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 | 95.1 | ||
Root | \(-0.539169 - 0.933868i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.95 |
Dual form | 576.2.p.c.479.1 |
$q$-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 | ||||||||
\(3\) | −1.68071 | + | 0.418594i | −0.970357 | + | 0.241675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.312371 | + | 0.541042i | −0.139697 | + | 0.241962i | −0.927382 | − | 0.374116i | \(-0.877946\pi\) |
0.787685 | + | 0.616078i | \(0.211279\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.751481 | − | 0.433868i | 0.284033 | − | 0.163987i | −0.351215 | − | 0.936295i | \(-0.614231\pi\) |
0.635248 | + | 0.772308i | \(0.280898\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.64956 | − | 1.40707i | 0.883186 | − | 0.469023i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.70560 | + | 0.984726i | −0.514256 | + | 0.296906i | −0.734582 | − | 0.678520i | \(-0.762621\pi\) |
0.220325 | + | 0.975426i | \(0.429288\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.75578 | + | 1.59105i | 0.764316 | + | 0.441278i | 0.830843 | − | 0.556506i | \(-0.187859\pi\) |
−0.0665271 | + | 0.997785i | \(0.521192\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.298527 | − | 1.04009i | 0.0770794 | − | 0.268550i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.45005i | − | 0.351689i | −0.984418 | − | 0.175845i | \(-0.943734\pi\) | ||
0.984418 | − | 0.175845i | \(-0.0562656\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.81414 | −0.645607 | −0.322803 | − | 0.946466i | \(-0.604625\pi\) | ||||
−0.322803 | + | 0.946466i | \(0.604625\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.08141 | + | 1.04377i | −0.235982 | + | 0.227769i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.88357 | + | 4.99450i | −0.601267 | + | 1.04142i | 0.391363 | + | 0.920237i | \(0.372004\pi\) |
−0.992630 | + | 0.121188i | \(0.961330\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.30485 | + | 3.99212i | 0.460970 | + | 0.798423i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.86414 | + | 3.47396i | −0.743655 | + | 0.668564i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.41107 | + | 7.64020i | 0.819115 | + | 1.41875i | 0.906335 | + | 0.422560i | \(0.138869\pi\) |
−0.0872193 | + | 0.996189i | \(0.527798\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.14776 | + | 4.12676i | 1.28378 | + | 0.741188i | 0.977537 | − | 0.210766i | \(-0.0675959\pi\) |
0.306239 | + | 0.951955i | \(0.400929\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.45441 | − | 2.36899i | 0.427257 | − | 0.412388i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.542111i | 0.0916335i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.26419i | 0.701028i | 0.936557 | + | 0.350514i | \(0.113993\pi\) | ||||
−0.936557 | + | 0.350514i | \(0.886007\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.29767 | − | 1.52054i | −0.848306 | − | 0.243481i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.79610 | − | 4.50108i | −1.21755 | − | 0.702951i | −0.253154 | − | 0.967426i | \(-0.581468\pi\) |
−0.964393 | + | 0.264475i | \(0.914801\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.15855 | − | 3.73872i | −0.329176 | − | 0.570149i | 0.653173 | − | 0.757209i | \(-0.273437\pi\) |
−0.982349 | + | 0.187060i | \(0.940104\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.0663618 | + | 1.87305i | −0.00989264 | + | 0.279218i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.29767 | + | 9.17583i | 0.772744 | + | 1.33843i | 0.936054 | + | 0.351857i | \(0.114450\pi\) |
−0.163309 | + | 0.986575i | \(0.552217\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.12352 | + | 5.41009i | −0.446217 | + | 0.772870i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.606982 | + | 2.43711i | 0.0849945 | + | 0.341264i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.19740 | −1.12600 | −0.563000 | − | 0.826457i | \(-0.690353\pi\) | ||||
−0.563000 | + | 0.826457i | \(0.690353\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.23040i | − | 0.165907i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.72974 | − | 1.17798i | 0.626469 | − | 0.156027i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.80475 | + | 5.08343i | 1.14628 | + | 0.661806i | 0.947978 | − | 0.318335i | \(-0.103124\pi\) |
0.198303 | + | 0.980141i | \(0.436457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.23321 | − | 4.17610i | 0.926118 | − | 0.534695i | 0.0405364 | − | 0.999178i | \(-0.487093\pi\) |
0.885582 | + | 0.464483i | \(0.153760\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.38061 | − | 2.20694i | 0.173941 | − | 0.278049i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.72165 | + | 0.993996i | −0.213545 | + | 0.123290i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.55859 | − | 4.43161i | 0.312582 | − | 0.541407i | −0.666339 | − | 0.745649i | \(-0.732140\pi\) |
0.978920 | + | 0.204242i | \(0.0654729\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.75578 | − | 9.60134i | 0.331757 | − | 1.15587i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.6284 | −1.26136 | −0.630679 | − | 0.776044i | \(-0.717224\pi\) | ||||
−0.630679 | + | 0.776044i | \(0.717224\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.776091 | −0.0908346 | −0.0454173 | − | 0.998968i | \(-0.514462\pi\) | ||||
−0.0454173 | + | 0.998968i | \(0.514462\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.54485 | − | 5.74478i | −0.640264 | − | 0.663351i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.854482 | + | 1.48001i | −0.0973773 | + | 0.168662i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.1148 | − | 6.99450i | 1.36302 | − | 0.786943i | 0.372999 | − | 0.927832i | \(-0.378329\pi\) |
0.990025 | + | 0.140889i | \(0.0449961\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.04032 | − | 7.45622i | 0.560036 | − | 0.828469i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.55157 | − | 0.895797i | 0.170307 | − | 0.0983265i | −0.412424 | − | 0.910992i | \(-0.635318\pi\) |
0.582730 | + | 0.812666i | \(0.301984\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.784539 | + | 0.452954i | 0.0850952 | + | 0.0491298i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.6119 | − | 10.9945i | −1.13771 | − | 1.17873i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.66402i | 0.282385i | 0.989982 | + | 0.141193i | \(0.0450937\pi\) | ||||
−0.989982 | + | 0.141193i | \(0.954906\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.76122 | 0.289455 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.7407 | − | 3.94387i | −1.42485 | − | 0.408961i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.879054 | − | 1.52257i | 0.0901891 | − | 0.156212i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.06063 | + | 10.4973i | 0.615364 | + | 1.06584i | 0.990321 | + | 0.138799i | \(0.0443242\pi\) |
−0.374957 | + | 0.927042i | \(0.622342\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.13350 | + | 5.00898i | −0.314928 | + | 0.503421i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.47922 | − | 2.56209i | −0.147188 | − | 0.254938i | 0.782999 | − | 0.622023i | \(-0.213689\pi\) |
−0.930187 | + | 0.367085i | \(0.880356\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.20966 | − | 0.698396i | −0.119191 | − | 0.0688150i | 0.439219 | − | 0.898380i | \(-0.355255\pi\) |
−0.558410 | + | 0.829565i | \(0.688588\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.226924 | − | 0.911130i | −0.0221455 | − | 0.0889172i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 8.37526i | − | 0.809667i | −0.914390 | − | 0.404833i | \(-0.867330\pi\) | ||
0.914390 | − | 0.404833i | \(-0.132670\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 16.3625i | − | 1.56724i | −0.621239 | − | 0.783621i | \(-0.713371\pi\) | ||
0.621239 | − | 0.783621i | \(-0.286629\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.78496 | − | 7.16685i | −0.169421 | − | 0.680248i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.3229 | − | 8.26933i | −1.34739 | − | 0.777913i | −0.359507 | − | 0.933142i | \(-0.617055\pi\) |
−0.987878 | + | 0.155229i | \(0.950388\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.80149 | − | 3.12027i | −0.167990 | − | 0.290967i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.54032 | + | 0.338012i | 0.882003 | + | 0.0312492i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.629131 | − | 1.08969i | −0.0576723 | − | 0.0998914i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.56063 | + | 6.16719i | −0.323694 | + | 0.560654i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.9871 | + | 4.30160i | 1.35134 | + | 0.387863i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.00358 | −0.536977 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.73547i | − | 0.153998i | −0.997031 | − | 0.0769991i | \(-0.975466\pi\) | ||
0.997031 | − | 0.0769991i | \(-0.0245339\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.19289 | + | 5.38014i | 0.457209 | + | 0.473695i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.8109 | + | 8.55109i | 1.29404 | + | 0.747112i | 0.979367 | − | 0.202090i | \(-0.0647732\pi\) |
0.314669 | + | 0.949202i | \(0.398107\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.11477 | + | 1.22096i | −0.183374 | + | 0.105871i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.672512 | − | 3.17583i | −0.0578807 | − | 0.273332i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.19289 | + | 1.26607i | −0.187352 | + | 0.108167i | −0.590742 | − | 0.806860i | \(-0.701165\pi\) |
0.403391 | + | 0.915028i | \(0.367832\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.25857 | − | 7.37605i | 0.361207 | − | 0.625629i | −0.626953 | − | 0.779057i | \(-0.715698\pi\) |
0.988160 | + | 0.153428i | \(0.0490315\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.7448 | − | 13.2043i | −1.07330 | − | 1.11200i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.26700 | −0.524073 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.51156 | −0.457710 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.98509 | − | 10.4003i | 0.246206 | − | 0.857800i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.34997 | − | 14.4626i | 0.684057 | − | 1.18482i | −0.289676 | − | 0.957125i | \(-0.593547\pi\) |
0.973732 | − | 0.227696i | \(-0.0731192\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.39854 | + | 1.38480i | −0.195191 | + | 0.112693i | −0.594410 | − | 0.804162i | \(-0.702614\pi\) |
0.399219 | + | 0.916855i | \(0.369281\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.04032 | − | 3.84200i | −0.164950 | − | 0.310607i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.46551 | + | 2.57816i | −0.358678 | + | 0.207083i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.02876 | − | 2.32600i | −0.321530 | − | 0.185635i | 0.330544 | − | 0.943790i | \(-0.392768\pi\) |
−0.652074 | + | 0.758155i | \(0.726101\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.7774 | − | 3.43138i | 1.09262 | − | 0.272126i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.00436i | 0.394399i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.82831 | 0.769812 | 0.384906 | − | 0.922956i | \(-0.374234\pi\) | ||||
0.384906 | + | 0.922956i | \(0.374234\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.515037 | + | 2.06794i | 0.0400956 | + | 0.160989i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.34854 | + | 2.33573i | −0.104353 | + | 0.180744i | −0.913474 | − | 0.406898i | \(-0.866610\pi\) |
0.809121 | + | 0.587642i | \(0.199944\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.43711 | − | 2.48915i | −0.110547 | − | 0.191473i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.45622 | + | 3.95968i | −0.570191 | + | 0.302804i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.13451 | + | 15.8214i | 0.694484 | + | 1.20288i | 0.970354 | + | 0.241687i | \(0.0777007\pi\) |
−0.275870 | + | 0.961195i | \(0.588966\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.46410 | + | 2.00000i | 0.261861 | + | 0.151186i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.9261 | − | 4.85814i | −1.27224 | − | 0.365160i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 15.1453i | − | 1.13201i | −0.824400 | − | 0.566007i | \(-0.808487\pi\) | ||
0.824400 | − | 0.566007i | \(-0.191513\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.2042i | 1.27878i | 0.768882 | + | 0.639391i | \(0.220813\pi\) | ||||
−0.768882 | + | 0.639391i | \(0.779187\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.4088 | + | 10.0466i | −0.769443 | + | 0.742665i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.30711 | − | 1.33201i | −0.169622 | − | 0.0979312i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.42790 | + | 2.47320i | 0.104419 | + | 0.180858i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.39659 | + | 4.28714i | −0.101587 | + | 0.311844i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.17672 | + | 10.6984i | 0.446932 | + | 0.774109i | 0.998185 | − | 0.0602296i | \(-0.0191833\pi\) |
−0.551253 | + | 0.834338i | \(0.685850\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.18640 | − | 2.05491i | 0.0853993 | − | 0.147916i | −0.820162 | − | 0.572131i | \(-0.806117\pi\) |
0.905561 | + | 0.424215i | \(0.139450\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.47751 | − | 2.39129i | 0.177418 | − | 0.171244i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.8095 | −1.26888 | −0.634439 | − | 0.772973i | \(-0.718769\pi\) | ||||
−0.634439 | + | 0.772973i | \(0.718769\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.90187i | − | 0.134820i | −0.997725 | − | 0.0674098i | \(-0.978527\pi\) | ||
0.997725 | − | 0.0674098i | \(-0.0214735\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.44520 | + | 8.51925i | −0.172471 | + | 0.600902i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.62968 | + | 3.82765i | 0.465312 | + | 0.268648i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.87055 | − | 2.81201i | 0.340174 | − | 0.196400i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.612603 | + | 17.2906i | −0.0425788 | + | 1.20178i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.79978 | − | 2.77115i | 0.332007 | − | 0.191685i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.65449 | + | 4.59771i | −0.182742 | + | 0.316519i | −0.942813 | − | 0.333321i | \(-0.891831\pi\) |
0.760071 | + | 0.649840i | \(0.225164\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17.8632 | − | 4.44898i | 1.22397 | − | 0.304839i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.69707 | 0.183939 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.16188 | 0.486180 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.30438 | − | 0.324867i | 0.0881420 | − | 0.0219525i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.30711 | − | 3.99602i | 0.155193 | − | 0.268802i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.71855 | + | 3.30160i | −0.382942 | + | 0.221092i | −0.679098 | − | 0.734048i | \(-0.737629\pi\) |
0.296155 | + | 0.955140i | \(0.404295\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.7240 | + | 7.33426i | 0.781601 | + | 0.488951i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.3972 | + | 11.7763i | −1.35381 | + | 0.781622i | −0.988781 | − | 0.149375i | \(-0.952274\pi\) |
−0.365028 | + | 0.930997i | \(0.618941\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.42555 | + | 4.28714i | 0.490694 | + | 0.283302i | 0.724862 | − | 0.688894i | \(-0.241903\pi\) |
−0.234168 | + | 0.972196i | \(0.575237\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.816613 | − | 2.84514i | 0.0537292 | − | 0.187196i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.35596i | 0.154344i | 0.997018 | + | 0.0771720i | \(0.0245891\pi\) | ||||
−0.997018 | + | 0.0771720i | \(0.975411\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.61935 | −0.431799 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −17.4336 | + | 16.8269i | −1.13244 | + | 1.09302i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.3147 | − | 19.5977i | 0.731890 | − | 1.26767i | −0.224185 | − | 0.974547i | \(-0.571972\pi\) |
0.956075 | − | 0.293124i | \(-0.0946947\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.8858 | − | 18.8547i | −0.701215 | − | 1.21454i | −0.968040 | − | 0.250795i | \(-0.919308\pi\) |
0.266825 | − | 0.963745i | \(-0.414025\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.35018 | + | 14.6416i | −0.343214 | + | 0.939257i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.95139 | − | 3.37991i | −0.124670 | − | 0.215935i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.75514 | − | 4.47743i | −0.493448 | − | 0.284892i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.23276 | + | 2.15505i | −0.141495 | + | 0.136571i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 10.8742i | − | 0.686375i | −0.939267 | − | 0.343188i | \(-0.888493\pi\) | ||
0.939267 | − | 0.343188i | \(-0.111507\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 11.3581i | − | 0.714079i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.50819 | − | 0.432880i | −0.0944462 | − | 0.0271080i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.7490 | + | 11.9794i | 1.29429 | + | 0.747257i | 0.979411 | − | 0.201875i | \(-0.0647036\pi\) |
0.314876 | + | 0.949133i | \(0.398037\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.85009 | + | 3.20446i | 0.114959 | + | 0.199115i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.4377 | + | 14.0365i | 1.38886 | + | 0.868836i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.58645 | − | 6.21192i | −0.221150 | − | 0.383043i | 0.734007 | − | 0.679142i | \(-0.237648\pi\) |
−0.955157 | + | 0.296098i | \(0.904314\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.56063 | − | 4.43514i | 0.157298 | − | 0.272449i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.11514 | − | 4.47743i | −0.0682455 | − | 0.274014i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.0301 | 0.794458 | 0.397229 | − | 0.917720i | \(-0.369972\pi\) | ||||
0.397229 | + | 0.917720i | \(0.369972\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.21940i | 0.438547i | 0.975663 | + | 0.219274i | \(0.0703687\pi\) | ||||
−0.975663 | + | 0.219274i | \(0.929631\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.64081 | + | 1.15583i | −0.280875 | + | 0.0699541i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.86228 | − | 4.53929i | −0.474113 | − | 0.273729i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.1861 | + | 15.1186i | −1.57337 | + | 0.908387i | −0.577620 | + | 0.816306i | \(0.696018\pi\) |
−0.995752 | + | 0.0920808i | \(0.970648\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24.7450 | + | 0.876713i | 1.48145 | + | 0.0524874i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.8706 | − | 13.2043i | 1.36434 | − | 0.787704i | 0.374144 | − | 0.927371i | \(-0.377937\pi\) |
0.990199 | + | 0.139667i | \(0.0446032\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.4760 | + | 25.0732i | −0.860509 | + | 1.49045i | 0.0109287 | + | 0.999940i | \(0.496521\pi\) |
−0.871438 | + | 0.490506i | \(0.836812\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.840097 | + | 2.92696i | −0.0497630 | + | 0.173378i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.81150 | −0.461098 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.8974 | 0.876315 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.5803 | − | 15.1060i | −0.854710 | − | 0.885529i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.05188 | − | 15.6783i | 0.528817 | − | 0.915937i | −0.470619 | − | 0.882337i | \(-0.655969\pi\) |
0.999435 | − | 0.0336006i | \(-0.0106974\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.50070 | + | 3.17583i | −0.320263 | + | 0.184904i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.16977 | − | 9.73029i | 0.183929 | − | 0.564609i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.8930 | + | 9.17583i | −0.919116 | + | 0.530652i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.24422 | − | 1.87305i | −0.186994 | − | 0.107961i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.55862 | + | 3.68693i | 0.204437 | + | 0.211809i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.21797i | 0.298780i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.6127 | −1.34765 | −0.673825 | − | 0.738891i | \(-0.735350\pi\) | ||||
−0.673825 | + | 0.738891i | \(0.735350\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.32543 | + | 0.667445i | 0.132289 | + | 0.0379696i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.70159 | − | 8.14340i | 0.266603 | − | 0.461770i | −0.701379 | − | 0.712788i | \(-0.747432\pi\) |
0.967982 | + | 0.251018i | \(0.0807655\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.84517 | − | 6.66003i | −0.217342 | − | 0.376447i | 0.736653 | − | 0.676271i | \(-0.236405\pi\) |
−0.953994 | + | 0.299824i | \(0.903072\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.762787 | + | 1.43635i | 0.0429782 | + | 0.0809294i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.4647 | + | 28.5178i | 0.924752 | + | 1.60172i | 0.791959 | + | 0.610574i | \(0.209061\pi\) |
0.132793 | + | 0.991144i | \(0.457605\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.0470 | − | 8.68739i | −0.842471 | − | 0.486401i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.50583 | + | 14.0764i | 0.195676 | + | 0.785666i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.08064i | 0.227053i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.6685i | 0.813664i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.84923 | + | 27.5006i | 0.378764 | + | 1.52078i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.96220 | + | 4.59698i | 0.438970 | + | 0.253440i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.74858 | + | 3.02863i | 0.0961106 | + | 0.166468i | 0.910072 | − | 0.414451i | \(-0.136026\pi\) |
−0.813961 | + | 0.580920i | \(0.802693\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.00000 | + | 11.2982i | 0.328798 | + | 0.619138i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.59846 | + | 2.76861i | 0.0873332 | + | 0.151265i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.4890 | − | 23.3636i | 0.734792 | − | 1.27270i | −0.220022 | − | 0.975495i | \(-0.570613\pi\) |
0.954814 | − | 0.297203i | \(-0.0960538\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 27.5341 | + | 7.90285i | 1.49545 | + | 0.429224i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.2549 | −0.880253 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.4949i | 0.620668i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.33391 | + | 4.49017i | 0.233330 | + | 0.241743i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.6779 | − | 9.62901i | −0.895319 | − | 0.516912i | −0.0196402 | − | 0.999807i | \(-0.506252\pi\) |
−0.875678 | + | 0.482895i | \(0.839585\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.3570 | − | 8.86639i | 0.822043 | − | 0.474607i | −0.0290775 | − | 0.999577i | \(-0.509257\pi\) |
0.851120 | + | 0.524970i | \(0.175924\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.1760 | + | 3.42542i | −0.863410 | + | 0.182835i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.2735 | − | 8.81818i | 0.812928 | − | 0.469344i | −0.0350435 | − | 0.999386i | \(-0.511157\pi\) |
0.847972 | + | 0.530041i | \(0.177824\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.32000 | − | 5.75041i | 0.176207 | − | 0.305200i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.51352 | + | 1.56809i | 0.0801040 | + | 0.0829924i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.1550 | 1.53874 | 0.769372 | − | 0.638801i | \(-0.220569\pi\) | ||||
0.769372 | + | 0.638801i | \(0.220569\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0806 | −0.583192 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.40283 | − | 11.8557i | 0.178602 | − | 0.622263i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.242428 | − | 0.419898i | 0.0126893 | − | 0.0219785i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.2952 | + | 14.6042i | −1.32040 | + | 0.762333i | −0.983792 | − | 0.179312i | \(-0.942613\pi\) |
−0.336607 | + | 0.941645i | \(0.609279\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −26.9896 | − | 0.956235i | −1.40502 | − | 0.0497796i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.16019 | + | 3.55659i | −0.319821 | + | 0.184649i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.99633 | − | 5.19403i | −0.465812 | − | 0.268937i | 0.248673 | − | 0.968588i | \(-0.420006\pi\) |
−0.714485 | + | 0.699651i | \(0.753339\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.0903 | − | 2.51306i | 0.521059 | − | 0.129774i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 28.0730i | 1.44583i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.40043 | 0.482868 | 0.241434 | − | 0.970417i | \(-0.422382\pi\) | ||||
0.241434 | + | 0.970417i | \(0.422382\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.726458 | + | 2.91682i | 0.0372176 | + | 0.149433i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.1080 | − | 24.4358i | 0.720887 | − | 1.24861i | −0.239757 | − | 0.970833i | \(-0.577068\pi\) |
0.960645 | − | 0.277780i | \(-0.0895988\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.533831 | − | 0.924622i | −0.0272065 | − | 0.0471231i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.9798 | − | 6.86872i | −0.558136 | − | 0.349157i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.67663 | − | 16.7604i | −0.490624 | − | 0.849786i | 0.509317 | − | 0.860579i | \(-0.329898\pi\) |
−0.999942 | + | 0.0107924i | \(0.996565\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.24228 | + | 4.18133i | 0.366258 | + | 0.211459i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −28.4723 | − | 8.17212i | −1.43624 | − | 0.412229i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.73951i | 0.439733i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.42212i | 0.221940i | 0.993824 | + | 0.110970i | \(0.0353958\pi\) | ||||
−0.993824 | + | 0.110970i | \(0.964604\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.04322 | − | 2.93731i | 0.152352 | − | 0.147050i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.31867 | − | 5.38014i | −0.465352 | − | 0.268671i | 0.248940 | − | 0.968519i | \(-0.419918\pi\) |
−0.714292 | + | 0.699848i | \(0.753251\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.1318 | + | 22.7449i | 0.654140 | + | 1.13300i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.45968 | + | 5.05613i | 0.122222 | + | 0.251241i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.19905 | − | 7.27298i | −0.208139 | − | 0.360508i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.62126 | − | 13.2004i | 0.376847 | − | 0.652718i | −0.613755 | − | 0.789497i | \(-0.710342\pi\) |
0.990602 | + | 0.136779i | \(0.0436749\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.15565 | − | 3.04582i | 0.155657 | − | 0.150239i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.82214 | 0.434109 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.11928i | 0.0549435i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.06984 | + | 14.1796i | −0.199301 | + | 0.694378i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.87593 | + | 5.70187i | 0.482471 | + | 0.278555i | 0.721446 | − | 0.692471i | \(-0.243478\pi\) |
−0.238975 | + | 0.971026i | \(0.576811\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.3821 | + | 12.9223i | −1.09084 | + | 0.629795i | −0.933799 | − | 0.357797i | \(-0.883528\pi\) |
−0.157038 | + | 0.987593i | \(0.550195\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 26.9475 | + | 16.8577i | 1.31023 | + | 0.819650i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.78877 | − | 3.34215i | 0.280797 | − | 0.162118i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.62375 | − | 6.27652i | 0.175366 | − | 0.303742i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.5330 | − | 2.62333i | 0.508538 | − | 0.126655i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.4831 | −1.66099 | −0.830496 | − | 0.557025i | \(-0.811943\pi\) | ||||
−0.830496 | + | 0.557025i | \(0.811943\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.5245 | −1.08246 | −0.541230 | − | 0.840874i | \(-0.682041\pi\) | ||||
−0.541230 | + | 0.840874i | \(0.682041\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.26333 | − | 2.30711i | 0.444143 | − | 0.110617i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.11477 | − | 14.0552i | 0.388182 | − | 0.672351i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.11034 | + | 1.21841i | −0.100721 | + | 0.0581514i | −0.549514 | − | 0.835484i | \(-0.685187\pi\) |
0.448793 | + | 0.893636i | \(0.351854\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.663578 | + | 18.7294i | −0.0315989 | + | 0.891874i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.57955 | − | 4.37605i | 0.360115 | − | 0.207913i | −0.309016 | − | 0.951057i | \(-0.600000\pi\) |
0.669131 | + | 0.743144i | \(0.266666\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.44135 | − | 0.832161i | −0.0683263 | − | 0.0394482i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.97992 | + | 27.8026i | −0.377437 | + | 1.31502i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.1485i | 0.714903i | 0.933932 | + | 0.357451i | \(0.116354\pi\) | ||||
−0.933932 | + | 0.357451i | \(0.883646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.7293 | 0.834841 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.45158 | − | 3.33146i | 0.162170 | − | 0.156526i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.862526 | + | 1.49394i | −0.0404359 | + | 0.0700370i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.54907 | − | 11.3433i | −0.306352 | − | 0.530618i | 0.671209 | − | 0.741268i | \(-0.265775\pi\) |
−0.977562 | + | 0.210650i | \(0.932442\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.03742 | + | 5.60321i | 0.235127 | + | 0.261535i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.472168 | + | 0.817819i | 0.0219911 | + | 0.0380896i | 0.876812 | − | 0.480834i | \(-0.159666\pi\) |
−0.854820 | + | 0.518924i | \(0.826333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.0864 | − | 15.6383i | −1.25881 | − | 0.726775i | −0.285967 | − | 0.958239i | \(-0.592315\pi\) |
−0.972843 | + | 0.231465i | \(0.925648\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.42601 | − | 6.20237i | 0.297999 | − | 0.287628i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 37.1248i | − | 1.71793i | −0.512033 | − | 0.858966i | \(-0.671107\pi\) | ||
0.512033 | − | 0.858966i | \(-0.328893\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 4.44036i | − | 0.205037i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.74482 | + | 2.22292i | 0.356862 | + | 0.102427i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.36322 | + | 4.25116i | 0.338561 | + | 0.195468i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.48616 | − | 11.2344i | −0.297605 | − | 0.515467i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.7195 | + | 11.5343i | −0.994467 | + | 0.528119i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.922436 | − | 1.59771i | −0.0421472 | − | 0.0730010i | 0.844182 | − | 0.536056i | \(-0.180087\pi\) |
−0.886329 | + | 0.463055i | \(0.846753\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.78454 | + | 11.7512i | −0.309348 | + | 0.535807i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.09480 | − | 8.41087i | −0.0953165 | − | 0.382708i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.57266 | −0.343857 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 15.0231i | − | 0.680763i | −0.940287 | − | 0.340381i | \(-0.889444\pi\) | ||
0.940287 | − | 0.340381i | \(-0.110556\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.5185 | + | 4.11407i | −0.746993 | + | 0.186045i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.61877 | + | 3.82135i | 0.298701 | + | 0.172455i | 0.641859 | − | 0.766823i | \(-0.278163\pi\) |
−0.343158 | + | 0.939278i | \(0.611497\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.0787 | − | 6.39628i | 0.498959 | − | 0.288074i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.73125 | − | 3.26001i | −0.0778141 | − | 0.146527i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.98704 | + | 4.61132i | −0.358268 | + | 0.206846i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.5388 | + | 25.1820i | −0.650848 | + | 1.12730i | 0.332069 | + | 0.943255i | \(0.392253\pi\) |
−0.982917 | + | 0.184047i | \(0.941080\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.28877 | − | 4.49017i | 0.0575781 | − | 0.200606i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.4130 | 1.40064 | 0.700318 | − | 0.713831i | \(-0.253041\pi\) | ||||
0.700318 | + | 0.713831i | \(0.253041\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.84827 | 0.0822468 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.45731 | + | 3.58197i | 0.153545 | + | 0.159081i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.59946 | − | 16.6268i | 0.425489 | − | 0.736968i | −0.570977 | − | 0.820966i | \(-0.693436\pi\) |
0.996466 | + | 0.0839980i | \(0.0267689\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.583218 | + | 0.336721i | −0.0258000 | + | 0.0148957i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.8742 | − | 9.77619i | 0.480109 | − | 0.431629i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.755724 | − | 0.436317i | 0.0333012 | − | 0.0192264i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.0714 | − | 10.4335i | −0.794777 | − | 0.458865i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.9752 | − | 22.7676i | −0.964605 | − | 0.999386i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 25.7108i | − | 1.12641i | −0.826317 | − | 0.563205i | \(-0.809568\pi\) | ||
0.826317 | − | 0.563205i | \(-0.190432\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.4567 | 0.894509 | 0.447254 | − | 0.894407i | \(-0.352402\pi\) | ||||
0.447254 | + | 0.894407i | \(0.352402\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.65933 | − | 1.91136i | −0.290637 | − | 0.0834188i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.98402 | − | 10.3646i | 0.260668 | − | 0.451490i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.13001 | − | 8.88543i | −0.223044 | − | 0.386323i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 30.4814 | + | 1.07995i | 1.32278 | + | 0.0468659i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.3229 | − | 24.8080i | −0.620394 | − | 1.07455i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.53137 | + | 2.61619i | 0.195908 | + | 0.113108i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.33974 | + | 25.4549i | 0.273580 | + | 1.09846i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 12.3032i | − | 0.529938i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 25.9547i | − | 1.11588i | −0.829881 | − | 0.557940i | \(-0.811592\pi\) | ||
0.829881 | − | 0.557940i | \(-0.188408\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.20159 | − | 28.9153i | −0.309050 | − | 1.24087i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.85280 | + | 5.11117i | 0.379212 | + | 0.218938i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.48679 | − | 16.4316i | −0.405626 | − | 0.702565i | 0.588768 | − | 0.808302i | \(-0.299613\pi\) |
−0.994394 | + | 0.105737i | \(0.966280\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.2888 | − | 21.2424i | 0.567151 | − | 0.906605i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.4134 | − | 21.5006i | −0.528827 | − | 0.915955i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.06938 | − | 10.5125i | 0.258096 | − | 0.447036i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.43514 | + | 1.27298i | 0.188261 | + | 0.0540348i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.319595 | 0.0135417 | 0.00677083 | − | 0.999977i | \(-0.497845\pi\) | ||||
0.00677083 | + | 0.999977i | \(0.497845\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 13.7374i | − | 0.581032i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.43515 | − | 3.55902i | −0.145032 | − | 0.150262i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.97840 | − | 3.45163i | −0.251959 | − | 0.145469i | 0.368702 | − | 0.929548i | \(-0.379802\pi\) |
−0.620661 | + | 0.784079i | \(0.713136\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.94812 | − | 5.16620i | 0.376450 | − | 0.217344i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.552693 | − | 7.79004i | 0.0232109 | − | 0.327151i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.6038 | + | 7.85414i | −0.570300 | + | 0.329263i | −0.757269 | − | 0.653103i | \(-0.773467\pi\) |
0.186969 | + | 0.982366i | \(0.440133\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.9368 | − | 18.9432i | 0.457693 | − | 0.792747i | −0.541146 | − | 0.840929i | \(-0.682009\pi\) |
0.998839 | + | 0.0481816i | \(0.0153426\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.8595 | − | 15.3953i | −0.620767 | − | 0.643150i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −26.5848 | −1.10866 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.5347 | 0.729979 | 0.364989 | − | 0.931012i | \(-0.381073\pi\) | ||||
0.364989 | + | 0.931012i | \(0.381073\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.13383 | + | 3.95033i | −0.0471202 | + | 0.164170i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.777316 | − | 1.34635i | 0.0322485 | − | 0.0558560i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.9814 | − | 8.07219i | 0.579052 | − | 0.334316i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.16300 | + | 5.05613i | −0.130774 | + | 0.209045i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.86502 | − | 5.69557i | 0.407173 | − | 0.235081i | −0.282401 | − | 0.959296i | \(-0.591131\pi\) |
0.689574 | + | 0.724215i | \(0.257798\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.1148 | − | 11.6133i | −0.828815 | − | 0.478516i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 29.9326 | − | 7.45497i | 1.23126 | − | 0.306656i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 14.5507i | − | 0.597524i | −0.954328 | − | 0.298762i | \(-0.903426\pi\) | ||
0.954328 | − | 0.298762i | \(-0.0965737\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.786089 | 0.0322265 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.796109 | + | 3.19648i | 0.0325826 | + | 0.130823i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.01255 | + | 6.94994i | −0.163948 | + | 0.283967i | −0.936281 | − | 0.351251i | \(-0.885756\pi\) |
0.772333 | + | 0.635218i | \(0.219090\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.02650 | + | 13.9023i | 0.327408 | + | 0.567087i | 0.981997 | − | 0.188898i | \(-0.0604916\pi\) |
−0.654589 | + | 0.755985i | \(0.727158\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.543562 | − | 15.3419i | 0.0221355 | − | 0.624771i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.22447 | − | 3.85290i | −0.0904378 | − | 0.156643i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.03660 | − | 1.17583i | −0.0826629 | − | 0.0477255i | 0.458099 | − | 0.888901i | \(-0.348531\pi\) |
−0.540762 | + | 0.841176i | \(0.681864\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.7448 | − | 3.65801i | −0.516444 | − | 0.148230i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33.7154i | 1.36398i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.7623i | 0.596244i | 0.954528 | + | 0.298122i | \(0.0963603\pi\) | ||||
−0.954528 | + | 0.298122i | \(0.903640\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.00888 | + | 6.76496i | −0.282625 | + | 0.272789i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.2845 | + | 8.24718i | 0.575074 | + | 0.332019i | 0.759173 | − | 0.650889i | \(-0.225603\pi\) |
−0.184099 | + | 0.982908i | \(0.558937\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.6263 | + | 35.7258i | 0.829040 | + | 1.43594i | 0.898792 | + | 0.438375i | \(0.144446\pi\) |
−0.0697522 | + | 0.997564i | \(0.522221\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.20813 | − | 29.3169i | −0.249124 | − | 1.17645i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.15583 | + | 2.00196i | 0.0463074 | + | 0.0802068i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.64890 | + | 16.7124i | −0.385956 | + | 0.668495i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.90703 | + | 6.66665i | −0.275840 | + | 0.266240i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.18329 | 0.246544 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.49407i | 0.0992873i | 0.998767 | + | 0.0496437i | \(0.0158086\pi\) | ||||
−0.998767 | + | 0.0496437i | \(0.984191\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.53685 | − | 8.83855i | 0.100831 | − | 0.351301i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.938964 | + | 0.542111i | 0.0372616 | + | 0.0215130i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.2155 | + | 9.93935i | −0.682101 | + | 0.393811i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −28.1605 | + | 14.9549i | −1.11401 | + | 0.591605i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.03469 | − | 1.75208i | 0.119863 | − | 0.0692029i | −0.438870 | − | 0.898551i | \(-0.644621\pi\) |
0.558733 | + | 0.829348i | \(0.311288\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.6711 | − | 37.5354i | 0.854623 | − | 1.48025i | −0.0223710 | − | 0.999750i | \(-0.507121\pi\) |
0.876994 | − | 0.480501i | \(-0.159545\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.53299 | + | 1.12898i | −0.178486 | + | 0.0444535i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.1547 | 1.18551 | 0.592753 | − | 0.805385i | \(-0.298041\pi\) | ||||
0.592753 | + | 0.805385i | \(0.298041\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.0231 | −0.785976 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.0370 | + | 2.99792i | −0.471768 | + | 0.117498i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.50977 | + | 14.7394i | −0.333013 | + | 0.576796i | −0.983101 | − | 0.183063i | \(-0.941399\pi\) |
0.650088 | + | 0.759859i | \(0.274732\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.25300 | + | 5.34222i | −0.361545 | + | 0.208738i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.05630 | + | 1.09201i | −0.0802238 | + | 0.0426035i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.1524 | − | 12.7897i | 0.862934 | − | 0.498215i | −0.00205997 | − | 0.999998i | \(-0.500656\pi\) |
0.864994 | + | 0.501783i | \(0.167322\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.6746 | + | 22.3288i | 1.50427 | + | 0.868488i | 0.999988 | + | 0.00494722i | \(0.00157475\pi\) |
0.504278 | + | 0.863541i | \(0.331759\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.20486 | + | 7.68189i | −0.0856297 | + | 0.298340i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.52557i | − | 0.0591592i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −50.8786 | −1.97003 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.22917 | − | 7.94278i | 0.318158 | − | 0.307086i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.22462 | + | 14.2455i | −0.317508 | + | 0.549940i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.87704 | + | 15.3755i | 0.342185 | + | 0.592681i | 0.984838 | − | 0.173476i | \(-0.0554998\pi\) |
−0.642653 | + | 0.766157i | \(0.722166\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −22.7747 | − | 7.41916i | −0.876599 | − | 0.285564i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.79339 | + | 8.30239i | 0.184225 | + | 0.319087i | 0.943315 | − | 0.331899i | \(-0.107689\pi\) |
−0.759090 | + | 0.650985i | \(0.774356\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.10890 | + | 5.25903i | 0.349568 | + | 0.201823i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.3522 | − | 28.3307i | 1.12478 | − | 1.08563i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.7701i | 0.947800i | 0.880579 | + | 0.473900i | \(0.157154\pi\) | ||||
−0.880579 | + | 0.473900i | \(0.842846\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1.58193i | − | 0.0604425i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.2748 | − | 4.09715i | −0.544616 | − | 0.156316i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.5902 | − | 13.0425i | −0.860620 | − | 0.496879i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.61477 | − | 16.6533i | −0.365763 | − | 0.633520i | 0.623135 | − | 0.782114i | \(-0.285859\pi\) |
−0.988898 | + | 0.148594i | \(0.952525\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.181531 | + | 5.12368i | −0.00689579 | + | 0.194632i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.66051 | + | 4.60813i | 0.100919 | + | 0.174796i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.52680 | + | 11.3047i | −0.247220 | + | 0.428198i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.986190 | − | 3.95968i | −0.0373011 | − | 0.149769i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.5311 | −0.397754 | −0.198877 | − | 0.980024i | \(-0.563729\pi\) | ||||
−0.198877 | + | 0.980024i | \(0.563729\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 12.0000i | − | 0.452589i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.1252 | − | 2.77082i | 0.418999 | − | 0.104355i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.22322 | − | 1.28358i | −0.0836127 | − | 0.0482738i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.7893 | − | 9.69332i | 0.630537 | − | 0.364040i | −0.150423 | − | 0.988622i | \(-0.548064\pi\) |
0.780960 | + | 0.624581i | \(0.214730\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22.2572 | − | 35.5787i | 0.834710 | − | 1.33431i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −41.2222 | + | 23.7997i | −1.54378 | + | 0.891304i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.95763 | − | 3.39071i | 0.0732111 | − | 0.126805i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.8133 | + | 37.6743i | −0.403830 | + | 1.40697i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.9401 | −0.482583 | −0.241291 | − | 0.970453i | \(-0.577571\pi\) | ||||
−0.241291 | + | 0.970453i | \(0.577571\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.21205 | −0.0451390 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.1883 | + | 27.1326i | 0.973954 | + | 1.00907i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.3337 | + | 35.2190i | −0.755175 | + | 1.30800i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.6566 | − | 6.72997i | 0.432321 | − | 0.249601i | −0.268014 | − | 0.963415i | \(-0.586367\pi\) |
0.700335 | + | 0.713814i | \(0.253034\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.86322 | − | 26.8478i | 0.106045 | − | 0.994361i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.42133 | + | 3.13001i | −0.200515 | + | 0.115767i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.61900 | + | 4.97618i | 0.318350 | + | 0.183800i | 0.650657 | − | 0.759372i | \(-0.274494\pi\) |
−0.332307 | + | 0.943171i | \(0.607827\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.69453 | + | 4.86380i | 0.173160 | + | 0.179404i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.0780i | 0.371230i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.2128 | 0.743540 | 0.371770 | − | 0.928325i | \(-0.378751\pi\) | ||||
0.371770 | + | 0.928325i | \(0.378751\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.9084 | + | 4.27900i | 0.547672 | + | 0.157193i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.5392 | + | 39.0391i | −0.826883 | + | 1.43220i | 0.0735881 | + | 0.997289i | \(0.476555\pi\) |
−0.900471 | + | 0.434915i | \(0.856778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.21658 | + | 9.03538i | 0.191121 | + | 0.331031i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.85052 | − | 4.55663i | 0.104295 | − | 0.166718i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.63376 | − | 6.29385i | −0.132775 | − | 0.229972i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.1455 | + | 21.4460i | 1.35546 | + | 0.782575i | 0.989008 | − | 0.147862i | \(-0.0472390\pi\) |
0.366452 | + | 0.930437i | \(0.380572\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.55188 | + | 18.2764i | 0.165880 | + | 0.666029i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1.73029i | − | 0.0629715i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 18.3964i | − | 0.668628i | −0.942462 | − | 0.334314i | \(-0.891495\pi\) | ||
0.942462 | − | 0.334314i | \(-0.108505\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.75444 | + | 19.0897i | 0.172575 | + | 0.692912i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.0623 | − | 17.3565i | −1.08976 | − | 0.629172i | −0.156246 | − | 0.987718i | \(-0.549939\pi\) |
−0.933512 | + | 0.358546i | \(0.883273\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.09916 | − | 12.2961i | −0.257007 | − | 0.445149i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.71602 | + | 0.0962281i | 0.0981979 | + | 0.00347913i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.1760 | + | 28.0176i | 0.584081 | + | 1.01166i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.41906 | − | 5.92199i | 0.123294 | − | 0.213552i | −0.797771 | − | 0.602961i | \(-0.793987\pi\) |
0.921065 | + | 0.389409i | \(0.127321\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −39.8875 | − | 11.4485i | −1.43651 | − | 0.412309i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.5131 | 1.45715 | 0.728577 | − | 0.684964i | \(-0.240182\pi\) | ||||
0.728577 | + | 0.684964i | \(0.240182\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38.0463i | 1.36666i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.45083 | − | 4.61132i | −0.159673 | − | 0.165430i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21.9393 | + | 12.6667i | 0.786057 | + | 0.453830i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.1277 | − | 10.4661i | 0.648661 | − | 0.374505i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −43.5868 | − | 14.1990i | −1.55766 | − | 0.507429i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.51693 | − | 1.45315i | 0.0898332 | − | 0.0518652i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.6672 | + | 37.5286i | −0.772351 | + | 1.33775i | 0.163921 | + | 0.986473i | \(0.447586\pi\) |
−0.936272 | + | 0.351277i | \(0.885748\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.62805 | + | 8.93915i | 0.307167 | + | 0.318242i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.3512 | −0.510270 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.5775 | 0.943796 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.44715 | + | 8.52604i | −0.0867914 | + | 0.302388i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.1110 | + | 36.5654i | −0.747791 | + | 1.29521i | 0.201089 | + | 0.979573i | \(0.435552\pi\) |
−0.948880 | + | 0.315639i | \(0.897781\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.3054 | − | 7.68189i | 0.470712 | − | 0.271766i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.74845 | + | 7.05847i | 0.132445 | + | 0.249399i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.32370 | − | 0.764237i | 0.0467122 | − | 0.0269693i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.70757 | − | 1.56322i | −0.0954294 | − | 0.0550962i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.8998 | + | 5.45431i | −0.770908 | + | 0.192001i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 31.6048i | − | 1.11117i | −0.831461 | − | 0.555583i | \(-0.812495\pi\) | ||
0.831461 | − | 0.555583i | \(-0.187505\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.9542 | 0.700688 | 0.350344 | − | 0.936621i | \(-0.386065\pi\) | ||||
0.350344 | + | 0.936621i | \(0.386065\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.02199 | − | 12.1337i | −0.105986 | − | 0.425547i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.07008 | + | 5.31753i | −0.107540 | + | 0.186265i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.07445 | + | 10.5213i | 0.212518 | + | 0.368092i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.31603 | − | 3.88523i | 0.255643 | − | 0.135761i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.1074 | + | 26.1669i | 0.527253 | + | 0.913230i | 0.999496 | + | 0.0317607i | \(0.0101114\pi\) |
−0.472242 | + | 0.881469i | \(0.656555\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.8460 | + | 15.4996i | 0.935794 | + | 0.540281i | 0.888639 | − | 0.458607i | \(-0.151651\pi\) |
0.0471548 | + | 0.998888i | \(0.484985\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.1143 | + | 4.33812i | 0.526213 | + | 0.151034i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 25.1412i | − | 0.874245i | −0.899402 | − | 0.437122i | \(-0.855998\pi\) | ||
0.899402 | − | 0.437122i | \(-0.144002\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.9471i | 1.14430i | 0.820149 | + | 0.572149i | \(0.193890\pi\) | ||||
−0.820149 | + | 0.572149i | \(0.806110\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 37.6827 | − | 36.3712i | 1.30720 | − | 1.26170i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.84491 | + | 4.52926i | 0.271810 | + | 0.156930i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.842487 | − | 1.45923i | −0.0291555 | − | 0.0504987i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −41.9562 | + | 8.88462i | −1.45022 | + | 0.307098i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.28863 | − | 2.23197i | −0.0444883 | − | 0.0770560i | 0.842924 | − | 0.538033i | \(-0.180832\pi\) |
−0.887412 | + | 0.460977i | \(0.847499\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.4151 | + | 42.2882i | −0.841900 | + | 1.45821i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32.9115 | + | 31.7661i | −1.13353 | + | 1.09408i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.79565 | 0.0617722 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.17937i | 0.212326i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.8345 | − | 48.2003i | 0.474798 | − | 1.65423i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.2975 | − | 12.2961i | −0.730068 | − | 0.421505i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.50789 | − | 1.44793i | 0.0858685 | − | 0.0495762i | −0.456451 | − | 0.889749i | \(-0.650880\pi\) |
0.542319 | + | 0.840172i | \(0.317546\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.186751 | − | 5.27102i | 0.00638676 | − | 0.180265i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.9352 | − | 9.77752i | 0.578494 | − | 0.333994i | −0.182041 | − | 0.983291i | \(-0.558270\pi\) |
0.760535 | + | 0.649297i | \(0.224937\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.09073 | + | 8.81740i | −0.173693 | + | 0.300846i | −0.939708 | − | 0.341977i | \(-0.888904\pi\) |
0.766015 | + | 0.642823i | \(0.222237\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.1289 | − | 3.26985i | 0.447430 | − | 0.111436i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.38174 | 0.183197 | 0.0915983 | − | 0.995796i | \(-0.470802\pi\) | ||||
0.0915983 | + | 0.995796i | \(0.470802\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.4134 | −0.388068 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −25.0381 | + | 6.23594i | −0.850338 | + | 0.211784i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.7753 | + | 23.8596i | −0.467296 | + | 0.809380i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.1018 | − | 8.14170i | 0.477823 | − | 0.275871i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30.8284 | + | 19.2855i | 1.04338 | + | 0.652717i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.51158 | + | 2.60476i | −0.152519 | + | 0.0880570i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.0499 | + | 21.3908i | 1.25109 | + | 0.722315i | 0.971325 | − | 0.237754i | \(-0.0764112\pi\) |
0.279762 | + | 0.960069i | \(0.409745\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.65072 | + | 30.1397i | −0.291782 | + | 1.01659i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 20.4046i | − | 0.687448i | −0.939071 | − | 0.343724i | \(-0.888312\pi\) | ||
0.939071 | − | 0.343724i | \(-0.111688\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.0790 | −1.71895 | −0.859473 | − | 0.511181i | \(-0.829208\pi\) | ||||
−0.859473 | + | 0.511181i | \(0.829208\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.91568 | − | 7.64020i | 0.266083 | − | 0.256823i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.2192 | + | 33.2886i | −0.645318 | + | 1.11772i | 0.338910 | + | 0.940819i | \(0.389942\pi\) |
−0.984228 | + | 0.176904i | \(0.943392\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.752966 | − | 1.30417i | −0.0252537 | − | 0.0437406i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.25442 | + | 17.6806i | −0.0420246 | + | 0.592323i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.9084 | − | 25.8220i | −0.498889 | − | 0.864101i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.19426 | + | 4.73096i | 0.273904 | + | 0.158138i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.8706 | − | 22.0746i | 0.763625 | − | 0.737050i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 72.8138i | 2.42848i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.8867i | 0.396002i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.23663 | + | 1.79004i | 0.207542 | + | 0.0595688i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.30822 | − | 5.37411i | −0.309416 | − | 0.178641i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.8075 | − | 49.8961i | −0.956538 | − | 1.65677i | −0.730809 | − | 0.682582i | \(-0.760857\pi\) |
−0.225729 | − | 0.974190i | \(-0.572476\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.52433 | − | 4.70704i | −0.249566 | − | 0.156123i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.2250 | + | 29.8346i | 0.570690 | + | 0.988464i | 0.996495 | + | 0.0836493i | \(0.0266576\pi\) |
−0.425805 | + | 0.904815i | \(0.640009\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.76423 | + | 3.05574i | −0.0583875 | + | 0.101130i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.18421 | − | 8.76988i | −0.0722077 | − | 0.289923i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.8402 | 0.490066 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 41.9650i | − | 1.38430i | −0.721755 | − | 0.692149i | \(-0.756664\pi\) | ||
0.721755 | − | 0.692149i | \(-0.243336\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.6861 | − | 9.88415i | 1.30770 | − | 0.325694i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.2895 | − | 16.9103i | −0.964076 | − | 0.556610i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.0231 | + | 9.82831i | −0.559717 | + | 0.323153i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.18775 | − | 0.148371i | −0.137544 | − | 0.00487315i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.6300 | + | 9.60134i | −0.545613 | + | 0.315010i | −0.747351 | − | 0.664430i | \(-0.768674\pi\) |
0.201738 | + | 0.979440i | \(0.435341\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.79000 | − | 15.2247i | 0.288081 | − | 0.498970i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.49323 | + | 15.6547i | −0.147102 | + | 0.512513i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.78414 | −0.0583477 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 56.0541 | 1.83121 | 0.915604 | − | 0.402081i | \(-0.131713\pi\) | ||||
0.915604 | + | 0.402081i | \(0.131713\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.25045 | + | 9.58400i | 0.301877 | + | 0.312762i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.98561 | + | 10.3674i | −0.195125 | + | 0.337967i | −0.946942 | − | 0.321406i | \(-0.895845\pi\) |
0.751816 | + | 0.659373i | \(0.229178\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.9613 | − | 25.9584i | 1.46414 | − | 0.845322i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.88327 | − | 2.09480i | −0.0612628 | − | 0.0681437i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.4040 | − | 16.3991i | 0.923007 | − | 0.532898i | 0.0384138 | − | 0.999262i | \(-0.487770\pi\) |
0.884593 | + | 0.466364i | \(0.154436\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.13874 | − | 1.23480i | −0.0694263 | − | 0.0400833i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −39.6098 | − | 41.0380i | −1.28444 | − | 1.33075i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.01998i | 0.162613i | 0.996689 | + | 0.0813065i | \(0.0259093\pi\) | ||||
−0.996689 | + | 0.0813065i | \(0.974091\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.71771 | −0.249739 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 28.9261 | + | 8.30239i | 0.935048 | + | 0.268378i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.09861 | + | 1.90285i | −0.0354761 | + | 0.0614463i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.5603 | + | 32.1474i | 0.598720 | + | 1.03701i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.7846 | − | 22.1907i | −0.379752 | − | 0.715086i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.741197 | + | 1.28379i | 0.0238600 | + | 0.0413267i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.2768 | − | 22.0991i | −1.23090 | − | 0.710660i | −0.263682 | − | 0.964610i | \(-0.584937\pi\) |
−0.967217 | + | 0.253950i | \(0.918270\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.70813 | − | 6.85837i | −0.0548731 | − | 0.220322i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51.9018i | 1.66561i | 0.553567 | + | 0.832805i | \(0.313266\pi\) | ||||
−0.553567 | + | 0.832805i | \(0.686734\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 7.39062i | − | 0.236932i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.14015 | − | 24.6535i | −0.196642 | − | 0.789544i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.6452 | + | 6.72338i | 0.372564 | + | 0.215100i | 0.674578 | − | 0.738203i | \(-0.264326\pi\) |
−0.302014 | + | 0.953304i | \(0.597659\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.62333 | − | 4.54373i | −0.0838419 | − | 0.145218i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.0231 | − | 43.3534i | −0.735072 | − | 1.38417i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.0997 | − | 22.6894i | −0.417816 | − | 0.723678i | 0.577904 | − | 0.816105i | \(-0.303871\pi\) |
−0.995719 | + | 0.0924270i | \(0.970538\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.56319 | − | 9.63572i | 0.177258 | − | 0.307020i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.3064 | − | 4.39325i | −0.487208 | − | 0.139839i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.8974 | 0.791690 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.2335i | 1.27806i | 0.769182 | + | 0.639030i | \(0.220664\pi\) | ||||
−0.769182 | + | 0.639030i | \(0.779336\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.20661 | − | 4.35829i | −0.133493 | − | 0.138306i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.02899 | + | 0.594087i | 0.0326212 | + | 0.0188338i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.5866 | − | 25.1647i | 1.38040 | − | 0.796975i | 0.388194 | − | 0.921578i | \(-0.373099\pi\) |
0.992207 | + | 0.124603i | \(0.0397658\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.8136 | − | 16.4774i | −0.468682 | − | 0.521323i |
(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.95.1 | yes | 16 | |
3.2 | odd | 2 | 1728.2.p.a.287.6 | 16 | |||
4.3 | odd | 2 | inner | 576.2.p.c.95.8 | yes | 16 | |
8.3 | odd | 2 | 576.2.p.a.95.1 | ✓ | 16 | ||
8.5 | even | 2 | 576.2.p.a.95.8 | yes | 16 | ||
9.2 | odd | 6 | 576.2.p.a.479.1 | yes | 16 | ||
9.4 | even | 3 | 5184.2.f.a.2591.11 | 16 | |||
9.5 | odd | 6 | 5184.2.f.f.2591.7 | 16 | |||
9.7 | even | 3 | 1728.2.p.c.1439.3 | 16 | |||
12.11 | even | 2 | 1728.2.p.a.287.5 | 16 | |||
24.5 | odd | 2 | 1728.2.p.c.287.4 | 16 | |||
24.11 | even | 2 | 1728.2.p.c.287.3 | 16 | |||
36.7 | odd | 6 | 1728.2.p.c.1439.4 | 16 | |||
36.11 | even | 6 | 576.2.p.a.479.8 | yes | 16 | ||
36.23 | even | 6 | 5184.2.f.f.2591.5 | 16 | |||
36.31 | odd | 6 | 5184.2.f.a.2591.9 | 16 | |||
72.5 | odd | 6 | 5184.2.f.a.2591.12 | 16 | |||
72.11 | even | 6 | inner | 576.2.p.c.479.1 | yes | 16 | |
72.13 | even | 6 | 5184.2.f.f.2591.8 | 16 | |||
72.29 | odd | 6 | inner | 576.2.p.c.479.8 | yes | 16 | |
72.43 | odd | 6 | 1728.2.p.a.1439.6 | 16 | |||
72.59 | even | 6 | 5184.2.f.a.2591.10 | 16 | |||
72.61 | even | 6 | 1728.2.p.a.1439.5 | 16 | |||
72.67 | odd | 6 | 5184.2.f.f.2591.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.2.p.a.95.1 | ✓ | 16 | 8.3 | odd | 2 | ||
576.2.p.a.95.8 | yes | 16 | 8.5 | even | 2 | ||
576.2.p.a.479.1 | yes | 16 | 9.2 | odd | 6 | ||
576.2.p.a.479.8 | yes | 16 | 36.11 | even | 6 | ||
576.2.p.c.95.1 | yes | 16 | 1.1 | even | 1 | trivial | |
576.2.p.c.95.8 | yes | 16 | 4.3 | odd | 2 | inner | |
576.2.p.c.479.1 | yes | 16 | 72.11 | even | 6 | inner | |
576.2.p.c.479.8 | yes | 16 | 72.29 | odd | 6 | inner | |
1728.2.p.a.287.5 | 16 | 12.11 | even | 2 | |||
1728.2.p.a.287.6 | 16 | 3.2 | odd | 2 | |||
1728.2.p.a.1439.5 | 16 | 72.61 | even | 6 | |||
1728.2.p.a.1439.6 | 16 | 72.43 | odd | 6 | |||
1728.2.p.c.287.3 | 16 | 24.11 | even | 2 | |||
1728.2.p.c.287.4 | 16 | 24.5 | odd | 2 | |||
1728.2.p.c.1439.3 | 16 | 9.7 | even | 3 | |||
1728.2.p.c.1439.4 | 16 | 36.7 | odd | 6 | |||
5184.2.f.a.2591.9 | 16 | 36.31 | odd | 6 | |||
5184.2.f.a.2591.10 | 16 | 72.59 | even | 6 | |||
5184.2.f.a.2591.11 | 16 | 9.4 | even | 3 | |||
5184.2.f.a.2591.12 | 16 | 72.5 | odd | 6 | |||
5184.2.f.f.2591.5 | 16 | 36.23 | even | 6 | |||
5184.2.f.f.2591.6 | 16 | 72.67 | odd | 6 | |||
5184.2.f.f.2591.7 | 16 | 9.5 | odd | 6 | |||
5184.2.f.f.2591.8 | 16 | 72.13 | even | 6 |