Newspace parameters
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.w (of order \(6\), degree \(2\), not minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(18.1100711784\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.17213603549184.1 |
|
|
Defining polynomial: |
\( x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{9} \) |
Twist minimal: | no (minimal twist has level 756) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.4 | ||
Root | \(-0.385418 + 0.222521i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.269 |
Dual form | 2268.2.w.i.1349.4 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(5\) | 0.385418 | − | 0.667563i | 0.172364 | − | 0.298543i | −0.766882 | − | 0.641788i | \(-0.778193\pi\) |
0.939246 | + | 0.343245i | \(0.111526\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.37047 | − | 1.17511i | 0.895953 | − | 0.444148i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.68157 | − | 2.70291i | 1.41155 | − | 0.814957i | 0.416013 | − | 0.909359i | \(-0.363427\pi\) |
0.995534 | + | 0.0944018i | \(0.0300938\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.57338 | − | 2.64044i | 1.26843 | − | 0.732326i | 0.293736 | − | 0.955887i | \(-0.405101\pi\) |
0.974690 | + | 0.223560i | \(0.0717680\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.85433 | + | 4.94385i | −0.692277 | + | 1.19906i | 0.278813 | + | 0.960345i | \(0.410059\pi\) |
−0.971090 | + | 0.238713i | \(0.923274\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.535344 | − | 0.309081i | 0.122816 | − | 0.0709080i | −0.437333 | − | 0.899300i | \(-0.644077\pi\) |
0.560150 | + | 0.828391i | \(0.310744\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.83782 | + | 3.37047i | 1.21727 | + | 0.702791i | 0.964333 | − | 0.264691i | \(-0.0852700\pi\) |
0.252937 | + | 0.967483i | \(0.418603\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.20291 | + | 3.81555i | 0.440581 | + | 0.763109i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.99408 | − | 4.03803i | −1.29877 | − | 0.749844i | −0.318576 | − | 0.947897i | \(-0.603205\pi\) |
−0.980191 | + | 0.198053i | \(0.936538\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.580455i | − | 0.104253i | −0.998640 | − | 0.0521264i | \(-0.983400\pi\) | ||
0.998640 | − | 0.0521264i | \(-0.0165999\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.129163 | − | 2.03534i | 0.0218326 | − | 0.344036i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.53803 | − | 7.86010i | −0.746048 | − | 1.29219i | −0.949704 | − | 0.313150i | \(-0.898616\pi\) |
0.203656 | − | 0.979043i | \(-0.434718\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.29615 | + | 7.44116i | 0.670947 | + | 1.16211i | 0.977636 | + | 0.210304i | \(0.0674453\pi\) |
−0.306690 | + | 0.951810i | \(0.599221\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.70291 | + | 2.94952i | −0.259691 | + | 0.449798i | −0.966159 | − | 0.257947i | \(-0.916954\pi\) |
0.706468 | + | 0.707745i | \(0.250287\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.770835 | −0.112438 | −0.0562189 | − | 0.998418i | \(-0.517904\pi\) | ||||
−0.0562189 | + | 0.998418i | \(0.517904\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.23825 | − | 5.57111i | 0.605464 | − | 0.795872i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.63798 | − | 3.83244i | −0.911796 | − | 0.526426i | −0.0307875 | − | 0.999526i | \(-0.509802\pi\) |
−0.881009 | + | 0.473100i | \(0.843135\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.16699i | − | 0.561877i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.7885 | −1.79510 | −0.897552 | − | 0.440908i | \(-0.854657\pi\) | ||||
−0.897552 | + | 0.440908i | \(0.854657\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.12928i | − | 0.528701i | −0.964427 | − | 0.264350i | \(-0.914842\pi\) | ||
0.964427 | − | 0.264350i | \(-0.0851575\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 4.07069i | − | 0.504907i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.5526 | 1.65571 | 0.827855 | − | 0.560943i | \(-0.189561\pi\) | ||||
0.827855 | + | 0.560943i | \(0.189561\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.25906i | 0.268101i | 0.990974 | + | 0.134051i | \(0.0427985\pi\) | ||||
−0.990974 | + | 0.134051i | \(0.957202\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.96197 | + | 1.13274i | 0.229631 | + | 0.132577i | 0.610402 | − | 0.792092i | \(-0.291008\pi\) |
−0.380771 | + | 0.924669i | \(0.624341\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.92132 | − | 11.9085i | 0.902718 | − | 1.35710i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.07069 | −0.908023 | −0.454012 | − | 0.890996i | \(-0.650008\pi\) | ||||
−0.454012 | + | 0.890996i | \(0.650008\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.92709 | − | 3.33781i | 0.211525 | − | 0.366373i | −0.740667 | − | 0.671873i | \(-0.765490\pi\) |
0.952192 | + | 0.305500i | \(0.0988236\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.20022 | + | 3.81089i | 0.238647 | + | 0.413349i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.59808 | + | 4.50000i | 0.275396 | + | 0.476999i | 0.970235 | − | 0.242166i | \(-0.0778579\pi\) |
−0.694839 | + | 0.719165i | \(0.744525\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.73825 | − | 11.6333i | 0.811189 | − | 1.21950i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.476501i | − | 0.0488880i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.1468 | + | 7.01293i | 1.23332 | + | 0.712055i | 0.967720 | − | 0.252029i | \(-0.0810979\pi\) |
0.265596 | + | 0.964084i | \(0.414431\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.35241 | + | 11.0027i | 0.632088 | + | 1.09481i | 0.987124 | + | 0.159956i | \(0.0511352\pi\) |
−0.355036 | + | 0.934853i | \(0.615531\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.57069 | + | 1.48419i | 0.253297 | + | 0.146241i | 0.621273 | − | 0.783594i | \(-0.286616\pi\) |
−0.367976 | + | 0.929835i | \(0.619949\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.26891 | + | 2.46466i | −0.412691 | + | 0.238267i | −0.691945 | − | 0.721950i | \(-0.743246\pi\) |
0.279254 | + | 0.960217i | \(0.409913\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.40581 | − | 5.89904i | 0.326218 | − | 0.565026i | −0.655540 | − | 0.755160i | \(-0.727559\pi\) |
0.981758 | + | 0.190134i | \(0.0608924\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.48172 | − | 3.16487i | 0.515677 | − | 0.297726i | −0.219487 | − | 0.975615i | \(-0.570438\pi\) |
0.735164 | + | 0.677889i | \(0.237105\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.50000 | − | 2.59808i | 0.419627 | − | 0.242272i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.956559 | + | 15.0734i | −0.0876876 | + | 1.38177i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.11141 | − | 15.7814i | 0.828310 | − | 1.43467i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.25033 | 0.648489 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.41119 | −0.391430 | −0.195715 | − | 0.980661i | \(-0.562703\pi\) | ||||
−0.195715 | + | 0.980661i | \(0.562703\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.39600 | + | 7.61410i | −0.384080 | + | 0.665247i | −0.991641 | − | 0.129026i | \(-0.958815\pi\) |
0.607561 | + | 0.794273i | \(0.292148\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.905813 | − | 1.36175i | 0.0785440 | − | 0.118079i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.91281 | − | 2.25906i | 0.334294 | − | 0.193005i | −0.323452 | − | 0.946245i | \(-0.604843\pi\) |
0.657746 | + | 0.753240i | \(0.271510\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.64944 | − | 3.83906i | 0.563998 | − | 0.325624i | −0.190750 | − | 0.981639i | \(-0.561092\pi\) |
0.754749 | + | 0.656014i | \(0.227759\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.2737 | − | 24.7228i | 1.19363 | − | 2.06743i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.39128 | + | 3.11266i | −0.447721 | + | 0.258492i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.40674 | − | 4.27628i | −0.606784 | − | 0.350327i | 0.164922 | − | 0.986307i | \(-0.447263\pi\) |
−0.771706 | + | 0.635980i | \(0.780596\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.53803 | + | 6.12805i | 0.287921 | + | 0.498694i | 0.973313 | − | 0.229480i | \(-0.0737026\pi\) |
−0.685392 | + | 0.728174i | \(0.740369\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.387490 | − | 0.223717i | −0.0311239 | − | 0.0179694i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.6465i | − | 0.849682i | −0.905268 | − | 0.424841i | \(-0.860330\pi\) | ||
0.905268 | − | 0.424841i | \(-0.139670\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.7990 | + | 1.12953i | 1.40276 | + | 0.0890195i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.53534 | − | 13.0516i | −0.590214 | − | 1.02228i | −0.994203 | − | 0.107517i | \(-0.965710\pi\) |
0.403990 | − | 0.914764i | \(-0.367623\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.69215 | − | 15.0553i | −0.672619 | − | 1.16501i | −0.977159 | − | 0.212511i | \(-0.931836\pi\) |
0.304540 | − | 0.952500i | \(-0.401497\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.44385 | − | 12.8931i | 0.572603 | − | 0.991778i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.7554 | −1.50198 | −0.750989 | − | 0.660314i | \(-0.770423\pi\) | ||||
−0.750989 | + | 0.660314i | \(0.770423\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.70560 | + | 6.45599i | 0.733674 | + | 0.488027i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.1444 | − | 8.74363i | −1.13195 | − | 0.653529i | −0.187522 | − | 0.982260i | \(-0.560046\pi\) |
−0.944424 | + | 0.328731i | \(0.893379\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.11997i | 0.306235i | 0.988208 | + | 0.153118i | \(0.0489313\pi\) | ||||
−0.988208 | + | 0.153118i | \(0.951069\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.99615 | −0.514367 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 30.8600i | 2.25670i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.3696i | 1.03975i | 0.854244 | + | 0.519873i | \(0.174021\pi\) | ||||
−0.854244 | + | 0.519873i | \(0.825979\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.07069 | 0.149051 | 0.0745257 | − | 0.997219i | \(-0.476256\pi\) | ||||
0.0745257 | + | 0.997219i | \(0.476256\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.2881i | 1.44547i | 0.691126 | + | 0.722735i | \(0.257115\pi\) | ||||
−0.691126 | + | 0.722735i | \(0.742885\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.42394 | + | 3.13151i | 0.384493 | + | 0.221987i | 0.679771 | − | 0.733424i | \(-0.262079\pi\) |
−0.295279 | + | 0.955411i | \(0.595412\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −21.3244 | − | 1.35325i | −1.49668 | − | 0.0949794i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.62325 | 0.462588 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.67083 | − | 2.89397i | 0.115574 | − | 0.200180i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.86778 | − | 3.23509i | −0.128583 | − | 0.222713i | 0.794545 | − | 0.607206i | \(-0.207710\pi\) |
−0.923128 | + | 0.384493i | \(0.874376\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.31266 | + | 2.27359i | 0.0895227 | + | 0.155058i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.682096 | − | 1.37595i | −0.0463037 | − | 0.0934056i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30.1468i | 2.02789i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.7201 | − | 7.92132i | −0.918768 | − | 0.530451i | −0.0355260 | − | 0.999369i | \(-0.511311\pi\) |
−0.883242 | + | 0.468918i | \(0.844644\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.95640 | + | 3.38859i | 0.129851 | + | 0.224909i | 0.923619 | − | 0.383312i | \(-0.125217\pi\) |
−0.793768 | + | 0.608221i | \(0.791883\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.39397 | − | 2.53686i | −0.290362 | − | 0.167640i | 0.347743 | − | 0.937590i | \(-0.386948\pi\) |
−0.638105 | + | 0.769949i | \(0.720281\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.56891 | + | 0.905813i | −0.102783 | + | 0.0593418i | −0.550510 | − | 0.834828i | \(-0.685567\pi\) |
0.447727 | + | 0.894170i | \(0.352234\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.297093 | + | 0.514581i | −0.0193802 | + | 0.0335676i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.43813 | − | 4.29440i | 0.481132 | − | 0.277782i | −0.239756 | − | 0.970833i | \(-0.577067\pi\) |
0.720888 | + | 0.693051i | \(0.243734\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.6521 | − | 11.9235i | 1.33032 | − | 0.768061i | 0.344972 | − | 0.938613i | \(-0.387888\pi\) |
0.985349 | + | 0.170552i | \(0.0545551\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.08557 | − | 4.97650i | −0.133242 | − | 0.317937i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.63222 | − | 2.82709i | 0.103856 | − | 0.179883i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.25033 | −0.457637 | −0.228818 | − | 0.973469i | \(-0.573486\pi\) | ||||
−0.228818 | + | 0.973469i | \(0.573486\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36.4403 | 2.29098 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.2737 | − | 24.7228i | 0.890370 | − | 1.54217i | 0.0509387 | − | 0.998702i | \(-0.483779\pi\) |
0.839432 | − | 0.543465i | \(-0.182888\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.9937 | − | 13.2995i | −1.24235 | − | 0.826388i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.95640 | − | 1.12953i | 0.120637 | − | 0.0696498i | −0.438467 | − | 0.898747i | \(-0.644478\pi\) |
0.559104 | + | 0.829097i | \(0.311145\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.11679 | + | 2.95418i | −0.314322 | + | 0.181474i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.33605 | − | 14.4385i | 0.508258 | − | 0.880329i | −0.491696 | − | 0.870767i | \(-0.663623\pi\) |
0.999954 | − | 0.00956210i | \(-0.00304376\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.2528 | + | 15.7344i | −1.65549 | + | 0.955797i | −0.680730 | + | 0.732534i | \(0.738337\pi\) |
−0.974758 | + | 0.223263i | \(0.928329\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 20.6261 | + | 11.9085i | 1.24380 | + | 0.718110i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.51991 | − | 16.4890i | −0.571996 | − | 0.990726i | −0.996361 | − | 0.0852348i | \(-0.972836\pi\) |
0.424365 | − | 0.905491i | \(-0.360497\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.58142 | − | 3.79978i | −0.392614 | − | 0.226676i | 0.290678 | − | 0.956821i | \(-0.406119\pi\) |
−0.683292 | + | 0.730145i | \(0.739453\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.9824i | 1.84171i | 0.389903 | + | 0.920856i | \(0.372509\pi\) | ||||
−0.389903 | + | 0.920856i | \(0.627491\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.9281 | + | 12.5906i | 1.11729 | + | 0.743199i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.79440 | − | 13.5003i | −0.458494 | − | 0.794136i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.46891 | − | 4.27628i | −0.144235 | − | 0.249823i | 0.784852 | − | 0.619683i | \(-0.212739\pi\) |
−0.929087 | + | 0.369860i | \(0.879406\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.31431 | + | 9.20466i | −0.309411 | + | 0.535916i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 35.5981 | 2.05869 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.570688 | + | 8.99284i | −0.0328939 | + | 0.518339i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.75656 | − | 1.59150i | −0.157840 | − | 0.0911289i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.95736i | 0.454151i | 0.973877 | + | 0.227075i | \(0.0729164\pi\) | ||||
−0.973877 | + | 0.227075i | \(0.927084\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.87565 | 0.559997 | 0.279998 | − | 0.960000i | \(-0.409666\pi\) | ||||
0.279998 | + | 0.960000i | \(0.409666\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.8248i | 0.950993i | 0.879718 | + | 0.475496i | \(0.157732\pi\) | ||||
−0.879718 | + | 0.475496i | \(0.842268\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 24.7700i | − | 1.39122i | −0.718419 | − | 0.695611i | \(-0.755134\pi\) | ||
0.718419 | − | 0.695611i | \(-0.244866\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −43.6577 | −2.44436 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.52888i | 0.196352i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.1494 | + | 11.6333i | 1.11769 | + | 0.645299i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.82724 | + | 0.905813i | −0.100739 | + | 0.0499391i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.0054 | −0.989665 | −0.494833 | − | 0.868988i | \(-0.664771\pi\) | ||||
−0.494833 | + | 0.868988i | \(0.664771\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.22340 | − | 9.04719i | 0.285385 | − | 0.494301i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.60872 | − | 4.51844i | −0.142106 | − | 0.246135i | 0.786183 | − | 0.617993i | \(-0.212054\pi\) |
−0.928290 | + | 0.371858i | \(0.878721\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.56891 | − | 2.71744i | −0.0849615 | − | 0.147158i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.50000 | − | 18.1865i | 0.188982 | − | 0.981981i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.2828i | 0.874104i | 0.899436 | + | 0.437052i | \(0.143977\pi\) | ||||
−0.899436 | + | 0.437052i | \(0.856023\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.0734 | + | 8.70262i | 0.806859 | + | 0.465840i | 0.845864 | − | 0.533399i | \(-0.179085\pi\) |
−0.0390047 | + | 0.999239i | \(0.512419\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.9447 | + | 25.8850i | 0.795427 | + | 1.37772i | 0.922568 | + | 0.385835i | \(0.126087\pi\) |
−0.127141 | + | 0.991885i | \(0.540580\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.50807 | + | 0.870682i | 0.0800398 | + | 0.0462110i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.2700 | + | 11.7029i | −1.06981 | + | 0.617656i | −0.928130 | − | 0.372257i | \(-0.878584\pi\) |
−0.141681 | + | 0.989912i | \(0.545251\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.30894 | + | 16.1236i | −0.489944 | + | 0.848608i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.51235 | − | 0.873158i | 0.0791602 | − | 0.0457032i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.3696 | + | 10.0283i | −0.906684 | + | 0.523474i | −0.879363 | − | 0.476152i | \(-0.842031\pi\) |
−0.0273213 | + | 0.999627i | \(0.508698\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.2386 | − | 1.28435i | −1.05074 | − | 0.0666800i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.99462 | − | 6.91889i | 0.206834 | − | 0.358247i | −0.743882 | − | 0.668311i | \(-0.767017\pi\) |
0.950715 | + | 0.310065i | \(0.100351\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −42.6487 | −2.19652 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.5816 | −1.77634 | −0.888170 | − | 0.459516i | \(-0.848023\pi\) | ||||
−0.888170 | + | 0.459516i | \(0.848023\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.01058 | − | 6.94653i | 0.204931 | − | 0.354951i | −0.745180 | − | 0.666864i | \(-0.767636\pi\) |
0.950111 | + | 0.311913i | \(0.100970\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.89666 | − | 9.87772i | −0.249557 | − | 0.503415i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.9446 | − | 9.20560i | 0.808421 | − | 0.466742i | −0.0379861 | − | 0.999278i | \(-0.512094\pi\) |
0.846407 | + | 0.532536i | \(0.178761\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −33.3262 | + | 19.2409i | −1.68538 | + | 0.973052i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.11058 | + | 5.38769i | −0.156511 | + | 0.271084i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.9973 | + | 12.7002i | −1.10401 | + | 0.637402i | −0.937272 | − | 0.348598i | \(-0.886658\pi\) |
−0.166741 | + | 0.986001i | \(0.553324\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.43813 | − | 4.29440i | −0.371442 | − | 0.214452i | 0.302646 | − | 0.953103i | \(-0.402130\pi\) |
−0.674088 | + | 0.738651i | \(0.735463\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.53266 | − | 2.65464i | −0.0763470 | − | 0.132237i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −42.4902 | − | 24.5318i | −2.10616 | − | 1.21599i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.51112i | 0.173614i | 0.996225 | + | 0.0868069i | \(0.0276663\pi\) | ||||
−0.996225 | + | 0.0868069i | \(0.972334\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −32.6851 | + | 16.2029i | −1.60833 | + | 0.797293i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.48547 | − | 2.57290i | −0.0729187 | − | 0.126299i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.7862 | + | 25.6105i | 0.722355 | + | 1.25116i | 0.960054 | + | 0.279816i | \(0.0902735\pi\) |
−0.237699 | + | 0.971339i | \(0.576393\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.5172 | − | 19.9484i | 0.561315 | − | 0.972226i | −0.436067 | − | 0.899914i | \(-0.643629\pi\) |
0.997382 | − | 0.0723120i | \(-0.0230377\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −25.1513 | −1.22002 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.85235 | − | 9.78834i | −0.234822 | − | 0.473691i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.2386 | + | 11.6848i | 0.974861 | + | 0.562836i | 0.900715 | − | 0.434411i | \(-0.143043\pi\) |
0.0741463 | + | 0.997247i | \(0.476377\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.9199i | 1.82231i | 0.412059 | + | 0.911157i | \(0.364810\pi\) | ||||
−0.412059 | + | 0.911157i | \(0.635190\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.16699 | 0.199334 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 3.13783i | − | 0.149760i | −0.997193 | − | 0.0748802i | \(-0.976143\pi\) | ||
0.997193 | − | 0.0748802i | \(-0.0238574\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 24.2282i | − | 1.15112i | −0.817761 | − | 0.575558i | \(-0.804785\pi\) | ||
0.817761 | − | 0.575558i | \(-0.195215\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.00538 | 0.189873 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 25.1812i | − | 1.18837i | −0.804327 | − | 0.594187i | \(-0.797474\pi\) | ||
0.804327 | − | 0.594187i | \(-0.202526\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.2255 | + | 23.2242i | 1.89415 | + | 1.09359i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.78349 | − | 9.64944i | −0.224253 | − | 0.452373i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.2121 | −1.22615 | −0.613074 | − | 0.790025i | \(-0.710067\pi\) | ||||
−0.613074 | + | 0.790025i | \(0.710067\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.899998 | + | 1.55884i | −0.0419171 | + | 0.0726026i | −0.886223 | − | 0.463259i | \(-0.846680\pi\) |
0.844306 | + | 0.535862i | \(0.180013\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.2228 | + | 17.7064i | 0.475095 | + | 0.822888i | 0.999593 | − | 0.0285234i | \(-0.00908051\pi\) |
−0.524499 | + | 0.851411i | \(0.675747\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.25271 | − | 9.09797i | −0.243067 | − | 0.421004i | 0.718520 | − | 0.695507i | \(-0.244820\pi\) |
−0.961586 | + | 0.274503i | \(0.911487\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.1259 | − | 15.9257i | 1.48344 | − | 0.735381i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.4112i | 0.846547i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.35862 | + | 1.36175i | 0.108221 | + | 0.0624815i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.98349 | − | 5.16756i | −0.136319 | − | 0.236112i | 0.789781 | − | 0.613388i | \(-0.210194\pi\) |
−0.926101 | + | 0.377276i | \(0.876861\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.5083 | − | 23.9648i | −1.89261 | − | 1.09270i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.36314 | − | 5.40581i | 0.425158 | − | 0.245465i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.0199 | + | 20.8191i | −0.544674 | + | 0.943403i | 0.453953 | + | 0.891026i | \(0.350013\pi\) |
−0.998627 | + | 0.0523777i | \(0.983320\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.6697 | − | 10.7790i | 0.842553 | − | 0.486448i | −0.0155783 | − | 0.999879i | \(-0.504959\pi\) |
0.858131 | + | 0.513430i | \(0.171626\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.9268 | − | 23.0518i | 1.79821 | − | 1.03820i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.65464 | + | 5.35504i | 0.119077 | + | 0.240206i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.4257 | + | 24.9861i | −0.645784 | + | 1.11853i | 0.338336 | + | 0.941025i | \(0.390136\pi\) |
−0.984120 | + | 0.177505i | \(0.943197\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.7805 | 0.926555 | 0.463278 | − | 0.886213i | \(-0.346673\pi\) | ||||
0.463278 | + | 0.886213i | \(0.346673\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.79331 | 0.435797 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.7027 | + | 22.0018i | −0.563039 | + | 0.975212i | 0.434190 | + | 0.900821i | \(0.357035\pi\) |
−0.997229 | + | 0.0743909i | \(0.976299\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.98188 | + | 0.379611i | 0.264623 | + | 0.0167930i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.98158 | − | 1.14406i | 0.0873187 | − | 0.0504135i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.60872 | + | 2.08350i | −0.158711 | + | 0.0916320i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.02709 | + | 1.77897i | −0.0449976 | + | 0.0779381i | −0.887647 | − | 0.460524i | \(-0.847661\pi\) |
0.842649 | + | 0.538463i | \(0.180995\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.81790 | + | 5.66837i | −0.429307 | + | 0.247860i | −0.699051 | − | 0.715071i | \(-0.746394\pi\) |
0.269744 | + | 0.962932i | \(0.413061\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.86968 | + | 1.65681i | 0.125005 | + | 0.0721717i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2201 | + | 19.4338i | 0.487832 | + | 0.844949i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 39.2959 | + | 22.6875i | 1.70209 | + | 0.982704i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.79969i | 0.164275i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.78349 | − | 37.5371i | 0.206040 | − | 1.61684i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.39128 | − | 16.2662i | −0.403763 | − | 0.699337i | 0.590414 | − | 0.807101i | \(-0.298965\pi\) |
−0.994177 | + | 0.107763i | \(0.965631\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.62532 | − | 4.54719i | −0.112456 | − | 0.194780i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.45928 | − | 5.99165i | 0.147908 | − | 0.256184i | −0.782546 | − | 0.622593i | \(-0.786079\pi\) |
0.930454 | + | 0.366408i | \(0.119413\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.99231 | −0.212680 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.1313 | + | 9.48392i | −0.813546 | + | 0.403297i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.00704 | − | 5.20022i | −0.381641 | − | 0.220340i | 0.296891 | − | 0.954911i | \(-0.404050\pi\) |
−0.678532 | + | 0.734571i | \(0.737383\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.9857i | 0.760714i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.02148 | −0.253775 | −0.126887 | − | 0.991917i | \(-0.540499\pi\) | ||||
−0.126887 | + | 0.991917i | \(0.540499\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 4.87919i | − | 0.205269i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.3534i | 1.23056i | 0.788309 | + | 0.615280i | \(0.210957\pi\) | ||||
−0.788309 | + | 0.615280i | \(0.789043\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.2282 | 0.720977 | 0.360489 | − | 0.932764i | \(-0.382610\pi\) | ||||
0.360489 | + | 0.932764i | \(0.382610\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29.6993i | 1.23855i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.85594 | + | 1.07153i | 0.0772636 | + | 0.0446082i | 0.538134 | − | 0.842859i | \(-0.319129\pi\) |
−0.460870 | + | 0.887467i | \(0.652463\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.645816 | − | 10.1767i | 0.0267930 | − | 0.422201i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −41.4349 | −1.71606 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.79200 | + | 15.2282i | −0.362885 | + | 0.628535i | −0.988434 | − | 0.151650i | \(-0.951541\pi\) |
0.625550 | + | 0.780184i | \(0.284875\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.179407 | − | 0.310743i | −0.00739235 | − | 0.0128039i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.1469 | + | 21.0391i | 0.498815 | + | 0.863973i | 0.999999 | − | 0.00136757i | \(-0.000435311\pi\) |
−0.501184 | + | 0.865341i | \(0.667102\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.69375 | + | 6.44811i | 0.397405 | + | 0.264347i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 37.8116i | − | 1.54494i | −0.635051 | − | 0.772471i | \(-0.719021\pi\) | ||
0.635051 | − | 0.772471i | \(-0.280979\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.51344 | − | 1.45114i | −0.102525 | − | 0.0591931i | 0.447861 | − | 0.894103i | \(-0.352186\pi\) |
−0.550386 | + | 0.834910i | \(0.685519\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.02339 | − | 12.1649i | −0.285542 | − | 0.494572i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.67403 | − | 5.58530i | −0.392657 | − | 0.226701i | 0.290654 | − | 0.956828i | \(-0.406127\pi\) |
−0.683311 | + | 0.730128i | \(0.739461\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.52532 | + | 2.03534i | −0.142619 | + | 0.0823412i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.12953 | + | 14.0808i | −0.328349 | + | 0.568717i | −0.982184 | − | 0.187920i | \(-0.939825\pi\) |
0.653836 | + | 0.756637i | \(0.273159\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.62501 | − | 2.67025i | 0.186196 | − | 0.107500i | −0.404005 | − | 0.914757i | \(-0.632382\pi\) |
0.590200 | + | 0.807257i | \(0.299049\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.3669 | + | 10.6041i | −0.738227 | + | 0.426216i | −0.821424 | − | 0.570317i | \(-0.806820\pi\) |
0.0831972 | + | 0.996533i | \(0.473487\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.4466 | + | 7.61410i | 0.458600 | + | 0.305052i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.22013 | + | 14.2377i | −0.328805 | + | 0.569507i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 51.8122 | 2.06589 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.7338 | 1.78082 | 0.890411 | − | 0.455157i | \(-0.150417\pi\) | ||||
0.890411 | + | 0.455157i | \(0.150417\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.70015 | + | 2.94475i | −0.0674684 | + | 0.116859i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.67294 | − | 36.6696i | 0.185149 | − | 1.45290i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.6508 | − | 13.6548i | 0.934152 | − | 0.539333i | 0.0460296 | − | 0.998940i | \(-0.485343\pi\) |
0.888122 | + | 0.459607i | \(0.152010\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.9429 | + | 17.8649i | −1.22027 | + | 0.704524i | −0.964976 | − | 0.262340i | \(-0.915506\pi\) |
−0.255295 | + | 0.966863i | \(0.582173\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.4537 | + | 35.4268i | −0.804117 | + | 1.39277i | 0.112768 | + | 0.993621i | \(0.464028\pi\) |
−0.916885 | + | 0.399150i | \(0.869305\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −64.5517 | + | 37.2689i | −2.53387 | + | 1.46293i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.5825 | − | 13.0380i | −0.883723 | − | 0.510218i | −0.0118388 | − | 0.999930i | \(-0.503768\pi\) |
−0.871884 | + | 0.489712i | \(0.837102\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.38859 | + | 5.86921i | 0.132403 | + | 0.229329i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.3830 | + | 20.4284i | 1.37833 | + | 0.795778i | 0.991958 | − | 0.126566i | \(-0.0403956\pi\) |
0.386370 | + | 0.922344i | \(0.373729\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.25780i | 0.282296i | 0.989989 | + | 0.141148i | \(0.0450793\pi\) | ||||
−0.989989 | + | 0.141148i | \(0.954921\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.559939 | − | 1.12953i | −0.0217135 | − | 0.0438013i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −27.2201 | − | 47.1466i | −1.05397 | − | 1.82553i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.1611 | − | 19.3315i | −0.430868 | − | 0.746286i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.6233 | + | 30.5244i | −0.679326 | + | 1.17663i | 0.295858 | + | 0.955232i | \(0.404395\pi\) |
−0.975184 | + | 0.221396i | \(0.928939\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.9634 | −0.421359 | −0.210680 | − | 0.977555i | \(-0.567568\pi\) | ||||
−0.210680 | + | 0.977555i | \(0.567568\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.0344 | + | 2.35021i | 1.42125 | + | 0.0901929i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.70628 | − | 4.44922i | −0.294873 | − | 0.170245i | 0.345265 | − | 0.938505i | \(-0.387789\pi\) |
−0.640137 | + | 0.768261i | \(0.721123\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 3.48273i | − | 0.133068i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −40.4773 | −1.54206 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.40607i | 0.319782i | 0.987135 | + | 0.159891i | \(0.0511143\pi\) | ||||
−0.987135 | + | 0.159891i | \(0.948886\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 5.91856i | − | 0.224504i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −49.0506 | −1.85792 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 28.3351i | − | 1.07020i | −0.844788 | − | 0.535101i | \(-0.820273\pi\) | ||
0.844788 | − | 0.535101i | \(-0.179727\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.85881 | − | 2.80524i | −0.183254 | − | 0.105802i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.9875 | + | 18.6168i | 1.05258 | + | 0.700156i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.0868 | −0.904599 | −0.452300 | − | 0.891866i | \(-0.649396\pi\) | ||||
−0.452300 | + | 0.891866i | \(0.649396\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.95640 | − | 3.38859i | 0.0732679 | − | 0.126904i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.0027 | − | 19.0572i | −0.411477 | − | 0.712699i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.57083 | − | 4.45281i | −0.0958759 | − | 0.166062i | 0.814098 | − | 0.580728i | \(-0.197232\pi\) |
−0.909974 | + | 0.414666i | \(0.863899\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.83781 | + | 0.497389i | 0.291895 | + | 0.0185237i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 35.5816i | − | 1.32147i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.99193 | − | 3.45945i | −0.222229 | − | 0.128304i | 0.384753 | − | 0.923019i | \(-0.374287\pi\) |
−0.606982 | + | 0.794716i | \(0.707620\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.72132 | − | 16.8378i | −0.359556 | − | 0.622769i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.8940 | − | 8.59904i | −0.550121 | − | 0.317613i | 0.199050 | − | 0.979989i | \(-0.436215\pi\) |
−0.749171 | + | 0.662377i | \(0.769548\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 63.4473 | − | 36.6313i | 2.33711 | − | 1.34933i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.6114 | − | 18.3795i | 0.390347 | − | 0.676101i | −0.602148 | − | 0.798384i | \(-0.705688\pi\) |
0.992495 | + | 0.122284i | \(0.0390217\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.1891 | + | 16.8523i | −1.07085 | + | 0.618253i | −0.928412 | − | 0.371552i | \(-0.878826\pi\) |
−0.142433 | + | 0.989804i | \(0.545492\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.70937 | + | 3.29631i | −0.209175 | + | 0.120767i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.22309 | + | 10.8588i | −0.263926 | + | 0.396772i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.41119 | + | 4.17630i | −0.0879856 | + | 0.152395i | −0.906660 | − | 0.421863i | \(-0.861376\pi\) |
0.818674 | + | 0.574259i | \(0.194710\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.45448 | 0.198509 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.30426 | −0.265478 | −0.132739 | − | 0.991151i | \(-0.542377\pi\) | ||||
−0.132739 | + | 0.991151i | \(0.542377\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.91925 | + | 13.7165i | −0.287072 | + | 0.497224i | −0.973110 | − | 0.230342i | \(-0.926015\pi\) |
0.686037 | + | 0.727566i | \(0.259349\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.14138 | − | 17.9857i | 0.0413206 | − | 0.651126i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −63.0598 | + | 36.4076i | −2.27696 | + | 1.31460i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.9810 | − | 23.6604i | 1.47781 | − | 0.853215i | 0.478126 | − | 0.878291i | \(-0.341316\pi\) |
0.999686 | + | 0.0250761i | \(0.00798279\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.5173 | − | 18.2165i | 0.378282 | − | 0.655203i | −0.612531 | − | 0.790447i | \(-0.709848\pi\) |
0.990812 | + | 0.135244i | \(0.0431817\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.21475 | − | 1.27869i | 0.0795562 | − | 0.0459318i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.59984 | + | 2.65572i | 0.164806 | + | 0.0951510i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.10603 | + | 10.5760i | 0.218491 | + | 0.378437i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.10720 | − | 4.10334i | −0.253667 | − | 0.146455i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.0152i | 1.39074i | 0.718652 | + | 0.695370i | \(0.244760\pi\) | ||||
−0.718652 | + | 0.695370i | \(0.755240\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.27519 | − | 13.9438i | 0.329788 | − | 0.495786i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.9031 | − | 18.8848i | −0.387181 | − | 0.670618i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.8426 | + | 27.4403i | 0.561175 | + | 0.971984i | 0.997394 | + | 0.0721433i | \(0.0229839\pi\) |
−0.436219 | + | 0.899840i | \(0.643683\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.20022 | − | 3.81089i | 0.0778381 | − | 0.134820i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.2468 | 0.432180 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.61410 | − | 11.4466i | 0.268362 | − | 0.403441i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.93123 | + | 1.11500i | 0.0678985 | + | 0.0392012i | 0.533565 | − | 0.845759i | \(-0.320852\pi\) |
−0.465666 | + | 0.884960i | \(0.654185\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 55.3535i | 1.94373i | 0.235548 | + | 0.971863i | \(0.424312\pi\) | ||||
−0.235548 | + | 0.971863i | \(0.575688\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.6170 | −0.406926 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.10534i | 0.0736566i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45.9821i | 1.60479i | 0.596797 | + | 0.802393i | \(0.296440\pi\) | ||||
−0.596797 | + | 0.802393i | \(0.703560\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.2989 | 1.47445 | 0.737223 | − | 0.675649i | \(-0.236137\pi\) | ||||
0.737223 | + | 0.675649i | \(0.236137\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.1105i | 0.734084i | 0.930204 | + | 0.367042i | \(0.119630\pi\) | ||||
−0.930204 | + | 0.367042i | \(0.880370\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.3615 | + | 27.3442i | 1.64493 | + | 0.949703i | 0.979043 | + | 0.203652i | \(0.0652812\pi\) |
0.665890 | + | 0.746050i | \(0.268052\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.4453 | + | 36.8550i | 0.535149 | + | 1.27695i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.4004 | −0.463741 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.6825 | + | 37.5553i | −0.748564 | + | 1.29655i | 0.199947 | + | 0.979807i | \(0.435923\pi\) |
−0.948511 | + | 0.316745i | \(0.897410\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.1114 | + | 31.3699i | 0.624531 | + | 1.08172i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.73798 | − | 9.93847i | −0.197392 | − | 0.341894i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.05347 | − | 48.1163i | 0.104918 | − | 1.65329i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 61.1812i | − | 2.09726i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.0353 | + | 13.2995i | 0.788715 | + | 0.455365i | 0.839510 | − | 0.543344i | \(-0.182842\pi\) |
−0.0507949 | + | 0.998709i | \(0.516175\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.8155 | − | 25.6613i | −0.506090 | − | 0.876573i | −0.999975 | − | 0.00704593i | \(-0.997757\pi\) |
0.493886 | − | 0.869527i | \(-0.335576\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.19285 | − | 2.42074i | −0.143058 | − | 0.0825947i | 0.426763 | − | 0.904364i | \(-0.359654\pi\) |
−0.569821 | + | 0.821769i | \(0.692987\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.0258 | + | 10.9846i | −0.647647 | + | 0.373919i | −0.787554 | − | 0.616246i | \(-0.788653\pi\) |
0.139907 | + | 0.990165i | \(0.455320\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.61410 | + | 13.1880i | −0.258887 | + | 0.448406i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −37.7835 | + | 21.8143i | −1.28172 | + | 0.740000i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 61.9810 | − | 35.7847i | 2.10015 | − | 1.21252i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.1867 | − | 8.51991i | 0.581016 | − | 0.288026i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.2989 | − | 36.8907i | 0.719212 | − | 1.24571i | −0.242100 | − | 0.970251i | \(-0.577836\pi\) |
0.961312 | − | 0.275461i | \(-0.0888304\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.2523 | −1.38982 | −0.694912 | − | 0.719095i | \(-0.744557\pi\) | ||||
−0.694912 | + | 0.719095i | \(0.744557\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.21206 | 0.141747 | 0.0708736 | − | 0.997485i | \(-0.477421\pi\) | ||||
0.0708736 | + | 0.997485i | \(0.477421\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.79585 | − | 3.11051i | 0.0602988 | − | 0.104441i | −0.834300 | − | 0.551310i | \(-0.814128\pi\) |
0.894599 | + | 0.446870i | \(0.147461\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.4566 | + | 5.18362i | −0.350703 | + | 0.173853i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.412662 | + | 0.238250i | −0.0138092 | + | 0.00797275i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.6738 | + | 6.73989i | −0.390213 | + | 0.225290i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.34389 | + | 4.05974i | −0.0781733 | + | 0.135400i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.8940 | − | 21.8781i | 1.26243 | − | 0.728865i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.75034 | + | 1.58791i | 0.0914244 | + | 0.0527839i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.92394 | − | 5.06440i | −0.0970877 | − | 0.168161i | 0.813390 | − | 0.581718i | \(-0.197619\pi\) |
−0.910478 | + | 0.413558i | \(0.864286\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.58142 | + | 3.79978i | 0.218052 | + | 0.125892i | 0.605048 | − | 0.796189i | \(-0.293154\pi\) |
−0.386996 | + | 0.922081i | \(0.626487\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 20.8350i | − | 0.689536i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.47321 | + | 23.2148i | −0.0486498 | + | 0.766619i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.3062 | − | 23.0471i | −0.438933 | − | 0.760254i | 0.558675 | − | 0.829387i | \(-0.311310\pi\) |
−0.997607 | + | 0.0691331i | \(0.977977\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.96492 | + | 10.3315i | 0.196338 | + | 0.340067i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.9937 | − | 34.6301i | 0.657390 | − | 1.13863i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52.4113 | 1.71956 | 0.859779 | − | 0.510667i | \(-0.170601\pi\) | ||||
0.859779 | + | 0.510667i | \(0.170601\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.546998 | − | 4.29242i | 0.0179271 | − | 0.140678i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.6010 | + | 11.8940i | 0.673723 | + | 0.388974i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 49.0719i | − | 1.60311i | −0.597922 | − | 0.801554i | \(-0.704007\pi\) | ||
0.597922 | − | 0.801554i | \(-0.295993\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.4638 | 0.895294 | 0.447647 | − | 0.894210i | \(-0.352262\pi\) | ||||
0.447647 | + | 0.894210i | \(0.352262\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 57.9202i | 1.88614i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 58.9512i | − | 1.91566i | −0.287341 | − | 0.957828i | \(-0.592771\pi\) | ||
0.287341 | − | 0.957828i | \(-0.407229\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.9638 | 0.388360 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 16.6649i | − | 0.539828i | −0.962884 | − | 0.269914i | \(-0.913005\pi\) | ||
0.962884 | − | 0.269914i | \(-0.0869953\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.59259 | + | 5.53828i | 0.310409 | + | 0.179215i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.62056 | − | 9.95300i | 0.213789 | − | 0.321399i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.6631 | 0.989131 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.798079 | − | 1.38231i | 0.0256911 | − | 0.0444983i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.6729 | − | 20.2181i | −0.375376 | − | 0.650171i | 0.615007 | − | 0.788522i | \(-0.289153\pi\) |
−0.990383 | + | 0.138351i | \(0.955820\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.66507 | − | 13.2763i | −0.245984 | − | 0.426056i | 0.716424 | − | 0.697665i | \(-0.245778\pi\) |
−0.962408 | + | 0.271609i | \(0.912444\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.2510 | − | 16.9142i | 0.360690 | − | 0.542243i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 19.7463i | − | 0.631741i | −0.948802 | − | 0.315870i | \(-0.897704\pi\) | ||
0.948802 | − | 0.315870i | \(-0.102296\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.3262 | + | 14.0447i | 0.777467 | + | 0.448871i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.4194 | − | 19.7790i | −0.364222 | − | 0.630851i | 0.624429 | − | 0.781082i | \(-0.285332\pi\) |
−0.988651 | + | 0.150230i | \(0.951998\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.5436 | + | 7.81940i | 0.431535 | + | 0.249147i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.8825 | + | 11.4792i | −0.632228 | + | 0.365017i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.92125 | + | 6.79180i | −0.124563 | + | 0.215749i | −0.921562 | − | 0.388232i | \(-0.873086\pi\) |
0.796999 | + | 0.603980i | \(0.206419\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.18096 | − | 2.41388i | 0.132545 | − | 0.0765251i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.608720 | + | 0.351445i | −0.0192783 | + | 0.0111304i | −0.509608 | − | 0.860407i | \(-0.670210\pi\) |
0.490330 | + | 0.871537i | \(0.336876\pi\) | |||||||
\(998\) | 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 | 2268.2.w.i.269.4 | 12 | ||
3.2 | odd | 2 | inner | 2268.2.w.i.269.3 | 12 | ||
7.5 | odd | 6 | 2268.2.bm.i.593.4 | 12 | |||
9.2 | odd | 6 | 756.2.t.e.269.3 | ✓ | 12 | ||
9.4 | even | 3 | 2268.2.bm.i.1025.3 | 12 | |||
9.5 | odd | 6 | 2268.2.bm.i.1025.4 | 12 | |||
9.7 | even | 3 | 756.2.t.e.269.4 | yes | 12 | ||
21.5 | even | 6 | 2268.2.bm.i.593.3 | 12 | |||
63.5 | even | 6 | inner | 2268.2.w.i.1349.4 | 12 | ||
63.11 | odd | 6 | 5292.2.f.e.2645.7 | 12 | |||
63.25 | even | 3 | 5292.2.f.e.2645.6 | 12 | |||
63.38 | even | 6 | 5292.2.f.e.2645.5 | 12 | |||
63.40 | odd | 6 | inner | 2268.2.w.i.1349.3 | 12 | ||
63.47 | even | 6 | 756.2.t.e.593.4 | yes | 12 | ||
63.52 | odd | 6 | 5292.2.f.e.2645.8 | 12 | |||
63.61 | odd | 6 | 756.2.t.e.593.3 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.t.e.269.3 | ✓ | 12 | 9.2 | odd | 6 | ||
756.2.t.e.269.4 | yes | 12 | 9.7 | even | 3 | ||
756.2.t.e.593.3 | yes | 12 | 63.61 | odd | 6 | ||
756.2.t.e.593.4 | yes | 12 | 63.47 | even | 6 | ||
2268.2.w.i.269.3 | 12 | 3.2 | odd | 2 | inner | ||
2268.2.w.i.269.4 | 12 | 1.1 | even | 1 | trivial | ||
2268.2.w.i.1349.3 | 12 | 63.40 | odd | 6 | inner | ||
2268.2.w.i.1349.4 | 12 | 63.5 | even | 6 | inner | ||
2268.2.bm.i.593.3 | 12 | 21.5 | even | 6 | |||
2268.2.bm.i.593.4 | 12 | 7.5 | odd | 6 | |||
2268.2.bm.i.1025.3 | 12 | 9.4 | even | 3 | |||
2268.2.bm.i.1025.4 | 12 | 9.5 | odd | 6 | |||
5292.2.f.e.2645.5 | 12 | 63.38 | even | 6 | |||
5292.2.f.e.2645.6 | 12 | 63.25 | even | 3 | |||
5292.2.f.e.2645.7 | 12 | 63.11 | odd | 6 | |||
5292.2.f.e.2645.8 | 12 | 63.52 | odd | 6 |