Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3276,2,Mod(2521,3276)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3276, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3276.2521");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3276 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3276.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(26.1589917022\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1092) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2521.2 | ||
Root | \(-1.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3276.2521 |
Dual form | 3276.2.e.e.2521.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3276\mathbb{Z}\right)^\times\).
\(n\) | \(1639\) | \(2017\) | \(2341\) | \(2549\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 0.561553i | − | 0.251134i | −0.992085 | − | 0.125567i | \(-0.959925\pi\) | ||
0.992085 | − | 0.125567i | \(-0.0400750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.12311i | 0.941652i | 0.882226 | + | 0.470826i | \(0.156044\pi\) | ||||
−0.882226 | + | 0.470826i | \(0.843956\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.56155 | − | 0.561553i | −0.987797 | − | 0.155747i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.56155i | − | 0.587661i | −0.955858 | − | 0.293830i | \(-0.905070\pi\) | ||
0.955858 | − | 0.293830i | \(-0.0949300\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.68466 | 0.768304 | 0.384152 | − | 0.923270i | \(-0.374494\pi\) | ||||
0.384152 | + | 0.923270i | \(0.374494\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.68466 | 0.936932 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.43845 | −0.638504 | −0.319252 | − | 0.947670i | \(-0.603432\pi\) | ||||
−0.319252 | + | 0.947670i | \(0.603432\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.56155i | − | 0.460068i | −0.973183 | − | 0.230034i | \(-0.926116\pi\) | ||
0.973183 | − | 0.230034i | \(-0.0738838\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.561553 | 0.0949197 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0000i | 1.56174i | 0.624695 | + | 0.780869i | \(0.285223\pi\) | ||||
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.43845 | 0.219361 | 0.109681 | − | 0.993967i | \(-0.465017\pi\) | ||||
0.109681 | + | 0.993967i | \(0.465017\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.56155i | 0.665371i | 0.943038 | + | 0.332685i | \(0.107955\pi\) | ||||
−0.943038 | + | 0.332685i | \(0.892045\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.561553 | 0.0771352 | 0.0385676 | − | 0.999256i | \(-0.487721\pi\) | ||||
0.0385676 | + | 0.999256i | \(0.487721\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.75379 | 0.236481 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 15.1231i | 1.96886i | 0.175775 | + | 0.984430i | \(0.443757\pi\) | ||||
−0.175775 | + | 0.984430i | \(0.556243\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.1231 | −1.42417 | −0.712084 | − | 0.702094i | \(-0.752248\pi\) | ||||
−0.712084 | + | 0.702094i | \(0.752248\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.315342 | + | 2.00000i | −0.0391133 | + | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 13.1231i | − | 1.60324i | −0.597832 | − | 0.801621i | \(-0.703971\pi\) | ||
0.597832 | − | 0.801621i | \(-0.296029\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.36932i | 1.11193i | 0.831205 | + | 0.555967i | \(0.187652\pi\) | ||||
−0.831205 | + | 0.555967i | \(0.812348\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.5616i | 1.23614i | 0.786125 | + | 0.618068i | \(0.212084\pi\) | ||||
−0.786125 | + | 0.618068i | \(0.787916\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.12311 | −0.355911 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.68466 | −0.414556 | −0.207278 | − | 0.978282i | \(-0.566461\pi\) | ||||
−0.207278 | + | 0.978282i | \(0.566461\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.68466i | 0.623972i | 0.950087 | + | 0.311986i | \(0.100994\pi\) | ||||
−0.950087 | + | 0.311986i | \(0.899006\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1.12311i | − | 0.121818i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.68466i | 0.602573i | 0.953534 | + | 0.301286i | \(0.0974160\pi\) | ||||
−0.953534 | + | 0.301286i | \(0.902584\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.561553 | − | 3.56155i | 0.0588667 | − | 0.373352i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.43845 | −0.147582 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.6847i | 1.59254i | 0.604944 | + | 0.796268i | \(0.293195\pi\) | ||||
−0.604944 | + | 0.796268i | \(0.706805\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.36932 | 0.932282 | 0.466141 | − | 0.884710i | \(-0.345644\pi\) | ||||
0.466141 | + | 0.884710i | \(0.345644\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.75379 | −0.172806 | −0.0864030 | − | 0.996260i | \(-0.527537\pi\) | ||||
−0.0864030 | + | 0.996260i | \(0.527537\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.4924 | 1.59438 | 0.797191 | − | 0.603727i | \(-0.206318\pi\) | ||||
0.797191 | + | 0.603727i | \(0.206318\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.12311i | − | 0.107574i | −0.998552 | − | 0.0537870i | \(-0.982871\pi\) | ||
0.998552 | − | 0.0537870i | \(-0.0171292\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.8078 | −1.39300 | −0.696499 | − | 0.717558i | \(-0.745260\pi\) | ||||
−0.696499 | + | 0.717558i | \(0.745260\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.06913i | − | 0.192947i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00000i | 0.183340i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.24621 | 0.113292 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 5.43845i | − | 0.486430i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.4924 | 1.10852 | 0.554262 | − | 0.832343i | \(-0.313001\pi\) | ||||
0.554262 | + | 0.832343i | \(0.313001\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.87689 | −0.600837 | −0.300419 | − | 0.953807i | \(-0.597126\pi\) | ||||
−0.300419 | + | 0.953807i | \(0.597126\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.56155 | 0.222115 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.36932i | 0.458732i | 0.973340 | + | 0.229366i | \(0.0736652\pi\) | ||||
−0.973340 | + | 0.229366i | \(0.926335\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.75379 | 0.488030 | 0.244015 | − | 0.969771i | \(-0.421535\pi\) | ||||
0.244015 | + | 0.969771i | \(0.421535\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.75379 | − | 11.1231i | 0.146659 | − | 0.930161i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.93087i | 0.160350i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 5.36932i | − | 0.439872i | −0.975514 | − | 0.219936i | \(-0.929415\pi\) | ||
0.975514 | − | 0.219936i | \(-0.0705848\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000i | 0.976546i | 0.872691 | + | 0.488273i | \(0.162373\pi\) | ||||
−0.872691 | + | 0.488273i | \(0.837627\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.43845 | −0.115539 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.24621 | −0.658119 | −0.329060 | − | 0.944309i | \(-0.606732\pi\) | ||||
−0.329060 | + | 0.944309i | \(0.606732\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.68466i | 0.290392i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 6.87689i | − | 0.538640i | −0.963051 | − | 0.269320i | \(-0.913201\pi\) | ||
0.963051 | − | 0.269320i | \(-0.0867989\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 0.561553i | − | 0.0434543i | −0.999764 | − | 0.0217271i | \(-0.993083\pi\) | ||
0.999764 | − | 0.0217271i | \(-0.00691650\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.3693 | + | 4.00000i | 0.951486 | + | 0.307692i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.87689 | 0.370783 | 0.185392 | − | 0.982665i | \(-0.440645\pi\) | ||||
0.185392 | + | 0.982665i | \(0.440645\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.68466i | 0.354127i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.5616 | −0.789408 | −0.394704 | − | 0.918808i | \(-0.629153\pi\) | ||||
−0.394704 | + | 0.918808i | \(0.629153\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3693 | 1.29105 | 0.645526 | − | 0.763739i | \(-0.276638\pi\) | ||||
0.645526 | + | 0.763739i | \(0.276638\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.24621i | 0.456768i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.0000 | 1.15772 | 0.578860 | − | 0.815427i | \(-0.303498\pi\) | ||||
0.578860 | + | 0.815427i | \(0.303498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.3693i | 1.10631i | 0.833079 | + | 0.553154i | \(0.186576\pi\) | ||||
−0.833079 | + | 0.553154i | \(0.813424\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.3693i | 1.52250i | 0.648458 | + | 0.761250i | \(0.275414\pi\) | ||||
−0.648458 | + | 0.761250i | \(0.724586\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.6155 | −1.81584 | −0.907918 | − | 0.419147i | \(-0.862329\pi\) | ||||
−0.907918 | + | 0.419147i | \(0.862329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 3.43845i | − | 0.241332i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.61553 | 0.392205 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.56155 | 0.176345 | 0.0881723 | − | 0.996105i | \(-0.471897\pi\) | ||||
0.0881723 | + | 0.996105i | \(0.471897\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 0.807764i | − | 0.0550891i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.56155 | 0.173890 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.12311 | − | 1.12311i | −0.479152 | − | 0.0755483i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.5616i | 0.707254i | 0.935387 | + | 0.353627i | \(0.115052\pi\) | ||||
−0.935387 | + | 0.353627i | \(0.884948\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 7.12311i | − | 0.472777i | −0.971659 | − | 0.236389i | \(-0.924036\pi\) | ||
0.971659 | − | 0.236389i | \(-0.0759638\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.3693i | 1.27996i | 0.768391 | + | 0.639980i | \(0.221057\pi\) | ||||
−0.768391 | + | 0.639980i | \(0.778943\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.6847 | 1.15856 | 0.579280 | − | 0.815128i | \(-0.303334\pi\) | ||||
0.579280 | + | 0.815128i | \(0.303334\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.56155 | 0.167097 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.24621i | − | 0.533403i | −0.963779 | − | 0.266702i | \(-0.914066\pi\) | ||
0.963779 | − | 0.266702i | \(-0.0859338\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.0540i | 1.48504i | 0.669826 | + | 0.742519i | \(0.266369\pi\) | ||||
−0.669826 | + | 0.742519i | \(0.733631\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.561553i | 0.0358763i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.43845 | + | 9.12311i | −0.0915262 | + | 0.580489i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.00000 | 0.252478 | 0.126239 | − | 0.992000i | \(-0.459709\pi\) | ||||
0.126239 | + | 0.992000i | \(0.459709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.5076i | 0.723475i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.36932 | 0.334929 | 0.167464 | − | 0.985878i | \(-0.446442\pi\) | ||||
0.167464 | + | 0.985878i | \(0.446442\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.0540 | −1.66822 | −0.834110 | − | 0.551598i | \(-0.814018\pi\) | ||||
−0.834110 | + | 0.551598i | \(0.814018\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.315342i | − | 0.0193713i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.0000 | −0.609711 | −0.304855 | − | 0.952399i | \(-0.598608\pi\) | ||||
−0.304855 | + | 0.952399i | \(0.598608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 22.7386i | − | 1.38127i | −0.723202 | − | 0.690637i | \(-0.757330\pi\) | ||
0.723202 | − | 0.690637i | \(-0.242670\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.6307i | 0.882263i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.5616 | 0.754751 | 0.377375 | − | 0.926060i | \(-0.376827\pi\) | ||||
0.377375 | + | 0.926060i | \(0.376827\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.0000i | − | 1.07379i | −0.843649 | − | 0.536895i | \(-0.819597\pi\) | ||
0.843649 | − | 0.536895i | \(-0.180403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.75379 | −0.579803 | −0.289901 | − | 0.957057i | \(-0.593622\pi\) | ||||
−0.289901 | + | 0.957057i | \(0.593622\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.0000 | −0.590281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 7.93087i | − | 0.463326i | −0.972796 | − | 0.231663i | \(-0.925583\pi\) | ||
0.972796 | − | 0.231663i | \(-0.0744167\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.49242 | 0.494448 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.1231 | − | 2.06913i | −0.758929 | − | 0.119661i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.43845i | 0.0829107i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.24621i | 0.357657i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.80776i | − | 0.502686i | −0.967898 | − | 0.251343i | \(-0.919128\pi\) | ||
0.967898 | − | 0.251343i | \(-0.0808722\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.6155 | 1.45252 | 0.726262 | − | 0.687418i | \(-0.241256\pi\) | ||||
0.726262 | + | 0.687418i | \(0.241256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.8769 | −0.953938 | −0.476969 | − | 0.878920i | \(-0.658265\pi\) | ||||
−0.476969 | + | 0.878920i | \(0.658265\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000i | 0.336994i | 0.985702 | + | 0.168497i | \(0.0538913\pi\) | ||||
−0.985702 | + | 0.168497i | \(0.946109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 10.7386i | − | 0.601248i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.12311i | − | 0.285057i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.6847 | − | 2.63068i | −0.925498 | − | 0.145924i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.56155 | −0.251487 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.2462i | 1.44262i | 0.692611 | + | 0.721311i | \(0.256460\pi\) | ||||
−0.692611 | + | 0.721311i | \(0.743540\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.36932 | −0.402629 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.68466 | −0.0917692 | −0.0458846 | − | 0.998947i | \(-0.514611\pi\) | ||||
−0.0458846 | + | 0.998947i | \(0.514611\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.00000 | 0.433224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.49242 | −0.455897 | −0.227949 | − | 0.973673i | \(-0.573202\pi\) | ||||
−0.227949 | + | 0.973673i | \(0.573202\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 26.4233i | − | 1.41441i | −0.707010 | − | 0.707203i | \(-0.749957\pi\) | ||
0.707010 | − | 0.707203i | \(-0.250043\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.2462i | 1.50339i | 0.659509 | + | 0.751697i | \(0.270764\pi\) | ||||
−0.659509 | + | 0.751697i | \(0.729236\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.26137 | 0.279244 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 20.2462i | − | 1.06855i | −0.845309 | − | 0.534277i | \(-0.820584\pi\) | ||
0.845309 | − | 0.534277i | \(-0.179416\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.4384 | 0.654655 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.93087 | 0.310436 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.3693 | −0.593474 | −0.296737 | − | 0.954959i | \(-0.595898\pi\) | ||||
−0.296737 | + | 0.954959i | \(0.595898\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.561553i | 0.0291544i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.00000 | 0.310668 | 0.155334 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.2462 | + | 1.93087i | 0.630712 | + | 0.0994448i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 36.9848i | − | 1.89978i | −0.312578 | − | 0.949892i | \(-0.601193\pi\) | ||
0.312578 | − | 0.949892i | \(-0.398807\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 20.8769i | − | 1.06676i | −0.845876 | − | 0.533380i | \(-0.820922\pi\) | ||
0.845876 | − | 0.533380i | \(-0.179078\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.75379i | 0.0893814i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.24621 | −0.215291 | −0.107646 | − | 0.994189i | \(-0.534331\pi\) | ||||
−0.107646 | + | 0.994189i | \(0.534331\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.36932 | 0.372682 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.06913i | 0.104109i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.0540i | 0.554783i | 0.960757 | + | 0.277392i | \(0.0894699\pi\) | ||||
−0.960757 | + | 0.277392i | \(0.910530\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 2.49242i | − | 0.124466i | −0.998062 | − | 0.0622328i | \(-0.980178\pi\) | ||
0.998062 | − | 0.0622328i | \(-0.0198221\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.43845 | + | 9.12311i | −0.0716542 | + | 0.454454i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 2.56155i | − | 0.126661i | −0.997993 | − | 0.0633303i | \(-0.979828\pi\) | ||
0.997993 | − | 0.0633303i | \(-0.0201722\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.1231 | −0.744159 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.19224 | 0.156701 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.00000 | 0.195413 | 0.0977064 | − | 0.995215i | \(-0.468849\pi\) | ||||
0.0977064 | + | 0.995215i | \(0.468849\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 4.63068i | − | 0.225686i | −0.993613 | − | 0.112843i | \(-0.964004\pi\) | ||
0.993613 | − | 0.112843i | \(-0.0359957\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.36932 | 0.454479 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 11.1231i | − | 0.538285i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.87689i | 0.427585i | 0.976879 | + | 0.213792i | \(0.0685816\pi\) | ||||
−0.976879 | + | 0.213792i | \(0.931418\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.7386 | 0.996635 | 0.498318 | − | 0.866995i | \(-0.333951\pi\) | ||||
0.498318 | + | 0.866995i | \(0.333951\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 9.43845i | − | 0.451502i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.24621 | 0.298115 | 0.149058 | − | 0.988828i | \(-0.452376\pi\) | ||||
0.149058 | + | 0.988828i | \(0.452376\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.3153 | 1.15526 | 0.577628 | − | 0.816300i | \(-0.303978\pi\) | ||||
0.577628 | + | 0.816300i | \(0.303978\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.19224 | 0.151326 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.0000i | 0.471929i | 0.971762 | + | 0.235965i | \(0.0758249\pi\) | ||||
−0.971762 | + | 0.235965i | \(0.924175\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.2311 | −1.47061 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.00000 | − | 0.315342i | −0.0937614 | − | 0.0147834i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 4.63068i | − | 0.216614i | −0.994117 | − | 0.108307i | \(-0.965457\pi\) | ||
0.994117 | − | 0.108307i | \(-0.0345430\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.75379i | 0.174831i | 0.996172 | + | 0.0874157i | \(0.0278608\pi\) | ||||
−0.996172 | + | 0.0874157i | \(0.972139\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.6155i | 0.818663i | 0.912386 | + | 0.409332i | \(0.134238\pi\) | ||||
−0.912386 | + | 0.409332i | \(0.865762\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.1231 | −0.792363 | −0.396181 | − | 0.918172i | \(-0.629665\pi\) | ||||
−0.396181 | + | 0.918172i | \(0.629665\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.1231 | 0.605969 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.49242i | 0.206562i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 12.0000i | − | 0.550598i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 35.3002i | − | 1.61291i | −0.591298 | − | 0.806453i | \(-0.701384\pi\) | ||
0.591298 | − | 0.806453i | \(-0.298616\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.80776 | 0.399940 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.24621i | 0.283043i | 0.989935 | + | 0.141521i | \(0.0451994\pi\) | ||||
−0.989935 | + | 0.141521i | \(0.954801\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.24621 | −0.281888 | −0.140944 | − | 0.990018i | \(-0.545014\pi\) | ||||
−0.140944 | + | 0.990018i | \(0.545014\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.87689 | −0.309720 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.36932 | −0.420271 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 41.6155i | − | 1.86297i | −0.363784 | − | 0.931483i | \(-0.618515\pi\) | ||
0.363784 | − | 0.931483i | \(-0.381485\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.4924 | −1.27041 | −0.635207 | − | 0.772342i | \(-0.719085\pi\) | ||||
−0.635207 | + | 0.772342i | \(0.719085\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 5.26137i | − | 0.234128i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 41.6847i | 1.84764i | 0.382827 | + | 0.923820i | \(0.374950\pi\) | ||||
−0.382827 | + | 0.923820i | \(0.625050\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.5616 | −0.467216 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.984845i | 0.0433975i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.2462 | −0.626548 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.3693 | −0.936207 | −0.468103 | − | 0.883674i | \(-0.655063\pi\) | ||||
−0.468103 | + | 0.883674i | \(0.655063\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.75379 | 0.251596 | 0.125798 | − | 0.992056i | \(-0.459851\pi\) | ||||
0.125798 | + | 0.992056i | \(0.459851\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 5.12311i | − | 0.223166i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.42329 | −0.409708 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.61553 | − | 35.6155i | 0.243236 | − | 1.54268i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 9.26137i | − | 0.400404i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 3.12311i | − | 0.134522i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 20.9848i | − | 0.902209i | −0.892471 | − | 0.451104i | \(-0.851030\pi\) | ||
0.892471 | − | 0.451104i | \(-0.148970\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.630683 | −0.0270155 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.1771 | 1.37579 | 0.687896 | − | 0.725809i | \(-0.258534\pi\) | ||||
0.687896 | + | 0.725809i | \(0.258534\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.80776i | 0.375223i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 3.68466i | − | 0.156688i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.12311i | 0.132330i | 0.997809 | + | 0.0661651i | \(0.0210764\pi\) | ||||
−0.997809 | + | 0.0661651i | \(0.978924\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.12311 | − | 0.807764i | −0.216684 | − | 0.0341648i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.36932 | −0.142000 | −0.0709999 | − | 0.997476i | \(-0.522619\pi\) | ||||
−0.0709999 | + | 0.997476i | \(0.522619\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.31534i | 0.349829i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.4233 | 1.35926 | 0.679628 | − | 0.733557i | \(-0.262141\pi\) | ||||
0.679628 | + | 0.733557i | \(0.262141\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.8078 | −0.535988 | −0.267994 | − | 0.963421i | \(-0.586361\pi\) | ||||
−0.267994 | + | 0.963421i | \(0.586361\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.2614 | 0.719849 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 33.6155i | − | 1.39943i | −0.714421 | − | 0.699716i | \(-0.753310\pi\) | ||
0.714421 | − | 0.699716i | \(-0.246690\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.68466 | −0.235839 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.75379i | 0.0726345i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.4384i | 0.472115i | 0.971739 | + | 0.236058i | \(0.0758554\pi\) | ||||
−0.971739 | + | 0.236058i | \(0.924145\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.56155 | −0.270364 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 24.4233i | − | 1.00294i | −0.865174 | − | 0.501472i | \(-0.832792\pi\) | ||
0.865174 | − | 0.501472i | \(-0.167208\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.12311 | 0.0460428 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.5616 | 0.921840 | 0.460920 | − | 0.887442i | \(-0.347519\pi\) | ||||
0.460920 | + | 0.887442i | \(0.347519\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.4924 | 0.917485 | 0.458743 | − | 0.888569i | \(-0.348300\pi\) | ||||
0.458743 | + | 0.888569i | \(0.348300\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 0.699813i | − | 0.0284515i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.492423 | 0.0199868 | 0.00999341 | − | 0.999950i | \(-0.496819\pi\) | ||||
0.00999341 | + | 0.999950i | \(0.496819\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.56155 | − | 16.2462i | 0.103629 | − | 0.657251i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 5.12311i | − | 0.206920i | −0.994634 | − | 0.103460i | \(-0.967009\pi\) | ||
0.994634 | − | 0.103460i | \(-0.0329914\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.8617i | 1.52426i | 0.647426 | + | 0.762128i | \(0.275845\pi\) | ||||
−0.647426 | + | 0.762128i | \(0.724155\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 2.24621i | − | 0.0902829i | −0.998981 | − | 0.0451414i | \(-0.985626\pi\) | ||
0.998981 | − | 0.0451414i | \(-0.0143738\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.68466 | −0.227751 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.3693 | 0.814773 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 26.7386i | − | 1.06445i | −0.846604 | − | 0.532224i | \(-0.821356\pi\) | ||
0.846604 | − | 0.532224i | \(-0.178644\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 7.01515i | − | 0.278388i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.56155 | + | 0.561553i | 0.141114 | + | 0.0222495i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.6847 | −1.33046 | −0.665232 | − | 0.746637i | \(-0.731667\pi\) | ||||
−0.665232 | + | 0.746637i | \(0.731667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.7538i | 0.857886i | 0.903332 | + | 0.428943i | \(0.141114\pi\) | ||||
−0.903332 | + | 0.428943i | \(0.858886\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.36932 | 0.289718 | 0.144859 | − | 0.989452i | \(-0.453727\pi\) | ||||
0.144859 | + | 0.989452i | \(0.453727\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −47.2311 | −1.85398 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.7538 | 0.459961 | 0.229981 | − | 0.973195i | \(-0.426134\pi\) | ||||
0.229981 | + | 0.973195i | \(0.426134\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.86174i | 0.150891i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.6695 | 1.27262 | 0.636312 | − | 0.771432i | \(-0.280459\pi\) | ||||
0.636312 | + | 0.771432i | \(0.280459\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 4.94602i | − | 0.192378i | −0.995363 | − | 0.0961890i | \(-0.969335\pi\) | ||
0.995363 | − | 0.0961890i | \(-0.0306653\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.43845i | − | 0.0557806i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.6695 | −0.490565 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 34.7386i | − | 1.34107i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.1771 | −0.392298 | −0.196149 | − | 0.980574i | \(-0.562844\pi\) | ||||
−0.196149 | + | 0.980574i | \(0.562844\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.73863 | −0.182120 | −0.0910602 | − | 0.995845i | \(-0.529026\pi\) | ||||
−0.0910602 | + | 0.995845i | \(0.529026\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.6847 | −0.601922 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1.36932i | − | 0.0523955i | −0.999657 | − | 0.0261977i | \(-0.991660\pi\) | ||
0.999657 | − | 0.0261977i | \(-0.00833995\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.01515 | 0.115203 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.00000 | − | 0.315342i | −0.0761939 | − | 0.0120136i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 5.93087i | − | 0.225621i | −0.993617 | − | 0.112810i | \(-0.964015\pi\) | ||
0.993617 | − | 0.112810i | \(-0.0359853\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 3.23106i | − | 0.122561i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.0000i | 0.757554i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.6695 | −1.15837 | −0.579186 | − | 0.815196i | \(-0.696629\pi\) | ||||
−0.579186 | + | 0.815196i | \(0.696629\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.36932i | 0.352369i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.7538i | 0.666758i | 0.942793 | + | 0.333379i | \(0.108189\pi\) | ||||
−0.942793 | + | 0.333379i | \(0.891811\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 9.43845i | − | 0.353473i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.24621 | − | 0.984845i | −0.233595 | − | 0.0368311i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.3542 | −1.50496 | −0.752478 | − | 0.658617i | \(-0.771142\pi\) | ||||
−0.752478 | + | 0.658617i | \(0.771142\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 1.75379i | − | 0.0653145i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.1080 | −0.598234 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.6155 | 0.653324 | 0.326662 | − | 0.945141i | \(-0.394076\pi\) | ||||
0.326662 | + | 0.945141i | \(0.394076\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.87689 | 0.106406 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 42.5616i | − | 1.57205i | −0.618197 | − | 0.786023i | \(-0.712136\pi\) | ||
0.618197 | − | 0.786023i | \(-0.287864\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 40.9848 | 1.50970 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 50.2462i | − | 1.84834i | −0.381985 | − | 0.924168i | \(-0.624760\pi\) | ||
0.381985 | − | 0.924168i | \(-0.375240\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 28.7386i | − | 1.05432i | −0.849767 | − | 0.527159i | \(-0.823257\pi\) | ||
0.849767 | − | 0.527159i | \(-0.176743\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.01515 | −0.110467 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.4924i | 0.602620i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.4384 | 1.07422 | 0.537112 | − | 0.843511i | \(-0.319515\pi\) | ||||
0.537112 | + | 0.843511i | \(0.319515\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.73863 | 0.245244 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.05398 | −0.329072 | −0.164536 | − | 0.986371i | \(-0.552613\pi\) | ||||
−0.164536 | + | 0.986371i | \(0.552613\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 23.9309i | − | 0.867493i | −0.901035 | − | 0.433747i | \(-0.857191\pi\) | ||
0.901035 | − | 0.433747i | \(-0.142809\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.12311 | 0.0406592 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.49242 | − | 53.8617i | 0.306644 | − | 1.94483i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 48.1771i | − | 1.73731i | −0.495418 | − | 0.868655i | \(-0.664985\pi\) | ||
0.495418 | − | 0.868655i | \(-0.335015\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.7538i | 0.566624i | 0.959028 | + | 0.283312i | \(0.0914333\pi\) | ||||
−0.959028 | + | 0.283312i | \(0.908567\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 12.0000i | − | 0.431053i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.6155 | 0.917772 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.2614 | −1.04705 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.63068i | 0.165276i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.80776i | 0.313963i | 0.987602 | + | 0.156981i | \(0.0501763\pi\) | ||||
−0.987602 | + | 0.156981i | \(0.949824\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 14.8078i | − | 0.526503i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 39.6155 | + | 6.24621i | 1.40679 | + | 0.221809i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.2311 | 1.46048 | 0.730239 | − | 0.683191i | \(-0.239408\pi\) | ||||
0.730239 | + | 0.683191i | \(0.239408\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.12311i | 0.322752i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −32.9848 | −1.16401 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.06913 | 0.0729273 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42.3153 | −1.48773 | −0.743864 | − | 0.668331i | \(-0.767009\pi\) | ||||
−0.743864 | + | 0.668331i | \(0.767009\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 36.0000i | − | 1.26413i | −0.774915 | − | 0.632065i | \(-0.782207\pi\) | ||
0.774915 | − | 0.632065i | \(-0.217793\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.86174 | −0.135271 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 3.68466i | − | 0.128910i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.50758i | 0.192216i | 0.995371 | + | 0.0961079i | \(0.0306394\pi\) | ||||
−0.995371 | + | 0.0961079i | \(0.969361\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.7386 | 1.48978 | 0.744888 | − | 0.667190i | \(-0.232503\pi\) | ||||
0.744888 | + | 0.667190i | \(0.232503\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 16.7386i | − | 0.582059i | −0.956714 | − | 0.291030i | \(-0.906002\pi\) | ||
0.956714 | − | 0.291030i | \(-0.0939978\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.7386 | −0.720283 | −0.360141 | − | 0.932898i | \(-0.617272\pi\) | ||||
−0.360141 | + | 0.932898i | \(0.617272\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.00000 | −0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.315342 | −0.0109128 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 3.12311i | − | 0.107822i | −0.998546 | − | 0.0539108i | \(-0.982831\pi\) | ||
0.998546 | − | 0.0539108i | \(-0.0171687\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.1771 | −0.592313 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.24621 | − | 6.94602i | 0.0772720 | − | 0.238951i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.24621i | 0.0428203i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.9309i | 1.57264i | 0.617818 | + | 0.786322i | \(0.288017\pi\) | ||||
−0.617818 | + | 0.786322i | \(0.711983\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.3693 | −0.866599 | −0.433300 | − | 0.901250i | \(-0.642651\pi\) | ||||
−0.433300 | + | 0.901250i | \(0.642651\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.12311 | −0.0383199 | −0.0191599 | − | 0.999816i | \(-0.506099\pi\) | ||||
−0.0191599 | + | 0.999816i | \(0.506099\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 40.1080i | − | 1.36529i | −0.730750 | − | 0.682645i | \(-0.760829\pi\) | ||
0.730750 | − | 0.682645i | \(-0.239171\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 2.73863i | − | 0.0931163i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 11.5076i | − | 0.390368i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.36932 | + | 46.7386i | −0.249700 | + | 1.58368i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.43845 | 0.183853 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 9.61553i | − | 0.324693i | −0.986734 | − | 0.162347i | \(-0.948094\pi\) | ||
0.986734 | − | 0.162347i | \(-0.0519063\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.2462 | 1.35593 | 0.677965 | − | 0.735095i | \(-0.262862\pi\) | ||||
0.677965 | + | 0.735095i | \(0.262862\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.75379 | 0.328241 | 0.164121 | − | 0.986440i | \(-0.447521\pi\) | ||||
0.164121 | + | 0.986440i | \(0.447521\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.8617 | −1.47273 | −0.736367 | − | 0.676583i | \(-0.763460\pi\) | ||||
−0.736367 | + | 0.676583i | \(0.763460\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.4924i | 0.418982i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.6847 | 0.391012 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.93087i | 0.198247i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.80776i | 0.293755i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.12311 | 0.0374161 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 9.75379i | − | 0.324227i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50.5616 | −1.67887 | −0.839434 | − | 0.543461i | \(-0.817114\pi\) | ||||
−0.839434 | + | 0.543461i | \(0.817114\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.8078 | −0.821918 | −0.410959 | − | 0.911654i | \(-0.634806\pi\) | ||||
−0.410959 | + | 0.911654i | \(0.634806\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.7538 | −0.587565 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 6.87689i | − | 0.227095i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.4924 | 0.412087 | 0.206043 | − | 0.978543i | \(-0.433941\pi\) | ||||
0.206043 | + | 0.978543i | \(0.433941\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.26137 | − | 33.3693i | 0.173180 | − | 1.09836i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.9309i | 1.31009i | 0.755590 | + | 0.655045i | \(0.227350\pi\) | ||||
−0.755590 | + | 0.655045i | \(0.772650\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.56155i | 0.0839515i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.50758 | 0.114710 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.8617 | 0.844866 | 0.422433 | − | 0.906394i | \(-0.361176\pi\) | ||||
0.422433 | + | 0.906394i | \(0.361176\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 43.9309i | − | 1.43211i | −0.698046 | − | 0.716053i | \(-0.745947\pi\) | ||
0.698046 | − | 0.716053i | \(-0.254053\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.8466i | 1.19989i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 18.4924i | − | 0.600923i | −0.953794 | − | 0.300461i | \(-0.902859\pi\) | ||
0.953794 | − | 0.300461i | \(-0.0971407\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.93087 | − | 37.6155i | 0.192524 | − | 1.22105i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.3153 | 1.11158 | 0.555791 | − | 0.831322i | \(-0.312415\pi\) | ||||
0.555791 | + | 0.831322i | \(0.312415\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 8.98485i | − | 0.290743i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.36932 | −0.173384 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.4384 | 0.788337 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.63068 | 0.277832 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 0.492423i | − | 0.0158352i | −0.999969 | − | 0.00791762i | \(-0.997480\pi\) | ||
0.999969 | − | 0.00791762i | \(-0.00252028\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.4773 | −1.33107 | −0.665534 | − | 0.746367i | \(-0.731796\pi\) | ||||
−0.665534 | + | 0.746367i | \(0.731796\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.75379i | 0.184458i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 61.3693i | 1.96338i | 0.190490 | + | 0.981689i | \(0.438992\pi\) | ||||
−0.190490 | + | 0.981689i | \(0.561008\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.7538 | −0.567414 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 36.5616i | − | 1.16613i | −0.812425 | − | 0.583066i | \(-0.801853\pi\) | ||
0.812425 | − | 0.583066i | \(-0.198147\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.0000 | 0.382352 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.30019 | 0.168536 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.75379 | −0.0557109 | −0.0278555 | − | 0.999612i | \(-0.508868\pi\) | ||||
−0.0278555 | + | 0.999612i | \(0.508868\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.3845i | 0.456018i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.1080 | 1.39691 | 0.698456 | − | 0.715653i | \(-0.253871\pi\) | ||||
0.698456 | + | 0.715653i | \(0.253871\pi\) | |||||||
\(998\) | 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 | 3276.2.e.e.2521.2 | 4 | ||
3.2 | odd | 2 | 1092.2.e.e.337.3 | yes | 4 | ||
12.11 | even | 2 | 4368.2.h.l.337.3 | 4 | |||
13.12 | even | 2 | inner | 3276.2.e.e.2521.3 | 4 | ||
21.20 | even | 2 | 7644.2.e.i.4705.2 | 4 | |||
39.38 | odd | 2 | 1092.2.e.e.337.2 | ✓ | 4 | ||
156.155 | even | 2 | 4368.2.h.l.337.2 | 4 | |||
273.272 | even | 2 | 7644.2.e.i.4705.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1092.2.e.e.337.2 | ✓ | 4 | 39.38 | odd | 2 | ||
1092.2.e.e.337.3 | yes | 4 | 3.2 | odd | 2 | ||
3276.2.e.e.2521.2 | 4 | 1.1 | even | 1 | trivial | ||
3276.2.e.e.2521.3 | 4 | 13.12 | even | 2 | inner | ||
4368.2.h.l.337.2 | 4 | 156.155 | even | 2 | |||
4368.2.h.l.337.3 | 4 | 12.11 | even | 2 | |||
7644.2.e.i.4705.2 | 4 | 21.20 | even | 2 | |||
7644.2.e.i.4705.3 | 4 | 273.272 | even | 2 |