Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(1151,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.cg (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.7 | ||
Character | \(\chi\) | \(=\) | 2736.1151 |
Dual form | 2736.2.cg.c.2591.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.34408 | − | 0.776006i | −0.601092 | − | 0.347040i | 0.168379 | − | 0.985722i | \(-0.446147\pi\) |
−0.769471 | + | 0.638682i | \(0.779480\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.95486i | − | 1.11683i | −0.829561 | − | 0.558416i | \(-0.811409\pi\) | ||
0.829561 | − | 0.558416i | \(-0.188591\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.57750 | 1.07866 | 0.539328 | − | 0.842096i | \(-0.318678\pi\) | ||||
0.539328 | + | 0.842096i | \(0.318678\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.39307 | + | 4.14491i | 0.663718 | + | 1.14959i | 0.979631 | + | 0.200805i | \(0.0643556\pi\) |
−0.315914 | + | 0.948788i | \(0.602311\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.37866 | + | 1.95067i | 0.819446 | + | 0.473108i | 0.850226 | − | 0.526419i | \(-0.176466\pi\) |
−0.0307791 | + | 0.999526i | \(0.509799\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.61248 | + | 3.48926i | −0.599343 | + | 0.800492i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.64157 | + | 4.57534i | 0.550806 | + | 0.954025i | 0.998217 | + | 0.0596959i | \(0.0190131\pi\) |
−0.447410 | + | 0.894329i | \(0.647654\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.29563 | − | 2.24410i | −0.259126 | − | 0.448819i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.08654 | + | 4.09142i | −1.31594 | + | 0.759757i | −0.983072 | − | 0.183218i | \(-0.941349\pi\) |
−0.332865 | + | 0.942975i | \(0.608015\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.52123i | − | 1.35085i | −0.737427 | − | 0.675427i | \(-0.763959\pi\) | ||
0.737427 | − | 0.675427i | \(-0.236041\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.29299 | + | 3.97157i | −0.387586 | + | 0.671319i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.32246 | 0.381810 | 0.190905 | − | 0.981609i | \(-0.438858\pi\) | ||||
0.190905 | + | 0.981609i | \(0.438858\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.70788 | + | 2.14074i | 0.579073 | + | 0.334328i | 0.760765 | − | 0.649028i | \(-0.224824\pi\) |
−0.181692 | + | 0.983355i | \(0.558157\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.48460 | + | 2.01183i | 0.531396 | + | 0.306802i | 0.741585 | − | 0.670859i | \(-0.234074\pi\) |
−0.210189 | + | 0.977661i | \(0.567408\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.08174 | + | 7.06978i | 0.595383 | + | 1.03123i | 0.993493 | + | 0.113896i | \(0.0363329\pi\) |
−0.398110 | + | 0.917338i | \(0.630334\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.73120 | −0.247314 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.03458 | + | 1.17467i | −0.279471 | + | 0.161353i | −0.633184 | − | 0.774001i | \(-0.718252\pi\) |
0.353713 | + | 0.935354i | \(0.384919\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.80845 | − | 2.77616i | −0.648371 | − | 0.374337i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.14582 | + | 5.44871i | −0.409550 | + | 0.709362i | −0.994839 | − | 0.101463i | \(-0.967648\pi\) |
0.585289 | + | 0.810825i | \(0.300981\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.24917 | − | 10.8239i | −0.800125 | − | 1.38586i | −0.919534 | − | 0.393011i | \(-0.871433\pi\) |
0.119409 | − | 0.992845i | \(-0.461900\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 7.42814i | − | 0.921347i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.02949 | − | 5.21318i | 1.10313 | − | 0.636891i | 0.166087 | − | 0.986111i | \(-0.446887\pi\) |
0.937041 | + | 0.349220i | \(0.113553\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.72467 | − | 4.71927i | 0.323359 | − | 0.560074i | −0.657820 | − | 0.753175i | \(-0.728521\pi\) |
0.981179 | + | 0.193101i | \(0.0618545\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.18870 | + | 8.98709i | −0.607291 | + | 1.05186i | 0.384394 | + | 0.923169i | \(0.374410\pi\) |
−0.991685 | + | 0.128690i | \(0.958923\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 10.5710i | − | 1.20468i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.60257 | + | 4.96669i | 0.967864 | + | 0.558797i | 0.898585 | − | 0.438801i | \(-0.144597\pi\) |
0.0692799 | + | 0.997597i | \(0.477930\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.9858 | 1.97419 | 0.987097 | − | 0.160126i | \(-0.0511900\pi\) | ||||
0.987097 | + | 0.160126i | \(0.0511900\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.02747 | − | 5.24373i | −0.328375 | − | 0.568762i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.70648 | − | 4.44934i | 0.816885 | − | 0.471629i | −0.0324559 | − | 0.999473i | \(-0.510333\pi\) |
0.849341 | + | 0.527844i | \(0.177000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.2476 | − | 7.07118i | 1.28390 | − | 0.741261i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.21907 | − | 2.66256i | 0.638063 | − | 0.273173i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.08794 | − | 10.5446i | 0.618137 | − | 1.07064i | −0.371688 | − | 0.928358i | \(-0.621221\pi\) |
0.989825 | − | 0.142287i | \(-0.0454457\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.47913 | − | 5.47278i | 0.943209 | − | 0.544562i | 0.0522441 | − | 0.998634i | \(-0.483363\pi\) |
0.890965 | + | 0.454072i | \(0.150029\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.4264i | − | 1.02734i | −0.857988 | − | 0.513670i | \(-0.828286\pi\) | ||
0.857988 | − | 0.513670i | \(-0.171714\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.6914 | 1.90364 | 0.951820 | − | 0.306657i | \(-0.0992104\pi\) | ||||
0.951820 | + | 0.306657i | \(0.0992104\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.94405 | + | 13.7595i | −0.760902 | + | 1.31792i | 0.181484 | + | 0.983394i | \(0.441910\pi\) |
−0.942386 | + | 0.334527i | \(0.891423\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.66966i | 0.627429i | 0.949517 | + | 0.313715i | \(0.101574\pi\) | ||||
−0.949517 | + | 0.313715i | \(0.898426\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 8.19951i | − | 0.764608i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.76397 | − | 9.98348i | 0.528382 | − | 0.915184i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.79849 | 0.163500 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.7817i | 1.05379i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.29254 | + | 1.32360i | −0.203430 | + | 0.117450i | −0.598254 | − | 0.801306i | \(-0.704139\pi\) |
0.394825 | + | 0.918757i | \(0.370805\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.36489 | + | 16.2205i | −0.818214 | + | 1.41719i | 0.0887828 | + | 0.996051i | \(0.471702\pi\) |
−0.906997 | + | 0.421137i | \(0.861631\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.3103 | + | 7.71951i | 0.894015 | + | 0.669366i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.1197 | + | 7.57468i | −1.12089 | + | 0.647148i | −0.941629 | − | 0.336652i | \(-0.890705\pi\) |
−0.179265 | + | 0.983801i | \(0.557372\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.86612 | − | 4.54151i | 0.667196 | − | 0.385206i | −0.127818 | − | 0.991798i | \(-0.540797\pi\) |
0.795013 | + | 0.606592i | \(0.207464\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.56120 | + | 14.8284i | 0.715923 | + | 1.24002i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.6999 | 1.05467 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.72619 | − | 5.03807i | −0.714877 | − | 0.412735i | 0.0979869 | − | 0.995188i | \(-0.468760\pi\) |
−0.812864 | + | 0.582453i | \(0.802093\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 15.1780i | − | 1.23517i | −0.786504 | − | 0.617586i | \(-0.788111\pi\) | ||
0.786504 | − | 0.617586i | \(-0.211889\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.83652 | + | 10.1092i | −0.468801 | + | 0.811987i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.25867 | − | 5.64418i | 0.260070 | − | 0.450454i | −0.706190 | − | 0.708022i | \(-0.749588\pi\) |
0.966260 | + | 0.257568i | \(0.0829210\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.5195 | − | 7.80549i | 1.06549 | − | 0.615158i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.36702i | 0.420377i | 0.977661 | + | 0.210189i | \(0.0674078\pi\) | ||||
−0.977661 | + | 0.210189i | \(0.932592\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.55271 | − | 13.0817i | −0.584447 | − | 1.01229i | −0.994944 | − | 0.100429i | \(-0.967978\pi\) |
0.410498 | − | 0.911862i | \(-0.365355\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.95354 | + | 8.57979i | −0.381042 | + | 0.659984i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.97214 | + | 1.13862i | 0.149939 | + | 0.0865674i | 0.573093 | − | 0.819491i | \(-0.305744\pi\) |
−0.423153 | + | 0.906058i | \(0.639077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.63099 | + | 3.82840i | −0.501256 | + | 0.289400i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.3998 | 1.00155 | 0.500773 | − | 0.865579i | \(-0.333049\pi\) | ||||
0.500773 | + | 0.865579i | \(0.333049\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.72566 | + | 8.18508i | 0.351255 | + | 0.608392i | 0.986470 | − | 0.163944i | \(-0.0524215\pi\) |
−0.635214 | + | 0.772336i | \(0.719088\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.12157 | − | 1.80224i | −0.229503 | − | 0.132503i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.0872 | + | 6.97853i | 0.883901 | + | 0.510321i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.87185 | −0.135442 | −0.0677210 | − | 0.997704i | \(-0.521573\pi\) | ||||
−0.0677210 | + | 0.997704i | \(0.521573\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.91040 | − | 15.4333i | 0.641385 | − | 1.11091i | −0.343739 | − | 0.939065i | \(-0.611694\pi\) |
0.985124 | − | 0.171846i | \(-0.0549731\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3.51742i | − | 0.250606i | −0.992119 | − | 0.125303i | \(-0.960010\pi\) | ||
0.992119 | − | 0.125303i | \(-0.0399903\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.896925 | + | 0.517840i | −0.0635813 | + | 0.0367087i | −0.531454 | − | 0.847087i | \(-0.678354\pi\) |
0.467872 | + | 0.883796i | \(0.345021\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.0896 | + | 20.9397i | 0.848521 | + | 1.46968i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.32246 | − | 5.75467i | −0.232051 | − | 0.401923i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.34613 | + | 12.4828i | −0.646486 | + | 0.863456i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.51358 | + | 3.76062i | 0.448413 | + | 0.258892i | 0.707160 | − | 0.707054i | \(-0.249976\pi\) |
−0.258747 | + | 0.965945i | \(0.583309\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.12239 | − | 5.40814i | −0.212945 | − | 0.368832i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.2242 | −1.50868 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.6724i | 1.25604i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.7471 | + | 12.5557i | 1.45630 | + | 0.840793i | 0.998826 | − | 0.0484325i | \(-0.0154226\pi\) |
0.457469 | + | 0.889225i | \(0.348756\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.58598 | −0.304382 | −0.152191 | − | 0.988351i | \(-0.548633\pi\) | ||||
−0.152191 | + | 0.988351i | \(0.548633\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.3584 | −0.684503 | −0.342251 | − | 0.939608i | \(-0.611189\pi\) | ||||
−0.342251 | + | 0.939608i | \(0.611189\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.5657 | − | 9.56419i | −1.08525 | − | 0.626571i | −0.152945 | − | 0.988235i | \(-0.548876\pi\) |
−0.932309 | + | 0.361664i | \(0.882209\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 12.6698i | − | 0.826488i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.95891 | −0.579504 | −0.289752 | − | 0.957102i | \(-0.593573\pi\) | ||||
−0.289752 | + | 0.957102i | \(0.593573\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.04028 | − | 1.80181i | −0.0670101 | − | 0.116065i | 0.830574 | − | 0.556909i | \(-0.188013\pi\) |
−0.897584 | + | 0.440844i | \(0.854679\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.32687 | + | 1.34342i | 0.148659 | + | 0.0858281i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.7145 | − | 2.47845i | −1.31803 | − | 0.157700i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.49712 | + | 16.4495i | 0.599453 | + | 1.03828i | 0.992902 | + | 0.118936i | \(0.0379484\pi\) |
−0.393449 | + | 0.919346i | \(0.628718\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.45023 | + | 16.3683i | 0.594131 | + | 1.02906i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.1578 | + | 11.0607i | −1.19503 | + | 0.689950i | −0.959443 | − | 0.281904i | \(-0.909034\pi\) |
−0.235585 | + | 0.971854i | \(0.575701\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 6.86254i | − | 0.426418i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.31065 | − | 12.6624i | 0.450794 | − | 0.780798i | −0.547641 | − | 0.836713i | \(-0.684474\pi\) |
0.998436 | + | 0.0559148i | \(0.0178075\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.64619 | 0.223984 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.7954 | + | 7.38740i | 0.780147 | + | 0.450418i | 0.836482 | − | 0.547994i | \(-0.184608\pi\) |
−0.0563356 | + | 0.998412i | \(0.517942\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.3521 | − | 14.6370i | −1.54003 | − | 0.889136i | −0.998836 | − | 0.0482382i | \(-0.984639\pi\) |
−0.541193 | − | 0.840898i | \(-0.682027\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.63511 | − | 8.02825i | −0.279508 | − | 0.484122i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.08628 | −0.425773 | −0.212887 | − | 0.977077i | \(-0.568287\pi\) | ||||
−0.212887 | + | 0.977077i | \(0.568287\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.7896 | − | 6.22936i | 0.643652 | − | 0.371613i | −0.142368 | − | 0.989814i | \(-0.545472\pi\) |
0.786020 | + | 0.618201i | \(0.212138\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.6722 | − | 9.62572i | −0.991062 | − | 0.572190i | −0.0854701 | − | 0.996341i | \(-0.527239\pi\) |
−0.905591 | + | 0.424151i | \(0.860573\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.32560 | − | 10.9563i | 0.373388 | − | 0.646727i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.889753 | − | 1.54110i | −0.0523384 | − | 0.0906528i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.82121i | − | 0.106396i | −0.998584 | − | 0.0531980i | \(-0.983059\pi\) | ||
0.998584 | − | 0.0531980i | \(-0.0169415\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.45647 | − | 4.88234i | 0.492355 | − | 0.284261i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.6429 | + | 21.8982i | −0.731160 | + | 1.26641i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.94469 | − | 10.2965i | 0.342646 | − | 0.593480i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.3976i | 1.11070i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0734 | + | 10.4347i | 1.03150 | + | 0.595538i | 0.917414 | − | 0.397933i | \(-0.130272\pi\) |
0.114087 | + | 0.993471i | \(0.463606\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.2309 | 1.20389 | 0.601946 | − | 0.798537i | \(-0.294392\pi\) | ||||
0.601946 | + | 0.798537i | \(0.294392\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.62822 | + | 2.82016i | 0.0920324 | + | 0.159405i | 0.908366 | − | 0.418176i | \(-0.137330\pi\) |
−0.816334 | + | 0.577580i | \(0.803997\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.0712 | − | 6.96932i | 0.677987 | − | 0.391436i | −0.121109 | − | 0.992639i | \(-0.538645\pi\) |
0.799096 | + | 0.601203i | \(0.205312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.3521 | + | 14.6370i | −1.41944 | + | 0.819516i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.6331 | + | 6.69296i | −0.869849 | + | 0.372406i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.20106 | − | 10.7405i | 0.343973 | − | 0.595778i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.8902 | − | 12.0610i | 1.15171 | − | 0.664943i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.14723i | 0.392847i | 0.980519 | + | 0.196424i | \(0.0629328\pi\) | ||||
−0.980519 | + | 0.196424i | \(0.937067\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.1818 | −0.884108 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.47152 | + | 11.2090i | −0.352526 | + | 0.610593i | −0.986691 | − | 0.162605i | \(-0.948011\pi\) |
0.634165 | + | 0.773197i | \(0.281344\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 26.9072i | − | 1.45711i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 15.5686i | − | 0.840624i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.70837 | − | 13.3513i | 0.413807 | − | 0.716735i | −0.581495 | − | 0.813550i | \(-0.697532\pi\) |
0.995302 | + | 0.0968150i | \(0.0308655\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.4727 | 1.57764 | 0.788820 | − | 0.614625i | \(-0.210693\pi\) | ||||
0.788820 | + | 0.614625i | \(0.210693\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 19.7000i | − | 1.04853i | −0.851556 | − | 0.524264i | \(-0.824341\pi\) | ||
0.851556 | − | 0.524264i | \(-0.175659\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.32437 | + | 4.22873i | −0.388737 | + | 0.224437i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.64022 | − | 11.5012i | 0.350457 | − | 0.607010i | −0.635872 | − | 0.771794i | \(-0.719360\pi\) |
0.986330 | + | 0.164785i | \(0.0526929\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.34993 | − | 18.2312i | −0.281575 | − | 0.959539i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.9481 | − | 8.05292i | 0.730075 | − | 0.421509i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.4570 | + | 8.34674i | −0.754648 | + | 0.435696i | −0.827371 | − | 0.561656i | \(-0.810165\pi\) |
0.0727227 | + | 0.997352i | \(0.476831\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.47098 | + | 6.01191i | 0.180204 | + | 0.312123i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.7828 | −1.59387 | −0.796937 | − | 0.604062i | \(-0.793548\pi\) | ||||
−0.796937 | + | 0.604062i | \(0.793548\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −33.9171 | − | 19.5821i | −1.74682 | − | 1.00853i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.9927i | 0.770125i | 0.922890 | + | 0.385063i | \(0.125820\pi\) | ||||
−0.922890 | + | 0.385063i | \(0.874180\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.26956 | + | 3.93100i | −0.115969 | + | 0.200865i | −0.918167 | − | 0.396194i | \(-0.870331\pi\) |
0.802197 | + | 0.597059i | \(0.203664\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.20317 | + | 14.2083i | −0.418072 | + | 0.724122i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.79236 | + | 1.61217i | −0.141578 | + | 0.0817404i | −0.569116 | − | 0.822257i | \(-0.692714\pi\) |
0.427538 | + | 0.903998i | \(0.359381\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.6114i | 1.04236i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.70837 | − | 13.3513i | −0.387850 | − | 0.671776i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.15174 | − | 10.6551i | 0.308747 | − | 0.534765i | −0.669342 | − | 0.742955i | \(-0.733424\pi\) |
0.978088 | + | 0.208190i | \(0.0667571\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.1635 | + | 12.2188i | 1.05686 | + | 0.610176i | 0.924561 | − | 0.381034i | \(-0.124432\pi\) |
0.132296 | + | 0.991210i | \(0.457765\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 31.1749 | − | 17.9988i | 1.55293 | − | 0.896585i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.30859 | 0.411842 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.96304 | + | 13.7924i | 0.393747 | + | 0.681990i | 0.992940 | − | 0.118615i | \(-0.0378453\pi\) |
−0.599193 | + | 0.800604i | \(0.704512\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.1002 | + | 9.29544i | 0.792238 | + | 0.457399i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.1743 | − | 13.9571i | −1.18667 | − | 0.685125i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −38.2550 | −1.86888 | −0.934439 | − | 0.356123i | \(-0.884099\pi\) | ||||
−0.934439 | + | 0.356123i | \(0.884099\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.06443 | − | 10.5039i | 0.295562 | − | 0.511929i | −0.679553 | − | 0.733626i | \(-0.737826\pi\) |
0.975116 | + | 0.221697i | \(0.0711597\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 10.1094i | − | 0.490378i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −31.9831 | + | 18.4654i | −1.54777 | + | 0.893605i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.9424 | − | 22.4169i | −0.623413 | − | 1.07978i | −0.988845 | − | 0.148945i | \(-0.952412\pi\) |
0.365433 | − | 0.930838i | \(-0.380921\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.3701 | + | 19.6936i | 0.546413 | + | 0.946416i | 0.998516 | + | 0.0544501i | \(0.0173406\pi\) |
−0.452103 | + | 0.891966i | \(0.649326\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.8656 | − | 2.73582i | −1.09381 | − | 0.130872i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.1175 | + | 17.3883i | 1.43743 | + | 0.829900i | 0.997671 | − | 0.0682169i | \(-0.0217310\pi\) |
0.439758 | + | 0.898116i | \(0.355064\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.93456 | − | 8.54692i | −0.234448 | − | 0.406076i | 0.724664 | − | 0.689102i | \(-0.241995\pi\) |
−0.959112 | + | 0.283026i | \(0.908662\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.8109 | −0.654697 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 7.88038i | − | 0.371898i | −0.982559 | − | 0.185949i | \(-0.940464\pi\) | ||
0.982559 | − | 0.185949i | \(-0.0595359\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.2649 | + | 7.65850i | 0.624621 | + | 0.360625i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −21.9491 | −1.02899 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.32909 | 0.342840 | 0.171420 | − | 0.985198i | \(-0.445164\pi\) | ||||
0.171420 | + | 0.985198i | \(0.445164\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.1717 | + | 10.4914i | 0.846340 | + | 0.488634i | 0.859414 | − | 0.511280i | \(-0.170829\pi\) |
−0.0130745 | + | 0.999915i | \(0.504162\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.7207i | 0.730605i | 0.930889 | + | 0.365302i | \(0.119034\pi\) | ||||
−0.930889 | + | 0.365302i | \(0.880966\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.8549 | −1.28897 | −0.644485 | − | 0.764617i | \(-0.722928\pi\) | ||||
−0.644485 | + | 0.764617i | \(0.722928\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.4042 | − | 26.6809i | −0.711301 | − | 1.23201i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.4661 | + | 7.19733i | 0.573194 | + | 0.330934i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.2150 | + | 1.34186i | 0.514582 | + | 0.0615686i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.78739 | − | 10.0241i | −0.264433 | − | 0.458011i | 0.702982 | − | 0.711207i | \(-0.251851\pi\) |
−0.967415 | + | 0.253197i | \(0.918518\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.55780 | + | 9.62639i | 0.253414 | + | 0.438926i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.3654 | + | 9.44856i | −0.743114 | + | 0.429037i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.00714i | 0.181581i | 0.995870 | + | 0.0907905i | \(0.0289394\pi\) | ||||
−0.995870 | + | 0.0907905i | \(0.971061\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.72467 | + | 4.71927i | −0.122963 | + | 0.212978i | −0.920935 | − | 0.389717i | \(-0.872573\pi\) |
0.797972 | + | 0.602695i | \(0.205906\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31.9240 | −1.43779 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.9448 | − | 8.05103i | −0.625509 | − | 0.361138i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.76253 | + | 1.59495i | 0.123668 | + | 0.0713997i | 0.560558 | − | 0.828115i | \(-0.310587\pi\) |
−0.436890 | + | 0.899515i | \(0.643920\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.2446 | − | 33.3326i | −0.858072 | − | 1.48623i | −0.873765 | − | 0.486348i | \(-0.838329\pi\) |
0.0156927 | − | 0.999877i | \(-0.495005\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.9876 | −0.755940 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.72135 | + | 5.03527i | −0.386567 | + | 0.223185i | −0.680672 | − | 0.732589i | \(-0.738312\pi\) |
0.294105 | + | 0.955773i | \(0.404979\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.5556 | + | 15.3319i | 1.17475 | + | 0.678242i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.09092 | + | 14.0139i | −0.356529 | + | 0.617526i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.6024 | + | 25.2921i | 0.642213 | + | 1.11235i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.7688i | 1.52325i | 0.648018 | + | 0.761625i | \(0.275598\pi\) | ||||
−0.648018 | + | 0.761625i | \(0.724402\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.64797 | + | 2.68351i | −0.203242 | + | 0.117342i | −0.598167 | − | 0.801372i | \(-0.704104\pi\) |
0.394925 | + | 0.918713i | \(0.370771\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.6715 | − | 25.4117i | 0.639099 | − | 1.10695i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.45584 | + | 4.25363i | −0.106775 | + | 0.184941i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.4918i | 0.887597i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26.4669 | − | 15.2807i | −1.14426 | − | 0.660640i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.19337 | −0.266767 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.23120 | − | 10.7928i | −0.267900 | − | 0.464017i | 0.700419 | − | 0.713732i | \(-0.252996\pi\) |
−0.968319 | + | 0.249715i | \(0.919663\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21.3549 | − | 12.3293i | 0.914744 | − | 0.528128i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.10047 | − | 0.635358i | 0.0470528 | − | 0.0271659i | −0.476289 | − | 0.879289i | \(-0.658018\pi\) |
0.523342 | + | 0.852123i | \(0.324685\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.23739 | − | 35.4155i | 0.180519 | − | 1.50875i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.6759 | − | 25.4194i | 0.624082 | − | 1.08094i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −37.0099 | + | 21.3677i | −1.56816 | + | 0.905378i | −0.571776 | + | 0.820409i | \(0.693746\pi\) |
−0.996384 | + | 0.0849682i | \(0.972921\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.2578i | 0.814519i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.0540 | −0.634451 | −0.317226 | − | 0.948350i | \(-0.602751\pi\) | ||||
−0.317226 | + | 0.948350i | \(0.602751\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.17570 | − | 8.96457i | 0.217743 | − | 0.377142i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.3871i | 1.14813i | 0.818811 | + | 0.574064i | \(0.194634\pi\) | ||||
−0.818811 | + | 0.574064i | \(0.805366\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0687i | 0.839848i | 0.907559 | + | 0.419924i | \(0.137943\pi\) | ||||
−0.907559 | + | 0.419924i | \(0.862057\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.84500 | − | 11.8559i | 0.285456 | − | 0.494425i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.6632 | 1.15163 | 0.575816 | − | 0.817579i | \(-0.304684\pi\) | ||||
0.575816 | + | 0.817579i | \(0.304684\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 53.1454i | − | 2.20484i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.27871 | + | 4.20237i | −0.301454 | + | 0.174044i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.24250 | − | 10.8123i | 0.257655 | − | 0.446272i | −0.707958 | − | 0.706255i | \(-0.750383\pi\) |
0.965613 | + | 0.259982i | \(0.0837167\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.2436 | + | 19.6490i | 1.08135 | + | 0.809625i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.7999 | + | 13.1635i | −0.936280 | + | 0.540562i | −0.888792 | − | 0.458310i | \(-0.848455\pi\) |
−0.0474878 | + | 0.998872i | \(0.515122\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.4945 | + | 8.94574i | −0.635212 | + | 0.366740i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.90978 | + | 15.4322i | 0.364044 | + | 0.630542i | 0.988622 | − | 0.150420i | \(-0.0480625\pi\) |
−0.624578 | + | 0.780962i | \(0.714729\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.14657 | 0.169142 | 0.0845711 | − | 0.996417i | \(-0.473048\pi\) | ||||
0.0845711 | + | 0.996417i | \(0.473048\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.41732 | − | 1.39564i | −0.0982782 | − | 0.0567409i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.01676i | 0.365979i | 0.983115 | + | 0.182989i | \(0.0585774\pi\) | ||||
−0.983115 | + | 0.182989i | \(0.941423\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.5358 | + | 33.8369i | −0.790332 | + | 1.36890i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.07558 | − | 15.7194i | 0.366559 | − | 0.634900i | −0.622466 | − | 0.782647i | \(-0.713869\pi\) |
0.989025 | + | 0.147748i | \(0.0472023\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.3186 | + | 9.99891i | −0.697221 | + | 0.402541i | −0.806312 | − | 0.591491i | \(-0.798540\pi\) |
0.109090 | + | 0.994032i | \(0.465206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 6.82304i | − | 0.274241i | −0.990554 | − | 0.137120i | \(-0.956215\pi\) | ||
0.990554 | − | 0.137120i | \(-0.0437848\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.1472 | − | 22.7716i | −0.526730 | − | 0.912324i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.66454 | − | 4.61513i | 0.106582 | − | 0.184605i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.84681 | + | 4.53036i | 0.312873 | + | 0.180637i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.3500 | + | 19.2546i | −1.32764 | + | 0.766515i | −0.984935 | − | 0.172927i | \(-0.944677\pi\) |
−0.342708 | + | 0.939442i | \(0.611344\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.10847 | 0.163040 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.14288 | − | 7.17568i | −0.164147 | − | 0.284311i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.7653 | + | 11.9889i | 0.820181 | + | 0.473532i | 0.850479 | − | 0.526009i | \(-0.176312\pi\) |
−0.0302978 | + | 0.999541i | \(0.509646\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.05767 | − | 1.76535i | −0.120583 | − | 0.0696185i | 0.438495 | − | 0.898733i | \(-0.355512\pi\) |
−0.559078 | + | 0.829115i | \(0.688845\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.83957 | 0.347519 | 0.173760 | − | 0.984788i | \(-0.444408\pi\) | ||||
0.173760 | + | 0.984788i | \(0.444408\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.2541 | + | 19.4928i | −0.441764 | + | 0.765158i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.10915i | 0.0434042i | 0.999764 | + | 0.0217021i | \(0.00690854\pi\) | ||||
−0.999764 | + | 0.0217021i | \(0.993091\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.1744 | − | 14.5344i | 0.983643 | − | 0.567907i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.73179 | − | 13.3919i | −0.301188 | − | 0.521673i | 0.675217 | − | 0.737619i | \(-0.264050\pi\) |
−0.976405 | + | 0.215946i | \(0.930716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.32246 | + | 9.21877i | 0.207020 | + | 0.358569i | 0.950774 | − | 0.309884i | \(-0.100290\pi\) |
−0.743755 | + | 0.668453i | \(0.766957\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.86749 | − | 18.3765i | −0.305088 | − | 0.712610i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −37.4392 | − | 21.6156i | −1.44965 | − | 0.836958i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.3564 | − | 38.7224i | −0.863060 | − | 1.49486i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.8299 | −1.53533 | −0.767664 | − | 0.640852i | \(-0.778581\pi\) | ||||
−0.767664 | + | 0.640852i | \(0.778581\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.7547i | 1.18200i | 0.806671 | + | 0.591000i | \(0.201267\pi\) | ||||
−0.806671 | + | 0.591000i | \(0.798733\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −31.1579 | − | 17.9890i | −1.19573 | − | 0.690355i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.2903 | 0.776387 | 0.388194 | − | 0.921578i | \(-0.373099\pi\) | ||||
0.388194 | + | 0.921578i | \(0.373099\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.5120 | 0.898347 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.73778 | − | 5.62211i | −0.370980 | − | 0.214185i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.66267i | 0.329544i | 0.986332 | + | 0.164772i | \(0.0526888\pi\) | ||||
−0.986332 | + | 0.164772i | \(0.947311\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.0969 | −0.534728 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.35178 | + | 14.4657i | 0.316346 | + | 0.547927i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.2447 | − | 11.6883i | −0.764634 | − | 0.441461i | 0.0663234 | − | 0.997798i | \(-0.478873\pi\) |
−0.830957 | + | 0.556337i | \(0.812206\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.06737 | + | 8.10367i | −0.228835 | + | 0.305636i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.1713 | − | 28.0095i | −0.608184 | − | 1.05341i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.0163 | + | 45.0616i | 0.977063 | + | 1.69232i | 0.672951 | + | 0.739687i | \(0.265027\pi\) |
0.304113 | + | 0.952636i | \(0.401640\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 34.4122 | − | 19.8679i | 1.28875 | − | 0.744059i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 26.5742i | − | 0.993817i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.2859 | + | 19.5477i | −0.420892 | + | 0.729006i | −0.996027 | − | 0.0890524i | \(-0.971616\pi\) |
0.575135 | + | 0.818058i | \(0.304949\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.8084 | −1.14737 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.3631 | + | 10.6019i | 0.681987 | + | 0.393745i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.24947 | − | 1.29873i | −0.0834281 | − | 0.0481672i | 0.457706 | − | 0.889104i | \(-0.348671\pi\) |
−0.541134 | + | 0.840937i | \(0.682005\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.84886 | + | 13.5946i | 0.290300 | + | 0.502815i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.7135 | −0.912813 | −0.456407 | − | 0.889771i | \(-0.650864\pi\) | ||||
−0.456407 | + | 0.889771i | \(0.650864\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.3030 | − | 18.6501i | 1.18990 | − | 0.686987i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.8487 | + | 19.5425i | 1.24514 | + | 0.718884i | 0.970137 | − | 0.242558i | \(-0.0779865\pi\) |
0.275007 | + | 0.961442i | \(0.411320\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.14989 | + | 8.91988i | −0.188931 | + | 0.327238i | −0.944894 | − | 0.327376i | \(-0.893836\pi\) |
0.755963 | + | 0.654614i | \(0.227169\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.81914 | + | 13.5432i | 0.286471 | + | 0.496183i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 58.1854i | − | 2.12605i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.7889 | + | 21.8174i | −1.37894 | + | 0.796129i | −0.992031 | − | 0.125990i | \(-0.959789\pi\) |
−0.386905 | + | 0.922120i | \(0.626456\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.7783 | + | 20.4005i | −0.428654 | + | 0.742451i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.69201 | + | 16.7871i | −0.352262 | + | 0.610136i | −0.986645 | − | 0.162883i | \(-0.947921\pi\) |
0.634383 | + | 0.773019i | \(0.281254\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.1351i | 1.49115i | 0.666423 | + | 0.745574i | \(0.267824\pi\) | ||||
−0.666423 | + | 0.745574i | \(0.732176\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 40.6574 | + | 23.4736i | 1.47190 | + | 0.849800i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −30.1126 | −1.08730 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.9257 | − | 36.2444i | −0.754600 | − | 1.30701i | −0.945573 | − | 0.325410i | \(-0.894498\pi\) |
0.190973 | − | 0.981595i | \(-0.438836\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.7846 | − | 16.0414i | 0.999342 | − | 0.576970i | 0.0912886 | − | 0.995824i | \(-0.470901\pi\) |
0.908054 | + | 0.418854i | \(0.137568\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.8784 | + | 9.74473i | −0.606289 | + | 0.350041i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.1564 | + | 7.34511i | −0.614690 | + | 0.263166i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.74751 | − | 16.8832i | 0.348793 | − | 0.604128i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.75983 | + | 5.05749i | −0.312652 | + | 0.180510i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 9.20538i | − | 0.328136i | −0.986449 | − | 0.164068i | \(-0.947538\pi\) | ||
0.986449 | − | 0.164068i | \(-0.0524617\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.7079 | 0.700733 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.9094 | − | 51.8046i | 1.06211 | − | 1.83963i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 23.2175i | − | 0.822404i | −0.911544 | − | 0.411202i | \(-0.865109\pi\) | ||
0.911544 | − | 0.411202i | \(-0.134891\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.8485i | 1.12672i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.5626 | + | 32.1513i | −0.655058 | + | 1.13459i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.2284 | −0.853939 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 53.1510i | − | 1.86869i | −0.356371 | − | 0.934345i | \(-0.615986\pi\) | ||
0.356371 | − | 0.934345i | \(-0.384014\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.76280 | + | 2.74980i | −0.167244 | + | 0.0965586i | −0.581286 | − | 0.813699i | \(-0.697450\pi\) |
0.414041 | + | 0.910258i | \(0.364117\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.16484 | − | 7.21371i | 0.145888 | − | 0.252685i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.1233 | + | 6.90281i | −0.564081 | + | 0.241499i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.0362 | + | 20.2282i | −1.22277 | + | 0.705968i | −0.965508 | − | 0.260373i | \(-0.916154\pi\) |
−0.257264 | + | 0.966341i | \(0.582821\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.3542 | + | 11.1741i | −0.674643 | + | 0.389506i | −0.797834 | − | 0.602878i | \(-0.794021\pi\) |
0.123190 | + | 0.992383i | \(0.460687\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.6175 | − | 40.9067i | −0.821261 | − | 1.42247i | −0.904744 | − | 0.425956i | \(-0.859938\pi\) |
0.0834832 | − | 0.996509i | \(-0.473395\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.4010 | 0.812750 | 0.406375 | − | 0.913706i | \(-0.366793\pi\) | ||||
0.406375 | + | 0.913706i | \(0.366793\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.84914 | − | 3.37700i | −0.202661 | − | 0.117006i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.4438i | 0.811306i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.1780 | − | 26.2890i | 0.524002 | − | 0.907599i | −0.475607 | − | 0.879658i | \(-0.657772\pi\) |
0.999610 | − | 0.0279408i | \(-0.00889500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.9794 | − | 32.8732i | 0.654461 | − | 1.13356i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.3159 | − | 7.68796i | 0.458082 | − | 0.264474i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 5.31430i | − | 0.182602i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.13495 | + | 10.6260i | 0.210303 | + | 0.364256i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.86624 | + | 6.69652i | −0.132377 | + | 0.229285i | −0.924593 | − | 0.380957i | \(-0.875594\pi\) |
0.792215 | + | 0.610242i | \(0.208928\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.16835 | + | 1.25190i | 0.0740695 | + | 0.0427641i | 0.536577 | − | 0.843851i | \(-0.319717\pi\) |
−0.462508 | + | 0.886615i | \(0.653050\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.8497 | − | 8.57348i | 0.506665 | − | 0.292523i | −0.224797 | − | 0.974406i | \(-0.572172\pi\) |
0.731462 | + | 0.681882i | \(0.238838\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −56.7183 | −1.93071 | −0.965356 | − | 0.260937i | \(-0.915969\pi\) | ||||
−0.965356 | + | 0.260937i | \(0.915969\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.76715 | − | 3.06079i | −0.0600848 | − | 0.104070i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30.7757 | + | 17.7683i | 1.04399 | + | 0.602750i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.2164 | + | 24.9510i | 1.46433 | + | 0.845432i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 34.8134 | 1.17691 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.0768 | + | 33.0420i | −0.644178 | + | 1.11575i | 0.340313 | + | 0.940312i | \(0.389467\pi\) |
−0.984491 | + | 0.175436i | \(0.943866\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.3654i | 0.787202i | 0.919281 | + | 0.393601i | \(0.128771\pi\) | ||||
−0.919281 | + | 0.393601i | \(0.871229\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.0755 | + | 5.81707i | −0.339066 | + | 0.195760i | −0.659859 | − | 0.751389i | \(-0.729384\pi\) |
0.320793 | + | 0.947149i | \(0.396051\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.63103 | + | 4.55708i | 0.0883415 | + | 0.153012i | 0.906810 | − | 0.421539i | \(-0.138510\pi\) |
−0.818469 | + | 0.574551i | \(0.805177\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.91104 | + | 6.77412i | 0.131172 | + | 0.227197i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −35.3318 | − | 4.22737i | −1.18233 | − | 0.141464i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.0104 | − | 10.3983i | −0.602021 | − | 0.347577i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.7725 | + | 53.2995i | 1.02632 | + | 1.77764i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.16556 | −0.305349 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 14.6686i | − | 0.487599i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.4669 | − | 15.8580i | −0.912023 | − | 0.526557i | −0.0309416 | − | 0.999521i | \(-0.509851\pi\) |
−0.881082 | + | 0.472964i | \(0.843184\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.4605 | −0.876677 | −0.438338 | − | 0.898810i | \(-0.644433\pi\) | ||||
−0.438338 | + | 0.898810i | \(0.644433\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 64.3440 | 2.12948 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 47.9292 | + | 27.6719i | 1.58276 | + | 0.913808i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 53.0421i | − | 1.74970i | −0.484395 | − | 0.874849i | \(-0.660960\pi\) | ||
0.484395 | − | 0.874849i | \(-0.339040\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 26.0813 | 0.858477 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.00905 | − | 5.21182i | −0.0989368 | − | 0.171364i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.56206 | − | 4.94331i | −0.280912 | − | 0.162185i | 0.352924 | − | 0.935652i | \(-0.385187\pi\) |
−0.633836 | + | 0.773467i | \(0.718521\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.52272 | − | 6.04061i | 0.148226 | − | 0.197973i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.8308 | − | 18.7594i | −0.354204 | − | 0.613499i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.5017 | − | 19.9215i | −0.375743 | − | 0.650806i | 0.614695 | − | 0.788765i | \(-0.289279\pi\) |
−0.990438 | + | 0.137959i | \(0.955946\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.2656 | + | 23.8247i | −1.34522 | + | 0.776663i | −0.987568 | − | 0.157192i | \(-0.949756\pi\) |
−0.357652 | + | 0.933855i | \(0.616423\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.6197i | 0.736600i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.94511 | + | 8.56517i | −0.160694 | + | 0.278331i | −0.935118 | − | 0.354337i | \(-0.884707\pi\) |
0.774424 | + | 0.632667i | \(0.218040\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −49.6676 | −1.61228 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.5341 | + | 15.8968i | 0.891915 | + | 0.514948i | 0.874569 | − | 0.484902i | \(-0.161145\pi\) |
0.0173469 | + | 0.999850i | \(0.494478\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.51592 | + | 1.45256i | 0.0814131 | + | 0.0470039i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.3821 | + | 38.7670i | 0.722756 | + | 1.25185i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.5689 | −0.824805 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.9526 | + | 13.8291i | −0.771062 | + | 0.445173i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.3678 | − | 22.7290i | −1.26598 | − | 0.730915i | −0.291757 | − | 0.956493i | \(-0.594240\pi\) |
−0.974225 | + | 0.225578i | \(0.927573\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.8498 | − | 20.5244i | 0.380278 | − | 0.658660i | −0.610824 | − | 0.791766i | \(-0.709162\pi\) |
0.991102 | + | 0.133106i | \(0.0424951\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.4195 | − | 23.2433i | −0.430210 | − | 0.745146i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 21.4168i | − | 0.685184i | −0.939484 | − | 0.342592i | \(-0.888695\pi\) | ||
0.939484 | − | 0.342592i | \(-0.111305\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.5699 | − | 15.9175i | 0.881138 | − | 0.508726i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.17570 | + | 2.03638i | −0.0374991 | + | 0.0649504i | −0.884166 | − | 0.467173i | \(-0.845272\pi\) |
0.846667 | + | 0.532124i | \(0.178606\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.72954 | + | 4.72770i | −0.0869703 | + | 0.150637i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.2576i | 0.675954i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.7179 | − | 26.9726i | −1.48404 | − | 0.856813i | −0.484209 | − | 0.874952i | \(-0.660893\pi\) |
−0.999835 | + | 0.0181390i | \(0.994226\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.60739 | 0.0509576 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.0931 | + | 26.1420i | 0.478004 | + | 0.827926i | 0.999682 | − | 0.0252157i | \(-0.00802727\pi\) |
−0.521678 | + | 0.853142i | \(0.674694\pi\) | |||||||
\(998\) | 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 | 2736.2.cg.c.1151.7 | ✓ | 32 | |
3.2 | odd | 2 | inner | 2736.2.cg.c.1151.9 | yes | 32 | |
4.3 | odd | 2 | inner | 2736.2.cg.c.1151.8 | yes | 32 | |
12.11 | even | 2 | inner | 2736.2.cg.c.1151.10 | yes | 32 | |
19.7 | even | 3 | inner | 2736.2.cg.c.2591.10 | yes | 32 | |
57.26 | odd | 6 | inner | 2736.2.cg.c.2591.8 | yes | 32 | |
76.7 | odd | 6 | inner | 2736.2.cg.c.2591.9 | yes | 32 | |
228.83 | even | 6 | inner | 2736.2.cg.c.2591.7 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2736.2.cg.c.1151.7 | ✓ | 32 | 1.1 | even | 1 | trivial | |
2736.2.cg.c.1151.8 | yes | 32 | 4.3 | odd | 2 | inner | |
2736.2.cg.c.1151.9 | yes | 32 | 3.2 | odd | 2 | inner | |
2736.2.cg.c.1151.10 | yes | 32 | 12.11 | even | 2 | inner | |
2736.2.cg.c.2591.7 | yes | 32 | 228.83 | even | 6 | inner | |
2736.2.cg.c.2591.8 | yes | 32 | 57.26 | odd | 6 | inner | |
2736.2.cg.c.2591.9 | yes | 32 | 76.7 | odd | 6 | inner | |
2736.2.cg.c.2591.10 | yes | 32 | 19.7 | even | 3 | inner |