Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(191,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 16.0.9349208943630483456.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 \) |
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 | 959.2 | ||
Root | \(0.500000 - 2.74530i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.959 |
Dual form | 1152.2.p.e.191.2 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.65068 | − | 0.524648i | −0.953021 | − | 0.302905i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.57313 | − | 2.72474i | 0.703526 | − | 1.21854i | −0.263695 | − | 0.964606i | \(-0.584941\pi\) |
0.967221 | − | 0.253937i | \(-0.0817255\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.21650 | + | 1.27970i | −0.837759 | + | 0.483680i | −0.856502 | − | 0.516144i | \(-0.827367\pi\) |
0.0187428 | + | 0.999824i | \(0.494034\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.44949 | + | 1.73205i | 0.816497 | + | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.02166 | + | 1.16721i | −0.609554 | + | 0.351926i | −0.772791 | − | 0.634661i | \(-0.781140\pi\) |
0.163237 | + | 0.986587i | \(0.447807\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.59808 | + | 1.50000i | 0.720577 | + | 0.416025i | 0.814965 | − | 0.579510i | \(-0.196756\pi\) |
−0.0943882 | + | 0.995535i | \(0.530089\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.02627 | + | 3.67234i | −1.03958 | + | 0.948195i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.24264i | 1.02899i | 0.857493 | + | 0.514496i | \(0.172021\pi\) | ||||
−0.857493 | + | 0.514496i | \(0.827979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.08665 | 1.85520 | 0.927602 | − | 0.373570i | \(-0.121866\pi\) | ||||
0.927602 | + | 0.373570i | \(0.121866\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.33013 | − | 0.949490i | 0.944911 | − | 0.207196i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.642559 | − | 1.11295i | 0.133983 | − | 0.232065i | −0.791226 | − | 0.611524i | \(-0.790557\pi\) |
0.925208 | + | 0.379459i | \(0.123890\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.44949 | − | 4.24264i | −0.489898 | − | 0.848528i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.13461 | − | 4.14418i | −0.603256 | − | 0.797548i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.18386 | + | 2.05051i | 0.219838 | + | 0.380770i | 0.954758 | − | 0.297383i | \(-0.0961139\pi\) |
−0.734920 | + | 0.678153i | \(0.762781\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.64580 | + | 4.41431i | 1.37323 | + | 0.792833i | 0.991333 | − | 0.131374i | \(-0.0419387\pi\) |
0.381894 | + | 0.924206i | \(0.375272\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.94949 | − | 0.866025i | 0.687518 | − | 0.150756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.05254i | 1.36113i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.34847i | − | 1.20808i | −0.796954 | − | 0.604040i | \(-0.793557\pi\) | ||
0.796954 | − | 0.604040i | \(-0.206443\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.50162 | − | 3.83909i | −0.560708 | − | 0.614747i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.17423 | − | 4.71940i | −1.27660 | − | 0.737046i | −0.300379 | − | 0.953820i | \(-0.597113\pi\) |
−0.976222 | + | 0.216774i | \(0.930447\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.11295 | − | 1.92768i | −0.169723 | − | 0.293968i | 0.768600 | − | 0.639730i | \(-0.220954\pi\) |
−0.938322 | + | 0.345762i | \(0.887621\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.57277 | − | 3.94949i | 1.27795 | − | 0.588755i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.78674 | − | 8.29088i | −0.698218 | − | 1.20935i | −0.969084 | − | 0.246732i | \(-0.920643\pi\) |
0.270866 | − | 0.962617i | \(-0.412690\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.224745 | + | 0.389270i | −0.0321064 | + | 0.0556099i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.22589 | − | 7.00324i | 0.311687 | − | 0.980650i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.34242 | 1.14592 | 0.572960 | − | 0.819584i | \(-0.305795\pi\) | ||||
0.572960 | + | 0.819584i | \(0.305795\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.34468i | 0.990357i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13.3485 | − | 4.24264i | −1.76805 | − | 0.561951i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.11295 | + | 0.642559i | 0.144893 | + | 0.0836541i | 0.570694 | − | 0.821163i | \(-0.306674\pi\) |
−0.425801 | + | 0.904817i | \(0.640008\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.79423 | − | 4.50000i | 0.997949 | − | 0.576166i | 0.0903080 | − | 0.995914i | \(-0.471215\pi\) |
0.907641 | + | 0.419748i | \(0.137882\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.64580 | − | 0.704487i | −0.963281 | − | 0.0887570i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.17423 | − | 4.71940i | 1.01389 | − | 0.585369i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.204229 | + | 0.353736i | −0.0249506 | + | 0.0432157i | −0.878231 | − | 0.478237i | \(-0.841276\pi\) |
0.853281 | + | 0.521452i | \(0.174610\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.64456 | + | 1.50000i | −0.197982 | + | 0.180579i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.5841 | 1.73082 | 0.865409 | − | 0.501066i | \(-0.167059\pi\) | ||||
0.865409 | + | 0.501066i | \(0.167059\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.55051 | −0.181473 | −0.0907367 | − | 0.995875i | \(-0.528922\pi\) | ||||
−0.0907367 | + | 0.995875i | \(0.528922\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.81743 | + | 8.28836i | 0.209859 | + | 0.957058i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.98735 | − | 5.17423i | 0.340440 | − | 0.589659i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.93092 | − | 5.15627i | 1.00481 | − | 0.580126i | 0.0951401 | − | 0.995464i | \(-0.469670\pi\) |
0.909667 | + | 0.415338i | \(0.136337\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.00000 | + | 8.48528i | 0.333333 | + | 0.942809i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.93038 | + | 1.69185i | −0.321651 | + | 0.185705i | −0.652128 | − | 0.758109i | \(-0.726124\pi\) |
0.330477 | + | 0.943814i | \(0.392790\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.5601 | + | 6.67423i | 1.25387 | + | 0.723922i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.878383 | − | 4.00585i | −0.0941726 | − | 0.429472i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.14966i | 0.651863i | 0.945393 | + | 0.325932i | \(0.105678\pi\) | ||||
−0.945393 | + | 0.325932i | \(0.894322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.67819 | −0.804893 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.3048 | − | 11.2980i | −1.06856 | − | 1.17154i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.7214 | − | 22.0341i | 1.30518 | − | 2.26065i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.62372 | + | 11.4726i | 0.672537 | + | 1.16487i | 0.977182 | + | 0.212403i | \(0.0681289\pi\) |
−0.304645 | + | 0.952466i | \(0.598538\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.97370 | − | 0.642559i | −0.700883 | − | 0.0645797i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.57313 | − | 2.72474i | −0.156533 | − | 0.271122i | 0.777083 | − | 0.629398i | \(-0.216698\pi\) |
−0.933616 | + | 0.358275i | \(0.883365\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.35698 | + | 4.24755i | 0.724905 | + | 0.418524i | 0.816555 | − | 0.577267i | \(-0.195881\pi\) |
−0.0916506 | + | 0.995791i | \(0.529214\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.22474 | − | 13.2922i | 0.412293 | − | 1.29718i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 18.2037i | − | 1.75981i | −0.475145 | − | 0.879907i | \(-0.657604\pi\) | ||
0.475145 | − | 0.879907i | \(-0.342396\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.34847i | − | 0.129160i | −0.997913 | − | 0.0645800i | \(-0.979429\pi\) | ||
0.997913 | − | 0.0645800i | \(-0.0205708\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.85536 | + | 12.1300i | −0.365934 | + | 1.15133i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.50000 | + | 2.59808i | 0.423324 | + | 0.244406i | 0.696499 | − | 0.717558i | \(-0.254740\pi\) |
−0.273174 | + | 0.961965i | \(0.588074\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.02166 | − | 3.50162i | −0.188521 | − | 0.326528i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.76588 | + | 8.17423i | 0.348156 | + | 0.755708i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.42930 | − | 9.40382i | −0.497703 | − | 0.862047i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.77526 | + | 4.80688i | −0.252296 | + | 0.436989i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.0170 | + | 12.0788i | 0.993372 | + | 1.08911i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.317837 | 0.0284282 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.2921i | 1.88937i | 0.327983 | + | 0.944684i | \(0.393631\pi\) | ||||
−0.327983 | + | 0.944684i | \(0.606369\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.825765 | + | 3.76588i | 0.0727046 | + | 0.331568i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.52140 | − | 0.878383i | −0.132926 | − | 0.0767447i | 0.432063 | − | 0.901844i | \(-0.357786\pi\) |
−0.564988 | + | 0.825099i | \(0.691119\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.9241 | + | 10.3485i | −1.55421 | + | 0.897326i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16.2230 | + | 2.02166i | −1.39625 | + | 0.173997i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.5227 | − | 8.96204i | 1.32619 | − | 0.765679i | 0.341485 | − | 0.939887i | \(-0.389070\pi\) |
0.984709 | + | 0.174209i | \(0.0557367\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.79114 | + | 15.2267i | −0.745654 | + | 1.29151i | 0.204234 | + | 0.978922i | \(0.434530\pi\) |
−0.949888 | + | 0.312589i | \(0.898804\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.55159 | + | 16.1969i | 0.299098 | + | 1.36403i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.00324 | −0.585641 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.44949 | 0.618646 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.575211 | − | 0.524648i | 0.0474426 | − | 0.0432722i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.74434 | + | 9.94949i | −0.470595 | + | 0.815094i | −0.999434 | − | 0.0336278i | \(-0.989294\pi\) |
0.528840 | + | 0.848722i | \(0.322627\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.49792 | − | 2.59687i | 0.366035 | − | 0.211331i | −0.305690 | − | 0.952131i | \(-0.598887\pi\) |
0.671725 | + | 0.740801i | \(0.265554\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.34847 | + | 10.3923i | −0.594089 | + | 0.840168i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 24.0557 | − | 13.8886i | 1.93220 | − | 1.11556i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.62642 | − | 3.82577i | −0.528846 | − | 0.305329i | 0.211700 | − | 0.977335i | \(-0.432100\pi\) |
−0.740546 | + | 0.672005i | \(0.765433\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.7707 | − | 4.37683i | −1.09208 | − | 0.347105i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.28913i | 0.259220i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.63487 | 0.284705 | 0.142352 | − | 0.989816i | \(-0.454533\pi\) | ||||
0.142352 | + | 0.989816i | \(0.454533\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.85337 | − | 12.1237i | 0.299985 | − | 0.943831i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.07186 | − | 10.5168i | 0.469855 | − | 0.813812i | −0.529551 | − | 0.848278i | \(-0.677640\pi\) |
0.999406 | + | 0.0344659i | \(0.0109730\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.00000 | − | 3.46410i | −0.153846 | − | 0.266469i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 19.8082 | + | 14.0065i | 1.51477 | + | 1.07110i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.52664 | − | 4.37628i | −0.192097 | − | 0.332722i | 0.753848 | − | 0.657049i | \(-0.228196\pi\) |
−0.945945 | + | 0.324327i | \(0.894862\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.8586 | + | 6.26922i | 0.820833 | + | 0.473908i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.50000 | − | 1.64456i | −0.112747 | − | 0.123613i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 3.04189i | − | 0.227361i | −0.993517 | − | 0.113681i | \(-0.963736\pi\) | ||
0.993517 | − | 0.113681i | \(-0.0362641\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 19.3485i | − | 1.43816i | −0.694927 | − | 0.719080i | \(-0.744563\pi\) | ||
0.694927 | − | 0.719080i | \(-0.255437\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.2267 | + | 3.33884i | −1.12559 | + | 0.246814i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −20.0227 | − | 11.5601i | −1.47210 | − | 0.849916i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.95204 | − | 8.57719i | −0.362129 | − | 0.627226i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.2512 | + | 5.17423i | 0.891141 | + | 0.376370i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.36439 | + | 9.29139i | 0.388153 | + | 0.672302i | 0.992201 | − | 0.124647i | \(-0.0397797\pi\) |
−0.604048 | + | 0.796948i | \(0.706446\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.72474 | − | 6.45145i | 0.268113 | − | 0.464385i | −0.700262 | − | 0.713886i | \(-0.746933\pi\) |
0.968375 | + | 0.249501i | \(0.0802666\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −15.9691 | + | 3.50162i | −1.14357 | + | 0.250756i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.6848 | −1.18875 | −0.594373 | − | 0.804190i | \(-0.702600\pi\) | ||||
−0.594373 | + | 0.804190i | \(0.702600\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.5068i | 1.17014i | 0.810984 | + | 0.585068i | \(0.198932\pi\) | ||||
−0.810984 | + | 0.585068i | \(0.801068\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.522704 | − | 0.476756i | 0.0368687 | − | 0.0336278i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.24807 | − | 3.02997i | −0.368342 | − | 0.212662i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −25.7183 | + | 14.8485i | −1.79624 | + | 1.03706i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.50162 | − | 1.61320i | 0.243380 | − | 0.112125i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.3485 | + | 9.43879i | −1.13085 | + | 0.652895i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.83909 | − | 6.64951i | 0.264294 | − | 0.457771i | −0.703084 | − | 0.711107i | \(-0.748194\pi\) |
0.967378 | + | 0.253336i | \(0.0815277\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −24.0737 | − | 7.65153i | −1.64951 | − | 0.524274i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.00324 | −0.477617 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.5959 | −1.53391 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.55940 | + | 0.813472i | 0.172948 | + | 0.0549693i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.36396 | + | 11.0227i | −0.428086 | + | 0.741467i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.8006 | + | 9.69985i | −1.12505 | + | 0.649550i | −0.942686 | − | 0.333680i | \(-0.891709\pi\) |
−0.182367 | + | 0.983230i | \(0.558376\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.34847 | − | 14.6349i | 0.0898979 | − | 0.975663i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.4208 | + | 11.7900i | −1.35538 | + | 0.782529i | −0.988997 | − | 0.147936i | \(-0.952737\pi\) |
−0.366382 | + | 0.930464i | \(0.619404\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.6900 | + | 12.5227i | 1.43331 | + | 0.827524i | 0.997372 | − | 0.0724517i | \(-0.0230823\pi\) |
0.435941 | + | 0.899975i | \(0.356416\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.64580 | + | 6.97370i | −0.503057 | + | 0.458836i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.48528i | 0.555889i | 0.960597 | + | 0.277945i | \(0.0896532\pi\) | ||||
−0.960597 | + | 0.277945i | \(0.910347\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −30.1207 | −1.96486 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −17.4473 | + | 3.82577i | −1.13333 | + | 0.248510i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.642559 | − | 1.11295i | 0.0415637 | − | 0.0719905i | −0.844495 | − | 0.535563i | \(-0.820099\pi\) |
0.886059 | + | 0.463573i | \(0.153433\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.84847 | − | 11.8619i | −0.441149 | − | 0.764092i | 0.556626 | − | 0.830763i | \(-0.312096\pi\) |
−0.997775 | + | 0.0666710i | \(0.978762\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500258 | − | 15.5804i | −0.0320915 | − | 0.999485i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.707107 | + | 1.22474i | 0.0451754 | + | 0.0782461i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.0097 | + | 12.1300i | 1.33682 | + | 0.771812i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.72474 | − | 1.25529i | 0.362791 | − | 0.0795511i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.71071i | 0.486696i | 0.969939 | + | 0.243348i | \(0.0782457\pi\) | ||||
−0.969939 | + | 0.243348i | \(0.921754\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.00000i | 0.188608i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15.5804 | − | 17.0820i | −0.975684 | − | 1.06972i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.8485 | + | 6.84072i | 0.739087 | + | 0.426712i | 0.821737 | − | 0.569866i | \(-0.193005\pi\) |
−0.0826501 | + | 0.996579i | \(0.526338\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.40382 | + | 16.2879i | 0.584325 | + | 1.01208i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.651729 | + | 7.07321i | −0.0403410 | + | 0.437821i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.0788 | − | 20.9211i | −0.744811 | − | 1.29005i | −0.950283 | − | 0.311388i | \(-0.899206\pi\) |
0.205472 | − | 0.978663i | \(-0.434127\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.1237 | − | 22.7310i | 0.806184 | − | 1.39635i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.22641 | − | 10.1511i | 0.197453 | − | 0.621239i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.32124 | −0.202499 | −0.101250 | − | 0.994861i | \(-0.532284\pi\) | ||||
−0.101250 | + | 0.994861i | \(0.532284\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 13.2054i | − | 0.802173i | −0.916040 | − | 0.401087i | \(-0.868633\pi\) | ||
0.916040 | − | 0.401087i | \(-0.131367\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.6742 | + | 4.02834i | 0.767080 | + | 0.243806i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.90408 | + | 5.71812i | 0.597239 | + | 0.344816i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.6900 | + | 12.5227i | −1.30322 | + | 0.752416i | −0.980956 | − | 0.194232i | \(-0.937778\pi\) |
−0.322268 | + | 0.946649i | \(0.604445\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.0825 | + | 24.0557i | 0.663493 | + | 1.44018i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.8712 | + | 8.00853i | −0.827485 | + | 0.477749i | −0.852991 | − | 0.521926i | \(-0.825214\pi\) |
0.0255059 | + | 0.999675i | \(0.491880\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.38216 | − | 12.7863i | 0.438824 | − | 0.760065i | −0.558775 | − | 0.829319i | \(-0.688729\pi\) |
0.997599 | + | 0.0692539i | \(0.0220618\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −32.5590 | + | 29.6969i | −1.92863 | + | 1.75909i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.1576 | 1.42598 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.91456 | − | 22.4128i | −0.288097 | − | 1.31386i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.89097 | − | 3.27526i | 0.110472 | − | 0.191342i | −0.805489 | − | 0.592611i | \(-0.798097\pi\) |
0.915961 | + | 0.401268i | \(0.131431\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.50162 | − | 2.02166i | 0.203872 | − | 0.117706i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.1742 | + | 4.71940i | 0.648395 | + | 0.273847i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.33884 | − | 1.92768i | 0.193090 | − | 0.111481i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.93369 | + | 2.84847i | 0.284373 | + | 0.164183i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.16721 | + | 5.32302i | 0.0670543 | + | 0.305800i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 28.3164i | − | 1.62139i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.4430 | 1.33796 | 0.668982 | − | 0.743279i | \(-0.266730\pi\) | ||||
0.668982 | + | 0.743279i | \(0.266730\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.91555 | − | 10.8712i | −0.564076 | − | 0.618439i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.7937 | − | 18.6952i | 0.612054 | − | 1.06011i | −0.378840 | − | 0.925462i | \(-0.623677\pi\) |
0.990894 | − | 0.134646i | \(-0.0429898\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.94949 | + | 15.5010i | 0.505855 | + | 0.876167i | 0.999977 | + | 0.00677410i | \(0.00215628\pi\) |
−0.494122 | + | 0.869393i | \(0.664510\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −13.9474 | + | 19.7246i | −0.785847 | + | 1.11136i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.69445 | + | 6.39898i | 0.207501 | + | 0.359402i | 0.950927 | − | 0.309416i | \(-0.100134\pi\) |
−0.743426 | + | 0.668819i | \(0.766800\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.78674 | − | 2.76363i | −0.268006 | − | 0.154733i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.55051 | + | 30.0484i | −0.533058 | + | 1.67714i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 34.3087i | 1.90899i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 14.6969i | − | 0.815239i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.707471 | + | 2.22589i | −0.0391232 | + | 0.123092i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21.2196 | + | 12.2512i | 1.16988 | + | 0.675429i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.69985 | + | 16.8006i | 0.533152 | + | 0.923446i | 0.999250 | + | 0.0387135i | \(0.0123260\pi\) |
−0.466098 | + | 0.884733i | \(0.654341\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.7279 | − | 18.0000i | 0.697486 | − | 0.986394i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.642559 | + | 1.11295i | 0.0351068 | + | 0.0608067i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.8485 | + | 23.9863i | −0.754374 | + | 1.30661i | 0.191311 | + | 0.981530i | \(0.438726\pi\) |
−0.945685 | + | 0.325085i | \(0.894607\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.06499 | − | 6.64951i | −0.329405 | − | 0.361152i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.6096 | −1.11607 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.0662i | − | 1.02948i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.50000 | + | 6.84072i | 0.0807573 | + | 0.368292i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.47344 | − | 3.73745i | −0.347513 | − | 0.200637i | 0.316077 | − | 0.948734i | \(-0.397634\pi\) |
−0.663589 | + | 0.748097i | \(0.730968\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.43027 | − | 0.825765i | 0.0765605 | − | 0.0442022i | −0.461231 | − | 0.887280i | \(-0.652592\pi\) |
0.537792 | + | 0.843078i | \(0.319259\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.92768 | − | 15.4688i | −0.102892 | − | 0.825664i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.82577 | + | 5.67291i | −0.522973 | + | 0.301938i | −0.738150 | − | 0.674637i | \(-0.764300\pi\) |
0.215177 | + | 0.976575i | \(0.430967\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.9428 | − | 39.7380i | 1.21768 | − | 2.10908i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.02834 | + | 18.3712i | 0.213203 | + | 0.972306i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.57024 | −0.135652 | −0.0678260 | − | 0.997697i | \(-0.521606\pi\) | ||||
−0.0678260 | + | 0.997697i | \(0.521606\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 46.3939 | 2.44178 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.10298 | − | 6.47860i | 0.372810 | − | 0.340038i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.43916 | + | 4.22474i | −0.127671 | + | 0.221133i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.50533 | − | 1.44645i | 0.130777 | − | 0.0755041i | −0.433184 | − | 0.901305i | \(-0.642610\pi\) |
0.563961 | + | 0.825801i | \(0.309277\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.8485 | − | 25.7183i | −0.616807 | − | 1.33884i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.4910 | + | 10.6758i | −0.960004 | + | 0.554259i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.262459 | − | 0.151531i | −0.0135896 | − | 0.00784597i | 0.493190 | − | 0.869922i | \(-0.335831\pi\) |
−0.506779 | + | 0.862076i | \(0.669164\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.524648 | − | 0.166753i | −0.0270927 | − | 0.00861106i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.10318i | 0.365832i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.26922 | 0.322028 | 0.161014 | − | 0.986952i | \(-0.448524\pi\) | ||||
0.161014 | + | 0.986952i | \(0.448524\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.1708 | − | 35.1464i | 0.572300 | − | 1.80061i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.78674 | + | 8.29088i | −0.244591 | + | 0.423644i | −0.962017 | − | 0.272991i | \(-0.911987\pi\) |
0.717426 | + | 0.696635i | \(0.245320\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.39898 | − | 16.2795i | −0.479016 | − | 0.829681i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.612688 | − | 6.64951i | 0.0311447 | − | 0.338013i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.0119 | + | 19.0732i | 0.558327 | + | 0.967050i | 0.997636 | + | 0.0687146i | \(0.0218898\pi\) |
−0.439310 | + | 0.898336i | \(0.644777\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.72183 | + | 2.72615i | 0.238793 | + | 0.137867i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.05051 | + | 2.24813i | 0.103435 | + | 0.113403i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 32.4460i | − | 1.63253i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 28.0454i | − | 1.40756i | −0.710419 | − | 0.703779i | \(-0.751494\pi\) | ||
0.710419 | − | 0.703779i | \(-0.248506\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 35.0162 | − | 7.67819i | 1.75300 | − | 0.384390i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.4773 | + | 6.62642i | 0.573149 | + | 0.330908i | 0.758406 | − | 0.651782i | \(-0.225978\pi\) |
−0.185257 | + | 0.982690i | \(0.559312\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.2429 | + | 22.9374i | 0.659677 | + | 1.14259i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 27.8396 | + | 5.17423i | 1.38336 | + | 0.257110i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.57719 | + | 14.8561i | 0.425155 | + | 0.736391i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.2980 | + | 23.0327i | −0.657542 | + | 1.13890i | 0.323708 | + | 0.946157i | \(0.395070\pi\) |
−0.981250 | + | 0.192739i | \(0.938263\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −30.3249 | + | 6.64951i | −1.49582 | + | 0.327996i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.28913 | −0.161847 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.6460i | 0.522594i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.5000 | − | 20.5222i | 1.10183 | − | 1.00497i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.7432 | + | 7.93463i | 0.671398 | + | 0.387632i | 0.796606 | − | 0.604499i | \(-0.206627\pi\) |
−0.125208 | + | 0.992131i | \(0.539960\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.3260 | + | 8.84847i | −0.746943 | + | 0.431248i | −0.824588 | − | 0.565733i | \(-0.808593\pi\) |
0.0776450 | + | 0.996981i | \(0.475260\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.63515 | − | 28.5993i | 0.128125 | − | 1.39055i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.0000 | − | 10.3923i | 0.873128 | − | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.5173 | + | 19.9485i | −0.557360 | + | 0.965377i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.5601 | + | 3.67423i | 0.558128 | + | 0.177394i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.57024 | −0.123804 | −0.0619020 | − | 0.998082i | \(-0.519717\pi\) | ||||
−0.0619020 | + | 0.998082i | \(0.519717\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.4495 | −1.07885 | −0.539427 | − | 0.842032i | \(-0.681359\pi\) | ||||
−0.539427 | + | 0.842032i | \(0.681359\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.2967 | − | 3.90836i | −0.589583 | − | 0.187391i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.19615 | − | 9.00000i | 0.248566 | − | 0.430528i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.9416 | − | 8.04917i | 0.665395 | − | 0.384166i | −0.128935 | − | 0.991653i | \(-0.541156\pi\) |
0.794330 | + | 0.607487i | \(0.207822\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.22474 | + | 0.564242i | −0.0583212 | + | 0.0268687i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.0165 | + | 5.78304i | −0.475899 | + | 0.274760i | −0.718706 | − | 0.695314i | \(-0.755265\pi\) |
0.242807 | + | 0.970075i | \(0.421932\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.7563 | + | 9.67423i | 0.794323 | + | 0.458603i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.7020 | − | 13.4097i | 0.695383 | − | 0.634256i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 31.6055i | − | 1.49156i | −0.666194 | − | 0.745778i | \(-0.732078\pi\) | ||
0.666194 | − | 0.745778i | \(-0.267922\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.0341 | 1.03754 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.78706 | + | 1.92679i | −0.412852 | + | 0.0905283i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.0788 | + | 20.9211i | −0.566263 | + | 0.980797i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.926786 | − | 1.60524i | −0.0433532 | − | 0.0750900i | 0.843535 | − | 0.537075i | \(-0.180471\pi\) |
−0.886888 | + | 0.461985i | \(0.847137\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.5823 | − | 13.2990i | 0.820670 | − | 0.620745i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.1797 | − | 21.0959i | −0.567267 | − | 0.982535i | −0.996835 | − | 0.0795004i | \(-0.974668\pi\) |
0.429568 | − | 0.903034i | \(-0.358666\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.6523 | − | 12.5010i | −1.00627 | − | 0.580969i | −0.0961706 | − | 0.995365i | \(-0.530659\pi\) |
−0.910097 | + | 0.414396i | \(0.863993\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −46.9949 | + | 10.3048i | −2.17934 | + | 0.477875i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.9144i | 1.19917i | 0.800309 | + | 0.599587i | \(0.204669\pi\) | ||||
−0.800309 | + | 0.599587i | \(0.795331\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.04541i | − | 0.0482724i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.93092 | + | 9.79165i | 0.411515 | + | 0.451175i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.50000 | + | 2.59808i | 0.206910 | + | 0.119460i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.8082 | − | 34.3087i | −0.908861 | − | 1.57419i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 20.4347 | + | 14.4495i | 0.935639 | + | 0.661597i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.22021 | − | 2.11346i | −0.0557527 | − | 0.0965665i | 0.836802 | − | 0.547506i | \(-0.184423\pi\) |
−0.892555 | + | 0.450939i | \(0.851089\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.0227 | − | 19.0919i | 0.502592 | − | 0.870515i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.72563 | − | 5.42930i | 0.0785191 | − | 0.247042i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 41.6800 | 1.89259 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.00000 | − | 1.90702i | −0.271329 | − | 0.0862386i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.97422 | − | 4.60392i | −0.359871 | − | 0.207772i | 0.309153 | − | 0.951012i | \(-0.399954\pi\) |
−0.669024 | + | 0.743240i | \(0.733288\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.69958 | + | 5.02270i | −0.391809 | + | 0.226211i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.7214 | + | 17.9907i | −0.571783 | + | 0.808623i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −32.3258 | + | 18.6633i | −1.45001 | + | 0.837163i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.19959 | + | 15.9342i | −0.411830 | + | 0.713311i | −0.995090 | − | 0.0989747i | \(-0.968444\pi\) |
0.583260 | + | 0.812286i | \(0.301777\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.5403 | + | 14.1742i | −0.694289 | + | 0.633258i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.8799 | −0.930989 | −0.465494 | − | 0.885051i | \(-0.654123\pi\) | ||||
−0.465494 | + | 0.885051i | \(0.654123\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.89898 | −0.440499 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.48393 | + | 6.76742i | 0.0659035 | + | 0.300552i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.2262 | − | 19.4444i | 0.497594 | − | 0.861857i | −0.502403 | − | 0.864634i | \(-0.667550\pi\) |
0.999996 | + | 0.00277650i | \(0.000883790\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.43671 | − | 1.98419i | 0.152031 | − | 0.0877752i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −25.3485 | − | 33.5125i | −1.11916 | − | 1.47961i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23.1470 | − | 13.3639i | 1.01998 | − | 0.588885i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.3543 | + | 11.1742i | 0.851203 | + | 0.491442i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.87468 | + | 8.54943i | 0.0822892 | + | 0.375278i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 18.8776i | − | 0.827042i | −0.910495 | − | 0.413521i | \(-0.864299\pi\) | ||
0.910495 | − | 0.413521i | \(-0.135701\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.4425 | −0.981343 | −0.490671 | − | 0.871345i | \(-0.663248\pi\) | ||||
−0.490671 | + | 0.871345i | \(0.663248\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −14.6349 | − | 16.0454i | −0.638721 | − | 0.700279i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.7283 | + | 32.4384i | −0.815818 | + | 1.41304i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.6742 | + | 18.4883i | 0.464097 | + | 0.803840i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.61320 | + | 3.50162i | 0.0700071 | + | 0.151957i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.1582 | − | 24.5227i | −0.613259 | − | 1.06220i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −49.6003 | − | 28.6368i | −2.14441 | − | 1.23808i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.59592 | + | 5.02118i | −0.0688689 | + | 0.216680i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.04930i | − | 0.0451963i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 8.69694i | − | 0.373911i | −0.982368 | − | 0.186955i | \(-0.940138\pi\) | ||
0.982368 | − | 0.186955i | \(-0.0598620\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.1511 | + | 31.9381i | −0.435627 | + | 1.37060i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.67423 | − | 2.12132i | −0.157387 | − | 0.0908674i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.88242 | − | 13.6527i | −0.337028 | − | 0.583749i | 0.646844 | − | 0.762622i | \(-0.276088\pi\) |
−0.983872 | + | 0.178873i | \(0.942755\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 26.8861 | + | 2.47730i | 1.14747 | + | 0.105728i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.57348 | + | 16.5818i | 0.407844 | + | 0.706407i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.1969 | + | 22.8578i | −0.561191 | + | 0.972011i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 26.9861 | + | 29.5869i | 1.14550 | + | 1.25589i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.6417 | 0.874619 | 0.437309 | − | 0.899311i | \(-0.355931\pi\) | ||||
0.437309 | + | 0.899311i | \(0.355931\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.67767i | − | 0.282436i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.67423 | + | 16.7563i | 0.155126 | + | 0.707450i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.5941 | − | 21.1276i | −1.54226 | − | 0.890424i | −0.998696 | − | 0.0510558i | \(-0.983741\pi\) |
−0.543564 | − | 0.839368i | \(-0.682925\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.1582 | − | 8.17423i | 0.595640 | − | 0.343893i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.5081 | − | 14.9686i | −0.735271 | − | 0.628620i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.5000 | − | 7.79423i | 0.565949 | − | 0.326751i | −0.189580 | − | 0.981865i | \(-0.560713\pi\) |
0.755530 | + | 0.655114i | \(0.227379\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.47344 | + | 11.2123i | −0.270905 | + | 0.469222i | −0.969094 | − | 0.246692i | \(-0.920656\pi\) |
0.698189 | + | 0.715914i | \(0.253990\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.98018 | − | 18.1515i | −0.166274 | − | 0.758291i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.29577 | −0.262552 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.34847 | 0.389182 | 0.194591 | − | 0.980884i | \(-0.437662\pi\) | ||||
0.194591 | + | 0.980884i | \(0.437662\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.53310 | + | 8.69510i | −0.396182 | + | 0.361356i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.33013 | − | 7.50000i | 0.179644 | − | 0.311152i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.8655 | + | 9.73733i | −0.698500 | + | 0.403279i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 28.1969 | + | 2.59808i | 1.16580 | + | 0.107417i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.2857 | − | 9.40257i | 0.672184 | − | 0.388086i | −0.124720 | − | 0.992192i | \(-0.539803\pi\) |
0.796904 | + | 0.604106i | \(0.206470\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 61.8289 | + | 35.6969i | 2.54762 | + | 1.47087i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.5413 | + | 8.75366i | 1.13290 | + | 0.360077i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 25.0273i | − | 1.02775i | −0.857866 | − | 0.513873i | \(-0.828210\pi\) | ||
0.857866 | − | 0.513873i | \(-0.171790\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −34.1640 | −1.40059 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.66025 | − | 27.2474i | 0.354441 | − | 1.11516i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.6453 | + | 27.0985i | −0.639251 | + | 1.10722i | 0.346346 | + | 0.938107i | \(0.387422\pi\) |
−0.985597 | + | 0.169109i | \(0.945911\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.623724 | − | 1.08032i | −0.0254422 | − | 0.0440673i | 0.853024 | − | 0.521872i | \(-0.174766\pi\) |
−0.878466 | + | 0.477805i | \(0.841433\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.11295 | + | 0.512736i | −0.0453227 | + | 0.0208802i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.73169 | + | 15.1237i | 0.354994 | + | 0.614867i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.5049 | − | 6.06499i | −0.426379 | − | 0.246170i | 0.271424 | − | 0.962460i | \(-0.412506\pi\) |
−0.697803 | + | 0.716290i | \(0.745839\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.07321 | + | 7.75490i | 0.286621 | + | 0.314245i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 28.7204i | − | 1.16190i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 40.0454i | − | 1.61742i | −0.588208 | − | 0.808709i | \(-0.700167\pi\) | ||
0.588208 | − | 0.808709i | \(-0.299833\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 50.2429 | − | 11.0170i | 2.02599 | − | 0.444249i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.8712 | + | 8.00853i | 0.558432 | + | 0.322411i | 0.752516 | − | 0.658574i | \(-0.228840\pi\) |
−0.194084 | + | 0.980985i | \(0.562173\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.612688 | − | 1.06121i | −0.0246260 | − | 0.0426535i | 0.853450 | − | 0.521175i | \(-0.174506\pi\) |
−0.878076 | + | 0.478522i | \(0.841173\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.62642 | + | 0.825765i | −0.265909 | + | 0.0331368i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.86971 | − | 13.6307i | −0.315293 | − | 0.546104i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.7474 | − | 22.0792i | 0.509898 | − | 0.883169i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 31.9381 | − | 7.00324i | 1.27549 | − | 0.279683i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.1769 | 1.24310 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.96786i | − | 0.118148i | −0.998254 | − | 0.0590742i | \(-0.981185\pi\) | ||
0.998254 | − | 0.0590742i | \(-0.0188149\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.82577 | + | 8.96204i | −0.390539 | + | 0.356209i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 58.0155 | + | 33.4953i | 2.30228 | + | 1.32922i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.16781 | + | 0.674235i | −0.0462703 | + | 0.0267141i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 35.7237 | + | 25.2605i | 1.41321 | + | 0.999288i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.1969 | + | 11.0834i | −0.758233 | + | 0.437766i | −0.828661 | − | 0.559751i | \(-0.810897\pi\) |
0.0704277 | + | 0.997517i | \(0.477564\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.204229 | + | 0.353736i | −0.00805402 | + | 0.0139500i | −0.870024 | − | 0.493009i | \(-0.835897\pi\) |
0.861970 | + | 0.506959i | \(0.169230\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.5601 | + | 3.67423i | 0.455179 | + | 0.144673i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.1470 | 0.752745 | 0.376372 | − | 0.926468i | \(-0.377171\pi\) | ||||
0.376372 | + | 0.926468i | \(0.377171\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.00000 | −0.117760 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 37.2986 | + | 11.8549i | 1.46185 | + | 0.464630i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.2546 | + | 26.4217i | −0.596957 | + | 1.03396i | 0.396310 | + | 0.918117i | \(0.370290\pi\) |
−0.993267 | + | 0.115844i | \(0.963043\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.78674 | + | 2.76363i | −0.187033 | + | 0.107984i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.79796 | − | 2.68556i | −0.148172 | − | 0.104774i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.20474 | − | 0.695560i | 0.0469302 | − | 0.0270952i | −0.476351 | − | 0.879255i | \(-0.658041\pi\) |
0.523282 | + | 0.852160i | \(0.324708\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.96204 | − | 5.17423i | −0.348583 | − | 0.201254i | 0.315478 | − | 0.948933i | \(-0.397835\pi\) |
−0.664061 | + | 0.747678i | \(0.731168\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.2879 | − | 14.8561i | 0.632570 | − | 0.576964i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 65.1180i | 2.52517i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.04281 | 0.117818 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 32.8215 | − | 7.19694i | 1.26895 | − | 0.278250i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.5049 | + | 18.1950i | −0.405536 | + | 0.702409i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.62372 | − | 16.6688i | −0.370967 | − | 0.642534i | 0.618747 | − | 0.785590i | \(-0.287640\pi\) |
−0.989715 | + | 0.143056i | \(0.954307\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.90408 | + | 23.4501i | −0.381208 | + | 0.902596i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.18010 | − | 8.97219i | −0.199087 | − | 0.344829i | 0.749145 | − | 0.662406i | \(-0.230464\pi\) |
−0.948233 | + | 0.317576i | \(0.897131\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.3630 | − | 16.9527i | −1.12685 | − | 0.650586i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 39.8939 | − | 8.74774i | 1.52874 | − | 0.335214i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 31.7385i | − | 1.21444i | −0.794534 | − | 0.607220i | \(-0.792285\pi\) | ||
0.794534 | − | 0.607220i | \(-0.207715\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 56.3939i | − | 2.15470i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −29.2332 | − | 32.0506i | −1.11532 | − | 1.22281i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.6742 | + | 12.5136i | 0.825723 | + | 0.476731i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.74730 | − | 6.49051i | −0.142554 | − | 0.246911i | 0.785904 | − | 0.618349i | \(-0.212198\pi\) |
−0.928458 | + | 0.371438i | \(0.878865\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.2795 | − | 7.50000i | 0.618407 | − | 0.284901i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 27.6592 | + | 47.9072i | 1.04917 | + | 1.81722i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.0227 | − | 34.6803i | 0.758414 | − | 1.31361i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.45178 | − | 14.0065i | 0.168382 | − | 0.529774i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.76416 | −0.0666314 | −0.0333157 | − | 0.999445i | \(-0.510607\pi\) | ||||
−0.0333157 | + | 0.999445i | \(0.510607\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 59.4245i | − | 2.24124i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 49.7196 | + | 15.8028i | 1.87255 | + | 0.595166i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.97370 | + | 4.02627i | 0.262273 | + | 0.151423i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.96204 | − | 5.17423i | 0.336576 | − | 0.194322i | −0.322181 | − | 0.946678i | \(-0.604416\pi\) |
0.658757 | + | 0.752356i | \(0.271083\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 30.8071 | + | 2.83858i | 1.15536 | + | 0.106455i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.82577 | − | 5.67291i | 0.367978 | − | 0.212452i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.0170 | + | 19.0820i | −0.412013 | + | 0.713628i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.64456 | + | 1.50000i | −0.0614174 | + | 0.0560185i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.0130 | −1.04471 | −0.522354 | − | 0.852729i | \(-0.674946\pi\) | ||||
−0.522354 | + | 0.852729i | \(0.674946\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.7423 | −0.809727 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.08132 | + | 23.1732i | 0.188976 | + | 0.861822i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.79972 | − | 10.0454i | 0.215396 | − | 0.373077i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.5109 | + | 18.7702i | −1.20576 | + | 0.696147i | −0.961831 | − | 0.273645i | \(-0.911771\pi\) |
−0.243931 | + | 0.969792i | \(0.578437\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.34847 | + | 25.9808i | −0.272166 | + | 0.962250i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.17845 | − | 4.72183i | 0.302491 | − | 0.174643i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.9904 | − | 7.50000i | −0.479811 | − | 0.277019i | 0.240527 | − | 0.970642i | \(-0.422680\pi\) |
−0.720338 | + | 0.693624i | \(0.756013\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.524648 | − | 2.39264i | −0.0193519 | − | 0.0882540i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 0.953512i | − | 0.0351231i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.00052 | −0.0368046 | −0.0184023 | − | 0.999831i | \(-0.505858\pi\) | ||||
−0.0184023 | + | 0.999831i | \(0.505858\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −28.3164 | − | 31.0454i | −1.04023 | − | 1.14048i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.7932 | + | 32.5508i | −0.689457 | + | 1.19417i | 0.282557 | + | 0.959250i | \(0.408817\pi\) |
−0.972014 | + | 0.234923i | \(0.924516\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.0732 | + | 31.3037i | 0.662151 | + | 1.14688i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.1083 | − | 0.931383i | −0.369844 | − | 0.0340775i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.2952 | + | 40.3485i | 0.851188 | + | 1.47430i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.8080 | + | 8.54943i | 0.540353 | + | 0.311973i | 0.745222 | − | 0.666816i | \(-0.232343\pi\) |
−0.204869 | + | 0.978789i | \(0.565677\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.04541 | − | 12.7279i | 0.147423 | − | 0.463831i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 16.3409i | − | 0.594706i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.0000i | 0.436147i | 0.975932 | + | 0.218074i | \(0.0699773\pi\) | ||||
−0.975932 | + | 0.218074i | \(0.930023\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.57394 | − | 4.95204i | 0.0571305 | − | 0.179748i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.5227 | − | 24.5505i | −1.54145 | − | 0.889955i | −0.998748 | − | 0.0500275i | \(-0.984069\pi\) |
−0.542699 | − | 0.839927i | \(-0.682598\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.72563 | + | 2.98889i | 0.0624721 | + | 0.108205i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.7563 | + | 36.3712i | 0.605824 | + | 1.31500i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.92768 | + | 3.33884i | 0.0696044 | + | 0.120558i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.2980 | + | 23.0327i | −0.479537 | + | 0.830582i | −0.999725 | − | 0.0234700i | \(-0.992529\pi\) |
0.520188 | + | 0.854052i | \(0.325862\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.9691 | − | 17.5081i | −0.575112 | − | 0.630539i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −42.9192 | −1.54370 | −0.771848 | − | 0.635807i | \(-0.780668\pi\) | ||||
−0.771848 | + | 0.635807i | \(0.780668\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 43.2512i | − | 1.55363i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.97730 | − | 31.8198i | −0.250309 | − | 1.14153i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −66.1022 | − | 38.1641i | −2.36836 | − | 1.36737i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.4842 | + | 17.0227i | −1.05503 | + | 0.609120i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.78674 | − | 11.3337i | 0.171064 | − | 0.405033i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.8485 | + | 12.0369i | −0.744114 | + | 0.429614i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.1037 | + | 33.0885i | −0.680972 | + | 1.17948i | 0.293712 | + | 0.955894i | \(0.405109\pi\) |
−0.974684 | + | 0.223585i | \(0.928224\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.96204 | + | 40.8712i | 0.319057 | + | 1.45505i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.2990 | −0.472859 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.0000 | 0.958798 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −33.5888 | + | 30.6362i | −1.19127 | + | 1.08655i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.0902 | − | 29.6010i | 0.605364 | − | 1.04852i | −0.386629 | − | 0.922235i | \(-0.626361\pi\) |
0.991994 | − | 0.126287i | \(-0.0403059\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.1752 | − | 20.3084i | 1.24441 | − | 0.718460i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.6515 | + | 15.0635i | −0.376353 | + | 0.532244i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.13461 | − | 1.80977i | 0.110618 | − | 0.0638653i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.96204 | + | 5.17423i | 0.315870 | + | 0.182368i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.48230 | + | 1.74248i | 0.192986 | + | 0.0613382i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.6349i | 0.514537i | 0.966340 | + | 0.257269i | \(0.0828225\pi\) | ||||
−0.966340 | + | 0.257269i | \(0.917177\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.6251 | 0.724244 | 0.362122 | − | 0.932131i | \(-0.382052\pi\) | ||||
0.362122 | + | 0.932131i | \(0.382052\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.92820 | + | 21.7980i | −0.242983 | + | 0.764488i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.71812 | − | 9.90408i | 0.200297 | − | 0.346925i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.00000 | − | 15.5885i | −0.314870 | − | 0.545371i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.8076 | − | 13.2990i | −0.657192 | − | 0.464705i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.7402 | + | 28.9949i | 0.584237 | + | 1.01193i | 0.994970 | + | 0.100173i | \(0.0319396\pi\) |
−0.410733 | + | 0.911756i | \(0.634727\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.80110 | + | 5.08132i | 0.306787 | + | 0.177124i | 0.645488 | − | 0.763771i | \(-0.276654\pi\) |
−0.338701 | + | 0.940894i | \(0.609987\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13.3485 | − | 14.6349i | −0.464734 | − | 0.509523i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.1683i | 1.01428i | 0.861864 | + | 0.507140i | \(0.169297\pi\) | ||||
−0.861864 | + | 0.507140i | \(0.830703\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.6515i | 1.20350i | 0.798685 | + | 0.601749i | \(0.205529\pi\) | ||||
−0.798685 | + | 0.601749i | \(0.794471\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.3732 | − | 9.29139i | 1.46991 | − | 0.322315i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.65153 | − | 0.953512i | −0.0572221 | − | 0.0330372i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.1037 | − | 33.0885i | −0.661110 | − | 1.14508i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.67291 | − | 45.5227i | −0.196084 | − | 1.57349i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.92397 | + | 5.06447i | 0.100947 | + | 0.174845i | 0.912075 | − | 0.410023i | \(-0.134479\pi\) |
−0.811128 | + | 0.584868i | \(0.801146\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.6969 | − | 20.2597i | 0.403343 | − | 0.698610i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.0985 | − | 5.94204i | 0.933323 | − | 0.204655i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.5851 | −0.432939 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 14.2060i | − | 0.488122i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.8939 | + | 17.2330i | −0.648436 | + | 0.591436i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.17845 | − | 4.72183i | −0.280354 | − | 0.161862i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.8509 | − | 9.15153i | 0.542725 | − | 0.313342i | −0.203458 | − | 0.979084i | \(-0.565218\pi\) |
0.746183 | + | 0.665741i | \(0.231885\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 69.3250 | − | 31.9381i | 2.37086 | − | 1.09226i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.1742 | − | 9.91555i | 0.586661 | − | 0.338709i | −0.177115 | − | 0.984190i | \(-0.556677\pi\) |
0.763776 | + | 0.645481i | \(0.223343\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.4647 | − | 44.1061i | 0.868844 | − | 1.50488i | 0.00566493 | − | 0.999984i | \(-0.498197\pi\) |
0.863179 | − | 0.504898i | \(-0.168470\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −39.8765 | − | 12.6742i | −1.35899 | − | 0.431937i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.4427 | −0.866081 | −0.433040 | − | 0.901375i | \(-0.642559\pi\) | ||||
−0.433040 | + | 0.901375i | \(0.642559\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.8990 | −0.540582 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.65068 | + | 0.524648i | 0.0560600 | + | 0.0178180i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0369 | + | 20.8485i | −0.408323 | + | 0.707236i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.06121 | + | 0.612688i | −0.0359576 | + | 0.0207601i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.64643 | + | 39.5747i | −0.123413 | + | 1.33940i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.704487 | + | 0.406736i | −0.0238160 | + | 0.0137502i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.4655 | + | 7.19694i | 0.420929 | + | 0.243023i | 0.695475 | − | 0.718551i | \(-0.255194\pi\) |
−0.274546 | + | 0.961574i | \(0.588528\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.83974 | + | 4.41431i | −0.163240 | + | 0.148891i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 26.9343i | − | 0.907439i | −0.891145 | − | 0.453719i | \(-0.850097\pi\) | ||
0.891145 | − | 0.453719i | \(-0.149903\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.3564 | 0.516783 | 0.258392 | − | 0.966040i | \(-0.416808\pi\) | ||||
0.258392 | + | 0.966040i | \(0.416808\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.84072 | + | 1.50000i | −0.229948 | + | 0.0504219i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.2299 | − | 38.5034i | 0.746408 | − | 1.29282i | −0.203126 | − | 0.979153i | \(-0.565110\pi\) |
0.949534 | − | 0.313664i | \(-0.101557\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.2474 | − | 47.1940i | −0.913850 | − | 1.58283i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.9691 | − | 13.6527i | −0.534984 | − | 0.457384i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −38.7087 | − | 67.0454i | −1.29534 | − | 2.24359i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.28836 | − | 4.78529i | −0.277049 | − | 0.159955i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.52270 | + | 1.43027i | −0.217787 | + | 0.0477552i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.9037i | 0.697178i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35.3939i | 1.17914i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.64951 | − | 7.29036i | −0.221282 | − | 0.242608i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −52.7196 | − | 30.4377i | −1.75246 | − | 1.01178i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.3301 | + | 38.6768i | 0.741458 | + | 1.28424i | 0.951831 | + | 0.306622i | \(0.0991988\pi\) |
−0.210373 | + | 0.977621i | \(0.567468\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.866025 | − | 9.39898i | 0.0287242 | − | 0.311744i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.3672 | + | 35.2770i | 0.674794 | + | 1.16878i | 0.976529 | + | 0.215386i | \(0.0691010\pi\) |
−0.301735 | + | 0.953392i | \(0.597566\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.94949 | − | 6.84072i | 0.130709 | − | 0.226395i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.8561 | + | 46.7413i | −0.491128 | + | 1.54522i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.49626 | 0.148480 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 18.4741i | − | 0.609406i | −0.952447 | − | 0.304703i | \(-0.901443\pi\) | ||
0.952447 | − | 0.304703i | \(-0.0985572\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −38.6969 | − | 12.2993i | −1.27511 | − | 0.405277i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37.8907 | + | 21.8762i | 1.24719 | + | 0.720064i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31.1769 | + | 18.0000i | −1.02509 | + | 0.591836i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.6639 | + | 23.1470i | 0.350247 | + | 0.760247i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.8712 | − | 18.4008i | 1.04566 | − | 0.603712i | 0.124228 | − | 0.992254i | \(-0.460354\pi\) |
0.921431 | + | 0.388542i | \(0.127021\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.81743 | + | 3.14789i | −0.0595640 | + | 0.103168i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27.6253 | + | 25.1969i | −0.904413 | + | 0.824911i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −31.1609 | −1.01907 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.1464 | −1.40953 | −0.704766 | − | 0.709440i | \(-0.748948\pi\) | ||||
−0.704766 | + | 0.709440i | \(0.748948\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.64020 | − | 30.2825i | −0.216695 | − | 0.988231i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.5006 | − | 38.9722i | 0.733499 | − | 1.27046i | −0.221880 | − | 0.975074i | \(-0.571219\pi\) |
0.955379 | − | 0.295383i | \(-0.0954473\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.5049 | + | 6.06499i | −0.342085 | + | 0.197503i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 33.3712 | − | 25.2415i | 1.08556 | − | 0.821108i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.1521 | + | 8.74810i | −0.492379 | + | 0.284275i | −0.725561 | − | 0.688158i | \(-0.758420\pi\) |
0.233182 | + | 0.972433i | \(0.425086\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.02834 | − | 2.32577i | −0.130766 | − | 0.0754975i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.74115 | − | 12.5010i | −0.0888879 | − | 0.405371i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.4490i | 0.597621i | 0.954312 | + | 0.298811i | \(0.0965899\pi\) | ||||
−0.954312 | + | 0.298811i | \(0.903410\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 33.7556 | 1.09230 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.45145 | + | 7.07321i | 0.208546 | + | 0.228645i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.9374 | + | 39.7288i | −0.740687 | + | 1.28291i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.4722 | + | 40.6550i | 0.757168 | + | 1.31145i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 31.5297 | − | 44.5897i | 1.01603 | − | 1.43688i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.7190 | − | 20.2980i | −0.377249 | − | 0.653414i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.8076 | − | 13.1680i | −0.733442 | − | 0.423453i | 0.0862378 | − | 0.996275i | \(-0.472516\pi\) |
−0.819680 | + | 0.572821i | \(0.805849\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.0000 | − | 56.6328i | 0.578243 | − | 1.81931i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.6957i | 1.43435i | 0.696892 | + | 0.717177i | \(0.254566\pi\) | ||||
−0.696892 | + | 0.717177i | \(0.745434\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 45.0000i | − | 1.44263i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.71071 | + | 24.2599i | −0.246940 | + | 0.776940i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.1515 | + | 19.1400i | 1.06061 | + | 0.612344i | 0.925601 | − | 0.378500i | \(-0.123560\pi\) |
0.135010 | + | 0.990844i | \(0.456893\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.17793 | − | 12.4325i | −0.229408 | − | 0.397346i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.33562 | − | 3.30306i | 0.0745705 | − | 0.105459i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.93092 | + | 15.4688i | 0.284852 | + | 0.493378i | 0.972573 | − | 0.232597i | \(-0.0747222\pi\) |
−0.687721 | + | 0.725975i | \(0.741389\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.2474 | + | 45.4619i | −0.836313 | + | 1.44854i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −28.5993 | − | 31.3556i | −0.910326 | − | 0.998059i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.86054 | −0.0909597 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 2.30084i | − | 0.0730887i | −0.999332 | − | 0.0365444i | \(-0.988365\pi\) | ||
0.999332 | − | 0.0365444i | \(-0.0116350\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.19694 | − | 32.8215i | −0.228388 | − | 1.04156i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 44.9768 | + | 25.9674i | 1.42586 | + | 0.823221i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.6900 | + | 12.5227i | −0.686928 | + | 0.396598i | −0.802460 | − | 0.596706i | \(-0.796476\pi\) |
0.115532 | + | 0.993304i | \(0.463143\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −30.4534 | + | 23.0346i | −0.963502 | + | 0.728781i |
(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 | 1152.2.p.e.959.2 | yes | 16 | |
3.2 | odd | 2 | 3456.2.p.e.2879.1 | 16 | |||
4.3 | odd | 2 | inner | 1152.2.p.e.959.8 | yes | 16 | |
8.3 | odd | 2 | inner | 1152.2.p.e.959.1 | yes | 16 | |
8.5 | even | 2 | inner | 1152.2.p.e.959.7 | yes | 16 | |
9.2 | odd | 6 | inner | 1152.2.p.e.191.1 | ✓ | 16 | |
9.7 | even | 3 | 3456.2.p.e.575.8 | 16 | |||
12.11 | even | 2 | 3456.2.p.e.2879.2 | 16 | |||
24.5 | odd | 2 | 3456.2.p.e.2879.7 | 16 | |||
24.11 | even | 2 | 3456.2.p.e.2879.8 | 16 | |||
36.7 | odd | 6 | 3456.2.p.e.575.7 | 16 | |||
36.11 | even | 6 | inner | 1152.2.p.e.191.7 | yes | 16 | |
72.11 | even | 6 | inner | 1152.2.p.e.191.2 | yes | 16 | |
72.29 | odd | 6 | inner | 1152.2.p.e.191.8 | yes | 16 | |
72.43 | odd | 6 | 3456.2.p.e.575.1 | 16 | |||
72.61 | even | 6 | 3456.2.p.e.575.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.p.e.191.1 | ✓ | 16 | 9.2 | odd | 6 | inner | |
1152.2.p.e.191.2 | yes | 16 | 72.11 | even | 6 | inner | |
1152.2.p.e.191.7 | yes | 16 | 36.11 | even | 6 | inner | |
1152.2.p.e.191.8 | yes | 16 | 72.29 | odd | 6 | inner | |
1152.2.p.e.959.1 | yes | 16 | 8.3 | odd | 2 | inner | |
1152.2.p.e.959.2 | yes | 16 | 1.1 | even | 1 | trivial | |
1152.2.p.e.959.7 | yes | 16 | 8.5 | even | 2 | inner | |
1152.2.p.e.959.8 | yes | 16 | 4.3 | odd | 2 | inner | |
3456.2.p.e.575.1 | 16 | 72.43 | odd | 6 | |||
3456.2.p.e.575.2 | 16 | 72.61 | even | 6 | |||
3456.2.p.e.575.7 | 16 | 36.7 | odd | 6 | |||
3456.2.p.e.575.8 | 16 | 9.7 | even | 3 | |||
3456.2.p.e.2879.1 | 16 | 3.2 | odd | 2 | |||
3456.2.p.e.2879.2 | 16 | 12.11 | even | 2 | |||
3456.2.p.e.2879.7 | 16 | 24.5 | odd | 2 | |||
3456.2.p.e.2879.8 | 16 | 24.11 | even | 2 |