Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,3,Mod(557,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("882.557");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.s (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: | \(24.0327593166\) |
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: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 557.1 | ||
Root | \(1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.557 |
Dual form | 882.3.s.c.863.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | + | 0.707107i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | − | 1.73205i | 0.250000 | − | 0.433013i | ||||
\(5\) | 1.22474 | − | 0.707107i | 0.244949 | − | 0.141421i | −0.372500 | − | 0.928032i | \(-0.621499\pi\) |
0.617449 | + | 0.786611i | \(0.288166\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | + | 1.73205i | −0.100000 | + | 0.173205i | ||||
\(11\) | 6.12372 | + | 3.53553i | 0.556702 | + | 0.321412i | 0.751821 | − | 0.659367i | \(-0.229176\pi\) |
−0.195119 | + | 0.980780i | \(0.562509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −15.0000 | −1.15385 | −0.576923 | − | 0.816798i | \(-0.695747\pi\) | ||||
−0.576923 | + | 0.816798i | \(0.695747\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | −9.79796 | − | 5.65685i | −0.576351 | − | 0.332756i | 0.183331 | − | 0.983051i | \(-0.441312\pi\) |
−0.759682 | + | 0.650295i | \(0.774645\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.50000 | − | 11.2583i | −0.342105 | − | 0.592544i | 0.642718 | − | 0.766103i | \(-0.277807\pi\) |
−0.984823 | + | 0.173559i | \(0.944473\pi\) | |||||||
\(20\) | − | 2.82843i | − | 0.141421i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −10.0000 | −0.454545 | ||||||||
\(23\) | 19.5959 | − | 11.3137i | 0.851996 | − | 0.491900i | −0.00932753 | − | 0.999956i | \(-0.502969\pi\) |
0.861324 | + | 0.508056i | \(0.169636\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.5000 | + | 19.9186i | −0.460000 | + | 0.796743i | ||||
\(26\) | 18.3712 | − | 10.6066i | 0.706584 | − | 0.407946i | ||||
\(27\) | 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 | \(0.151259\pi\) | |||||||
\(32\) | 4.89898 | + | 2.82843i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 16.0000 | 0.470588 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.50000 | − | 14.7224i | −0.229730 | − | 0.397904i | 0.727998 | − | 0.685579i | \(-0.240451\pi\) |
−0.957728 | + | 0.287675i | \(0.907118\pi\) | |||||||
\(38\) | 15.9217 | + | 9.19239i | 0.418992 | + | 0.241905i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.00000 | + | 3.46410i | 0.0500000 | + | 0.0866025i | ||||
\(41\) | 80.6102i | 1.96610i | 0.183333 | + | 0.983051i | \(0.441311\pi\) | ||||
−0.183333 | + | 0.983051i | \(0.558689\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −85.0000 | −1.97674 | −0.988372 | − | 0.152055i | \(-0.951411\pi\) | ||||
−0.988372 | + | 0.152055i | \(0.951411\pi\) | |||||||
\(44\) | 12.2474 | − | 7.07107i | 0.278351 | − | 0.160706i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −16.0000 | + | 27.7128i | −0.347826 | + | 0.602452i | ||||
\(47\) | 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 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 32.5269i | − | 0.650538i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −15.0000 | + | 25.9808i | −0.288462 | + | 0.499630i | ||||
\(53\) | −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 | ||||||||
\(58\) | 16.0000 | + | 27.7128i | 0.275862 | + | 0.477807i | ||||
\(59\) | −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 | \(-0.965730\pi\) |
0.404046 | − | 0.914739i | \(-0.367604\pi\) | |||||||
\(62\) | 4.24264i | 0.0684297i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | −18.3712 | + | 10.6066i | −0.282633 | + | 0.163178i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −21.5000 | + | 37.2391i | −0.320896 | + | 0.555807i | −0.980673 | − | 0.195654i | \(-0.937317\pi\) |
0.659778 | + | 0.751461i | \(0.270651\pi\) | |||||||
\(68\) | −19.5959 | + | 11.3137i | −0.288175 | + | 0.166378i | ||||
\(69\) | 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 | ||||||||
\(73\) | −47.5000 | + | 82.2724i | −0.650685 | + | 1.12702i | 0.332272 | + | 0.943184i | \(0.392185\pi\) |
−0.982957 | + | 0.183836i | \(0.941149\pi\) | |||||||
\(74\) | 20.8207 | + | 12.0208i | 0.281360 | + | 0.162443i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −26.0000 | −0.342105 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −34.5000 | − | 59.7558i | −0.436709 | − | 0.756402i | 0.560725 | − | 0.828002i | \(-0.310523\pi\) |
−0.997433 | + | 0.0716005i | \(0.977189\pi\) | |||||||
\(80\) | −4.89898 | − | 2.82843i | −0.0612372 | − | 0.0353553i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −57.0000 | − | 98.7269i | −0.695122 | − | 1.20399i | ||||
\(83\) | − | 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 | ||||||||
\(86\) | 104.103 | − | 60.1041i | 1.21050 | − | 0.698885i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.0000 | + | 17.3205i | −0.113636 | + | 0.196824i | ||||
\(89\) | 117.576 | − | 67.8823i | 1.32107 | − | 0.762722i | 0.337173 | − | 0.941443i | \(-0.390529\pi\) |
0.983900 | + | 0.178721i | \(0.0571958\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 45.2548i | − | 0.491900i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −51.0000 | + | 88.3346i | −0.542553 | + | 0.939730i | ||||
\(95\) | −15.9217 | − | 9.19239i | −0.167597 | − | 0.0967620i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.0000 | −0.164948 | −0.0824742 | − | 0.996593i | \(-0.526282\pi\) | ||||
−0.0824742 | + | 0.996593i | \(0.526282\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 23.0000 | + | 39.8372i | 0.230000 | + | 0.398372i | ||||
\(101\) | −60.0125 | − | 34.6482i | −0.594183 | − | 0.343052i | 0.172567 | − | 0.984998i | \(-0.444794\pi\) |
−0.766750 | + | 0.641946i | \(0.778127\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −30.5000 | − | 52.8275i | −0.296117 | − | 0.512889i | 0.679127 | − | 0.734020i | \(-0.262358\pi\) |
−0.975244 | + | 0.221131i | \(0.929025\pi\) | |||||||
\(104\) | − | 42.4264i | − | 0.407946i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 48.0000 | 0.452830 | ||||||||
\(107\) | −146.969 | + | 84.8528i | −1.37355 | + | 0.793017i | −0.991373 | − | 0.131074i | \(-0.958158\pi\) |
−0.382173 | + | 0.924091i | \(0.624824\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 32.5000 | − | 56.2917i | 0.298165 | − | 0.516437i | −0.677551 | − | 0.735476i | \(-0.736959\pi\) |
0.975716 | + | 0.219039i | \(0.0702921\pi\) | |||||||
\(110\) | −12.2474 | + | 7.07107i | −0.111340 | + | 0.0642824i | ||||
\(111\) | 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 | ||||
\(116\) | −39.1918 | − | 22.6274i | −0.337861 | − | 0.195064i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 128.000 | 1.08475 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −35.5000 | − | 61.4878i | −0.293388 | − | 0.508164i | ||||
\(122\) | 88.1816 | + | 50.9117i | 0.722800 | + | 0.417309i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.00000 | − | 5.19615i | −0.0241935 | − | 0.0419045i | ||||
\(125\) | 67.8823i | 0.543058i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −171.000 | −1.34646 | −0.673228 | − | 0.739435i | \(-0.735093\pi\) | ||||
−0.673228 | + | 0.739435i | \(0.735093\pi\) | |||||||
\(128\) | 9.79796 | − | 5.65685i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 15.0000 | − | 25.9808i | 0.115385 | − | 0.199852i | ||||
\(131\) | −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 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 60.8112i | − | 0.453815i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16.0000 | − | 27.7128i | 0.117647 | − | 0.203771i | ||||
\(137\) | −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 | ||||||||
\(142\) | −37.0000 | − | 64.0859i | −0.260563 | − | 0.451309i | ||||
\(143\) | −91.8559 | − | 53.0330i | −0.642349 | − | 0.370860i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.0000 | − | 27.7128i | −0.110345 | − | 0.191123i | ||||
\(146\) | − | 134.350i | − | 0.920207i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −34.0000 | −0.229730 | ||||||||
\(149\) | 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 | −0.924621 | − | 0.380889i | \(-0.875618\pi\) |
0.792170 | + | 0.610300i | \(0.208951\pi\) | |||||||
\(152\) | 31.8434 | − | 18.3848i | 0.209496 | − | 0.120952i | ||||
\(153\) | 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 | \(-0.441635\pi\) |
0.760340 | − | 0.649525i | \(-0.225032\pi\) | |||||||
\(158\) | 84.5074 | + | 48.7904i | 0.534857 | + | 0.308800i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.00000 | 0.0500000 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −64.0000 | − | 110.851i | −0.392638 | − | 0.680069i | 0.600159 | − | 0.799881i | \(-0.295104\pi\) |
−0.992797 | + | 0.119812i | \(0.961771\pi\) | |||||||
\(164\) | 139.621 | + | 80.6102i | 0.851347 | + | 0.491525i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 43.0000 | + | 74.4782i | 0.259036 | + | 0.448664i | ||||
\(167\) | 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 | ||||||||
\(170\) | 19.5959 | − | 11.3137i | 0.115270 | − | 0.0665512i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −85.0000 | + | 147.224i | −0.494186 | + | 0.855955i | ||||
\(173\) | −97.9796 | + | 56.5685i | −0.566356 | + | 0.326986i | −0.755693 | − | 0.654926i | \(-0.772700\pi\) |
0.189337 | + | 0.981912i | \(0.439366\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 28.2843i | − | 0.160706i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −96.0000 | + | 166.277i | −0.539326 | + | 0.934140i | ||||
\(179\) | 25.7196 | + | 14.8492i | 0.143685 | + | 0.0829567i | 0.570119 | − | 0.821562i | \(-0.306897\pi\) |
−0.426434 | + | 0.904519i | \(0.640230\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −81.0000 | −0.447514 | −0.223757 | − | 0.974645i | \(-0.571832\pi\) | ||||
−0.223757 | + | 0.974645i | \(0.571832\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 32.0000 | + | 55.4256i | 0.173913 | + | 0.301226i | ||||
\(185\) | −20.8207 | − | 12.0208i | −0.112544 | − | 0.0649774i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −40.0000 | − | 69.2820i | −0.213904 | − | 0.370492i | ||||
\(188\) | − | 144.250i | − | 0.767286i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 26.0000 | 0.136842 | ||||||||
\(191\) | −55.1135 | + | 31.8198i | −0.288552 | + | 0.166596i | −0.637289 | − | 0.770625i | \(-0.719944\pi\) |
0.348736 | + | 0.937221i | \(0.386611\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 111.500 | − | 193.124i | 0.577720 | − | 1.00064i | −0.418020 | − | 0.908438i | \(-0.637276\pi\) |
0.995740 | − | 0.0922029i | \(-0.0293909\pi\) | |||||||
\(194\) | 19.5959 | − | 11.3137i | 0.101010 | − | 0.0583181i | ||||
\(195\) | 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 | \(0.277672\pi\) | |||||||
\(200\) | −56.3383 | − | 32.5269i | −0.281691 | − | 0.162635i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 98.0000 | 0.485149 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 57.0000 | + | 98.7269i | 0.278049 | + | 0.481595i | ||||
\(206\) | 74.7094 | + | 43.1335i | 0.362667 | + | 0.209386i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 30.0000 | + | 51.9615i | 0.144231 | + | 0.249815i | ||||
\(209\) | − | 91.9239i | − | 0.439827i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 272.000 | 1.28910 | 0.644550 | − | 0.764562i | \(-0.277045\pi\) | ||||
0.644550 | + | 0.764562i | \(0.277045\pi\) | |||||||
\(212\) | −58.7878 | + | 33.9411i | −0.277301 | + | 0.160100i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 120.000 | − | 207.846i | 0.560748 | − | 0.971243i | ||||
\(215\) | −104.103 | + | 60.1041i | −0.484201 | + | 0.279554i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 91.9239i | 0.421669i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.0000 | − | 17.3205i | 0.0454545 | − | 0.0787296i | ||||
\(221\) | 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 | ||||||||
\(226\) | 97.0000 | + | 168.009i | 0.429204 | + | 0.743402i | ||||
\(227\) | 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 | \(0.227676\pi\) |
0.190496 | + | 0.981688i | \(0.438990\pi\) | |||||||
\(230\) | 45.2548i | 0.196760i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 64.0000 | 0.275862 | ||||||||
\(233\) | −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 | ||||
\(236\) | −156.767 | + | 90.5097i | −0.664268 | + | 0.383516i | ||||
\(237\) | 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 | ||||||||
\(241\) | 79.0000 | − | 136.832i | 0.327801 | − | 0.567768i | −0.654274 | − | 0.756257i | \(-0.727026\pi\) |
0.982075 | + | 0.188490i | \(0.0603592\pi\) | |||||||
\(242\) | 86.9569 | + | 50.2046i | 0.359326 | + | 0.207457i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −144.000 | −0.590164 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 97.5000 | + | 168.875i | 0.394737 | + | 0.683704i | ||||
\(248\) | 7.34847 | + | 4.24264i | 0.0296309 | + | 0.0171074i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −48.0000 | − | 83.1384i | −0.192000 | − | 0.332554i | ||||
\(251\) | 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 | ||||||||
\(254\) | 209.431 | − | 120.915i | 0.824533 | − | 0.476044i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 275.568 | − | 159.099i | 1.07225 | − | 0.619062i | 0.143453 | − | 0.989657i | \(-0.454179\pi\) |
0.928795 | + | 0.370595i | \(0.120846\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 42.4264i | 0.163178i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 83.0000 | − | 143.760i | 0.316794 | − | 0.548703i | ||||
\(263\) | 146.969 | + | 84.8528i | 0.558819 | + | 0.322634i | 0.752671 | − | 0.658396i | \(-0.228765\pi\) |
−0.193852 | + | 0.981031i | \(0.562098\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −48.0000 | −0.181132 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 43.0000 | + | 74.4782i | 0.160448 | + | 0.277904i | ||||
\(269\) | −420.087 | − | 242.538i | −1.56166 | − | 0.901627i | −0.997089 | − | 0.0762447i | \(-0.975707\pi\) |
−0.564574 | − | 0.825382i | \(-0.690960\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 108.000 | + | 187.061i | 0.398524 | + | 0.690264i | 0.993544 | − | 0.113447i | \(-0.0361892\pi\) |
−0.595020 | + | 0.803711i | \(0.702856\pi\) | |||||||
\(272\) | 45.2548i | 0.166378i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 304.000 | 1.10949 | ||||||||
\(275\) | −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 | \(0.981088\pi\) | |||||||
\(278\) | −101.654 | + | 58.6899i | −0.365661 | + | 0.211115i | ||||
\(279\) | 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 | \(0.0771989\pi\) | |||||||
\(284\) | 90.6311 | + | 52.3259i | 0.319124 | + | 0.184246i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 150.000 | 0.524476 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −80.5000 | − | 139.430i | −0.278547 | − | 0.482457i | ||||
\(290\) | 39.1918 | + | 22.6274i | 0.135144 | + | 0.0780256i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 95.0000 | + | 164.545i | 0.325342 | + | 0.563510i | ||||
\(293\) | − | 101.823i | − | 0.347520i | −0.984788 | − | 0.173760i | \(-0.944408\pi\) | ||
0.984788 | − | 0.173760i | \(-0.0555917\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −128.000 | −0.433898 | ||||||||
\(296\) | 41.6413 | − | 24.0416i | 0.140680 | − | 0.0812217i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −72.0000 | + | 124.708i | −0.241611 | + | 0.418482i | ||||
\(299\) | −293.939 | + | 169.706i | −0.983073 | + | 0.567577i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 56.5685i | − | 0.187313i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −26.0000 | + | 45.0333i | −0.0855263 | + | 0.148136i | ||||
\(305\) | −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 | ||||||||
\(310\) | 3.00000 | + | 5.19615i | 0.00967742 | + | 0.0167618i | ||||
\(311\) | 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 | \(0.178076\pi\) |
0.0358348 | + | 0.999358i | \(0.488591\pi\) | |||||||
\(314\) | 418.607i | 1.33314i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −138.000 | −0.436709 | ||||||||
\(317\) | 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 | ||||
\(320\) | −9.79796 | + | 5.65685i | −0.0306186 | + | 0.0176777i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 147.078i | 0.455350i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 172.500 | − | 298.779i | 0.530769 | − | 0.919319i | ||||
\(326\) | 156.767 | + | 90.5097i | 0.480881 | + | 0.277637i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −228.000 | −0.695122 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.5000 | + | 52.8275i | 0.0921450 | + | 0.159600i | 0.908413 | − | 0.418073i | \(-0.137294\pi\) |
−0.816268 | + | 0.577673i | \(0.803961\pi\) | |||||||
\(332\) | −105.328 | − | 60.8112i | −0.317253 | − | 0.183166i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −43.0000 | − | 74.4782i | −0.128743 | − | 0.222989i | ||||
\(335\) | 60.8112i | 0.181526i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 135.000 | 0.400593 | 0.200297 | − | 0.979735i | \(-0.435809\pi\) | ||||
0.200297 | + | 0.979735i | \(0.435809\pi\) | |||||||
\(338\) | −68.5857 | + | 39.5980i | −0.202916 | + | 0.117154i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −16.0000 | + | 27.7128i | −0.0470588 | + | 0.0815083i | ||||
\(341\) | 18.3712 | − | 10.6066i | 0.0538744 | − | 0.0311044i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 240.416i | − | 0.698885i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 80.0000 | − | 138.564i | 0.231214 | − | 0.400474i | ||||
\(347\) | −88.1816 | − | 50.9117i | −0.254126 | − | 0.146720i | 0.367526 | − | 0.930013i | \(-0.380205\pi\) |
−0.621652 | + | 0.783294i | \(0.713538\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 152.000 | 0.435530 | 0.217765 | − | 0.976001i | \(-0.430123\pi\) | ||||
0.217765 | + | 0.976001i | \(0.430123\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 20.0000 | + | 34.6410i | 0.0568182 | + | 0.0984120i | ||||
\(353\) | 334.355 | + | 193.040i | 0.947182 | + | 0.546856i | 0.892205 | − | 0.451632i | \(-0.149158\pi\) |
0.0549778 | + | 0.998488i | \(0.482491\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 37.0000 | + | 64.0859i | 0.104225 | + | 0.180524i | ||||
\(356\) | − | 271.529i | − | 0.762722i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −42.0000 | −0.117318 | ||||||||
\(359\) | 39.1918 | − | 22.6274i | 0.109169 | − | 0.0630290i | −0.444421 | − | 0.895818i | \(-0.646591\pi\) |
0.553591 | + | 0.832789i | \(0.313257\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 96.0000 | − | 166.277i | 0.265928 | − | 0.460601i | ||||
\(362\) | 99.2043 | − | 57.2756i | 0.274045 | − | 0.158220i | ||||
\(363\) | 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 | \(0.122727\pi\) | |||||||
\(368\) | −78.3837 | − | 45.2548i | −0.212999 | − | 0.122975i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 34.0000 | 0.0918919 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 155.500 | + | 269.334i | 0.416890 | + | 0.722075i | 0.995625 | − | 0.0934411i | \(-0.0297867\pi\) |
−0.578735 | + | 0.815516i | \(0.696453\pi\) | |||||||
\(374\) | 97.9796 | + | 56.5685i | 0.261978 | + | 0.151253i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 102.000 | + | 176.669i | 0.271277 | + | 0.469865i | ||||
\(377\) | 339.411i | 0.900295i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 91.0000 | 0.240106 | 0.120053 | − | 0.992768i | \(-0.461694\pi\) | ||||
0.120053 | + | 0.992768i | \(0.461694\pi\) | |||||||
\(380\) | −31.8434 | + | 18.3848i | −0.0837983 | + | 0.0483810i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 45.0000 | − | 77.9423i | 0.117801 | − | 0.204037i | ||||
\(383\) | −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 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 315.370i | 0.817020i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.0000 | + | 27.7128i | −0.0412371 | + | 0.0714248i | ||||
\(389\) | 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 | ||||||||
\(394\) | −112.000 | − | 193.990i | −0.284264 | − | 0.492360i | ||||
\(395\) | −84.5074 | − | 48.7904i | −0.213943 | − | 0.123520i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −139.500 | − | 241.621i | −0.351385 | − | 0.608617i | 0.635107 | − | 0.772424i | \(-0.280956\pi\) |
−0.986492 | + | 0.163807i | \(0.947623\pi\) | |||||||
\(398\) | − | 192.333i | − | 0.483249i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 92.0000 | 0.230000 | ||||||||
\(401\) | 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 | ||||
\(404\) | −120.025 | + | 69.2965i | −0.297092 | + | 0.171526i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 120.208i | − | 0.295352i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −111.500 | + | 193.124i | −0.272616 | + | 0.472185i | −0.969531 | − | 0.244969i | \(-0.921222\pi\) |
0.696915 | + | 0.717154i | \(0.254556\pi\) | |||||||
\(410\) | −139.621 | − | 80.6102i | −0.340539 | − | 0.196610i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −122.000 | −0.296117 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −43.0000 | − | 74.4782i | −0.103614 | − | 0.179466i | ||||
\(416\) | −73.4847 | − | 42.4264i | −0.176646 | − | 0.101987i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 65.0000 | + | 112.583i | 0.155502 | + | 0.269338i | ||||
\(419\) | − | 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 | \(0.441837\pi\) | |||||||
\(422\) | −333.131 | + | 192.333i | −0.789409 | + | 0.455766i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 48.0000 | − | 83.1384i | 0.113208 | − | 0.196081i | ||||
\(425\) | 225.353 | − | 130.108i | 0.530242 | − | 0.306136i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 339.411i | 0.793017i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 85.0000 | − | 147.224i | 0.197674 | − | 0.342382i | ||||
\(431\) | 121.250 | + | 70.0036i | 0.281322 | + | 0.162421i | 0.634022 | − | 0.773315i | \(-0.281403\pi\) |
−0.352700 | + | 0.935737i | \(0.614736\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −137.000 | −0.316397 | −0.158199 | − | 0.987407i | \(-0.550569\pi\) | ||||
−0.158199 | + | 0.987407i | \(0.550569\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −65.0000 | − | 112.583i | −0.149083 | − | 0.258219i | ||||
\(437\) | −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 | \(-0.406154\pi\) | |||||||
\(440\) | 28.2843i | 0.0642824i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −240.000 | −0.542986 | ||||||||
\(443\) | 548.686 | − | 316.784i | 1.23857 | − | 0.715088i | 0.269767 | − | 0.962926i | \(-0.413053\pi\) |
0.968801 | + | 0.247838i | \(0.0797201\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 96.0000 | − | 166.277i | 0.215730 | − | 0.373656i | ||||
\(446\) | 303.737 | − | 175.362i | 0.681024 | − | 0.393189i | ||||
\(447\) | 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 | ||||
\(452\) | −237.601 | − | 137.179i | −0.525665 | − | 0.303493i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −234.000 | −0.515419 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 119.500 | + | 206.980i | 0.261488 | + | 0.452910i | 0.966638 | − | 0.256148i | \(-0.0824535\pi\) |
−0.705150 | + | 0.709059i | \(0.749120\pi\) | |||||||
\(458\) | −530.315 | − | 306.177i | −1.15789 | − | 0.668509i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −32.0000 | − | 55.4256i | −0.0695652 | − | 0.120490i | ||||
\(461\) | − | 452.548i | − | 0.981667i | −0.871253 | − | 0.490833i | \(-0.836692\pi\) | ||
0.871253 | − | 0.490833i | \(-0.163308\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 211.000 | 0.455724 | 0.227862 | − | 0.973693i | \(-0.426827\pi\) | ||||
0.227862 | + | 0.973693i | \(0.426827\pi\) | |||||||
\(464\) | −78.3837 | + | 45.2548i | −0.168930 | + | 0.0975320i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 161.000 | − | 278.860i | 0.345494 | − | 0.598412i | ||||
\(467\) | −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 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 144.250i | 0.306914i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 128.000 | − | 221.703i | 0.271186 | − | 0.469709i | ||||
\(473\) | −520.517 | − | 300.520i | −1.10046 | − | 0.635350i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 299.000 | 0.629474 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −243.000 | − | 420.888i | −0.508368 | − | 0.880520i | ||||
\(479\) | 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 | ||||
\(482\) | 223.446i | 0.463580i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −142.000 | −0.293388 | ||||||||
\(485\) | −19.5959 | + | 11.3137i | −0.0404040 | + | 0.0233272i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −209.500 | + | 362.865i | −0.430185 | + | 0.745102i | −0.996889 | − | 0.0788195i | \(-0.974885\pi\) |
0.566704 | + | 0.823921i | \(0.308218\pi\) | |||||||
\(488\) | 176.363 | − | 101.823i | 0.361400 | − | 0.208654i | ||||
\(489\) | 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 | ||||||||
\(493\) | −128.000 | + | 221.703i | −0.259635 | + | 0.449701i | ||||
\(494\) | −238.825 | − | 137.886i | −0.483452 | − | 0.279121i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.0000 | −0.0241935 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −93.5000 | − | 161.947i | −0.187375 | − | 0.324543i | 0.756999 | − | 0.653416i | \(-0.226665\pi\) |
−0.944374 | + | 0.328873i | \(0.893331\pi\) | |||||||
\(500\) | 117.576 | + | 67.8823i | 0.235151 | + | 0.135765i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −168.000 | − | 290.985i | −0.334661 | − | 0.579650i | ||||
\(503\) | 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 | ||||||||
\(506\) | −195.959 | + | 113.137i | −0.387271 | + | 0.223591i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −171.000 | + | 296.181i | −0.336614 | + | 0.583033i | ||||
\(509\) | 224.128 | − | 129.401i | 0.440331 | − | 0.254225i | −0.263407 | − | 0.964685i | \(-0.584846\pi\) |
0.703738 | + | 0.710460i | \(0.251513\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −225.000 | + | 389.711i | −0.437743 | + | 0.758193i | ||||
\(515\) | −74.7094 | − | 43.1335i | −0.145067 | − | 0.0837544i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 510.000 | 0.986460 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −30.0000 | − | 51.9615i | −0.0576923 | − | 0.0999260i | ||||
\(521\) | −352.727 | − | 203.647i | −0.677018 | − | 0.390877i | 0.121712 | − | 0.992565i | \(-0.461161\pi\) |
−0.798731 | + | 0.601689i | \(0.794495\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −405.500 | − | 702.347i | −0.775335 | − | 1.34292i | −0.934606 | − | 0.355684i | \(-0.884248\pi\) |
0.159272 | − | 0.987235i | \(-0.449085\pi\) | |||||||
\(524\) | 234.759i | 0.448014i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −240.000 | −0.456274 | ||||||||
\(527\) | −29.3939 | + | 16.9706i | −0.0557759 | + | 0.0322022i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.50000 | + | 14.7224i | −0.0160681 | + | 0.0278307i | ||||
\(530\) | 58.7878 | − | 33.9411i | 0.110920 | − | 0.0640399i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1209.15i | − | 2.26858i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −120.000 | + | 207.846i | −0.224299 | + | 0.388497i | ||||
\(536\) | −105.328 | − | 60.8112i | −0.196508 | − | 0.113454i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 686.000 | 1.27509 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 172.500 | + | 298.779i | 0.318854 | + | 0.552271i | 0.980249 | − | 0.197766i | \(-0.0633687\pi\) |
−0.661395 | + | 0.750038i | \(0.730035\pi\) | |||||||
\(542\) | −264.545 | − | 152.735i | −0.488090 | − | 0.281799i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −32.0000 | − | 55.4256i | −0.0588235 | − | 0.101885i | ||||
\(545\) | − | 91.9239i | − | 0.168668i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −864.000 | −1.57952 | −0.789762 | − | 0.613413i | \(-0.789796\pi\) | ||||
−0.789762 | + | 0.613413i | \(0.789796\pi\) | |||||||
\(548\) | −372.322 | + | 214.960i | −0.679421 | + | 0.392264i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 115.000 | − | 199.186i | 0.209091 | − | 0.362156i | ||||
\(551\) | −254.747 | + | 147.078i | −0.462336 | + | 0.266930i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 431.335i | − | 0.778583i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 83.0000 | − | 143.760i | 0.149281 | − | 0.258562i | ||||
\(557\) | −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 | ||||||||
\(562\) | −16.0000 | − | 27.7128i | −0.0284698 | − | 0.0493111i | ||||
\(563\) | 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 | ||||
\(566\) | 222.032i | 0.392282i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −148.000 | −0.260563 | ||||||||
\(569\) | 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 | −0.995706 | − | 0.0925665i | \(-0.970493\pi\) |
0.578018 | + | 0.816024i | \(0.303826\pi\) | |||||||
\(572\) | −183.712 | + | 106.066i | −0.321174 | + | 0.185430i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 520.431i | 0.905097i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −131.500 | + | 227.765i | −0.227903 | + | 0.394739i | −0.957186 | − | 0.289472i | \(-0.906520\pi\) |
0.729283 | + | 0.684212i | \(0.239854\pi\) | |||||||
\(578\) | 197.184 | + | 113.844i | 0.341149 | + | 0.196962i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −64.0000 | −0.110345 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −120.000 | − | 207.846i | −0.205832 | − | 0.356511i | ||||
\(584\) | −232.702 | − | 134.350i | −0.398462 | − | 0.230052i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 72.0000 | + | 124.708i | 0.122867 | + | 0.212812i | ||||
\(587\) | − | 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 | ||||||||
\(590\) | 156.767 | − | 90.5097i | 0.265707 | − | 0.153406i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −34.0000 | + | 58.8897i | −0.0574324 | + | 0.0994759i | ||||
\(593\) | 694.430 | − | 400.930i | 1.17105 | − | 0.676104i | 0.217120 | − | 0.976145i | \(-0.430334\pi\) |
0.953926 | + | 0.300041i | \(0.0970004\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 203.647i | − | 0.341689i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 240.000 | − | 415.692i | 0.401338 | − | 0.695137i | ||||
\(599\) | 676.059 | + | 390.323i | 1.12865 | + | 0.651624i | 0.943594 | − | 0.331104i | \(-0.107421\pi\) |
0.185052 | + | 0.982729i | \(0.440755\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −383.000 | −0.637271 | −0.318636 | − | 0.947877i | \(-0.603225\pi\) | ||||
−0.318636 | + | 0.947877i | \(0.603225\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 40.0000 | + | 69.2820i | 0.0662252 | + | 0.114705i | ||||
\(605\) | −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 | \(-0.383673\pi\) | |||||||
\(608\) | − | 73.5391i | − | 0.120952i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 144.000 | 0.236066 | ||||||||
\(611\) | −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 | \(0.274657\pi\) | |||||||
\(614\) | −13.4722 | + | 7.77817i | −0.0219417 | + | 0.0126680i | ||||
\(615\) | 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 | \(0.889434\pi\) | |||||||
\(620\) | −7.34847 | − | 4.24264i | −0.0118524 | − | 0.00684297i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −742.000 | −1.19293 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −239.500 | − | 414.826i | −0.383200 | − | 0.663722i | ||||
\(626\) | −677.284 | − | 391.030i | −1.08192 | − | 0.624649i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −296.000 | − | 512.687i | −0.471338 | − | 0.816381i | ||||
\(629\) | 192.333i | 0.305776i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −760.000 | −1.20444 | −0.602219 | − | 0.798331i | \(-0.705716\pi\) | ||||
−0.602219 | + | 0.798331i | \(0.705716\pi\) | |||||||
\(632\) | 169.015 | − | 97.5807i | 0.267428 | − | 0.154400i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −96.0000 | + | 166.277i | −0.151420 | + | 0.262266i | ||||
\(635\) | −209.431 | + | 120.915i | −0.329813 | + | 0.190418i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 226.274i | 0.354662i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.00000 | − | 13.8564i | 0.0125000 | − | 0.0216506i | ||||
\(641\) | −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 | ||||||||
\(646\) | −104.000 | − | 180.133i | −0.160991 | − | 0.278844i | ||||
\(647\) | −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 | ||||
\(650\) | 487.904i | 0.750621i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −256.000 | −0.392638 | ||||||||
\(653\) | 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 | ||||
\(656\) | 279.242 | − | 161.220i | 0.425674 | − | 0.245763i | ||||
\(657\) | 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 | ||||||||
\(661\) | −200.500 | + | 347.276i | −0.303328 | + | 0.525380i | −0.976888 | − | 0.213753i | \(-0.931431\pi\) |
0.673559 | + | 0.739133i | \(0.264765\pi\) | |||||||
\(662\) | −74.7094 | − | 43.1335i | −0.112854 | − | 0.0651564i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 172.000 | 0.259036 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −256.000 | − | 443.405i | −0.383808 | − | 0.664775i | ||||
\(668\) | 105.328 | + | 60.8112i | 0.157677 | + | 0.0910347i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −43.0000 | − | 74.4782i | −0.0641791 | − | 0.111161i | ||||
\(671\) | − | 509.117i | − | 0.758743i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 665.000 | 0.988113 | 0.494056 | − | 0.869430i | \(-0.335514\pi\) | ||||
0.494056 | + | 0.869430i | \(0.335514\pi\) | |||||||
\(674\) | −165.341 | + | 95.4594i | −0.245312 | + | 0.141631i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 56.0000 | − | 96.9948i | 0.0828402 | − | 0.143483i | ||||
\(677\) | 793.635 | − | 458.205i | 1.17228 | − | 0.676817i | 0.218065 | − | 0.975934i | \(-0.430025\pi\) |
0.954216 | + | 0.299117i | \(0.0966921\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 45.2548i | − | 0.0665512i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −15.0000 | + | 25.9808i | −0.0219941 | + | 0.0380950i | ||||
\(683\) | −117.576 | − | 67.8823i | −0.172146 | − | 0.0993884i | 0.411452 | − | 0.911432i | \(-0.365022\pi\) |
−0.583597 | + | 0.812043i | \(0.698355\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −304.000 | −0.443796 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 170.000 | + | 294.449i | 0.247093 | + | 0.427978i | ||||
\(689\) | 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 | \(0.782212\pi\) | |||||||
\(692\) | 226.274i | 0.326986i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 144.000 | 0.207493 | ||||||||
\(695\) | 101.654 | − | 58.6899i | 0.146264 | − | 0.0844458i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 456.000 | − | 789.815i | 0.654232 | − | 1.13316i | ||||
\(698\) | −186.161 | + | 107.480i | −0.266707 | + | 0.153983i | ||||
\(699\) | 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 | ||||
\(704\) | −48.9898 | − | 28.2843i | −0.0695878 | − | 0.0401765i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −546.000 | −0.773371 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 164.000 | + | 284.056i | 0.231312 | + | 0.400644i | 0.958194 | − | 0.286118i | \(-0.0923649\pi\) |
−0.726883 | + | 0.686762i | \(0.759032\pi\) | |||||||
\(710\) | −90.6311 | − | 52.3259i | −0.127649 | − | 0.0736985i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 192.000 | + | 332.554i | 0.269663 | + | 0.467070i | ||||
\(713\) | − | 67.8823i | − | 0.0952065i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −150.000 | −0.209790 | ||||||||
\(716\) | 51.4393 | − | 29.6985i | 0.0718426 | − | 0.0414783i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −32.0000 | + | 55.4256i | −0.0445682 | + | 0.0771945i | ||||
\(719\) | 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 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 271.529i | 0.376079i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −81.0000 | + | 140.296i | −0.111878 | + | 0.193779i | ||||
\(725\) | 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 | ||||||||
\(730\) | −95.0000 | − | 164.545i | −0.130137 | − | 0.225404i | ||||
\(731\) | 832.827 | + | 480.833i | 1.13930 | + | 0.657774i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 247.500 | + | 428.683i | 0.337653 | + | 0.584833i | 0.983991 | − | 0.178219i | \(-0.0570335\pi\) |
−0.646337 | + | 0.763052i | \(0.723700\pi\) | |||||||
\(734\) | 142.836i | 0.194599i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 128.000 | 0.173913 | ||||||||
\(737\) | −263.320 | + | 152.028i | −0.357286 | + | 0.206279i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −226.500 | + | 392.310i | −0.306495 | + | 0.530865i | −0.977593 | − | 0.210503i | \(-0.932490\pi\) |
0.671098 | + | 0.741369i | \(0.265823\pi\) | |||||||
\(740\) | −41.6413 | + | 24.0416i | −0.0562721 | + | 0.0324887i | ||||
\(741\) | 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 | ||||||||
\(745\) | 72.0000 | − | 124.708i | 0.0966443 | − | 0.167393i | ||||
\(746\) | −380.896 | − | 219.910i | −0.510584 | − | 0.294786i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −160.000 | −0.213904 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 169.500 | + | 293.583i | 0.225699 | + | 0.390922i | 0.956529 | − | 0.291637i | \(-0.0942001\pi\) |
−0.730830 | + | 0.682560i | \(0.760867\pi\) | |||||||
\(752\) | −249.848 | − | 144.250i | −0.332245 | − | 0.191822i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −240.000 | − | 415.692i | −0.318302 | − | 0.551316i | ||||
\(755\) | 56.5685i | 0.0749252i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 198.000 | 0.261559 | 0.130779 | − | 0.991411i | \(-0.458252\pi\) | ||||
0.130779 | + | 0.991411i | \(0.458252\pi\) | |||||||
\(758\) | −111.452 | + | 64.3467i | −0.147034 | + | 0.0848901i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 26.0000 | − | 45.0333i | 0.0342105 | − | 0.0592544i | ||||
\(761\) | −313.535 | + | 181.019i | −0.412004 | + | 0.237870i | −0.691650 | − | 0.722233i | \(-0.743116\pi\) |
0.279647 | + | 0.960103i | \(0.409783\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 127.279i | 0.166596i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 232.000 | − | 401.836i | 0.302872 | − | 0.524590i | ||||
\(767\) | 1175.76 | + | 678.823i | 1.53293 | + | 0.885036i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 929.000 | 1.20806 | 0.604031 | − | 0.796961i | \(-0.293560\pi\) | ||||
0.604031 | + | 0.796961i | \(0.293560\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −223.000 | − | 386.247i | −0.288860 | − | 0.500320i | ||||
\(773\) | −148.194 | − | 85.5599i | −0.191713 | − | 0.110686i | 0.401071 | − | 0.916047i | \(-0.368638\pi\) |
−0.592784 | + | 0.805361i | \(0.701971\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34.5000 | + | 59.7558i | 0.0445161 | + | 0.0771042i | ||||
\(776\) | − | 45.2548i | − | 0.0583181i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −974.000 | −1.25193 | ||||||||
\(779\) | 907.536 | − | 523.966i | 1.16500 | − | 0.672614i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −185.000 | + | 320.429i | −0.236876 | + | 0.410281i | ||||
\(782\) | 313.535 | − | 181.019i | 0.400939 | − | 0.231483i | ||||
\(783\) | 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 | \(0.148456\pi\) | |||||||
\(788\) | 274.343 | + | 158.392i | 0.348151 | + | 0.201005i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 138.000 | 0.174684 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 540.000 | + | 935.307i | 0.680958 | + | 1.17945i | ||||
\(794\) | 341.704 | + | 197.283i | 0.430357 | + | 0.248467i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 136.000 | + | 235.559i | 0.170854 | + | 0.295928i | ||||
\(797\) | 1154.00i | 1.44793i | 0.689838 | + | 0.723964i | \(0.257682\pi\) | ||||
−0.689838 | + | 0.723964i | \(0.742318\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −816.000 | −1.02128 | ||||||||
\(800\) | −112.677 | + | 65.0538i | −0.140846 | + | 0.0813173i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −581.754 | + | 335.876i | −0.724475 | + | 0.418276i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 63.6396i | − | 0.0789573i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 98.0000 | − | 169.741i | 0.121287 | − | 0.210075i | ||||
\(809\) | 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 | ||||||||
\(814\) | 85.0000 | + | 147.224i | 0.104423 | + | 0.180865i | ||||
\(815\) | −156.767 | − | 90.5097i | −0.192353 | − | 0.111055i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 552.500 | + | 956.958i | 0.676255 | + | 1.17131i | ||||
\(818\) | − | 315.370i | − | 0.385537i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 228.000 | 0.278049 | ||||||||
\(821\) | 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 | \(0.340753\pi\) |
−0.999728 | + | 0.0233070i | \(0.992580\pi\) | |||||||
\(824\) | 149.419 | − | 86.2670i | 0.181334 | − | 0.104693i | ||||
\(825\) | 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 | ||||||||
\(829\) | 519.500 | − | 899.800i | 0.626659 | − | 1.08540i | −0.361559 | − | 0.932349i | \(-0.617755\pi\) |
0.988218 | − | 0.153055i | \(-0.0489113\pi\) | |||||||
\(830\) | 105.328 | + | 60.8112i | 0.126901 | + | 0.0732665i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 120.000 | 0.144231 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 43.0000 | + | 74.4782i | 0.0514970 | + | 0.0891954i | ||||
\(836\) | −159.217 | − | 91.9239i | −0.190451 | − | 0.109957i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 411.000 | + | 711.873i | 0.490453 | + | 0.849490i | ||||
\(839\) | 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 | ||||||||
\(842\) | −187.386 | + | 108.187i | −0.222549 | + | 0.128489i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 272.000 | − | 471.118i | 0.322275 | − | 0.558196i | ||||
\(845\) | 68.5857 | − | 39.5980i | 0.0811665 | − | 0.0468615i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 135.765i | 0.160100i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −184.000 | + | 318.697i | −0.216471 | + | 0.374938i | ||||
\(851\) | −333.131 | − | 192.333i | −0.391458 | − | 0.226008i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1463.00 | −1.71512 | −0.857562 | − | 0.514381i | \(-0.828022\pi\) | ||||
−0.857562 | + | 0.514381i | \(0.828022\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −240.000 | − | 415.692i | −0.280374 | − | 0.485622i | ||||
\(857\) | −58.7878 | − | 33.9411i | −0.0685971 | − | 0.0396046i | 0.465309 | − | 0.885148i | \(-0.345943\pi\) |
−0.533906 | + | 0.845544i | \(0.679276\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −731.000 | − | 1266.13i | −0.850990 | − | 1.47396i | −0.880316 | − | 0.474387i | \(-0.842670\pi\) |
0.0293268 | − | 0.999570i | \(-0.490664\pi\) | |||||||
\(860\) | 240.416i | 0.279554i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −198.000 | −0.229698 | ||||||||
\(863\) | −699.329 | + | 403.758i | −0.810347 | + | 0.467854i | −0.847076 | − | 0.531471i | \(-0.821639\pi\) |
0.0367295 | + | 0.999325i | \(0.488306\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −80.0000 | + | 138.564i | −0.0924855 | + | 0.160190i | ||||
\(866\) | 167.790 | − | 96.8736i | 0.193753 | − | 0.111863i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 487.904i | − | 0.561454i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 322.500 | − | 558.586i | 0.370264 | − | 0.641316i | ||||
\(872\) | 159.217 | + | 91.9239i | 0.182588 | + | 0.105417i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 416.000 | 0.475973 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −740.000 | − | 1281.72i | −0.843786 | − | 1.46148i | −0.886672 | − | 0.462400i | \(-0.846989\pi\) |
0.0428860 | − | 0.999080i | \(-0.486345\pi\) | |||||||
\(878\) | 734.847 | + | 424.264i | 0.836955 | + | 0.483216i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −20.0000 | − | 34.6410i | −0.0227273 | − | 0.0393648i | ||||
\(881\) | 712.764i | 0.809039i | 0.914529 | + | 0.404520i | \(0.132561\pi\) | ||||
−0.914529 | + | 0.404520i | \(0.867439\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −115.000 | −0.130238 | −0.0651189 | − | 0.997878i | \(-0.520743\pi\) | ||||
−0.0651189 | + | 0.997878i | \(0.520743\pi\) | |||||||
\(884\) | 293.939 | − | 169.706i | 0.332510 | − | 0.191975i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −448.000 | + | 775.959i | −0.505643 | + | 0.875800i | ||||
\(887\) | −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 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 271.529i | 0.305089i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −248.000 | + | 429.549i | −0.278027 | + | 0.481557i | ||||
\(893\) | −812.006 | − | 468.812i | −0.909301 | − | 0.524985i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 42.0000 | 0.0469274 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 271.000 | + | 469.386i | 0.301782 | + | 0.522701i | ||||
\(899\) | −58.7878 | − | 33.9411i | −0.0653924 | − | 0.0377543i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 192.000 | + | 332.554i | 0.213097 | + | 0.369094i | ||||
\(902\) | − | 806.102i | − | 0.893683i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 388.000 | 0.429204 | ||||||||
\(905\) | −99.2043 | + | 57.2756i | −0.109618 | + | 0.0632880i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 250.500 | − | 433.879i | 0.276185 | − | 0.478367i | −0.694248 | − | 0.719736i | \(-0.744263\pi\) |
0.970433 | + | 0.241369i | \(0.0775963\pi\) | |||||||
\(908\) | 286.590 | − | 165.463i | 0.315628 | − | 0.182228i | ||||
\(909\) | 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 | ||||||||
\(913\) | 215.000 | − | 372.391i | 0.235487 | − | 0.407876i | ||||
\(914\) | −292.714 | − | 168.999i | −0.320256 | − | 0.184900i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 866.000 | 0.945415 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 326.500 | + | 565.515i | 0.355277 | + | 0.615359i | 0.987165 | − | 0.159701i | \(-0.0510530\pi\) |
−0.631888 | + | 0.775060i | \(0.717720\pi\) | |||||||
\(920\) | 78.3837 | + | 45.2548i | 0.0851996 | + | 0.0491900i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 320.000 | + | 554.256i | 0.347072 | + | 0.601146i | ||||
\(923\) | − | 784.889i | − | 0.850367i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 391.000 | 0.422703 | ||||||||
\(926\) | −258.421 | + | 149.200i | −0.279073 | + | 0.161123i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 64.0000 | − | 110.851i | 0.0689655 | − | 0.119452i | ||||
\(929\) | −11.0227 | + | 6.36396i | −0.0118651 | + | 0.00685033i | −0.505921 | − | 0.862580i | \(-0.668847\pi\) |
0.494056 | + | 0.869430i | \(0.335514\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 455.377i | 0.488602i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 221.000 | − | 382.783i | 0.236617 | − | 0.409832i | ||||
\(935\) | −97.9796 | − | 56.5685i | −0.104791 | − | 0.0605011i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −761.000 | −0.812166 | −0.406083 | − | 0.913836i | \(-0.633106\pi\) | ||||
−0.406083 | + | 0.913836i | \(0.633106\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −102.000 | − | 176.669i | −0.108511 | − | 0.187946i | ||||
\(941\) | 244.949 | + | 141.421i | 0.260307 | + | 0.150288i | 0.624475 | − | 0.781045i | \(-0.285313\pi\) |
−0.364168 | + | 0.931333i | \(0.618646\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 912.000 | + | 1579.63i | 0.967126 | + | 1.67511i | ||||
\(944\) | 362.039i | 0.383516i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 850.000 | 0.898520 | ||||||||
\(947\) | −934.480 | + | 539.522i | −0.986780 | + | 0.569718i | −0.904310 | − | 0.426876i | \(-0.859614\pi\) |
−0.0824695 | + | 0.996594i | \(0.526281\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 712.500 | − | 1234.09i | 0.750790 | − | 1.30041i | ||||
\(950\) | −366.199 | + | 211.425i | −0.385472 | + | 0.222553i | ||||
\(951\) | 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 | ||||
\(956\) | 595.226 | + | 343.654i | 0.622621 | + | 0.359471i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −992.000 | −1.03549 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 476.000 | + | 824.456i | 0.495317 | + | 0.857915i | ||||
\(962\) | −312.310 | − | 180.312i | −0.324647 | − | 0.187435i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −158.000 | − | 273.664i | −0.163900 | − | 0.283884i | ||||
\(965\) | − | 315.370i | − | 0.326808i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1163.00 | 1.20269 | 0.601344 | − | 0.798990i | \(-0.294632\pi\) | ||||
0.601344 | + | 0.798990i | \(0.294632\pi\) | |||||||
\(968\) | 173.914 | − | 100.409i | 0.179663 | − | 0.103728i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 16.0000 | − | 27.7128i | 0.0164948 | − | 0.0285699i | ||||
\(971\) | −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 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 592.555i | − | 0.608373i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −144.000 | + | 249.415i | −0.147541 | + | 0.255548i | ||||
\(977\) | 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 | ||||||||
\(982\) | 120.000 | + | 207.846i | 0.122200 | + | 0.211656i | ||||
\(983\) | 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 | ||||
\(986\) | − | 362.039i | − | 0.367179i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 390.000 | 0.394737 | ||||||||
\(989\) | −1665.65 | + | 961.665i | −1.68418 | + | 0.972361i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 486.500 | − | 842.643i | 0.490918 | − | 0.850295i | −0.509027 | − | 0.860751i | \(-0.669995\pi\) |
0.999945 | + | 0.0104551i | \(0.00332803\pi\) | |||||||
\(992\) | 14.6969 | − | 8.48528i | 0.0148155 | − | 0.00855371i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 192.333i | 0.193300i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.5000 | + | 68.4160i | −0.0396189 | + | 0.0686219i | −0.885155 | − | 0.465296i | \(-0.845948\pi\) |
0.845536 | + | 0.533918i | \(0.179281\pi\) | |||||||
\(998\) | 229.027 | + | 132.229i | 0.229486 | + | 0.132494i | ||||
\(999\) | 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.s.c.557.1 | 4 | ||
3.2 | odd | 2 | inner | 882.3.s.c.557.2 | 4 | ||
7.2 | even | 3 | inner | 882.3.s.c.863.2 | 4 | ||
7.3 | odd | 6 | 882.3.b.c.197.1 | 2 | |||
7.4 | even | 3 | 882.3.b.d.197.1 | 2 | |||
7.5 | odd | 6 | 126.3.s.b.107.2 | yes | 4 | ||
7.6 | odd | 2 | 126.3.s.b.53.1 | ✓ | 4 | ||
21.2 | odd | 6 | inner | 882.3.s.c.863.1 | 4 | ||
21.5 | even | 6 | 126.3.s.b.107.1 | yes | 4 | ||
21.11 | odd | 6 | 882.3.b.d.197.2 | 2 | |||
21.17 | even | 6 | 882.3.b.c.197.2 | 2 | |||
21.20 | even | 2 | 126.3.s.b.53.2 | yes | 4 | ||
28.19 | even | 6 | 1008.3.dc.a.737.2 | 4 | |||
28.27 | even | 2 | 1008.3.dc.a.305.1 | 4 | |||
84.47 | odd | 6 | 1008.3.dc.a.737.1 | 4 | |||
84.83 | odd | 2 | 1008.3.dc.a.305.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.s.b.53.1 | ✓ | 4 | 7.6 | odd | 2 | ||
126.3.s.b.53.2 | yes | 4 | 21.20 | even | 2 | ||
126.3.s.b.107.1 | yes | 4 | 21.5 | even | 6 | ||
126.3.s.b.107.2 | yes | 4 | 7.5 | odd | 6 | ||
882.3.b.c.197.1 | 2 | 7.3 | odd | 6 | |||
882.3.b.c.197.2 | 2 | 21.17 | even | 6 | |||
882.3.b.d.197.1 | 2 | 7.4 | even | 3 | |||
882.3.b.d.197.2 | 2 | 21.11 | odd | 6 | |||
882.3.s.c.557.1 | 4 | 1.1 | even | 1 | trivial | ||
882.3.s.c.557.2 | 4 | 3.2 | odd | 2 | inner | ||
882.3.s.c.863.1 | 4 | 21.2 | odd | 6 | inner | ||
882.3.s.c.863.2 | 4 | 7.2 | even | 3 | inner | ||
1008.3.dc.a.305.1 | 4 | 28.27 | even | 2 | |||
1008.3.dc.a.305.2 | 4 | 84.83 | odd | 2 | |||
1008.3.dc.a.737.1 | 4 | 84.47 | odd | 6 | |||
1008.3.dc.a.737.2 | 4 | 28.19 | even | 6 |