Newspace parameters
Level: | \( N \) | \(=\) | \( 468 = 2^{2} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 468.bz (of order \(12\), degree \(4\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(3.73699881460\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 401.1 | ||
Character | \(\chi\) | \(=\) | 468.401 |
Dual form | 468.2.bz.a.461.1 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/468\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(209\) | \(235\) |
\(\chi(n)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.71575 | + | 0.237081i | −0.990588 | + | 0.136879i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.786297 | − | 2.93450i | −0.351642 | − | 1.31235i | −0.884657 | − | 0.466242i | \(-0.845608\pi\) |
0.533015 | − | 0.846106i | \(-0.321059\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.474592 | + | 0.474592i | −0.179379 | + | 0.179379i | −0.791085 | − | 0.611706i | \(-0.790483\pi\) |
0.611706 | + | 0.791085i | \(0.290483\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.88759 | − | 0.813543i | 0.962528 | − | 0.271181i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.52204 | + | 1.21168i | −1.36345 | + | 0.365335i | −0.865081 | − | 0.501632i | \(-0.832733\pi\) |
−0.498366 | + | 0.866967i | \(0.666066\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.60335 | + | 0.125867i | 0.999390 | + | 0.0349091i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.04480 | + | 4.84845i | 0.527965 | + | 1.25186i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.61521 | + | 6.26173i | −0.876817 | + | 1.51869i | −0.0220024 | + | 0.999758i | \(0.507004\pi\) |
−0.854815 | + | 0.518934i | \(0.826329\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.17267 | + | 1.11806i | −0.957277 | + | 0.256502i | −0.703447 | − | 0.710747i | \(-0.748357\pi\) |
−0.253830 | + | 0.967249i | \(0.581690\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.701763 | − | 0.926797i | 0.153137 | − | 0.202244i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.46204 | −0.304857 | −0.152428 | − | 0.988315i | \(-0.548709\pi\) | ||||
−0.152428 | + | 0.988315i | \(0.548709\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.66289 | + | 2.11477i | −0.732579 | + | 0.422954i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.76149 | + | 2.08043i | −0.916350 | + | 0.400378i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.82932 | − | 2.21086i | −0.711087 | − | 0.410546i | 0.100376 | − | 0.994950i | \(-0.467995\pi\) |
−0.811463 | + | 0.584403i | \(0.801329\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.38143 | + | 0.370153i | −0.248112 | + | 0.0664815i | −0.380732 | − | 0.924686i | \(-0.624328\pi\) |
0.132619 | + | 0.991167i | \(0.457661\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.47142 | − | 3.15102i | 1.30061 | − | 0.548523i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.76586 | + | 1.01952i | 0.298485 | + | 0.172330i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.14370 | − | 0.306454i | −0.188023 | − | 0.0503807i | 0.163579 | − | 0.986530i | \(-0.447696\pi\) |
−0.351602 | + | 0.936150i | \(0.614363\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.21229 | + | 0.638331i | −0.994762 | + | 0.102215i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.55355 | + | 5.55355i | −0.867319 | + | 0.867319i | −0.992175 | − | 0.124856i | \(-0.960153\pi\) |
0.124856 | + | 0.992175i | \(0.460153\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.46907i | 1.44402i | 0.691883 | + | 0.722010i | \(0.256782\pi\) | ||||
−0.691883 | + | 0.722010i | \(0.743218\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.65784 | − | 7.83393i | −0.694350 | − | 1.16781i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.93010 | − | 7.20323i | 0.281534 | − | 1.05070i | −0.669801 | − | 0.742541i | \(-0.733621\pi\) |
0.951335 | − | 0.308159i | \(-0.0997128\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.54953i | 0.935646i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.71825 | − | 11.6006i | 0.660687 | − | 1.62441i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 7.46793i | − | 1.02580i | −0.858449 | − | 0.512900i | \(-0.828571\pi\) | ||
0.858449 | − | 0.512900i | \(-0.171429\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.11133 | + | 12.3172i | 0.958892 | + | 1.66085i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.89419 | − | 2.90758i | 0.913157 | − | 0.385118i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.07072 | − | 3.99596i | 0.139395 | − | 0.520230i | −0.860546 | − | 0.509373i | \(-0.829877\pi\) |
0.999941 | − | 0.0108571i | \(-0.00345598\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.61574 | −0.719022 | −0.359511 | − | 0.933141i | \(-0.617056\pi\) | ||||
−0.359511 | + | 0.933141i | \(0.617056\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.984323 | + | 1.75652i | −0.124013 | + | 0.221301i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.46395 | − | 10.6730i | −0.305615 | − | 1.32382i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.82399 | − | 4.82399i | −0.589345 | − | 0.589345i | 0.348109 | − | 0.937454i | \(-0.386824\pi\) |
−0.937454 | + | 0.348109i | \(0.886824\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.50850 | − | 0.346623i | 0.301987 | − | 0.0417284i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.32349 | + | 8.67138i | 0.275747 | + | 1.02910i | 0.955339 | + | 0.295513i | \(0.0954904\pi\) |
−0.679591 | + | 0.733591i | \(0.737843\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.37710 | − | 8.37710i | 0.980466 | − | 0.980466i | −0.0193471 | − | 0.999813i | \(-0.506159\pi\) |
0.999813 | + | 0.0193471i | \(0.00615876\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.78323 | − | 4.49682i | 0.667790 | − | 0.519248i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.57107 | − | 2.72118i | 0.179040 | − | 0.310107i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.30240 | + | 10.9161i | 0.709076 | + | 1.22816i | 0.965200 | + | 0.261512i | \(0.0842210\pi\) |
−0.256125 | + | 0.966644i | \(0.582446\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.67630 | − | 4.69835i | 0.852922 | − | 0.522039i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.29206 | − | 1.15005i | −0.471114 | − | 0.126235i | 0.0154478 | − | 0.999881i | \(-0.495083\pi\) |
−0.486562 | + | 0.873646i | \(0.661749\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.2177 | + | 5.68525i | 2.30138 | + | 0.616652i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.09431 | + | 2.88542i | 0.760589 | + | 0.309349i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.16797 | + | 8.09097i | −0.229804 | + | 0.857641i | 0.750618 | + | 0.660736i | \(0.229756\pi\) |
−0.980423 | + | 0.196905i | \(0.936911\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.76986 | + | 1.65039i | −0.185531 | + | 0.173008i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.28243 | − | 0.962601i | 0.236677 | − | 0.0998170i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.56192 | + | 11.3656i | 0.673239 | + | 1.16608i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.0288 | − | 11.0288i | −1.11980 | − | 1.11980i | −0.991770 | − | 0.128034i | \(-0.959133\pi\) |
−0.128034 | − | 0.991770i | \(-0.540867\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.0720 | + | 7.17770i | −1.21328 | + | 0.721386i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.88792 | − | 8.46612i | 0.486366 | − | 0.842411i | −0.513511 | − | 0.858083i | \(-0.671655\pi\) |
0.999877 | + | 0.0156721i | \(0.00498879\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.73205 | − | 5.61880i | −0.958928 | − | 0.553637i | −0.0630850 | − | 0.998008i | \(-0.520094\pi\) |
−0.895843 | + | 0.444371i | \(0.853427\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.27148 | − | 1.33059i | −0.319264 | − | 0.129852i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.6940 | − | 8.48360i | 1.42052 | − | 0.820140i | 0.424181 | − | 0.905577i | \(-0.360562\pi\) |
0.996344 | + | 0.0854370i | \(0.0272286\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.514307 | + | 0.514307i | 0.0492617 | + | 0.0492617i | 0.731309 | − | 0.682047i | \(-0.238910\pi\) |
−0.682047 | + | 0.731309i | \(0.738910\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.03496 | + | 0.254648i | 0.193150 | + | 0.0241701i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.52098 | + | 4.91959i | −0.801586 | + | 0.462796i | −0.844026 | − | 0.536303i | \(-0.819820\pi\) |
0.0424393 | + | 0.999099i | \(0.486487\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.14960 | + | 4.29036i | 0.107201 | + | 0.400078i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.5074 | − | 2.56803i | 0.971408 | − | 0.237415i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.25601 | − | 4.68751i | −0.115139 | − | 0.429703i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.45443 | − | 5.45852i | 0.859493 | − | 0.496229i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.21186 | − | 10.8451i | 0.740438 | − | 0.977874i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.65509 | − | 1.65509i | −0.148036 | − | 0.148036i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.2584 | − | 7.07742i | 1.08776 | − | 0.628019i | 0.154782 | − | 0.987949i | \(-0.450533\pi\) |
0.932980 | + | 0.359929i | \(0.117199\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.24494 | − | 16.2465i | −0.197656 | − | 1.43043i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.29027 | − | 1.32229i | −0.200101 | − | 0.115529i | 0.396601 | − | 0.917991i | \(-0.370190\pi\) |
−0.596703 | + | 0.802462i | \(0.703523\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.44969 | − | 2.51094i | 0.125704 | − | 0.217726i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.84896 | + | 12.3368i | 0.847663 | + | 1.06178i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.0685980 | − | 0.0685980i | −0.00586072 | − | 0.00586072i | 0.704170 | − | 0.710031i | \(-0.251319\pi\) |
−0.710031 | + | 0.704170i | \(0.751319\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.04452 | − | 10.4694i | −0.512690 | − | 0.888004i | −0.999892 | − | 0.0147152i | \(-0.995316\pi\) |
0.487202 | − | 0.873289i | \(-0.338017\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.60382 | + | 12.8165i | −0.135066 | + | 1.07935i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.4470 | + | 3.79693i | −1.37537 | + | 0.317515i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.47678 | + | 12.9755i | −0.288731 | + | 1.07756i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.55277 | − | 11.2373i | −0.128070 | − | 0.926840i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.1989 | − | 3.26870i | −0.999377 | − | 0.267782i | −0.278192 | − | 0.960525i | \(-0.589735\pi\) |
−0.721184 | + | 0.692743i | \(0.756402\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.4834 | − | 3.88081i | −1.17864 | − | 0.315816i | −0.384253 | − | 0.923228i | \(-0.625541\pi\) |
−0.794387 | + | 0.607412i | \(0.792208\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.34504 | + | 21.0224i | −0.432121 | + | 1.69956i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.17243 | + | 3.76276i | 0.174494 | + | 0.302232i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.33213 | + | 2.30731i | −0.106315 | + | 0.184144i | −0.914275 | − | 0.405094i | \(-0.867239\pi\) |
0.807960 | + | 0.589238i | \(0.200572\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.77051 | + | 12.8131i | 0.140410 | + | 1.01614i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.693873 | − | 0.693873i | 0.0546849 | − | 0.0546849i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.21282 | − | 4.52631i | −0.0949955 | − | 0.354528i | 0.902023 | − | 0.431687i | \(-0.142082\pi\) |
−0.997019 | + | 0.0771594i | \(0.975415\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −15.1214 | − | 19.4472i | −1.17720 | − | 1.51397i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.0290 | − | 11.0290i | −0.853451 | − | 0.853451i | 0.137106 | − | 0.990556i | \(-0.456220\pi\) |
−0.990556 | + | 0.137106i | \(0.956220\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9683 | + | 0.907085i | 0.997563 | + | 0.0697757i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.1394 | + | 6.62316i | −0.851848 | + | 0.506485i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.0109 | −1.52140 | −0.760702 | − | 0.649101i | \(-0.775145\pi\) | ||||
−0.760702 | + | 0.649101i | \(0.775145\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.734725 | − | 2.74203i | 0.0555400 | − | 0.207278i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.889710 | + | 7.10991i | −0.0668747 | + | 0.534414i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.74519 | + | 9.95097i | 0.429416 | + | 0.743770i | 0.996821 | − | 0.0796682i | \(-0.0253861\pi\) |
−0.567405 | + | 0.823439i | \(0.692053\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 26.1318i | 1.94236i | 0.238350 | + | 0.971179i | \(0.423394\pi\) | ||||
−0.238350 | + | 0.971179i | \(0.576606\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.63519 | − | 1.33139i | 0.712254 | − | 0.0984188i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.59715i | 0.264468i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.76094 | − | 32.6963i | 0.640663 | − | 2.39099i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.27241 | − | 3.24712i | 0.0925544 | − | 0.236193i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.37903i | 0.172141i | 0.996289 | + | 0.0860703i | \(0.0274310\pi\) | ||||
−0.996289 | + | 0.0860703i | \(0.972569\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.7424 | + | 11.7424i | −0.845238 | + | 0.845238i | −0.989535 | − | 0.144296i | \(-0.953908\pi\) |
0.144296 | + | 0.989535i | \(0.453908\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.75788 | + | 17.7280i | 0.483942 | + | 1.26953i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.6064 | + | 6.32532i | 1.68189 | + | 0.450660i | 0.968276 | − | 0.249882i | \(-0.0803917\pi\) |
0.713611 | + | 0.700542i | \(0.247058\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.8808 | − | 6.85940i | −0.842210 | − | 0.486250i | 0.0158050 | − | 0.999875i | \(-0.494969\pi\) |
−0.858015 | + | 0.513625i | \(0.828302\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.42044 | + | 7.13308i | 0.664466 | + | 0.503129i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.86662 | − | 0.768109i | 0.201197 | − | 0.0539107i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.6636 | + | 11.9302i | 1.44321 | + | 0.833238i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.22177 | + | 1.18943i | −0.293433 | + | 0.0826714i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.5143 | − | 10.1119i | 1.21149 | − | 0.699453i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.7322 | −1.01420 | −0.507102 | − | 0.861886i | \(-0.669283\pi\) | ||||
−0.507102 | + | 0.861886i | \(0.669283\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.04234 | − | 14.3270i | −0.414014 | − | 0.981673i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 27.7870 | − | 7.44550i | 1.89506 | − | 0.507779i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.479944 | − | 0.831287i | 0.0325807 | − | 0.0564314i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.3869 | + | 16.3591i | −0.837032 | + | 1.10544i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.8150 | + | 22.1082i | −0.929299 | + | 1.48716i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.5686 | − | 6.85108i | 1.71220 | − | 0.458782i | 0.736236 | − | 0.676725i | \(-0.236601\pi\) |
0.975962 | + | 0.217942i | \(0.0699345\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.85646 | + | 9.08651i | −0.590430 | + | 0.605767i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.57813 | − | 2.57813i | 0.171117 | − | 0.171117i | −0.616353 | − | 0.787470i | \(-0.711391\pi\) |
0.787470 | + | 0.616353i | \(0.211391\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.18957 | − | 11.9036i | −0.210773 | − | 0.786614i | −0.987612 | − | 0.156915i | \(-0.949845\pi\) |
0.776840 | − | 0.629699i | \(-0.216822\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.05042 | + | 5.04132i | −0.134908 | + | 0.331695i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.46997 | 0.0963010 | 0.0481505 | − | 0.998840i | \(-0.484667\pi\) | ||||
0.0481505 | + | 0.998840i | \(0.484667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.6555 | −1.47788 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.4013 | − | 17.2351i | −0.870510 | − | 1.11954i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.07490 | + | 4.01157i | 0.0695293 | + | 0.259487i | 0.991937 | − | 0.126730i | \(-0.0404482\pi\) |
−0.922408 | + | 0.386217i | \(0.873782\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.19628 | + | 6.19628i | −0.399137 | + | 0.399137i | −0.877929 | − | 0.478791i | \(-0.841075\pi\) |
0.478791 | + | 0.877929i | \(0.341075\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.0567 | + | 9.88109i | −0.773438 | + | 0.633872i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 19.2196 | − | 5.14987i | 1.22789 | − | 0.329013i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.1763 | + | 3.50358i | −0.965648 | + | 0.222928i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.63674 | + | 0.955636i | 0.483959 | + | 0.0605610i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.12469 | + | 14.0724i | −0.512826 | + | 0.888240i | 0.487064 | + | 0.873367i | \(0.338068\pi\) |
−0.999889 | + | 0.0148739i | \(0.995265\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.61142 | − | 1.77152i | 0.415656 | − | 0.111375i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −37.7520 | − | 4.72416i | −2.36412 | − | 0.295838i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.63406 | 0.101930 | 0.0509648 | − | 0.998700i | \(-0.483770\pi\) | ||||
0.0509648 | + | 0.998700i | \(0.483770\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.688231 | − | 0.397350i | 0.0427646 | − | 0.0246902i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.8561 | − | 3.26873i | −0.795774 | − | 0.202329i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.9065 | + | 7.45155i | 0.795846 | + | 0.459482i | 0.842017 | − | 0.539452i | \(-0.181368\pi\) |
−0.0461705 | + | 0.998934i | \(0.514702\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.9146 | + | 5.87201i | −1.34621 | + | 0.360715i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.80147 | − | 14.3960i | 0.110248 | − | 0.881024i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.95682 | − | 1.70712i | −0.180280 | − | 0.104085i | 0.407144 | − | 0.913364i | \(-0.366525\pi\) |
−0.587424 | + | 0.809279i | \(0.699858\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.83826 | − | 2.36821i | −0.536886 | − | 0.143858i | −0.0198199 | − | 0.999804i | \(-0.506309\pi\) |
−0.517066 | + | 0.855945i | \(0.672976\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.64535 | − | 3.25125i | 0.160104 | − | 0.196774i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.0013 | − | 14.0013i | 0.844312 | − | 0.844312i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 8.61864i | − | 0.517844i | −0.965898 | − | 0.258922i | \(-0.916633\pi\) | ||
0.965898 | − | 0.258922i | \(-0.0833673\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.68786 | + | 2.19270i | −0.220787 | + | 0.131274i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.0542955 | − | 0.202633i | 0.00323900 | − | 0.0120881i | −0.964287 | − | 0.264858i | \(-0.914675\pi\) |
0.967526 | + | 0.252770i | \(0.0813416\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.0339i | 1.36922i | 0.728907 | + | 0.684612i | \(0.240028\pi\) | ||||
−0.728907 | + | 0.684612i | \(0.759972\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −13.9532 | − | 17.9448i | −0.826514 | − | 1.06296i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 5.27134i | − | 0.311157i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.6395 | − | 30.5525i | −1.03762 | − | 1.79720i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.5373 | + | 16.3079i | 1.26254 | + | 0.955986i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.67234 | + | 24.9015i | −0.389803 | + | 1.45476i | 0.440653 | + | 0.897678i | \(0.354747\pi\) |
−0.830455 | + | 0.557085i | \(0.811920\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.5680 | −0.731740 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 19.0109 | − | 15.1772i | 1.10312 | − | 0.880669i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.26825 | − | 0.184022i | −0.304671 | − | 0.0106423i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.49394 | − | 4.49394i | −0.259027 | − | 0.259027i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.37928 | + | 15.6846i | −0.366480 | + | 0.901055i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.41564 | + | 16.4794i | 0.252839 | + | 0.943606i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.1111 | − | 23.1111i | 1.31902 | − | 1.31902i | 0.404467 | − | 0.914553i | \(-0.367457\pi\) |
0.914553 | − | 0.404467i | \(-0.132543\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.0299 | + | 7.33317i | 1.02568 | + | 0.417169i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.87785 | + | 15.3769i | −0.503417 | + | 0.871943i | 0.496576 | + | 0.867993i | \(0.334591\pi\) |
−0.999992 | + | 0.00394966i | \(0.998743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.89955 | − | 8.48627i | −0.276939 | − | 0.479672i | 0.693684 | − | 0.720280i | \(-0.255987\pi\) |
−0.970622 | + | 0.240608i | \(0.922653\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.92849 | + | 1.50735i | 0.334033 | + | 0.0849293i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.1289 | + | 2.71402i | 0.568894 | + | 0.152435i | 0.531789 | − | 0.846877i | \(-0.321520\pi\) |
0.0371046 | + | 0.999311i | \(0.488187\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.9952 | + | 5.35770i | 1.11952 | + | 0.299974i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −23.1999 | + | 18.0394i | −1.29489 | + | 1.00686i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.08407 | − | 30.1702i | 0.449810 | − | 1.67871i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.4649 | + | 7.15924i | −0.746897 | + | 0.397123i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.00435 | − | 0.760489i | −0.0555409 | − | 0.0420552i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.50259 | + | 4.33461i | 0.137972 | + | 0.238975i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9971 | − | 10.9971i | −0.604458 | − | 0.604458i | 0.337034 | − | 0.941492i | \(-0.390576\pi\) |
−0.941492 | + | 0.337034i | \(0.890576\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.55185 | + | 0.0455386i | −0.194640 | + | 0.00249550i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.3629 | + | 17.9491i | −0.566187 | + | 0.980664i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.3011 | + | 9.41142i | 0.887975 | + | 0.512673i | 0.873280 | − | 0.487219i | \(-0.161989\pi\) |
0.0146957 | + | 0.999892i | \(0.495322\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.4535 | − | 10.4609i | 0.730695 | − | 0.568160i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.79838 | − | 3.34770i | 0.314000 | − | 0.181288i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.43049 | − | 6.43049i | −0.347214 | − | 0.347214i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.98959 | − | 7.08863i | −0.160954 | − | 0.381639i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.2620 | − | 6.50212i | 0.604576 | − | 0.349052i | −0.166264 | − | 0.986081i | \(-0.553170\pi\) |
0.770840 | + | 0.637029i | \(0.219837\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.09300 | + | 19.0073i | 0.272622 | + | 1.01744i | 0.957418 | + | 0.288705i | \(0.0932247\pi\) |
−0.684796 | + | 0.728735i | \(0.740109\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.4192 | + | 6.89720i | −0.929768 | + | 0.368145i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.521426 | − | 1.94599i | −0.0277527 | − | 0.103575i | 0.950660 | − | 0.310234i | \(-0.100407\pi\) |
−0.978413 | + | 0.206660i | \(0.933741\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.6192 | − | 13.6366i | 1.25358 | − | 0.723753i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.26633 | + | 7.74481i | 0.172872 | + | 0.409899i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.9143 | + | 12.9143i | 0.681589 | + | 0.681589i | 0.960358 | − | 0.278769i | \(-0.0899263\pi\) |
−0.278769 | + | 0.960358i | \(0.589926\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.293341 | + | 0.169361i | −0.0154390 | + | 0.00891372i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.9273 | + | 11.6069i | −0.783480 | + | 0.609205i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −31.1695 | − | 17.9957i | −1.63149 | − | 0.941938i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.46432 | + | 11.1965i | −0.337435 | + | 0.584454i | −0.983949 | − | 0.178447i | \(-0.942893\pi\) |
0.646515 | + | 0.762902i | \(0.276226\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.5183 | + | 20.5544i | −0.599619 | + | 1.07002i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.54422 | + | 3.54422i | 0.184007 | + | 0.184007i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.1109 | + | 19.2446i | 0.575301 | + | 0.996450i | 0.996009 | + | 0.0892538i | \(0.0284482\pi\) |
−0.420708 | + | 0.907196i | \(0.638218\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.23212 | + | 2.44733i | 0.166906 | + | 0.126380i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.5201 | − | 8.44850i | −0.696322 | − | 0.435120i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.09076 | − | 26.4631i | 0.364228 | − | 1.35932i | −0.504237 | − | 0.863565i | \(-0.668226\pi\) |
0.868465 | − | 0.495751i | \(-0.165107\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.3545 | + | 15.0493i | −0.991561 | + | 0.771000i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.64541 | − | 1.78063i | −0.339564 | − | 0.0909860i | 0.0850073 | − | 0.996380i | \(-0.472909\pi\) |
−0.424572 | + | 0.905394i | \(0.639575\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.22062 | − | 2.47066i | −0.469926 | − | 0.125916i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.70350 | + | 27.3428i | 0.391591 | + | 1.38991i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.10145 | + | 8.83597i | 0.258654 | + | 0.448002i | 0.965882 | − | 0.258984i | \(-0.0833878\pi\) |
−0.707228 | + | 0.706986i | \(0.750054\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.28559 | − | 9.15491i | 0.267304 | − | 0.462983i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.24301 | + | 1.72573i | 0.214032 | + | 0.0870516i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 27.0777 | − | 27.0777i | 1.36243 | − | 1.36243i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.15554 | − | 19.2407i | −0.258749 | − | 0.965665i | −0.965966 | − | 0.258669i | \(-0.916716\pi\) |
0.707217 | − | 0.706997i | \(-0.249950\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.89201 | + | 4.65184i | −0.0947190 | + | 0.232883i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.4659 | + | 18.4659i | 0.922144 | + | 0.922144i | 0.997181 | − | 0.0750371i | \(-0.0239075\pi\) |
−0.0750371 | + | 0.997181i | \(0.523908\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.02437 | + | 1.15992i | −0.250282 | + | 0.0577796i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −19.8231 | − | 18.8318i | −0.985020 | − | 0.935759i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.54319 | 0.274766 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.2504 | − | 38.2549i | 0.506849 | − | 1.89159i | 0.0572376 | − | 0.998361i | \(-0.481771\pi\) |
0.449611 | − | 0.893224i | \(-0.351563\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.133960 | + | 0.101434i | 0.00660777 | + | 0.00500335i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.38830 | + | 2.40460i | 0.0683137 | + | 0.118323i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.4993i | 0.662655i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.8530 | + | 16.5298i | 0.629413 | + | 0.809470i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 4.13333i | − | 0.201926i | −0.994890 | − | 0.100963i | \(-0.967808\pi\) | ||
0.994890 | − | 0.100963i | \(-0.0321924\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.174519 | + | 0.651312i | −0.00850551 | + | 0.0317430i | −0.970048 | − | 0.242913i | \(-0.921897\pi\) |
0.961543 | + | 0.274656i | \(0.0885638\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.286811 | − | 22.3702i | −0.0139452 | − | 1.08768i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 30.5814i | − | 1.48341i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.66518 | − | 2.66518i | 0.128977 | − | 0.128977i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 27.3188 | − | 10.4139i | 1.31896 | − | 0.502786i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.1112 | + | 4.04903i | 0.727879 | + | 0.195035i | 0.603685 | − | 0.797223i | \(-0.293699\pi\) |
0.124195 | + | 0.992258i | \(0.460365\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.7772 | + | 18.9239i | 1.57517 | + | 0.909427i | 0.995519 | + | 0.0945639i | \(0.0301457\pi\) |
0.579654 | + | 0.814863i | \(0.303188\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.88903 | − | 23.0870i | 0.138518 | − | 1.10694i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.10062 | − | 1.63466i | 0.291832 | − | 0.0781963i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.8319 | − | 10.8726i | −0.898799 | − | 0.518922i | −0.0219889 | − | 0.999758i | \(-0.507000\pi\) |
−0.876810 | + | 0.480836i | \(0.840333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.32832 | + | 18.9123i | 0.253730 | + | 0.900586i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.49013 | − | 0.860330i | 0.0707984 | − | 0.0408755i | −0.464183 | − | 0.885739i | \(-0.653652\pi\) |
0.534981 | + | 0.844864i | \(0.320319\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.4476 | 1.20633 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.7053 | + | 2.71612i | 1.02662 | + | 0.128468i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.08109 | + | 1.89737i | −0.334177 | + | 0.0895425i | −0.422006 | − | 0.906593i | \(-0.638674\pi\) |
0.0878286 | + | 0.996136i | \(0.472007\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.3843 | − | 31.8425i | 0.865682 | − | 1.49941i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 25.7699 | + | 3.22476i | 1.21078 | + | 0.151512i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.23469 | + | 3.89595i | 0.292287 | + | 0.182645i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.08759 | + | 1.09527i | −0.191210 | + | 0.0512345i | −0.353153 | − | 0.935566i | \(-0.614890\pi\) |
0.161943 | + | 0.986800i | \(0.448224\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.18673 | − | 37.3363i | 0.195420 | − | 1.74271i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.1299 | − | 17.1299i | 0.797821 | − | 0.797821i | −0.184931 | − | 0.982752i | \(-0.559206\pi\) |
0.982752 | + | 0.184931i | \(0.0592060\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.81468 | − | 6.77247i | −0.0843353 | − | 0.314744i | 0.910852 | − | 0.412733i | \(-0.135426\pi\) |
−0.995187 | + | 0.0979891i | \(0.968759\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.61942 | − | 5.94090i | −0.214220 | − | 0.275503i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.8585 | −1.70561 | −0.852804 | − | 0.522231i | \(-0.825100\pi\) | ||||
−0.852804 | + | 0.522231i | \(0.825100\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.57886 | 0.211432 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.73857 | − | 4.27459i | 0.0801093 | − | 0.196963i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.4735 | − | 42.8196i | −0.527550 | − | 1.96885i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.9196 | − | 12.9196i | 0.592792 | − | 0.592792i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.07548 | − | 21.5643i | −0.278177 | − | 0.987361i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.5400 | − | 4.43188i | 0.755732 | − | 0.202498i | 0.139673 | − | 0.990198i | \(-0.455395\pi\) |
0.616059 | + | 0.787700i | \(0.288728\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.08259 | − | 1.24821i | −0.186150 | − | 0.0569137i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.02601 | + | 1.35502i | −0.0466849 | + | 0.0616553i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.6921 | + | 41.0359i | −1.07580 | + | 1.86334i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.2868 | + | 3.02430i | −0.511455 | + | 0.137044i | −0.505311 | − | 0.862937i | \(-0.668622\pi\) |
−0.00614389 | + | 0.999981i | \(0.501956\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.15400 | + | 7.47847i | 0.142629 | + | 0.338188i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.9782 | 1.03699 | 0.518496 | − | 0.855080i | \(-0.326492\pi\) | ||||
0.518496 | + | 0.855080i | \(0.326492\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.6876 | − | 15.9854i | 1.24699 | − | 0.719948i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 30.5551 | + | 29.7816i | 1.37335 | + | 1.33858i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.21807 | − | 3.01266i | −0.234063 | − | 0.135136i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.3864 | + | 3.31892i | −0.554491 | + | 0.148575i | −0.525174 | − | 0.850995i | \(-0.676000\pi\) |
−0.0293168 | + | 0.999570i | \(0.509333\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.5378 | + | 16.3082i | 0.962237 | + | 0.728599i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.38363 | − | 0.798839i | −0.0616930 | − | 0.0356184i | 0.468836 | − | 0.883285i | \(-0.344673\pi\) |
−0.530529 | + | 0.847667i | \(0.678007\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.6872 | − | 7.68671i | −1.27656 | − | 0.342054i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.4654 | + | 1.51821i | −0.997724 | + | 0.0674262i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.0128 | + | 18.0128i | −0.798403 | + | 0.798403i | −0.982844 | − | 0.184441i | \(-0.940953\pi\) |
0.184441 | + | 0.982844i | \(0.440953\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.95141i | 0.351750i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.5421 | − | 14.0046i | 0.774503 | − | 0.618318i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.83609 | + | 32.9767i | −0.389365 | + | 1.45313i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.9120i | 1.53543i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 34.3337 | − | 4.74422i | 1.50708 | − | 0.208248i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 24.5314i | − | 1.07474i | −0.843346 | − | 0.537370i | \(-0.819418\pi\) | ||
0.843346 | − | 0.537370i | \(-0.180582\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.69447 | + | 6.39900i | 0.161548 | + | 0.279809i | 0.935424 | − | 0.353528i | \(-0.115018\pi\) |
−0.773876 | + | 0.633337i | \(0.781685\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.610520 | + | 4.87883i | −0.0266453 | + | 0.212929i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.67636 | − | 9.98832i | 0.116584 | − | 0.435098i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.8624 | −0.907062 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.159107 | − | 12.4098i | −0.00690465 | − | 0.538538i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20.7104 | + | 19.3124i | −0.897068 | + | 0.836513i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −36.4490 | − | 36.4490i | −1.57583 | − | 1.57583i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.2165 | − | 15.7113i | −0.527181 | − | 0.677992i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.93591 | − | 29.6172i | −0.341824 | − | 1.27570i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.03374 | + | 5.03374i | −0.216418 | + | 0.216418i | −0.806987 | − | 0.590569i | \(-0.798903\pi\) |
0.590569 | + | 0.806987i | \(0.298903\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.19535 | − | 44.8355i | −0.265868 | − | 1.92408i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.10484 | − | 1.91363i | 0.0473260 | − | 0.0819710i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.69757 | + | 16.7967i | 0.414638 | + | 0.718174i | 0.995390 | − | 0.0959061i | \(-0.0305748\pi\) |
−0.580752 | + | 0.814080i | \(0.697242\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.2159 | + | 4.56864i | −0.692079 | + | 0.194985i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.4504 | + | 4.94377i | 0.786013 | + | 0.210612i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.17175 | − | 2.18961i | −0.347498 | − | 0.0931119i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.852817 | − | 6.17181i | −0.0362000 | − | 0.261979i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.5583 | + | 39.4040i | −0.447368 | + | 1.66960i | 0.262238 | + | 0.965003i | \(0.415540\pi\) |
−0.709606 | + | 0.704598i | \(0.751127\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.19184 | + | 34.1204i | −0.0504095 | + | 1.44314i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.27990 | + | 58.1756i | −0.307357 | + | 2.45618i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.5011 | + | 21.6525i | 0.526858 | + | 0.912544i | 0.999510 | + | 0.0312954i | \(0.00996326\pi\) |
−0.472652 | + | 0.881249i | \(0.656703\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.1365 | + | 21.1365i | 0.889221 | + | 0.889221i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.41331 | + | 5.87290i | −0.0593534 | + | 0.246639i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.30226 | + | 9.18378i | −0.222282 | + | 0.385004i | −0.955501 | − | 0.294989i | \(-0.904684\pi\) |
0.733218 | + | 0.679993i | \(0.238017\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.4489 | + | 6.61000i | 0.479120 | + | 0.276620i | 0.720050 | − | 0.693923i | \(-0.244119\pi\) |
−0.240930 | + | 0.970543i | \(0.577452\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.564023 | − | 4.08182i | −0.0235624 | − | 0.170520i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.35530 | − | 3.09189i | 0.223332 | − | 0.128941i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.9959 | + | 17.9959i | 0.749178 | + | 0.749178i | 0.974325 | − | 0.225147i | \(-0.0722861\pi\) |
−0.225147 | + | 0.974325i | \(0.572286\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.3631 | − | 22.9310i | 0.721587 | − | 0.952978i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.58278 | − | 1.49117i | 0.107152 | − | 0.0618641i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.04872 | + | 33.7703i | 0.374760 | + | 1.39862i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.7978 | − | 28.8147i | −0.653159 | − | 1.19134i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.52782 | − | 20.6301i | −0.228158 | − | 0.851496i | −0.981115 | − | 0.193426i | \(-0.938040\pi\) |
0.752957 | − | 0.658069i | \(-0.228627\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.35040 | − | 3.08906i | 0.220460 | − | 0.127282i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −42.0023 | − | 5.25602i | −1.72774 | − | 0.216204i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.0256 | + | 22.0256i | 0.904484 | + | 0.904484i | 0.995820 | − | 0.0913365i | \(-0.0291139\pi\) |
−0.0913365 | + | 0.995820i | \(0.529114\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.7679 | + | 7.37155i | −0.523433 | + | 0.302204i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.0107 | + | 8.95228i | 0.900840 | + | 0.366393i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.0092 | + | 8.08823i | 0.572401 | + | 0.330476i | 0.758108 | − | 0.652129i | \(-0.226124\pi\) |
−0.185707 | + | 0.982605i | \(0.559457\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.07380 | − | 5.32398i | 0.125383 | − | 0.217170i | −0.796500 | − | 0.604639i | \(-0.793317\pi\) |
0.921883 | + | 0.387469i | \(0.126651\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.8542 | − | 10.0052i | −0.727080 | − | 0.407442i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23.4520 | − | 23.4520i | −0.953459 | − | 0.953459i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.0178799 | + | 0.0309689i | 0.000725723 | + | 0.00125699i | 0.866388 | − | 0.499371i | \(-0.166436\pi\) |
−0.865662 | + | 0.500628i | \(0.833102\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.73630 | + | 1.99750i | −0.191924 | + | 0.0809429i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.86148 | − | 25.7129i | 0.318042 | − | 1.04023i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.11344 | + | 7.88746i | −0.0853610 | + | 0.318572i | −0.995382 | − | 0.0959899i | \(-0.969398\pi\) |
0.910021 | + | 0.414561i | \(0.136065\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −38.2820 | − | 15.5702i | −1.54368 | − | 0.627851i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.5850 | + | 4.97983i | 0.748203 | + | 0.200480i | 0.612721 | − | 0.790299i | \(-0.290075\pi\) |
0.135482 | + | 0.990780i | \(0.456742\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.6220 | − | 4.72181i | −0.708290 | − | 0.189786i | −0.113349 | − | 0.993555i | \(-0.536158\pi\) |
−0.594941 | + | 0.803770i | \(0.702824\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.96150 | − | 3.04167i | 0.279356 | − | 0.122058i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.81101 | − | 4.86881i | −0.112621 | − | 0.195065i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.1293 | + | 24.4727i | −0.565174 | + | 0.978909i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −27.6528 | + | 21.5017i | −1.10434 | + | 0.858696i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.05365 | − | 6.05365i | 0.241375 | − | 0.241375i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.96498 | + | 33.4578i | 0.356890 | + | 1.33193i | 0.878089 | + | 0.478497i | \(0.158818\pi\) |
−0.521199 | + | 0.853435i | \(0.674515\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.2767 | − | 3.49272i | 1.00466 | − | 0.138823i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30.4074 | − | 30.4074i | −1.20668 | − | 1.20668i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.824367 | + | 23.6003i | −0.0326626 | + | 0.935076i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.7638 | + | 23.1491i | 0.544488 | + | 0.915764i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.60735 | −0.142482 | −0.0712409 | − | 0.997459i | \(-0.522696\pi\) | ||||
−0.0712409 | + | 0.997459i | \(0.522696\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.92452 | + | 14.6465i | −0.154768 | + | 0.577601i | 0.844357 | + | 0.535781i | \(0.179983\pi\) |
−0.999125 | + | 0.0418209i | \(0.986684\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −45.9103 | + | 19.3624i | −1.80772 | + | 0.762393i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.1852 | − | 40.1580i | −0.911505 | − | 1.57877i | −0.811939 | − | 0.583743i | \(-0.801588\pi\) |
−0.0995668 | − | 0.995031i | \(-0.531746\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.3673i | 0.760232i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.626380 | + | 1.54006i | −0.0245498 | + | 0.0603599i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.8522i | 0.424679i | 0.977196 | + | 0.212340i | \(0.0681083\pi\) | ||||
−0.977196 | + | 0.212340i | \(0.931892\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.07942 | + | 7.76049i | −0.0812496 | + | 0.303228i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.3745 | − | 31.0047i | 0.677842 | − | 1.20961i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.8367i | 0.850638i | 0.905043 | + | 0.425319i | \(0.139838\pi\) | ||||
−0.905043 | + | 0.425319i | \(0.860162\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.77396 | + | 6.77396i | −0.263477 | + | 0.263477i | −0.826465 | − | 0.562988i | \(-0.809652\pi\) |
0.562988 | + | 0.826465i | \(0.309652\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.4617 | − | 41.2073i | 0.716992 | − | 1.60036i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.50824 | − | 2.27978i | −0.329935 | − | 0.0884059i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.59863 | + | 3.23237i | 0.216780 | + | 0.125158i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −42.2450 | + | 17.8165i | −1.63328 | + | 0.688828i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.3946 | − | 6.80446i | 0.980348 | − | 0.262683i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.6123 | − | 18.8287i | −1.25711 | − | 0.725793i | −0.284599 | − | 0.958647i | \(-0.591860\pi\) |
−0.972512 | + | 0.232853i | \(0.925194\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.0412 | − | 17.6899i | 0.501956 | − | 0.680883i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.6548 | + | 11.9251i | −0.793829 | + | 0.458317i | −0.841309 | − | 0.540555i | \(-0.818214\pi\) |
0.0474798 | + | 0.998872i | \(0.484881\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.4683 | 0.401738 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.81220 | + | 5.03465i | −0.146084 | + | 0.192928i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −37.2984 | + | 9.99406i | −1.42718 | + | 0.382412i | −0.888026 | − | 0.459794i | \(-0.847923\pi\) |
−0.539156 | + | 0.842206i | \(0.681257\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.147362 | + | 0.255239i | −0.00563043 | + | 0.00975219i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.29462 | + | 19.6674i | 0.316459 | + | 0.750360i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.939964 | − | 26.9096i | 0.0358098 | − | 1.02517i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.4597 | + | 9.76934i | −1.38699 | + | 0.371643i | −0.873656 | − | 0.486545i | \(-0.838257\pi\) |
−0.513335 | + | 0.858188i | \(0.671590\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.32281 | − | 9.13576i | 0.0882362 | − | 0.347039i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.9697 | + | 25.9697i | −0.985087 | + | 0.985087i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.6976 | − | 54.8521i | −0.556710 | − | 2.07767i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.52210 | + | 0.348502i | −0.0953946 | + | 0.0131816i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −47.2060 | −1.78295 | −0.891473 | − | 0.453073i | \(-0.850328\pi\) | ||||
−0.891473 | + | 0.453073i | \(0.850328\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.11493 | 0.192913 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 38.8712 | − | 5.37119i | 1.46397 | − | 0.202291i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.69819 | + | 6.33772i | 0.0638669 | + | 0.238354i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.6959 | − | 20.6959i | 0.777251 | − | 0.777251i | −0.202112 | − | 0.979362i | \(-0.564780\pi\) |
0.979362 | + | 0.202112i | \(0.0647804\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.0794 | + | 26.3938i | 1.01556 | + | 0.989846i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.01971 | − | 0.541179i | 0.0756387 | − | 0.0202673i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0743 | + | 45.2783i | 0.900329 | + | 1.69331i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.79532 | − | 6.62801i | −0.104393 | − | 0.247527i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.4340 | + | 25.0004i | −0.538297 | + | 0.932357i | 0.460699 | + | 0.887556i | \(0.347599\pi\) |
−0.998996 | + | 0.0448010i | \(0.985735\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.28539 | − | 1.95211i | 0.271322 | − | 0.0727005i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.16223 | − | 12.1003i | 0.340747 | − | 0.450014i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.7019 | 0.694570 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.1912 | − | 19.1629i | 1.23099 | − | 0.710714i | 0.263755 | − | 0.964590i | \(-0.415039\pi\) |
0.967237 | + | 0.253876i | \(0.0817056\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.3436 | − | 19.8119i | 0.679394 | − | 0.733773i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −59.2927 | − | 34.2327i | −2.19302 | − | 1.26614i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.9931 | + | 10.4482i | −1.44024 | + | 0.385911i | −0.892618 | − | 0.450814i | \(-0.851134\pi\) |
−0.547623 | + | 0.836725i | \(0.684467\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −31.7550 | + | 13.3925i | −1.17130 | + | 0.493989i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27.6594 | + | 15.9692i | 1.01885 | + | 0.588232i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.38584 | − | 1.71108i | −0.234907 | − | 0.0629431i | 0.139445 | − | 0.990230i | \(-0.455468\pi\) |
−0.374352 | + | 0.927287i | \(0.622135\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.2082 | − | 9.60929i | 0.926045 | − | 0.353006i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.0339 | − | 12.0339i | 0.441479 | − | 0.441479i | −0.451030 | − | 0.892509i | \(-0.648943\pi\) |
0.892509 | + | 0.451030i | \(0.148943\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 38.3680i | 1.40569i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.3293 | + | 0.170896i | −0.487693 | + | 0.00625277i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.94742 | + | 10.9999i | −0.107696 | + | 0.401928i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 0.0965284i | − | 0.00352237i | −0.999998 | − | 0.00176119i | \(-0.999439\pi\) | ||
0.999998 | − | 0.00176119i | \(-0.000560603\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.6036 | − | 26.0709i | 0.386418 | − | 0.950075i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 45.5529i | 1.65784i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.1700 | − | 24.5432i | −0.515019 | − | 0.892039i | −0.999848 | − | 0.0174302i | \(-0.994452\pi\) |
0.484829 | − | 0.874609i | \(-0.338882\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.9235 | + | 4.60693i | −0.396499 | + | 0.167221i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.66031 | + | 13.6605i | −0.132686 | + | 0.495192i | −0.999997 | − | 0.00257596i | \(-0.999180\pi\) |
0.867311 | + | 0.497767i | \(0.165847\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.488172 | −0.0176730 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 65.8930 | − | 0.844821i | 2.38237 | − | 0.0305446i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.36112 | − | 14.2641i | 0.157471 | − | 0.515047i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.28647 | + | 3.28647i | 0.118513 | + | 0.118513i | 0.763876 | − | 0.645363i | \(-0.223294\pi\) |
−0.645363 | + | 0.763876i | \(0.723294\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.80363 | + | 0.387404i | −0.100970 | + | 0.0139520i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.37392 | − | 31.2519i | −0.301189 | − | 1.12405i | −0.936177 | − | 0.351530i | \(-0.885662\pi\) |
0.634988 | − | 0.772522i | \(-0.281005\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.27724 | − | 4.27724i | 0.153643 | − | 0.153643i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.08663 | + | 0.844920i | −0.0389825 | + | 0.0303113i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.9639 | − | 29.3824i | 0.607796 | − | 1.05273i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.0138 | − | 36.3970i | −0.751934 | − | 1.30239i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22.8328 | + | 2.56037i | 0.815979 | + | 0.0915002i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.81825 | + | 2.09489i | 0.279045 | + | 0.0747700i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.7742 | + | 5.83439i | 0.776167 | + | 0.207973i | 0.625094 | − | 0.780549i | \(-0.285060\pi\) |
0.151073 | + | 0.988523i | \(0.451727\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −23.9109 | − | 9.72510i | −0.851249 | − | 0.346223i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.70919 | − | 6.37878i | 0.0607718 | − | 0.226803i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.2355 | − | 0.706835i | −0.718583 | − | 0.0251004i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 36.2079 | − | 15.2704i | 1.28416 | − | 0.541586i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.95600 | + | 6.85199i | 0.140129 | + | 0.242710i | 0.927545 | − | 0.373712i | \(-0.121915\pi\) |
−0.787416 | + | 0.616422i | \(0.788582\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.1270 | + | 38.1270i | 1.34883 | + | 1.34883i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.322157 | + | 25.1271i | 0.0113829 | + | 0.887822i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −27.7313 | + | 48.0320i | −0.978615 | + | 1.69501i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.58176 | − | 1.49058i | −0.0909951 | − | 0.0525360i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.47788 | + | 2.22798i | 0.192830 | + | 0.0784286i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.5652 | + | 10.7186i | −0.652716 | + | 0.376846i | −0.789496 | − | 0.613756i | \(-0.789658\pi\) |
0.136780 | + | 0.990601i | \(0.456325\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.3538 | + | 22.3538i | 0.784949 | + | 0.784949i | 0.980661 | − | 0.195712i | \(-0.0627019\pi\) |
−0.195712 | + | 0.980661i | \(0.562702\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.7257 | + | 1.96786i | 0.551524 | + | 0.0690158i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.3288 | + | 7.11804i | −0.431859 | + | 0.249334i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.5870 | − | 39.5114i | −0.370394 | − | 1.38233i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.76795 | + | 6.20549i | −0.131663 | + | 0.216837i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.19464 | + | 34.3149i | 0.320895 | + | 1.19760i | 0.918374 | + | 0.395713i | \(0.129502\pi\) |
−0.597479 | + | 0.801884i | \(0.703831\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.1783 | − | 16.8461i | 1.01709 | − | 0.587218i | 0.103831 | − | 0.994595i | \(-0.466890\pi\) |
0.913260 | + | 0.407377i | \(0.133557\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −20.7033 | + | 27.3422i | −0.720797 | + | 0.951934i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.95015 | + | 3.95015i | 0.137360 | + | 0.137360i | 0.772444 | − | 0.635083i | \(-0.219034\pi\) |
−0.635083 | + | 0.772444i | \(0.719034\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.2862 | − | 14.0217i | 0.843495 | − | 0.486992i | −0.0149557 | − | 0.999888i | \(-0.504761\pi\) |
0.858451 | + | 0.512896i | \(0.171427\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.04332 | + | 14.7874i | 0.0708819 | + | 0.512970i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −41.0113 | − | 23.6779i | −1.42096 | − | 0.820391i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.6926 | + | 41.0367i | −0.819915 | + | 1.42013i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.80760 | − | 4.63645i | 0.200740 | − | 0.160259i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.2371 | − | 25.2371i | −0.871281 | − | 0.871281i | 0.121331 | − | 0.992612i | \(-0.461284\pi\) |
−0.992612 | + | 0.121331i | \(0.961284\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.72419 | − | 8.18255i | −0.162903 | − | 0.282157i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.0451168 | + | 0.360540i | −0.00155391 | + | 0.0124177i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.53510 | − | 38.7687i | −0.259215 | − | 1.33369i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.89643 | + | 7.07756i | −0.0651620 | + | 0.243188i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.46091 | − | 39.5204i | −0.187418 | − | 1.35634i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.67214 | + | 0.448048i | 0.0573202 | + | 0.0153589i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.4464 | + | 5.74656i | 0.734312 | + | 0.196758i | 0.606549 | − | 0.795046i | \(-0.292553\pi\) |
0.127763 | + | 0.991805i | \(0.459220\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 28.1945 | + | 27.4807i | 0.964231 | + | 0.939819i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.54760 | − | 16.5369i | −0.326140 | − | 0.564891i | 0.655603 | − | 0.755106i | \(-0.272415\pi\) |
−0.981742 | + | 0.190215i | \(0.939081\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.1199 | + | 46.9730i | −0.925319 | + | 1.60270i | −0.134272 | + | 0.990945i | \(0.542870\pi\) |
−0.791047 | + | 0.611755i | \(0.790464\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.24974 | + | 9.04429i | 0.0425909 | + | 0.308229i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.0822 | + | 10.0822i | −0.343201 | + | 0.343201i | −0.857569 | − | 0.514368i | \(-0.828026\pi\) |
0.514368 | + | 0.857569i | \(0.328026\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.7345 | + | 58.7221i | 0.534990 | + | 1.99661i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 37.5083 | + | 48.2383i | 1.27385 | + | 1.63826i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −41.7265 | − | 41.7265i | −1.41547 | − | 1.41547i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.7754 | − | 17.9897i | −0.568412 | − | 0.609559i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −40.8190 | − | 22.8742i | −1.38151 | − | 0.774173i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.57099 | 0.0531091 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.909826 | − | 3.39552i | 0.0307227 | − | 0.114658i | −0.948862 | − | 0.315692i | \(-0.897763\pi\) |
0.979584 | + | 0.201034i | \(0.0644300\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.54438 | − | 44.3066i | 0.187007 | − | 1.49443i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.0958 | + | 24.4146i | 0.474899 | + | 0.822549i | 0.999587 | − | 0.0287456i | \(-0.00915126\pi\) |
−0.524688 | + | 0.851295i | \(0.675818\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 8.66822i | − | 0.291709i | −0.989306 | − | 0.145854i | \(-0.953407\pi\) | ||
0.989306 | − | 0.145854i | \(-0.0465931\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21.5636 | − | 2.97965i | 0.724853 | − | 0.100160i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 10.0296i | − | 0.336760i | −0.985722 | − | 0.168380i | \(-0.946146\pi\) | ||
0.985722 | − | 0.168380i | \(-0.0538536\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.45887 | + | 9.17664i | −0.0824680 | + | 0.307775i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −29.0196 | + | 30.5473i | −0.972195 | + | 1.02337i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 32.2147i | 1.07802i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.6837 | − | 24.6837i | 0.825084 | − | 0.825084i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.08263 | − | 0.933267i | 0.303260 | − | 0.0311609i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.10830 | + | 1.63671i | 0.203723 | + | 0.0545875i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.7621 | + | 26.9981i | 1.55787 | + | 0.899438i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.77591 | + | 6.64505i | 0.292044 | + | 0.221133i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 76.6836 | − | 20.5473i | 2.54905 | − | 0.683016i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.2795 | − | 13.4404i | −0.772983 | − | 0.446282i | 0.0609549 | − | 0.998141i | \(-0.480585\pi\) |
−0.833938 | + | 0.551859i | \(0.813919\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.22673 | − | 28.4232i | 0.239695 | − | 0.942738i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.9403 | − | 21.9048i | 1.25702 | − | 0.725740i | 0.284525 | − | 0.958669i | \(-0.408164\pi\) |
0.972494 | + | 0.232929i | \(0.0748309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.8024 | 0.688457 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.4831 | − | 27.2276i | −0.379619 | − | 0.900117i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.71449 | − | 0.459395i | 0.0566174 | − | 0.0151706i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.847859 | + | 1.46853i | −0.0279683 | + | 0.0484425i | −0.879671 | − | 0.475583i | \(-0.842237\pi\) |
0.851702 | + | 0.524026i | \(0.175570\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −34.1736 | + | 45.1320i | −1.12606 | + | 1.48715i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.28091 | + | 31.5385i | 0.239654 | + | 1.03810i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.83733 | − | 1.29616i | 0.159051 | − | 0.0426175i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −32.6733 | − | 8.30733i | −1.07313 | − | 0.272849i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.1283 | − | 36.1283i | 1.18533 | − | 1.18533i | 0.206987 | − | 0.978344i | \(-0.433634\pi\) |
0.978344 | − | 0.206987i | \(-0.0663658\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.32279 | − | 27.3290i | −0.239995 | − | 0.895673i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.5866 | − | 28.4876i | 0.379328 | − | 0.932643i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −102.836 | −3.36309 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.45635 | −0.243588 | −0.121794 | − | 0.992555i | \(-0.538865\pi\) | ||||
−0.121794 | + | 0.992555i | \(0.538865\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.4183 | + | 13.3987i | 0.339989 | + | 0.437251i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.11870 | − | 26.5673i | −0.232063 | − | 0.866070i | −0.979451 | − | 0.201683i | \(-0.935359\pi\) |
0.747388 | − | 0.664388i | \(-0.231308\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.11953 | − | 8.11953i | 0.264408 | − | 0.264408i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.5292 | − | 1.18069i | −0.342514 | − | 0.0384080i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.9829 | + | 6.69414i | −0.811834 | + | 0.217530i | −0.640773 | − | 0.767730i | \(-0.721386\pi\) |
−0.171061 | + | 0.985260i | \(0.554719\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.2401 | − | 29.1313i | 1.01410 | − | 0.945641i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0220 | − | 2.25522i | −0.584404 | − | 0.0731304i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.8503 | − | 41.3099i | 0.772586 | − | 1.33816i | −0.163555 | − | 0.986534i | \(-0.552296\pi\) |
0.936141 | − | 0.351624i | \(-0.114371\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.98126 | − | 1.87062i | 0.225908 | − | 0.0605319i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −35.5770 | − | 4.45198i | −1.15004 | − | 0.143912i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.0651121 | 0.00210258 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.0755 | + | 14.4773i | −0.808886 | + | 0.467010i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 35.5285 | − | 36.4513i | 1.14489 | − | 1.17463i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 43.6912 | + | 25.2251i | 1.40647 | + | 0.812025i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53.1577 | + | 14.2436i | −1.70944 | + | 0.458042i | −0.975286 | − | 0.220944i | \(-0.929086\pi\) |
−0.734151 | + | 0.678986i | \(0.762419\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.71746 | + | 53.6810i | −0.215796 | + | 1.72448i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.0094 | − | 12.7071i | −0.706316 | − | 0.407792i | 0.103379 | − | 0.994642i | \(-0.467034\pi\) |
−0.809696 | + | 0.586850i | \(0.800368\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.83738 | + | 2.10002i | 0.251255 | + | 0.0673235i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 21.4050 | − | 15.4757i | 0.685509 | − | 0.495620i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.1030 | − | 31.1030i | 0.995074 | − | 0.995074i | −0.00491404 | − | 0.999988i | \(-0.501564\pi\) |
0.999988 | + | 0.00491404i | \(0.00156419\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 39.2146i | − | 1.25330i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.90352 | + | 1.06670i | 0.0607746 | + | 0.0340570i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.9175 | + | 44.4766i | −0.380108 | + | 1.41858i | 0.465627 | + | 0.884981i | \(0.345829\pi\) |
−0.845735 | + | 0.533603i | \(0.820838\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 74.2466i | − | 2.36569i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.32146 | − | 6.84378i | −0.169384 | − | 0.217840i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 13.8442i | − | 0.440219i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.6829 | − | 28.8957i | −0.529951 | − | 0.917901i | −0.999390 | − | 0.0349364i | \(-0.988877\pi\) |
0.469439 | − | 0.882965i | \(-0.344456\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.4756 | + | 16.2611i | 0.681506 | + | 0.516031i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.7870 | + | 40.2578i | −0.341972 | + | 1.27626i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.5089 | 0.554512 | 0.277256 | − | 0.960796i | \(-0.410575\pi\) | ||||
0.277256 | + | 0.960796i | \(0.410575\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.08328 | − | 0.920208i | 0.192466 | − | 0.0291141i |
(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 | 468.2.bz.a.401.1 | yes | 56 | |
3.2 | odd | 2 | 1404.2.cc.a.557.13 | 56 | |||
9.2 | odd | 6 | 468.2.bw.a.245.11 | yes | 56 | ||
9.7 | even | 3 | 1404.2.bz.a.89.13 | 56 | |||
13.6 | odd | 12 | 468.2.bw.a.149.11 | ✓ | 56 | ||
39.32 | even | 12 | 1404.2.bz.a.773.13 | 56 | |||
117.97 | odd | 12 | 1404.2.cc.a.305.13 | 56 | |||
117.110 | even | 12 | inner | 468.2.bz.a.461.1 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
468.2.bw.a.149.11 | ✓ | 56 | 13.6 | odd | 12 | ||
468.2.bw.a.245.11 | yes | 56 | 9.2 | odd | 6 | ||
468.2.bz.a.401.1 | yes | 56 | 1.1 | even | 1 | trivial | |
468.2.bz.a.461.1 | yes | 56 | 117.110 | even | 12 | inner | |
1404.2.bz.a.89.13 | 56 | 9.7 | even | 3 | |||
1404.2.bz.a.773.13 | 56 | 39.32 | even | 12 | |||
1404.2.cc.a.305.13 | 56 | 117.97 | odd | 12 | |||
1404.2.cc.a.557.13 | 56 | 3.2 | odd | 2 |