | − | 0.851829i | −0.475795 | − | 0.879556i | \(-0.657840\pi\) |
−0.999616 | + | 0.0277272i | \(0.991173\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1275.00 | 2.28086 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 640.542 | + | 369.817i | 1.13773 | + | 0.656868i | 0.945867 | − | 0.324554i | \(-0.105214\pi\) |
0.191862 | + | 0.981422i | \(0.438547\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 97.0000 | + | 168.009i | 0.171681 | + | 0.297361i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 665.036 | − | 383.959i | 1.16878 | − | 0.674796i | 0.215388 | − | 0.976528i | \(-0.430898\pi\) |
0.953393 | + | 0.301732i | \(0.0975649\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 238.500 | − | 413.094i | 0.417688 | − | 0.723457i | −0.578018 | − | 0.816024i | \(-0.696174\pi\) |
0.995706 | + | 0.0925665i | \(0.0295071\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 520.431i | − | 0.905097i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 131.500 | − | 227.765i | 0.227903 | − | 0.394739i | −0.729283 | − | 0.684212i | \(-0.760146\pi\) |
0.957186 | + | 0.289472i | \(0.0934798\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 157.992 | + | 395.273i | 0.271931 | + | 0.680332i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 120.000 | + | 207.846i | 0.205832 | + | 0.356511i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 531.744i | − | 0.905868i | −0.891544 | − | 0.452934i | \(-0.850377\pi\) | ||
0.891544 | − | 0.452934i | \(-0.149623\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −39.0000 | −0.0662139 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −694.430 | + | 400.930i | −1.17105 | + | 0.676104i | −0.953926 | − | 0.300041i | \(-0.903000\pi\) |
−0.217120 | + | 0.976145i | \(0.569666\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 104.000 | − | 41.5692i | 0.174790 | − | 0.0698642i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −676.059 | − | 390.323i | −1.12865 | − | 0.651624i | −0.185052 | − | 0.982729i | \(-0.559245\pi\) |
−0.943594 | + | 0.331104i | \(0.892579\pi\) | |||||||
\(600\) | 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 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 86.9569 | + | 50.2046i | 0.143730 | + | 0.0829828i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −382.500 | − | 662.509i | −0.630148 | − | 1.09145i | −0.987521 | − | 0.157487i | \(-0.949661\pi\) |
0.357373 | − | 0.933962i | \(-0.383673\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 936.930 | − | 540.937i | 1.53344 | − | 0.885330i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −204.000 | + | 353.338i | −0.332790 | + | 0.576408i | −0.983058 | − | 0.183296i | \(-0.941323\pi\) |
0.650268 | + | 0.759705i | \(0.274657\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 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 | ||||||||
\(619\) | −473.500 | + | 820.126i | −0.764943 | + | 1.32492i | 0.175333 | + | 0.984509i | \(0.443900\pi\) |
−0.940276 | + | 0.340412i | \(0.889434\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 587.878 | − | 746.705i | 0.943624 | − | 1.19856i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −239.500 | − | 414.826i | −0.383200 | − | 0.663722i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 192.333i | − | 0.305776i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 760.000 | 1.20444 | 0.602219 | − | 0.798331i | \(-0.294284\pi\) | ||||
0.602219 | + | 0.798331i | \(0.294284\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −209.431 | + | 120.915i | −0.329813 | + | 0.190418i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 532.500 | − | 506.625i | 0.835950 | − | 0.795329i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −401.716 | − | 231.931i | −0.626703 | − | 0.361827i | 0.152771 | − | 0.988262i | \(-0.451180\pi\) |
−0.779474 | + | 0.626435i | \(0.784514\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.0000 | 0.0295490 | 0.0147745 | − | 0.999891i | \(-0.495297\pi\) | ||||
0.0147745 | + | 0.999891i | \(0.495297\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1003.07 | − | 579.120i | −1.55033 | − | 0.895086i | −0.998114 | − | 0.0613872i | \(-0.980448\pi\) |
−0.552220 | − | 0.833698i | \(-0.686219\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 320.000 | + | 554.256i | 0.493066 | + | 0.854016i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 892.839 | − | 515.481i | 1.36729 | − | 0.789404i | 0.376707 | − | 0.926332i | \(-0.377056\pi\) |
0.990581 | + | 0.136928i | \(0.0437230\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 83.0000 | − | 143.760i | 0.126718 | − | 0.219481i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 972.979i | − | 1.47645i | −0.674556 | − | 0.738224i | \(-0.735665\pi\) | ||
0.674556 | − | 0.738224i | \(-0.264335\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 200.500 | − | 347.276i | 0.303328 | − | 0.525380i | −0.673559 | − | 0.739133i | \(-0.735235\pi\) |
0.976888 | + | 0.213753i | \(0.0685688\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −127.373 | − | 18.3848i | −0.191539 | − | 0.0276463i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 256.000 | + | 443.405i | 0.383808 | + | 0.664775i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 509.117i | − | 0.758743i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 665.000 | 0.988113 | 0.494056 | − | 0.869430i | \(-0.335514\pi\) | ||||
0.494056 | + | 0.869430i | \(0.335514\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −793.635 | + | 458.205i | −1.17228 | + | 0.676817i | −0.954216 | − | 0.299117i | \(-0.903308\pi\) |
−0.218065 | + | 0.975934i | \(0.569975\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −104.000 | + | 41.5692i | −0.153166 | + | 0.0612212i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 117.576 | + | 67.8823i | 0.172146 | + | 0.0993884i | 0.583597 | − | 0.812043i | \(-0.301645\pi\) |
−0.411452 | + | 0.911432i | \(0.634978\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 304.000 | 0.443796 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −440.908 | − | 254.558i | −0.639925 | − | 0.369461i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 110.500 | + | 191.392i | 0.159913 | + | 0.276978i | 0.934837 | − | 0.355077i | \(-0.115545\pi\) |
−0.774924 | + | 0.632054i | \(0.782212\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −101.654 | + | 58.6899i | −0.146264 | + | 0.0844458i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 456.000 | − | 789.815i | 0.654232 | − | 1.13316i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 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 | ||||||||
\(703\) | −110.500 | + | 191.392i | −0.157183 | + | 0.272250i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −480.100 | − | 69.2965i | −0.679066 | − | 0.0980148i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 164.000 | + | 284.056i | 0.231312 | + | 0.400644i | 0.958194 | − | 0.286118i | \(-0.0923649\pi\) |
−0.726883 | + | 0.686762i | \(0.759032\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 67.8823i | 0.0952065i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 150.000 | 0.209790 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 878.142 | − | 506.996i | 1.22134 | − | 0.705140i | 0.256135 | − | 0.966641i | \(-0.417551\pi\) |
0.965203 | + | 0.261501i | \(0.0842175\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 335.500 | + | 264.138i | 0.465326 | + | 0.366349i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 450.706 | + | 260.215i | 0.621664 | + | 0.358918i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1069.00 | −1.47043 | −0.735213 | − | 0.677836i | \(-0.762918\pi\) | ||||
−0.735213 | + | 0.677836i | \(0.762918\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 832.827 | + | 480.833i | 1.13930 | + | 0.657774i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −247.500 | − | 428.683i | −0.337653 | − | 0.584833i | 0.646337 | − | 0.763052i | \(-0.276300\pi\) |
−0.983991 | + | 0.178219i | \(0.942967\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −263.320 | + | 152.028i | −0.357286 | + | 0.206279i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 226.500 | − | 392.310i | 0.306495 | − | 0.530865i | −0.671098 | − | 0.741369i | \(-0.734177\pi\) |
0.977593 | + | 0.210503i | \(0.0675103\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 538.815i | 0.725189i | 0.931947 | + | 0.362594i | \(0.118109\pi\) | ||||
−0.931947 | + | 0.362594i | \(0.881891\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −72.0000 | + | 124.708i | −0.0966443 | + | 0.167393i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −734.847 | + | 933.381i | −0.981104 | + | 1.24617i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −169.500 | − | 293.583i | −0.225699 | − | 0.390922i | 0.730830 | − | 0.682560i | \(-0.239133\pi\) |
−0.956529 | + | 0.291637i | \(0.905800\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 56.5685i | 0.0749252i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 198.000 | 0.261559 | 0.130779 | − | 0.991411i | \(-0.458252\pi\) | ||||
0.130779 | + | 0.991411i | \(0.458252\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 313.535 | − | 181.019i | 0.412004 | − | 0.237870i | −0.279647 | − | 0.960103i | \(-0.590217\pi\) |
0.691650 | + | 0.722233i | \(0.256884\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −65.0000 | + | 450.333i | −0.0851900 | + | 0.590214i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1175.76 | − | 678.823i | −1.53293 | − | 0.885036i | ||||
\(768\) | 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 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 148.194 | + | 85.5599i | 0.191713 | + | 0.110686i | 0.592784 | − | 0.805361i | \(-0.298029\pi\) |
−0.401071 | + | 0.916047i | \(0.631362\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34.5000 | + | 59.7558i | 0.0445161 | + | 0.0771042i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −907.536 | + | 523.966i | −1.16500 | + | 0.672614i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −185.000 | + | 320.429i | −0.236876 | + | 0.410281i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 418.607i | − | 0.533258i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.0000 | − | 77.9423i | 0.0571792 | − | 0.0990372i | −0.836019 | − | 0.548701i | \(-0.815123\pi\) |
0.893198 | + | 0.449663i | \(0.148456\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 356.401 | + | 891.662i | 0.450570 | + | 1.12726i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 540.000 | + | 935.307i | 0.680958 | + | 1.17945i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 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 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −581.754 | + | 335.876i | −0.724475 | + | 0.418276i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −32.0000 | + | 221.703i | −0.0397516 | + | 0.275407i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 148.194 | + | 85.5599i | 0.183182 | + | 0.105760i | 0.588787 | − | 0.808288i | \(-0.299606\pi\) |
−0.405605 | + | 0.914049i | \(0.632939\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 554.000 | 0.683107 | 0.341554 | − | 0.939862i | \(-0.389047\pi\) | ||||
0.341554 | + | 0.939862i | \(0.389047\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −156.767 | − | 90.5097i | −0.192353 | − | 0.111055i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −552.500 | − | 956.958i | −0.676255 | − | 1.17131i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 919.783 | − | 531.037i | 1.12032 | − | 0.646818i | 0.178838 | − | 0.983879i | \(-0.442766\pi\) |
0.941483 | + | 0.337061i | \(0.109433\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 428.000 | − | 741.318i | 0.520049 | − | 0.900751i | −0.479680 | − | 0.877444i | \(-0.659247\pi\) |
0.999728 | − | 0.0233070i | \(-0.00741951\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1022.48i | − | 1.23637i | −0.786033 | − | 0.618184i | \(-0.787869\pi\) | ||
0.786033 | − | 0.618184i | \(-0.212131\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −519.500 | + | 899.800i | −0.626659 | + | 1.08540i | 0.361559 | + | 0.932349i | \(0.382245\pi\) |
−0.988218 | + | 0.153055i | \(0.951089\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 538.888 | − | 130.108i | 0.646924 | − | 0.156192i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −43.0000 | − | 74.4782i | −0.0514970 | − | 0.0891954i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 656.195i | 0.782116i | 0.920366 | + | 0.391058i | \(0.127891\pi\) | ||||
−0.920366 | + | 0.391058i | \(0.872109\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 329.000 | 0.391201 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −68.5857 | + | 39.5980i | −0.0811665 | + | 0.0468615i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 390.500 | + | 307.439i | 0.461039 | + | 0.362974i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 333.131 | + | 192.333i | 0.391458 | + | 0.226008i | ||||
\(852\) | 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 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 58.7878 | + | 33.9411i | 0.0685971 | + | 0.0396046i | 0.533906 | − | 0.845544i | \(-0.320724\pi\) |
−0.465309 | + | 0.885148i | \(0.654057\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −731.000 | − | 1266.13i | −0.850990 | − | 1.47396i | −0.880316 | − | 0.474387i | \(-0.842670\pi\) |
0.0293268 | − | 0.999570i | \(-0.490664\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 699.329 | − | 403.758i | 0.810347 | − | 0.467854i | −0.0367295 | − | 0.999325i | \(-0.511694\pi\) |
0.847076 | + | 0.531471i | \(0.178361\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −80.0000 | + | 138.564i | −0.0924855 | + | 0.160190i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 487.904i | − | 0.561454i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 322.500 | − | 558.586i | 0.370264 | − | 0.641316i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 176.363 | + | 441.235i | 0.201558 | + | 0.504268i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −740.000 | − | 1281.72i | −0.843786 | − | 1.46148i | −0.886672 | − | 0.462400i | \(-0.846989\pi\) |
0.0428860 | − | 0.999080i | \(-0.486345\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 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 | \(-0.479257\pi\) | ||||
0.0651189 | + | 0.997878i | \(0.479257\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1032.46 | + | 596.091i | −1.16399 | + | 0.672030i | −0.952257 | − | 0.305297i | \(-0.901244\pi\) |
−0.211734 | + | 0.977327i | \(0.567911\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1111.50 | + | 444.271i | −1.25028 | + | 0.499742i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −812.006 | − | 468.812i | −0.909301 | − | 0.524985i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 42.0000 | 0.0469274 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −58.7878 | − | 33.9411i | −0.0653924 | − | 0.0377543i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −192.000 | − | 332.554i | −0.213097 | − | 0.369094i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −99.2043 | + | 57.2756i | −0.109618 | + | 0.0632880i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −250.500 | + | 433.879i | −0.276185 | + | 0.478367i | −0.970433 | − | 0.241369i | \(-0.922404\pi\) |
0.694248 | + | 0.719736i | \(0.255737\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 203.647i | − | 0.223542i | −0.993734 | − | 0.111771i | \(-0.964348\pi\) | ||
0.993734 | − | 0.111771i | \(-0.0356523\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −215.000 | + | 372.391i | −0.235487 | + | 0.407876i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 508.269 | − | 645.588i | 0.554274 | − | 0.704022i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −326.500 | − | 565.515i | −0.355277 | − | 0.615359i | 0.631888 | − | 0.775060i | \(-0.282280\pi\) |
−0.987165 | + | 0.159701i | \(0.948947\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 784.889i | − | 0.850367i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 391.000 | 0.422703 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.0227 | − | 6.36396i | 0.0118651 | − | 0.00685033i | −0.494056 | − | 0.869430i | \(-0.664486\pi\) |
0.505921 | + | 0.862580i | \(0.331153\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −611.000 | − | 180.133i | −0.656284 | − | 0.193484i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 97.9796 | + | 56.5685i | 0.104791 | + | 0.0605011i | ||||
\(936\) | 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 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −244.949 | − | 141.421i | −0.260307 | − | 0.150288i | 0.364168 | − | 0.931333i | \(-0.381354\pi\) |
−0.624475 | + | 0.781045i | \(0.714687\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 912.000 | + | 1579.63i | 0.967126 | + | 1.67511i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 934.480 | − | 539.522i | 0.986780 | − | 0.569718i | 0.0824695 | − | 0.996594i | \(-0.473719\pi\) |
0.904310 | + | 0.426876i | \(0.140386\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 712.500 | − | 1234.09i | 0.750790 | − | 1.30041i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 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 | ||||||||
\(955\) | −45.0000 | + | 77.9423i | −0.0471204 | + | 0.0816150i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1489.29 | + | 214.960i | 1.55296 | + | 0.224151i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 476.000 | + | 824.456i | 0.495317 | + | 0.857915i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 315.370i | 0.326808i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1163.00 | −1.20269 | −0.601344 | − | 0.798990i | \(-0.705368\pi\) | ||||
−0.601344 | + | 0.798990i | \(0.705368\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1352.12 | + | 780.646i | −1.39250 | + | 0.803961i | −0.993592 | − | 0.113030i | \(-0.963944\pi\) |
−0.398909 | + | 0.916990i | \(0.630611\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −539.500 | + | 215.640i | −0.554471 | + | 0.221624i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 981.021 | + | 566.393i | 1.00412 | + | 0.579726i | 0.909463 | − | 0.415784i | \(-0.136493\pi\) |
0.0946520 | + | 0.995510i | \(0.469826\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 960.000 | 0.980592 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 264.545 | + | 152.735i | 0.269120 | + | 0.155376i | 0.628488 | − | 0.777820i | \(-0.283674\pi\) |
−0.359368 | + | 0.933196i | \(0.617008\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −112.000 | − | 193.990i | −0.113706 | − | 0.196944i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1665.65 | + | 961.665i | −1.68418 | + | 0.972361i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −486.500 | + | 842.643i | −0.490918 | + | 0.850295i | −0.999945 | − | 0.0104551i | \(-0.996672\pi\) |
0.509027 | + | 0.860751i | \(0.330005\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 192.333i | − | 0.193300i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.5000 | − | 68.4160i | 0.0396189 | − | 0.0686219i | −0.845536 | − | 0.533918i | \(-0.820719\pi\) |
0.885155 | + | 0.465296i | \(0.154052\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1008.3.dc.a.305.1 | 4 | ||
3.2 | odd | 2 | inner | 1008.3.dc.a.305.2 | 4 | ||
4.3 | odd | 2 | 126.3.s.b.53.1 | ✓ | 4 | ||
7.2 | even | 3 | inner | 1008.3.dc.a.737.2 | 4 | ||
12.11 | even | 2 | 126.3.s.b.53.2 | yes | 4 | ||
21.2 | odd | 6 | inner | 1008.3.dc.a.737.1 | 4 | ||
28.3 | even | 6 | 882.3.b.d.197.1 | 2 | |||
28.11 | odd | 6 | 882.3.b.c.197.1 | 2 | |||
28.19 | even | 6 | 882.3.s.c.863.2 | 4 | |||
28.23 | odd | 6 | 126.3.s.b.107.2 | yes | 4 | ||
28.27 | even | 2 | 882.3.s.c.557.1 | 4 | |||
84.11 | even | 6 | 882.3.b.c.197.2 | 2 | |||
84.23 | even | 6 | 126.3.s.b.107.1 | yes | 4 | ||
84.47 | odd | 6 | 882.3.s.c.863.1 | 4 | |||
84.59 | odd | 6 | 882.3.b.d.197.2 | 2 | |||
84.83 | odd | 2 | 882.3.s.c.557.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.s.b.53.1 | ✓ | 4 | 4.3 | odd | 2 | ||
126.3.s.b.53.2 | yes | 4 | 12.11 | even | 2 | ||
126.3.s.b.107.1 | yes | 4 | 84.23 | even | 6 | ||
126.3.s.b.107.2 | yes | 4 | 28.23 | odd | 6 | ||
882.3.b.c.197.1 | 2 | 28.11 | odd | 6 | |||
882.3.b.c.197.2 | 2 | 84.11 | even | 6 | |||
882.3.b.d.197.1 | 2 | 28.3 | even | 6 | |||
882.3.b.d.197.2 | 2 | 84.59 | odd | 6 | |||
882.3.s.c.557.1 | 4 | 28.27 | even | 2 | |||
882.3.s.c.557.2 | 4 | 84.83 | odd | 2 | |||
882.3.s.c.863.1 | 4 | 84.47 | odd | 6 | |||
882.3.s.c.863.2 | 4 | 28.19 | even | 6 | |||
1008.3.dc.a.305.1 | 4 | 1.1 | even | 1 | trivial | ||
1008.3.dc.a.305.2 | 4 | 3.2 | odd | 2 | inner | ||
1008.3.dc.a.737.1 | 4 | 21.2 | odd | 6 | inner | ||
1008.3.dc.a.737.2 | 4 | 7.2 | even | 3 | inner |