Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(95,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.95");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.p (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: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 11x^{14} + 85x^{12} + 332x^{10} + 940x^{8} + 1064x^{6} + 880x^{4} + 128x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 95.4 | ||
Root | \(-1.16543 - 2.01859i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.95 |
Dual form | 576.2.p.c.479.4 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −0.231865 | − | 1.71646i | −0.133867 | − | 0.990999i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.959555 | − | 1.66200i | 0.429126 | − | 0.743268i | −0.567670 | − | 0.823256i | \(-0.692155\pi\) |
0.996796 | + | 0.0799881i | \(0.0254882\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.63027 | − | 1.51859i | 0.994148 | − | 0.573972i | 0.0876366 | − | 0.996153i | \(-0.472069\pi\) |
0.906512 | + | 0.422181i | \(0.138735\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.89248 | + | 0.795973i | −0.964159 | + | 0.265324i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.87122 | − | 2.23505i | 1.16722 | − | 0.673892i | 0.214193 | − | 0.976791i | \(-0.431288\pi\) |
0.953023 | + | 0.302899i | \(0.0979545\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.64938 | − | 2.10697i | −1.01216 | − | 0.584369i | −0.100334 | − | 0.994954i | \(-0.531991\pi\) |
−0.911822 | + | 0.410585i | \(0.865325\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.07524 | − | 1.26168i | −0.794024 | − | 0.325765i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.94600i | 1.44212i | 0.692875 | + | 0.721058i | \(0.256344\pi\) | ||||
−0.692875 | + | 0.721058i | \(0.743656\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.59195 | 0.365218 | 0.182609 | − | 0.983186i | \(-0.441546\pi\) | ||||
0.182609 | + | 0.983186i | \(0.441546\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.21646 | − | 4.16265i | −0.701889 | − | 0.908364i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.13870 | − | 1.97229i | 0.237436 | − | 0.411251i | −0.722542 | − | 0.691327i | \(-0.757026\pi\) |
0.959978 | + | 0.280076i | \(0.0903597\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.658507 | + | 1.14057i | 0.131701 | + | 0.228114i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.03692 | + | 4.78027i | 0.392005 | + | 0.919963i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.90160 | + | 3.29367i | 0.353118 | + | 0.611619i | 0.986794 | − | 0.161980i | \(-0.0517879\pi\) |
−0.633676 | + | 0.773599i | \(0.718455\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.67664 | − | 5.00946i | −1.55837 | − | 0.899726i | −0.997413 | − | 0.0718819i | \(-0.977100\pi\) |
−0.560958 | − | 0.827844i | \(-0.689567\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.73397 | − | 6.12656i | −0.824078 | − | 1.06650i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 5.82867i | − | 0.985225i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.53794i | − | 1.23923i | −0.784906 | − | 0.619615i | \(-0.787289\pi\) | ||
0.784906 | − | 0.619615i | \(-0.212711\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.77037 | + | 6.75256i | −0.443615 | + | 1.08127i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.08347 | − | 2.35759i | −0.637731 | − | 0.368194i | 0.146009 | − | 0.989283i | \(-0.453357\pi\) |
−0.783740 | + | 0.621089i | \(0.786690\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.83430 | − | 3.17709i | −0.279727 | − | 0.484502i | 0.691589 | − | 0.722291i | \(-0.256911\pi\) |
−0.971317 | + | 0.237789i | \(0.923577\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.45259 | + | 5.57107i | −0.216539 | + | 0.830487i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.77037 | + | 4.79843i | 0.404101 | + | 0.699923i | 0.994216 | − | 0.107396i | \(-0.0342513\pi\) |
−0.590116 | + | 0.807319i | \(0.700918\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.11221 | − | 1.92640i | 0.158887 | − | 0.275201i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.2061 | − | 1.37867i | 1.42914 | − | 0.193052i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.72231 | −0.786020 | −0.393010 | − | 0.919534i | \(-0.628566\pi\) | ||||
−0.393010 | + | 0.919534i | \(0.628566\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 8.57861i | − | 1.15674i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.369116 | − | 2.73251i | −0.0488906 | − | 0.361930i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.08445 | + | 0.626109i | 0.141184 | + | 0.0815124i | 0.568928 | − | 0.822387i | \(-0.307358\pi\) |
−0.427744 | + | 0.903900i | \(0.640692\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.295196 | + | 0.170432i | −0.0377960 | + | 0.0218215i | −0.518779 | − | 0.854908i | \(-0.673613\pi\) |
0.480983 | + | 0.876730i | \(0.340280\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.39924 | + | 6.48610i | −0.806228 | + | 0.817172i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.00357 | + | 4.04351i | −0.868686 | + | 0.501536i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.66673 | + | 6.35096i | −0.447962 | + | 0.775893i | −0.998253 | − | 0.0590800i | \(-0.981183\pi\) |
0.550291 | + | 0.834973i | \(0.314517\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.64938 | − | 1.49723i | −0.439334 | − | 0.180246i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.9658 | 1.89480 | 0.947398 | − | 0.320058i | \(-0.103703\pi\) | ||||
0.947398 | + | 0.320058i | \(0.103703\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.3731 | 1.91633 | 0.958164 | − | 0.286220i | \(-0.0923988\pi\) | ||||
0.958164 | + | 0.286220i | \(0.0923988\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.80506 | − | 1.39476i | 0.208430 | − | 0.161053i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.78823 | − | 11.7576i | 0.773590 | − | 1.33990i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.0479956 | − | 0.0277103i | 0.00539992 | − | 0.00311765i | −0.497298 | − | 0.867580i | \(-0.665674\pi\) |
0.502698 | + | 0.864462i | \(0.332341\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.73285 | − | 4.60467i | 0.859206 | − | 0.511630i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.37177 | + | 4.83345i | −0.918922 | + | 0.530540i | −0.883291 | − | 0.468825i | \(-0.844677\pi\) |
−0.0356308 | + | 0.999365i | \(0.511344\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.88224 | + | 5.70551i | 1.07188 | + | 0.618850i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.21254 | − | 4.02771i | 0.558843 | − | 0.431816i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.4661i | 1.53341i | 0.642001 | + | 0.766704i | \(0.278105\pi\) | ||||
−0.642001 | + | 0.766704i | \(0.721895\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.7985 | −1.34165 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.58674 | + | 16.0546i | −0.683013 | + | 1.66479i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.52756 | − | 2.64581i | 0.156724 | − | 0.271455i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.99088 | − | 3.44830i | −0.202143 | − | 0.350122i | 0.747076 | − | 0.664739i | \(-0.231457\pi\) |
−0.949219 | + | 0.314617i | \(0.898124\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.41837 | + | 9.54621i | −0.946582 | + | 0.959430i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.70734 | + | 15.0816i | 0.866412 | + | 1.50067i | 0.865638 | + | 0.500671i | \(0.166913\pi\) |
0.000774625 | 1.00000i | \(0.499753\pi\) | ||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.42671 | + | 2.55576i | 0.436176 | + | 0.251826i | 0.701974 | − | 0.712202i | \(-0.252302\pi\) |
−0.265798 | + | 0.964029i | \(0.585635\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.0047 | + | 1.35146i | −0.976358 | + | 0.131889i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 10.9191i | − | 1.05559i | −0.849372 | − | 0.527795i | \(-0.823019\pi\) | ||
0.849372 | − | 0.527795i | \(-0.176981\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.26334i | − | 0.312572i | −0.987712 | − | 0.156286i | \(-0.950048\pi\) | ||
0.987712 | − | 0.156286i | \(-0.0499521\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.9386 | + | 1.74778i | −1.22808 | + | 0.165892i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.93476 | + | 5.73584i | 0.934584 | + | 0.539582i | 0.888258 | − | 0.459344i | \(-0.151915\pi\) |
0.0463256 | + | 0.998926i | \(0.485249\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.18530 | − | 3.78504i | −0.203780 | − | 0.352957i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.2329 | + | 3.18956i | 1.13093 | + | 0.294875i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.02951 | + | 15.6396i | 0.827734 | + | 1.43368i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.49088 | − | 7.77843i | 0.408261 | − | 0.707130i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.09990 | + | 7.55576i | −0.279509 | + | 0.681280i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1230 | 1.08432 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.07435i | − | 0.539011i | −0.962999 | − | 0.269506i | \(-0.913140\pi\) | ||
0.962999 | − | 0.269506i | \(-0.0868603\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.02805 | + | 3.88515i | −0.442695 | + | 0.342069i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.6351 | + | 6.71754i | 1.01656 | + | 0.586914i | 0.913107 | − | 0.407720i | \(-0.133676\pi\) |
0.103458 | + | 0.994634i | \(0.467009\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.18725 | − | 2.41751i | 0.363080 | − | 0.209625i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.89934 | + | 1.20157i | 0.851999 | + | 0.103415i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.02805 | − | 4.63500i | 0.685883 | − | 0.395994i | −0.116185 | − | 0.993228i | \(-0.537067\pi\) |
0.802068 | + | 0.597233i | \(0.203733\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.944348 | − | 1.63566i | 0.0800986 | − | 0.138735i | −0.823194 | − | 0.567761i | \(-0.807810\pi\) |
0.903292 | + | 0.429026i | \(0.141143\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.59396 | − | 5.86782i | 0.639527 | − | 0.494160i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.8367 | −1.57521 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.29877 | 0.606130 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.56448 | − | 1.46240i | −0.293993 | − | 0.120617i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.03859 | + | 12.1912i | −0.576624 | + | 0.998742i | 0.419239 | + | 0.907876i | \(0.362297\pi\) |
−0.995863 | + | 0.0908659i | \(0.971037\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.96519 | − | 2.28930i | 0.322683 | − | 0.186301i | −0.329905 | − | 0.944014i | \(-0.607017\pi\) |
0.652588 | + | 0.757713i | \(0.273683\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.73285 | − | 17.1987i | −0.382629 | − | 1.39043i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.6514 | + | 9.61371i | −1.33748 | + | 0.772192i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.5316 | − | 11.2766i | −1.55879 | − | 0.899970i | −0.997373 | − | 0.0724386i | \(-0.976922\pi\) |
−0.561420 | − | 0.827531i | \(-0.689745\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.32680 | + | 9.82213i | 0.105222 | + | 0.778945i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.91687i | − | 0.545126i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.96379 | −0.388794 | −0.194397 | − | 0.980923i | \(-0.562275\pi\) | ||||
−0.194397 | + | 0.980923i | \(0.562275\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.7248 | + | 1.98908i | −1.14633 | + | 0.154849i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.52022 | − | 6.09719i | 0.272403 | − | 0.471815i | −0.697074 | − | 0.716999i | \(-0.745515\pi\) |
0.969477 | + | 0.245184i | \(0.0788484\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.37867 | + | 4.11997i | 0.182974 | + | 0.316921i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.60467 | + | 1.26715i | −0.352128 | + | 0.0969011i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.84365 | + | 4.92534i | 0.216198 | + | 0.374467i | 0.953643 | − | 0.300941i | \(-0.0973008\pi\) |
−0.737444 | + | 0.675408i | \(0.763968\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.46410 | + | 2.00000i | 0.261861 | + | 0.151186i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.823246 | − | 2.00659i | 0.0618789 | − | 0.150825i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 15.2828i | − | 1.14229i | −0.820848 | − | 0.571147i | \(-0.806499\pi\) | ||
0.820848 | − | 0.571147i | \(-0.193501\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.4324i | 1.51873i | 0.650665 | + | 0.759365i | \(0.274490\pi\) | ||||
−0.650665 | + | 0.759365i | \(0.725510\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.360985 | + | 0.467176i | 0.0266848 | + | 0.0345346i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.5280 | − | 7.23307i | −0.921081 | − | 0.531786i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.2896 | + | 23.0182i | 0.971831 | + | 1.68326i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.6169 | + | 9.48015i | 0.917744 | + | 0.689579i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.29793 | + | 7.44424i | 0.310988 | + | 0.538646i | 0.978576 | − | 0.205884i | \(-0.0660069\pi\) |
−0.667589 | + | 0.744530i | \(0.732674\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.766456 | − | 1.32754i | 0.0551707 | − | 0.0955584i | −0.837121 | − | 0.547018i | \(-0.815763\pi\) |
0.892292 | + | 0.451459i | \(0.149096\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.56441 | + | 11.0838i | 0.613310 | + | 0.793728i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.4255 | −1.09902 | −0.549512 | − | 0.835486i | \(-0.685186\pi\) | ||||
−0.549512 | + | 0.835486i | \(0.685186\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.61578i | 0.539868i | 0.962879 | + | 0.269934i | \(0.0870020\pi\) | ||||
−0.962879 | + | 0.269934i | \(0.912998\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.7514 | + | 4.82123i | 0.828877 | + | 0.340063i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.0034 | + | 5.77549i | 0.702104 | + | 0.405360i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.83663 | + | 4.52448i | −0.547334 | + | 0.316003i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.72378 | + | 6.61118i | −0.119811 | + | 0.459509i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.16277 | − | 3.55808i | 0.426288 | − | 0.246117i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.38979 | + | 4.13923i | −0.164520 | + | 0.284956i | −0.936485 | − | 0.350709i | \(-0.885941\pi\) |
0.771965 | + | 0.635665i | \(0.219274\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.70191 | − | 27.4047i | −0.253651 | − | 1.87774i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.04043 | −0.480154 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −30.4292 | −2.06567 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.79635 | − | 28.1038i | −0.256533 | − | 1.89908i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.5280 | − | 21.6992i | 0.842728 | − | 1.45965i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.3549 | + | 6.55576i | −0.760381 | + | 0.439006i | −0.829432 | − | 0.558607i | \(-0.811336\pi\) |
0.0690516 | + | 0.997613i | \(0.478003\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.81258 | − | 2.77491i | −0.187505 | − | 0.184994i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.02631 | − | 2.90194i | 0.333608 | − | 0.192609i | −0.323834 | − | 0.946114i | \(-0.604972\pi\) |
0.657442 | + | 0.753505i | \(0.271639\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.4201 | + | 9.48015i | 1.08507 | + | 0.626466i | 0.932260 | − | 0.361790i | \(-0.117834\pi\) |
0.152811 | + | 0.988255i | \(0.451167\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −21.7553 | − | 8.92557i | −1.43140 | − | 0.587259i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.46503i | 0.358026i | 0.983847 | + | 0.179013i | \(0.0572904\pi\) | ||||
−0.983847 | + | 0.179013i | \(0.942710\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.6333 | 0.693640 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.0586921 | − | 0.0759575i | −0.00381246 | − | 0.00493397i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.0500 | − | 19.1392i | 0.714768 | − | 1.23801i | −0.248281 | − | 0.968688i | \(-0.579866\pi\) |
0.963049 | − | 0.269326i | \(-0.0868009\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.55610 | + | 16.5516i | 0.615562 | + | 1.06619i | 0.990286 | + | 0.139049i | \(0.0444044\pi\) |
−0.374723 | + | 0.927137i | \(0.622262\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.69671 | − | 12.2055i | −0.622044 | − | 0.782982i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.13445 | − | 3.69698i | −0.136365 | − | 0.236192i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.80962 | − | 3.35419i | −0.369657 | − | 0.213422i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.2375 | + | 13.2491i | 0.648778 | + | 0.839629i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 3.24267i | − | 0.204675i | −0.994750 | − | 0.102338i | \(-0.967368\pi\) | ||
0.994750 | − | 0.102338i | \(-0.0326322\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 10.1802i | − | 0.640025i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.50195 | − | 18.2854i | 0.469790 | − | 1.14508i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.2580 | − | 12.2733i | −1.32604 | − | 0.765589i | −0.341354 | − | 0.939935i | \(-0.610885\pi\) |
−0.984684 | + | 0.174346i | \(0.944219\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.4470 | − | 19.8268i | −0.711283 | − | 1.23198i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.12201 | − | 8.01324i | −0.502740 | − | 0.496007i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.1239 | − | 26.1953i | −0.932578 | − | 1.61527i | −0.778896 | − | 0.627153i | \(-0.784220\pi\) |
−0.153682 | − | 0.988120i | \(-0.549113\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.49088 | + | 9.51048i | −0.337302 | + | 0.584224i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.8306 | − | 3.35419i | 1.51961 | − | 0.205273i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.4497 | −1.06393 | −0.531963 | − | 0.846767i | \(-0.678546\pi\) | ||||
−0.531963 | + | 0.846767i | \(0.678546\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.634028i | 0.0385145i | 0.999815 | + | 0.0192572i | \(0.00613015\pi\) | ||||
−0.999815 | + | 0.0192572i | \(0.993870\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.96751 | + | 21.9681i | 0.179602 | + | 1.32957i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.09845 | + | 2.94359i | 0.307448 | + | 0.177505i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.6367 | − | 11.3372i | 1.17985 | − | 0.681189i | 0.223873 | − | 0.974618i | \(-0.428130\pi\) |
0.955981 | + | 0.293430i | \(0.0947966\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 29.0844 | + | 7.58338i | 1.74124 | + | 0.454005i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.1634 | − | 5.86782i | 0.606296 | − | 0.350045i | −0.165219 | − | 0.986257i | \(-0.552833\pi\) |
0.771514 | + | 0.636212i | \(0.219500\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.24946 | − | 12.5564i | 0.430936 | − | 0.746403i | −0.566018 | − | 0.824393i | \(-0.691517\pi\) |
0.996954 | + | 0.0779899i | \(0.0248502\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.89562 | − | 2.00853i | −0.289992 | − | 0.118975i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.3208 | −0.845332 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −18.3549 | −1.07970 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.45726 | + | 4.21680i | −0.319910 | + | 0.247193i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.06591 | + | 1.84622i | −0.0622713 | + | 0.107857i | −0.895480 | − | 0.445101i | \(-0.853168\pi\) |
0.833209 | + | 0.552958i | \(0.186501\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.08118 | − | 1.20157i | 0.121171 | − | 0.0699582i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.5695 | + | 13.9528i | 1.07751 | + | 0.809626i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.31112 | + | 4.79843i | −0.480645 | + | 0.277500i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.64938 | − | 5.57107i | −0.556181 | − | 0.321111i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 23.8680 | − | 18.4427i | 1.37118 | − | 1.05950i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.654154i | 0.0374568i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.4666 | 1.51053 | 0.755265 | − | 0.655419i | \(-0.227508\pi\) | ||||
0.755265 | + | 0.655419i | \(0.227508\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.36047 | − | 8.19086i | 0.191170 | − | 0.465962i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.70670 | + | 16.8125i | −0.550416 | + | 0.953349i | 0.447828 | + | 0.894120i | \(0.352198\pi\) |
−0.998244 | + | 0.0592293i | \(0.981136\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.89136 | − | 8.47208i | −0.276476 | − | 0.478871i | 0.694030 | − | 0.719946i | \(-0.255833\pi\) |
−0.970506 | + | 0.241075i | \(0.922500\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.63947 | + | 16.8593i | 0.261404 | + | 0.949914i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.22584 | − | 9.05141i | −0.293512 | − | 0.508378i | 0.681125 | − | 0.732167i | \(-0.261491\pi\) |
−0.974638 | + | 0.223789i | \(0.928157\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.7230 | + | 8.50034i | 0.824331 | + | 0.475928i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.7422 | + | 2.53176i | −1.04609 | + | 0.141309i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.46571i | 0.526686i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 5.54983i | − | 0.307849i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.60140 | + | 0.756654i | −0.309758 | + | 0.0418430i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.5737 | + | 8.41410i | 0.803472 | + | 0.463885i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.02124 | − | 15.6252i | −0.495852 | − | 0.858841i | 0.504136 | − | 0.863624i | \(-0.331811\pi\) |
−0.999989 | + | 0.00478295i | \(0.998478\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.00000 | + | 21.8033i | 0.328798 | + | 1.19482i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.03685 | + | 12.1882i | 0.384464 | + | 0.665912i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.444579 | + | 0.770034i | −0.0242178 | + | 0.0419464i | −0.877880 | − | 0.478880i | \(-0.841043\pi\) |
0.853663 | + | 0.520827i | \(0.174376\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.54182 | − | 18.3826i | 0.409616 | − | 0.998404i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −44.7856 | −2.42527 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.5043i | 0.783157i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.99019 | + | 4.62859i | −0.322501 | + | 0.249195i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.28499 | + | 3.62864i | 0.337396 | + | 0.194796i | 0.659120 | − | 0.752038i | \(-0.270929\pi\) |
−0.321724 | + | 0.946834i | \(0.604262\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.5877 | + | 11.8863i | −1.10204 | + | 0.636260i | −0.936755 | − | 0.349986i | \(-0.886186\pi\) |
−0.165280 | + | 0.986247i | \(0.552853\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.63839 | − | 21.7368i | 0.140827 | − | 1.16022i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.4377 | − | 6.02618i | 0.555540 | − | 0.320741i | −0.195813 | − | 0.980641i | \(-0.562735\pi\) |
0.751354 | + | 0.659900i | \(0.229401\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.3201 | − | 26.5352i | 0.813106 | − | 1.40834i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 24.7511 | − | 19.1251i | 1.30997 | − | 1.01221i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.3505 | −1.02128 | −0.510640 | − | 0.859795i | \(-0.670591\pi\) | ||||
−0.510640 | + | 0.859795i | \(0.670591\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.4657 | −0.866616 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.3926 | − | 5.90487i | −0.755418 | − | 0.309925i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.7109 | − | 27.2121i | 0.822347 | − | 1.42435i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.52528 | + | 4.34472i | −0.392817 | + | 0.226793i | −0.683380 | − | 0.730063i | \(-0.739491\pi\) |
0.290563 | + | 0.956856i | \(0.406157\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.6879 | + | 3.56895i | 0.712565 | + | 0.185792i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.0512 | + | 8.68983i | −0.781421 | + | 0.451153i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.92070 | − | 2.26362i | −0.203006 | − | 0.117206i | 0.395051 | − | 0.918659i | \(-0.370727\pi\) |
−0.598057 | + | 0.801454i | \(0.704060\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.81091 | − | 20.8087i | −0.145155 | − | 1.07456i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 16.0265i | − | 0.825406i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.28133 | 0.476750 | 0.238375 | − | 0.971173i | \(-0.423385\pi\) | ||||
0.238375 | + | 0.971173i | \(0.423385\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.4264 | + | 1.40843i | −0.534160 | + | 0.0721558i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.62746 | + | 8.01500i | −0.236452 | + | 0.409548i | −0.959694 | − | 0.281048i | \(-0.909318\pi\) |
0.723241 | + | 0.690595i | \(0.242651\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.0274 | − | 22.5640i | −0.663936 | − | 1.14997i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.83454 | + | 7.72962i | 0.398252 | + | 0.392919i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.98502 | + | 5.17021i | 0.151347 | + | 0.262140i | 0.931723 | − | 0.363170i | \(-0.118306\pi\) |
−0.780376 | + | 0.625310i | \(0.784972\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.7272 | + | 6.77072i | 0.593071 | + | 0.342410i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.83262 | − | 21.5288i | 0.445547 | − | 1.08598i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 0.106358i | − | 0.00535146i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.5213i | 0.879367i | 0.898153 | + | 0.439684i | \(0.144909\pi\) | ||||
−0.898153 | + | 0.439684i | \(0.855091\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.12043 | − | 6.62671i | −0.256342 | − | 0.331751i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.72928 | − | 3.88515i | −0.336044 | − | 0.194015i | 0.322477 | − | 0.946577i | \(-0.395484\pi\) |
−0.658521 | + | 0.752562i | \(0.728818\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.1096 | + | 36.5629i | 1.05154 | + | 1.82133i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.232853 | − | 17.2704i | −0.0115706 | − | 0.858174i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.8477 | − | 29.1810i | −0.835108 | − | 1.44645i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.48175 | + | 14.6908i | −0.419396 | + | 0.726415i | −0.995879 | − | 0.0906945i | \(-0.971091\pi\) |
0.576483 | + | 0.817109i | \(0.304425\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.81721 | − | 12.7051i | −0.484247 | − | 0.626698i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.80320 | 0.187143 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.5518i | 0.910674i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.02651 | − | 1.24169i | −0.148209 | − | 0.0608056i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.0314545 | + | 0.0181603i | 0.00153665 | + | 0.000887187i | 0.500768 | − | 0.865581i | \(-0.333051\pi\) |
−0.499231 | + | 0.866469i | \(0.666384\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.13540 | − | 1.81022i | 0.152810 | − | 0.0882249i | −0.421645 | − | 0.906761i | \(-0.638547\pi\) |
0.574455 | + | 0.818536i | \(0.305214\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.8327 | − | 11.6742i | −0.575324 | − | 0.567619i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.78181 | + | 3.91548i | −0.328966 | + | 0.189929i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.517630 | + | 0.896562i | −0.0250499 | + | 0.0433877i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.36757 | + | 32.3325i | 0.210868 | + | 1.56103i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.58181 | −0.461539 | −0.230770 | − | 0.973008i | \(-0.574124\pi\) | ||||
−0.230770 | + | 0.973008i | \(0.574124\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.88778 | 0.475176 | 0.237588 | − | 0.971366i | \(-0.423643\pi\) | ||||
0.237588 | + | 0.971366i | \(0.423643\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.69233 | − | 12.5280i | −0.0811408 | − | 0.600674i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.81275 | − | 3.13978i | 0.0867157 | − | 0.150196i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.7468 | + | 11.4008i | −0.942464 | + | 0.544132i | −0.890732 | − | 0.454529i | \(-0.849807\pi\) |
−0.0517319 | + | 0.998661i | \(0.516474\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.68368 | + | 6.45737i | −0.0801751 | + | 0.307494i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.36311 | + | 1.36434i | −0.112275 | + | 0.0648218i | −0.555086 | − | 0.831793i | \(-0.687315\pi\) |
0.442811 | + | 0.896615i | \(0.353981\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.0427 | + | 13.8811i | 1.13973 | + | 0.658026i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.5577 | + | 9.25476i | 1.06694 | + | 0.437735i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 17.1488i | − | 0.809302i | −0.914471 | − | 0.404651i | \(-0.867393\pi\) | ||
0.914471 | − | 0.404651i | \(-0.132607\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.0773 | −0.992493 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.84889 | − | 6.27529i | −0.227821 | − | 0.294839i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.2809 | + | 21.2711i | −0.575735 | + | 0.997203i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.3079 | − | 19.5858i | −0.528961 | − | 0.916187i | −0.999430 | − | 0.0337704i | \(-0.989249\pi\) |
0.470469 | − | 0.882417i | \(-0.344085\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −28.4234 | + | 12.1115i | −1.32669 | + | 0.565317i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.8418 | + | 18.7785i | 0.504953 | + | 0.874604i | 0.999984 | + | 0.00572824i | \(0.00182336\pi\) |
−0.495031 | + | 0.868875i | \(0.664843\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.9262 | + | 6.30823i | 0.507782 | + | 0.293168i | 0.731922 | − | 0.681389i | \(-0.238624\pi\) |
−0.224139 | + | 0.974557i | \(0.571957\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20.3624 | + | 26.3525i | 0.944286 | + | 1.22207i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.0822i | 1.34577i | 0.739749 | + | 0.672883i | \(0.234944\pi\) | ||||
−0.739749 | + | 0.672883i | \(0.765056\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.2730i | 1.02847i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.8271 | + | 36.1399i | −0.683198 | + | 1.66524i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.2019 | − | 8.19948i | −0.653005 | − | 0.377012i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.04831 | + | 1.81572i | 0.0480997 | + | 0.0833111i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.5517 | − | 4.55481i | 0.757849 | − | 0.208550i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.657735 | − | 1.13923i | −0.0300527 | − | 0.0520527i | 0.850608 | − | 0.525801i | \(-0.176234\pi\) |
−0.880661 | + | 0.473748i | \(0.842901\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.8822 | + | 27.5088i | −0.724168 | + | 1.25430i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.8725 | + | 1.60378i | −0.540219 | + | 0.0729744i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.64142 | −0.346979 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.5975i | 0.480220i | 0.970746 | + | 0.240110i | \(0.0771835\pi\) | ||||
−0.970746 | + | 0.240110i | \(0.922816\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.15093 | + | 8.52015i | 0.0520467 | + | 0.385294i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.2744 | + | 7.08665i | 0.553938 | + | 0.319816i | 0.750709 | − | 0.660633i | \(-0.229712\pi\) |
−0.196771 | + | 0.980450i | \(0.563045\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.5841 | + | 11.3069i | −0.882026 | + | 0.509238i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.82834 | + | 24.8134i | 0.306911 | + | 1.11528i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 41.9944 | − | 24.2455i | 1.88371 | − | 1.08756i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.3136 | + | 35.1842i | −0.909363 | + | 1.57506i | −0.0944115 | + | 0.995533i | \(0.530097\pi\) |
−0.814951 | + | 0.579529i | \(0.803236\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.2818 | − | 4.62859i | −0.504034 | − | 0.206790i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.81878 | 0.214859 | 0.107429 | − | 0.994213i | \(-0.465738\pi\) | ||||
0.107429 | + | 0.994213i | \(0.465738\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33.4207 | 1.48720 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.52024 | − | 5.03816i | 0.289574 | − | 0.223753i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.8768 | + | 18.8392i | −0.482106 | + | 0.835032i | −0.999789 | − | 0.0205402i | \(-0.993461\pi\) |
0.517683 | + | 0.855573i | \(0.326795\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 43.0657 | − | 24.8640i | 1.90511 | − | 1.09992i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.24267 | + | 7.60993i | 0.143167 | + | 0.335987i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.49534 | − | 4.90479i | 0.374349 | − | 0.216131i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.4494 | + | 12.3838i | 0.943345 | + | 0.544640i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.79482 | − | 6.02302i | 0.342154 | − | 0.264381i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 9.89853i | − | 0.433662i | −0.976209 | − | 0.216831i | \(-0.930428\pi\) | ||
0.976209 | − | 0.216831i | \(-0.0695721\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.9296 | −0.915188 | −0.457594 | − | 0.889161i | \(-0.651289\pi\) | ||||
−0.457594 | + | 0.889161i | \(0.651289\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.62972 | − | 6.40972i | 0.114770 | − | 0.279743i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 29.7862 | − | 51.5913i | 1.29751 | − | 2.24735i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.90672 | + | 15.4269i | 0.387248 | + | 0.670734i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.63512 | − | 0.947811i | −0.157751 | − | 0.0411315i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.93476 | + | 17.2075i | 0.430322 | + | 0.745340i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.1475 | − | 10.4775i | −0.784587 | − | 0.452981i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.2324 | + | 3.54355i | −1.13201 | + | 0.152916i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 9.94337i | − | 0.428291i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 24.6577i | − | 1.06012i | −0.847961 | − | 0.530058i | \(-0.822170\pi\) | ||
0.847961 | − | 0.530058i | \(-0.177830\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 35.0714 | − | 4.73755i | 1.50506 | − | 0.203308i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.42367 | − | 3.13136i | −0.232325 | − | 0.134133i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.26148 | − | 5.64904i | −0.139451 | − | 0.241536i | 0.787838 | − | 0.615882i | \(-0.211200\pi\) |
−0.927289 | + | 0.374347i | \(0.877867\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.718189 | − | 0.727938i | 0.0306516 | − | 0.0310676i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.02725 | + | 5.24335i | 0.128965 | + | 0.223374i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.0841609 | − | 0.145771i | 0.00357888 | − | 0.00619881i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.51048 | + | 23.1810i | −0.403697 | + | 0.983979i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.6027 | 1.00008 | 0.500039 | − | 0.866003i | \(-0.333319\pi\) | ||||
0.500039 | + | 0.866003i | \(0.333319\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.4592i | 0.653856i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 36.4285 | − | 28.1482i | 1.53801 | − | 1.18842i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.2685 | − | 22.0943i | −1.61283 | − | 0.931166i | −0.988711 | − | 0.149833i | \(-0.952126\pi\) |
−0.624115 | − | 0.781332i | \(-0.714540\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.0659 | − | 11.0077i | 0.802109 | − | 0.463098i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13.3469 | − | 23.8545i | 0.560517 | − | 1.00180i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.63183 | − | 3.82889i | 0.278021 | − | 0.160515i | −0.354506 | − | 0.935054i | \(-0.615351\pi\) |
0.632527 | + | 0.774538i | \(0.282018\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.68452 | + | 4.64972i | −0.112344 | + | 0.194585i | −0.916715 | − | 0.399542i | \(-0.869169\pi\) |
0.804371 | + | 0.594127i | \(0.202502\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.7812 | − | 9.10329i | 0.492167 | − | 0.380296i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.99937 | 0.125083 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.8963 | −0.869924 | −0.434962 | − | 0.900449i | \(-0.643238\pi\) | ||||
−0.434962 | + | 0.900449i | \(0.643238\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.45639 | − | 1.00778i | −0.102084 | − | 0.0418820i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.6800 | + | 25.4265i | −0.609030 | + | 1.05487i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.1523 | + | 12.7896i | −0.917455 | + | 0.529693i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 17.0391 | − | 17.2704i | 0.704482 | − | 0.714044i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.30245 | − | 1.32932i | 0.0950324 | − | 0.0548670i | −0.451731 | − | 0.892154i | \(-0.649193\pi\) |
0.546763 | + | 0.837287i | \(0.315860\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.8128 | − | 7.97480i | −0.569145 | − | 0.328596i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.57663 | + | 26.4773i | 0.147123 | + | 1.08913i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.5587i | 0.803180i | 0.915820 | + | 0.401590i | \(0.131542\pi\) | ||||
−0.915820 | + | 0.401590i | \(0.868458\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 34.6573 | 1.42081 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.0722 | − | 1.76583i | 0.535009 | − | 0.0722706i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.9459 | + | 18.9589i | −0.447239 | + | 0.774640i | −0.998205 | − | 0.0598874i | \(-0.980926\pi\) |
0.550967 | + | 0.834527i | \(0.314259\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.6621 | + | 20.1993i | 0.475706 | + | 0.823947i | 0.999613 | − | 0.0278286i | \(-0.00885926\pi\) |
−0.523907 | + | 0.851776i | \(0.675526\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.55073 | − | 21.2886i | 0.226043 | − | 0.866939i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.61849 | − | 14.9277i | −0.350391 | − | 0.606896i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.54529 | + | 3.20157i | 0.225076 | + | 0.129948i | 0.608299 | − | 0.793708i | \(-0.291852\pi\) |
−0.383222 | + | 0.923656i | \(0.625186\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.59396 | − | 18.5097i | 0.307723 | − | 0.750049i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 23.3484i | − | 0.944575i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.2674i | 1.02054i | 0.860014 | + | 0.510271i | \(0.170455\pi\) | ||||
−0.860014 | + | 0.510271i | \(0.829545\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.58313 | + | 12.4022i | 0.386429 | + | 0.500105i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.3822 | + | 13.4997i | 0.941333 | + | 0.543479i | 0.890378 | − | 0.455222i | \(-0.150440\pi\) |
0.0509554 | + | 0.998701i | \(0.483773\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.55480 | − | 14.8173i | −0.343846 | − | 0.595559i | 0.641297 | − | 0.767293i | \(-0.278397\pi\) |
−0.985143 | + | 0.171733i | \(0.945063\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.7475 | + | 1.42590i | 0.471412 | + | 0.0572195i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.9681 | + | 38.0499i | 0.880133 | + | 1.52444i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.34020 | − | 14.4457i | 0.333608 | − | 0.577826i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.53623 | − | 9.75316i | −0.300968 | − | 0.389504i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 44.8206 | 1.78711 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 14.4488i | − | 0.575199i | −0.957751 | − | 0.287600i | \(-0.907143\pi\) | ||
0.957751 | − | 0.287600i | \(-0.0928572\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.65893 | + | 3.14223i | 0.304415 | + | 0.124893i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.0956 | − | 5.82867i | −0.400630 | − | 0.231304i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.11776 | + | 4.68679i | −0.321637 | + | 0.185697i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −46.1808 | + | 12.7084i | −1.82688 | + | 0.502736i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.3963 | + | 20.4361i | −1.39807 | + | 0.807176i | −0.994190 | − | 0.107636i | \(-0.965672\pi\) |
−0.403879 | + | 0.914812i | \(0.632338\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.76272 | − | 6.51722i | 0.148387 | − | 0.257014i | −0.782244 | − | 0.622972i | \(-0.785925\pi\) |
0.930631 | + | 0.365958i | \(0.119259\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.63243 | + | 12.0846i | 0.0642768 | + | 0.475832i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.8778 | 0.899419 | 0.449709 | − | 0.893175i | \(-0.351528\pi\) | ||||
0.449709 | + | 0.893175i | \(0.351528\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.59753 | 0.219722 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.05546 | + | 52.2306i | 0.276525 | + | 2.04708i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.76276 | + | 8.24934i | −0.186381 | + | 0.322822i | −0.944041 | − | 0.329828i | \(-0.893009\pi\) |
0.757660 | + | 0.652650i | \(0.226343\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.3291 | − | 12.8917i | 0.872469 | − | 0.503720i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −47.3589 | + | 13.0326i | −1.84765 | + | 0.508449i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.1574 | + | 23.7622i | −1.60326 | + | 0.925645i | −0.612436 | + | 0.790520i | \(0.709810\pi\) |
−0.990829 | + | 0.135125i | \(0.956856\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.66209 | + | 3.26901i | 0.220230 | + | 0.127150i | 0.606057 | − | 0.795421i | \(-0.292750\pi\) |
−0.385827 | + | 0.922571i | \(0.626084\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −40.1507 | − | 16.4726i | −1.55932 | − | 0.639744i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 9.27893i | − | 0.359822i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.66143 | 0.335372 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.8855 | + | 17.9702i | 0.536845 | + | 0.694768i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.761845 | + | 1.31955i | −0.0294107 | + | 0.0509408i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.6311 | − | 23.6098i | −0.525442 | − | 0.910092i | −0.999561 | − | 0.0296310i | \(-0.990567\pi\) |
0.474119 | − | 0.880461i | \(-0.342767\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.11089 | + | 5.47109i | −0.158228 | + | 0.210582i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.7284 | − | 27.2424i | −0.604492 | − | 1.04701i | −0.992132 | − | 0.125200i | \(-0.960043\pi\) |
0.387639 | − | 0.921811i | \(-0.373291\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.4731 | − | 6.04664i | −0.401920 | − | 0.232049i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.14649 | − | 7.95461i | −0.235534 | − | 0.304821i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.3637i | 0.855725i | 0.903844 | + | 0.427862i | \(0.140733\pi\) | ||||
−0.903844 | + | 0.427862i | \(0.859267\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 17.7901i | − | 0.679726i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.4651 | − | 30.3826i | 0.475572 | − | 1.15917i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.8829 | + | 12.0568i | 0.795576 | + | 0.459326i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.43897 | − | 11.1526i | −0.244950 | − | 0.424265i | 0.717168 | − | 0.696901i | \(-0.245438\pi\) |
−0.962117 | + | 0.272635i | \(0.912105\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.2761 | + | 39.4117i | −0.390357 | + | 1.49713i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.81231 | − | 3.13901i | −0.0687448 | − | 0.119069i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.0182 | − | 24.2803i | 0.530979 | − | 0.919682i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.38051 | − | 1.26715i | 0.354803 | − | 0.0479279i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.77325 | 0.369131 | 0.184565 | − | 0.982820i | \(-0.440912\pi\) | ||||
0.184565 | + | 0.982820i | \(0.440912\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 12.0000i | − | 0.452589i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.46549 | − | 18.2517i | −0.0928556 | − | 0.687397i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 45.8053 | + | 26.4457i | 1.72268 | + | 0.994593i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.5252 | + | 13.0049i | −0.845950 | + | 0.488409i | −0.859282 | − | 0.511502i | \(-0.829089\pi\) |
0.0133323 | + | 0.999911i | \(0.495756\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.116770 | + | 0.118354i | −0.00437920 | + | 0.00443864i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.7602 | + | 11.4086i | −0.740026 | + | 0.427254i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.0749 | + | 31.3066i | −0.675963 | + | 1.17080i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −35.4139 | − | 14.5293i | −1.32255 | − | 0.542605i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.9704 | −1.04312 | −0.521559 | − | 0.853215i | \(-0.674649\pi\) | ||||
−0.521559 | + | 0.853215i | \(0.674649\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.5246 | 0.578165 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.1945 | − | 20.2404i | 0.974185 | − | 0.752749i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.50444 | + | 4.33781i | −0.0930124 | + | 0.161102i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.10497 | − | 4.10206i | 0.263509 | − | 0.152137i | −0.362425 | − | 0.932013i | \(-0.618051\pi\) |
0.625934 | + | 0.779876i | \(0.284718\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.7019 | + | 19.4740i | −0.692663 | + | 0.721261i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.8910 | − | 10.9067i | 0.698708 | − | 0.403399i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.3513 | − | 11.1725i | −0.714756 | − | 0.412665i | 0.0980633 | − | 0.995180i | \(-0.468735\pi\) |
−0.812820 | + | 0.582515i | \(0.802069\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.85082 | + | 4.52091i | −0.215811 | + | 0.166756i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.7812i | 1.20751i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.6888 | −1.31283 | −0.656417 | − | 0.754399i | \(-0.727929\pi\) | ||||
−0.656417 | + | 0.754399i | \(0.727929\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.41029 | + | 10.7497i | −0.162016 | + | 0.394900i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.56128 | + | 13.0965i | −0.277396 | + | 0.480465i | −0.970737 | − | 0.240145i | \(-0.922805\pi\) |
0.693341 | + | 0.720610i | \(0.256138\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.5078 | + | 23.3963i | 0.494889 | + | 0.857172i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20.3679 | − | 20.6443i | 0.745222 | − | 0.755337i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.5816 | − | 28.7202i | −0.605879 | − | 1.04941i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.4856 | − | 17.0235i | −1.07595 | − | 0.621197i | −0.146146 | − | 0.989263i | \(-0.546687\pi\) |
−0.929800 | + | 0.368066i | \(0.880020\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.56591 | + | 0.751860i | −0.202833 | + | 0.0273993i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 8.78686i | − | 0.319786i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 45.3866i | − | 1.64960i | −0.565423 | − | 0.824801i | \(-0.691287\pi\) | ||
0.565423 | − | 0.824801i | \(-0.308713\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17.4739 | + | 2.36043i | −0.634264 | + | 0.0856782i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.6558 | − | 7.30686i | −0.458774 | − | 0.264873i | 0.252755 | − | 0.967530i | \(-0.418663\pi\) |
−0.711529 | + | 0.702657i | \(0.751997\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.95567 | − | 8.58347i | −0.179407 | − | 0.310742i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −33.1256 | − | 8.63707i | −1.19766 | − | 0.312274i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.63839 | − | 4.56982i | −0.0952667 | − | 0.165007i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.2146 | − | 38.4768i | 0.801079 | − | 1.38751i | −0.117827 | − | 0.993034i | \(-0.537593\pi\) |
0.918906 | − | 0.394476i | \(-0.129074\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.1377 | + | 39.3343i | −0.581185 | + | 1.41659i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.7747 | −0.387539 | −0.193770 | − | 0.981047i | \(-0.562071\pi\) | ||||
−0.193770 | + | 0.981047i | \(0.562071\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 13.1951i | − | 0.473981i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −31.3778 | + | 24.2455i | −1.12567 | + | 0.869802i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.50067 | − | 3.75316i | −0.232911 | − | 0.134471i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 61.8072 | − | 35.6844i | 2.21164 | − | 1.27689i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.8712 | + | 15.7991i | −0.424243 | + | 0.564614i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −37.4833 | + | 21.6410i | −1.33784 | + | 0.772401i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.7959 | − | 29.0914i | 0.598710 | − | 1.03700i | −0.394301 | − | 0.918981i | \(-0.629013\pi\) |
0.993012 | − | 0.118016i | \(-0.0376533\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −41.4566 | + | 32.0333i | −1.47589 | + | 1.14042i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.8415 | 1.23882 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.43638 | 0.0510073 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17.5975 | + | 7.21973i | 0.624119 | + | 0.256058i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.1756 | − | 21.0887i | 0.431281 | − | 0.747001i | −0.565703 | − | 0.824609i | \(-0.691395\pi\) |
0.996984 | + | 0.0776084i | \(0.0247284\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.5314 | + | 16.4726i | −1.00937 | + | 0.582760i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.5147 | − | 41.8430i | −0.406851 | − | 1.47845i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 63.3839 | − | 36.5947i | 2.23677 | − | 1.29140i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.4958 | − | 6.63712i | −0.405175 | − | 0.233928i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.04597 | + | 29.9517i | 0.142425 | + | 1.05435i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 16.9318i | − | 0.595290i | −0.954677 | − | 0.297645i | \(-0.903799\pi\) | ||
0.954677 | − | 0.297645i | \(-0.0962012\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.5985 | 0.863771 | 0.431885 | − | 0.901929i | \(-0.357849\pi\) | ||||
0.431885 | + | 0.901929i | \(0.357849\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.08828 | − | 0.147009i | 0.0381678 | − | 0.00515582i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.76303 | + | 8.24981i | −0.166842 | + | 0.288978i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.92010 | − | 5.05776i | −0.102161 | − | 0.176949i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 37.0193 | − | 10.1872i | 1.29356 | − | 0.355971i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.0525282 | − | 0.0909815i | −0.00183325 | − | 0.00317528i | 0.865107 | − | 0.501587i | \(-0.167250\pi\) |
−0.866941 | + | 0.498412i | \(0.833917\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.56689 | + | 5.52345i | 0.333481 | + | 0.192535i | 0.657385 | − | 0.753554i | \(-0.271662\pi\) |
−0.323905 | + | 0.946090i | \(0.604996\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.87041 | − | 9.43380i | 0.134750 | − | 0.328443i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.4229i | 0.536308i | 0.963376 | + | 0.268154i | \(0.0864135\pi\) | ||||
−0.963376 | + | 0.268154i | \(0.913586\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.8278i | 0.897038i | 0.893773 | + | 0.448519i | \(0.148048\pi\) | ||||
−0.893773 | + | 0.448519i | \(0.851952\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.0130 | − | 31.0769i | −0.833001 | − | 1.07805i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.4544 | + | 6.61320i | 0.396871 | + | 0.229134i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.75569 | − | 11.7012i | −0.233790 | − | 0.404936i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.27294 | − | 51.6806i | 0.216824 | − | 1.78634i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.10290 | − | 14.0346i | −0.279743 | − | 0.484529i | 0.691578 | − | 0.722302i | \(-0.256916\pi\) |
−0.971321 | + | 0.237773i | \(0.923583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.26783 | − | 12.5882i | 0.250615 | − | 0.434077i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.4284 | − | 16.0845i | −0.428057 | − | 0.553979i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.12985 | 0.314076 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 27.2791i | − | 0.937322i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.2335 | − | 9.53203i | −0.797373 | − | 0.327138i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.8670 | − | 8.58347i | −0.509634 | − | 0.294238i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.3781 | + | 8.87853i | −0.526535 | + | 0.303995i | −0.739604 | − | 0.673042i | \(-0.764987\pi\) |
0.213069 | + | 0.977037i | \(0.431654\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.31244 | + | 8.86885i | −0.0790837 | + | 0.303308i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.9285 | + | 13.2378i | −0.783223 | + | 0.452194i | −0.837571 | − | 0.546328i | \(-0.816025\pi\) |
0.0543481 | + | 0.998522i | \(0.482692\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.9367 | − | 22.4071i | 0.441395 | − | 0.764519i | −0.556398 | − | 0.830916i | \(-0.687817\pi\) |
0.997793 | + | 0.0663970i | \(0.0211504\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.32049 | + | 24.5812i | 0.113162 | + | 0.837723i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48.6992 | 1.65774 | 0.828870 | − | 0.559441i | \(-0.188984\pi\) | ||||
0.828870 | + | 0.559441i | \(0.188984\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.9145 | 0.371106 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.25584 | + | 31.5054i | 0.144536 | + | 1.06998i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.123867 | − | 0.214545i | 0.00420192 | − | 0.00727793i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.7626 | − | 15.4514i | 0.906815 | − | 0.523550i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.50332 | + | 8.38944i | 0.287794 | + | 0.283940i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.8869 | − | 18.4099i | 1.07797 | − | 0.622368i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.11577 | − | 5.26299i | −0.307818 | − | 0.177719i | 0.338132 | − | 0.941099i | \(-0.390205\pi\) |
−0.645949 | + | 0.763380i | \(0.723538\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.41611 | + | 1.40153i | 0.115222 | + | 0.0472723i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.5758i | 0.794288i | 0.917756 | + | 0.397144i | \(0.129999\pi\) | ||||
−0.917756 | + | 0.397144i | \(0.870001\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −53.1293 | −1.78794 | −0.893971 | − | 0.448124i | \(-0.852092\pi\) | ||||
−0.893971 | + | 0.448124i | \(0.852092\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.54501 | − | 3.29367i | −0.0855494 | − | 0.110716i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.75882 | − | 13.4387i | 0.260516 | − | 0.451227i | −0.705863 | − | 0.708348i | \(-0.749441\pi\) |
0.966379 | + | 0.257122i | \(0.0827741\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.22442 | − | 15.9772i | −0.309377 | − | 0.535857i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.6439 | − | 35.1090i | 0.658095 | − | 1.17619i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.41029 | + | 7.63884i | 0.147585 | + | 0.255624i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.4001 | − | 14.6647i | −0.849031 | − | 0.490188i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.1634 | + | 13.1531i | 0.339345 | + | 0.439170i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 38.1040i | − | 1.27084i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 34.0249i | − | 1.13353i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.32518 | + | 17.8545i | −0.243767 | + | 0.594161i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33.9586 | + | 19.6060i | 1.12882 | + | 0.651727i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.92312 | + | 11.9912i | 0.229879 | + | 0.398161i | 0.957772 | − | 0.287529i | \(-0.0928338\pi\) |
−0.727893 | + | 0.685690i | \(0.759500\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −37.1903 | − | 36.6922i | −1.23352 | − | 1.21700i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.5442 | + | 26.9233i | 0.515002 | + | 0.892010i | 0.999848 | + | 0.0174104i | \(0.00554219\pi\) |
−0.484846 | + | 0.874599i | \(0.661124\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.6060 | + | 37.4226i | −0.715053 | + | 1.23851i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.12283 | − | 0.151675i | 0.0371196 | − | 0.00501423i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 40.8047 | 1.34749 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 33.6999i | − | 1.11166i | −0.831297 | − | 0.555828i | \(-0.812401\pi\) | ||
0.831297 | − | 0.555828i | \(-0.187599\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.13668 | − | 45.4290i | −0.202210 | − | 1.49693i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −58.2654 | − | 33.6396i | −1.91783 | − | 1.10726i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.59753 | − | 4.96379i | 0.282685 | − | 0.163208i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.8385 | − | 3.86894i | −0.487359 | − | 0.127073i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.59328 | + | 1.49723i | −0.0850829 | + | 0.0491226i | −0.541938 | − | 0.840419i | \(-0.682309\pi\) |
0.456855 | + | 0.889541i | \(0.348976\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.77058 | − | 3.06673i | 0.0580284 | − | 0.100508i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 31.1086 | + | 12.7629i | 1.01845 | + | 0.417840i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 51.0084 | 1.66815 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.83746 | 0.321376 | 0.160688 | − | 0.987005i | \(-0.448629\pi\) | ||||
0.160688 | + | 0.987005i | \(0.448629\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.4079 | + | 10.3602i | −0.437549 | + | 0.338093i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.6838 | + | 30.6293i | −0.576477 | + | 0.998487i | 0.419402 | + | 0.907800i | \(0.362240\pi\) |
−0.995879 | + | 0.0906870i | \(0.971094\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.29971 | + | 5.36919i | −0.302840 | + | 0.174845i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 27.8626 | − | 11.8725i | 0.906371 | − | 0.386214i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.27322 | − | 0.735095i | 0.0413741 | − | 0.0238874i | −0.479170 | − | 0.877722i | \(-0.659062\pi\) |
0.520544 | + | 0.853835i | \(0.325729\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −59.7518 | − | 34.4977i | −1.93962 | − | 1.11984i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.3247 | + | 11.0686i | −0.464511 | + | 0.358926i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.9312i | 0.645634i | 0.946461 | + | 0.322817i | \(0.104630\pi\) | ||||
−0.946461 | + | 0.322817i | \(0.895370\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.4964 | 0.533812 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.1768 | − | 27.2424i | 0.361293 | − | 0.880622i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.0773 | − | 24.3826i | 0.454579 | − | 0.787354i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34.6894 | + | 60.0839i | 1.11901 | + | 1.93819i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.69132 | + | 31.5833i | 0.280074 | + | 1.01776i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.47091 | − | 2.54770i | −0.0473504 | − | 0.0820133i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.7192 | − | 14.8490i | −0.827074 | − | 0.477511i | 0.0257760 | − | 0.999668i | \(-0.491794\pi\) |
−0.852850 | + | 0.522157i | \(0.825128\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.2475 | − | 2.19476i | 0.521945 | − | 0.0705059i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 21.5707i | − | 0.692236i | −0.938191 | − | 0.346118i | \(-0.887500\pi\) | ||
0.938191 | − | 0.346118i | \(-0.112500\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 5.73630i | − | 0.183897i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.52606 | + | 1.28681i | −0.305078 | + | 0.0412108i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.1262 | − | 5.84635i | −0.323965 | − | 0.187041i | 0.329193 | − | 0.944263i | \(-0.393223\pi\) |
−0.653159 | + | 0.757221i | \(0.726557\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.3325 | + | 56.0016i | 1.03335 | + | 1.78982i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.59753 | + | 9.43915i | 0.0829329 | + | 0.301369i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.9886 | − | 41.5495i | −0.765118 | − | 1.32522i | −0.940184 | − | 0.340667i | \(-0.889347\pi\) |
0.175066 | − | 0.984557i | \(-0.443986\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.8016 | + | 25.6372i | −0.471620 | + | 0.816869i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.0634 | − | 26.9660i | 0.352151 | − | 0.858339i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.35487 | −0.265669 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 39.4417i | − | 1.25291i | −0.779459 | − | 0.626453i | \(-0.784506\pi\) | ||
0.779459 | − | 0.626453i | \(-0.215494\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.7284 | + | 19.1075i | −0.784733 | + | 0.606360i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.6574 | + | 7.30776i | 0.401267 | + | 0.231672i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.96221 | + | 2.86494i | −0.157155 | + | 0.0907334i | −0.576515 | − | 0.817087i | \(-0.695588\pi\) |
0.419360 | + | 0.907820i | \(0.362254\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 36.0334 | − | 15.3542i | 1.14005 | − | 0.485785i |
(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 | 576.2.p.c.95.4 | yes | 16 | |
3.2 | odd | 2 | 1728.2.p.a.287.4 | 16 | |||
4.3 | odd | 2 | inner | 576.2.p.c.95.5 | yes | 16 | |
8.3 | odd | 2 | 576.2.p.a.95.4 | ✓ | 16 | ||
8.5 | even | 2 | 576.2.p.a.95.5 | yes | 16 | ||
9.2 | odd | 6 | 576.2.p.a.479.4 | yes | 16 | ||
9.4 | even | 3 | 5184.2.f.a.2591.8 | 16 | |||
9.5 | odd | 6 | 5184.2.f.f.2591.12 | 16 | |||
9.7 | even | 3 | 1728.2.p.c.1439.5 | 16 | |||
12.11 | even | 2 | 1728.2.p.a.287.3 | 16 | |||
24.5 | odd | 2 | 1728.2.p.c.287.6 | 16 | |||
24.11 | even | 2 | 1728.2.p.c.287.5 | 16 | |||
36.7 | odd | 6 | 1728.2.p.c.1439.6 | 16 | |||
36.11 | even | 6 | 576.2.p.a.479.5 | yes | 16 | ||
36.23 | even | 6 | 5184.2.f.f.2591.10 | 16 | |||
36.31 | odd | 6 | 5184.2.f.a.2591.6 | 16 | |||
72.5 | odd | 6 | 5184.2.f.a.2591.7 | 16 | |||
72.11 | even | 6 | inner | 576.2.p.c.479.4 | yes | 16 | |
72.13 | even | 6 | 5184.2.f.f.2591.11 | 16 | |||
72.29 | odd | 6 | inner | 576.2.p.c.479.5 | yes | 16 | |
72.43 | odd | 6 | 1728.2.p.a.1439.4 | 16 | |||
72.59 | even | 6 | 5184.2.f.a.2591.5 | 16 | |||
72.61 | even | 6 | 1728.2.p.a.1439.3 | 16 | |||
72.67 | odd | 6 | 5184.2.f.f.2591.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.2.p.a.95.4 | ✓ | 16 | 8.3 | odd | 2 | ||
576.2.p.a.95.5 | yes | 16 | 8.5 | even | 2 | ||
576.2.p.a.479.4 | yes | 16 | 9.2 | odd | 6 | ||
576.2.p.a.479.5 | yes | 16 | 36.11 | even | 6 | ||
576.2.p.c.95.4 | yes | 16 | 1.1 | even | 1 | trivial | |
576.2.p.c.95.5 | yes | 16 | 4.3 | odd | 2 | inner | |
576.2.p.c.479.4 | yes | 16 | 72.11 | even | 6 | inner | |
576.2.p.c.479.5 | yes | 16 | 72.29 | odd | 6 | inner | |
1728.2.p.a.287.3 | 16 | 12.11 | even | 2 | |||
1728.2.p.a.287.4 | 16 | 3.2 | odd | 2 | |||
1728.2.p.a.1439.3 | 16 | 72.61 | even | 6 | |||
1728.2.p.a.1439.4 | 16 | 72.43 | odd | 6 | |||
1728.2.p.c.287.5 | 16 | 24.11 | even | 2 | |||
1728.2.p.c.287.6 | 16 | 24.5 | odd | 2 | |||
1728.2.p.c.1439.5 | 16 | 9.7 | even | 3 | |||
1728.2.p.c.1439.6 | 16 | 36.7 | odd | 6 | |||
5184.2.f.a.2591.5 | 16 | 72.59 | even | 6 | |||
5184.2.f.a.2591.6 | 16 | 36.31 | odd | 6 | |||
5184.2.f.a.2591.7 | 16 | 72.5 | odd | 6 | |||
5184.2.f.a.2591.8 | 16 | 9.4 | even | 3 | |||
5184.2.f.f.2591.9 | 16 | 72.67 | odd | 6 | |||
5184.2.f.f.2591.10 | 16 | 36.23 | even | 6 | |||
5184.2.f.f.2591.11 | 16 | 72.13 | even | 6 | |||
5184.2.f.f.2591.12 | 16 | 9.5 | odd | 6 |