Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,2,Mod(129,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.g (of order \(8\), degree \(4\), 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: | \(8.17668116698\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\Q(\zeta_{48})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 385.2 | ||
Root | \(-0.608761 + 0.793353i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.385 |
Dual form | 1024.2.g.f.641.2 |
$q$-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 \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(e\left(\frac{5}{8}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.860919 | + | 0.356604i | −0.497052 | + | 0.205886i | −0.617103 | − | 0.786882i | \(-0.711694\pi\) |
0.120052 | + | 0.992768i | \(0.461694\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.366025 | + | 0.883663i | −0.163692 | + | 0.395186i | −0.984348 | − | 0.176236i | \(-0.943608\pi\) |
0.820656 | + | 0.571422i | \(0.193608\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.35207 | + | 2.35207i | 0.889000 | + | 0.889000i | 0.994427 | − | 0.105427i | \(-0.0336209\pi\) |
−0.105427 | + | 0.994427i | \(0.533621\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.50731 | + | 1.50731i | −0.502435 | + | 0.502435i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.81739 | + | 0.752787i | 0.547963 | + | 0.226974i | 0.639450 | − | 0.768832i | \(-0.279162\pi\) |
−0.0914869 | + | 0.995806i | \(0.529162\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.848387 | − | 2.04819i | −0.235300 | − | 0.568065i | 0.761485 | − | 0.648182i | \(-0.224471\pi\) |
−0.996785 | + | 0.0801172i | \(0.974471\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 0.891289i | − | 0.230130i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.00997i | 1.45763i | 0.684710 | + | 0.728816i | \(0.259929\pi\) | ||||
−0.684710 | + | 0.728816i | \(0.740071\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.54713 | − | 3.73510i | −0.354935 | − | 0.856890i | −0.995996 | − | 0.0893996i | \(-0.971505\pi\) |
0.641060 | − | 0.767490i | \(-0.278495\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.86370 | − | 1.18618i | −0.624911 | − | 0.258847i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.91236 | − | 2.91236i | 0.607269 | − | 0.607269i | −0.334962 | − | 0.942232i | \(-0.608724\pi\) |
0.942232 | + | 0.334962i | \(0.108724\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.88865 | + | 2.88865i | 0.577729 | + | 0.577729i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.82997 | − | 4.41794i | 0.352178 | − | 0.850232i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.69383 | + | 4.01532i | −1.80010 | + | 0.745625i | −0.813694 | + | 0.581293i | \(0.802547\pi\) |
−0.986405 | + | 0.164332i | \(0.947453\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.52140 | −1.35088 | −0.675442 | − | 0.737413i | \(-0.736047\pi\) | ||||
−0.675442 | + | 0.737413i | \(0.736047\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.83307 | −0.319097 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.93936 | + | 1.21752i | −0.496843 | + | 0.205799i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.994652 | + | 2.40130i | −0.163520 | + | 0.394772i | −0.984308 | − | 0.176462i | \(-0.943535\pi\) |
0.820788 | + | 0.571233i | \(0.193535\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.46078 | + | 1.46078i | 0.233913 | + | 0.233913i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.37894 | + | 1.37894i | −0.215354 | + | 0.215354i | −0.806537 | − | 0.591183i | \(-0.798661\pi\) |
0.591183 | + | 0.806537i | \(0.298661\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.8651 | + | 4.50046i | 1.65691 | + | 0.686314i | 0.997835 | − | 0.0657637i | \(-0.0209484\pi\) |
0.659074 | + | 0.752078i | \(0.270948\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.780239 | − | 1.88366i | −0.116311 | − | 0.280800i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.33173i | − | 0.485983i | −0.970028 | − | 0.242991i | \(-0.921871\pi\) | ||
0.970028 | − | 0.242991i | \(-0.0781286\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.06450i | 0.580643i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.14318 | − | 5.17409i | −0.300105 | − | 0.724518i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.02993 | − | 3.32611i | −1.10300 | − | 0.456876i | −0.244475 | − | 0.969656i | \(-0.578616\pi\) |
−0.858520 | + | 0.512780i | \(0.828616\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.33042 | + | 1.33042i | −0.179394 | + | 0.179394i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.66390 | + | 2.66390i | 0.352843 | + | 0.352843i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.70936 | + | 11.3694i | −0.613106 | + | 1.48017i | 0.246464 | + | 0.969152i | \(0.420731\pi\) |
−0.859570 | + | 0.511017i | \(0.829269\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.166225 | + | 0.0688525i | −0.0212829 | + | 0.00881566i | −0.393299 | − | 0.919410i | \(-0.628666\pi\) |
0.372017 | + | 0.928226i | \(0.378666\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.09059 | −0.893330 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.12044 | 0.263008 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.39629 | + | 3.47786i | −1.02577 | + | 0.424888i | −0.831184 | − | 0.555997i | \(-0.812336\pi\) |
−0.194587 | + | 0.980885i | \(0.562336\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.46875 | + | 3.54587i | −0.176816 | + | 0.426872i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.92235 | + | 7.92235i | 0.940210 | + | 0.940210i | 0.998311 | − | 0.0581008i | \(-0.0185045\pi\) |
−0.0581008 | + | 0.998311i | \(0.518504\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.84544 | + | 5.84544i | −0.684157 | + | 0.684157i | −0.960934 | − | 0.276777i | \(-0.910734\pi\) |
0.276777 | + | 0.960934i | \(0.410734\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.51699 | − | 1.45679i | −0.406108 | − | 0.168215i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.50402 | + | 6.04524i | 0.285360 | + | 0.688919i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.80100i | 0.202628i | 0.994855 | + | 0.101314i | \(0.0323046\pi\) | ||||
−0.994855 | + | 0.101314i | \(0.967695\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 1.93890i | − | 0.215433i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.98429 | + | 4.79049i | 0.217804 | + | 0.525825i | 0.994583 | − | 0.103949i | \(-0.0331478\pi\) |
−0.776779 | + | 0.629773i | \(0.783148\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.31079 | − | 2.19980i | −0.576036 | − | 0.238602i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.91372 | − | 6.91372i | 0.741229 | − | 0.741229i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.38134 | + | 6.38134i | 0.676421 | + | 0.676421i | 0.959188 | − | 0.282768i | \(-0.0912525\pi\) |
−0.282768 | + | 0.959188i | \(0.591253\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.82202 | − | 6.81296i | 0.295828 | − | 0.714192i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.47531 | − | 2.68216i | 0.671459 | − | 0.278127i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.86686 | 0.396731 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.874915 | 0.0888342 | 0.0444171 | − | 0.999013i | \(-0.485857\pi\) | ||||
0.0444171 | + | 0.999013i | \(0.485857\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.87404 | + | 1.60468i | −0.389356 | + | 0.161276i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.000704119 | 0.00169989i | −7.00625e−5 | 0.000169146i | −0.923915 | − | 0.382599i | \(-0.875029\pi\) | ||
0.923844 | + | 0.382768i | \(0.125029\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.93098 | − | 8.93098i | −0.879996 | − | 0.879996i | 0.113538 | − | 0.993534i | \(-0.463782\pi\) |
−0.993534 | + | 0.113538i | \(0.963782\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.09638 | − | 2.09638i | 0.204585 | − | 0.204585i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.07786 | + | 1.27489i | 0.297548 | + | 0.123248i | 0.526463 | − | 0.850198i | \(-0.323518\pi\) |
−0.228915 | + | 0.973446i | \(0.573518\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.19445 | − | 7.71209i | −0.305973 | − | 0.738684i | −0.999828 | − | 0.0185691i | \(-0.994089\pi\) |
0.693855 | − | 0.720115i | \(-0.255911\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 2.42202i | − | 0.229888i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.03528i | 0.661823i | 0.943662 | + | 0.330912i | \(0.107356\pi\) | ||||
−0.943662 | + | 0.330912i | \(0.892644\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.50755 | + | 3.63955i | 0.140580 | + | 0.339389i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.36603 | + | 1.80847i | 0.403639 | + | 0.167193i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.1359 | + | 14.1359i | −1.29583 | + | 1.29583i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.04196 | − | 5.04196i | −0.458360 | − | 0.458360i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.695418 | − | 1.67889i | 0.0627037 | − | 0.151380i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.02823 | + | 3.32540i | −0.718067 | + | 0.297433i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.09821 | −0.0974502 | −0.0487251 | − | 0.998812i | \(-0.515516\pi\) | ||||
−0.0487251 | + | 0.998812i | \(0.515516\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.9588 | −0.964872 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.0608 | − | 7.06683i | 1.49061 | − | 0.617431i | 0.519161 | − | 0.854676i | \(-0.326244\pi\) |
0.971450 | + | 0.237245i | \(0.0762443\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.14626 | − | 12.4242i | 0.446238 | − | 1.07731i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.23415 | + | 3.23415i | 0.278352 | + | 0.278352i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.83183 | − | 5.83183i | 0.498247 | − | 0.498247i | −0.412645 | − | 0.910892i | \(-0.635395\pi\) |
0.910892 | + | 0.412645i | \(0.135395\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.4088 | − | 5.13991i | −1.05250 | − | 0.435961i | −0.211719 | − | 0.977331i | \(-0.567906\pi\) |
−0.840785 | + | 0.541369i | \(0.817906\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.18811 | + | 2.86835i | 0.100057 | + | 0.241558i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 4.36101i | − | 0.364686i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 10.0358i | − | 0.833427i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.44942 | − | 3.49920i | −0.119546 | − | 0.288609i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.6186 | + | 6.88366i | 1.36145 | + | 0.563932i | 0.939457 | − | 0.342667i | \(-0.111330\pi\) |
0.421994 | + | 0.906598i | \(0.361330\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.54877 | − | 8.54877i | 0.695689 | − | 0.695689i | −0.267789 | − | 0.963478i | \(-0.586293\pi\) |
0.963478 | + | 0.267789i | \(0.0862929\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.05886 | − | 9.05886i | −0.732365 | − | 0.732365i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.75302 | − | 6.64639i | 0.221128 | − | 0.533851i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.46821 | − | 2.26500i | 0.436410 | − | 0.180767i | −0.153652 | − | 0.988125i | \(-0.549103\pi\) |
0.590062 | + | 0.807358i | \(0.299103\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.09922 | 0.642310 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.7002 | 1.07973 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.16282 | − | 2.96694i | 0.561035 | − | 0.232388i | −0.0840992 | − | 0.996457i | \(-0.526801\pi\) |
0.645135 | + | 0.764069i | \(0.276801\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.670951 | − | 1.61982i | 0.0522334 | − | 0.126103i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.5948 | − | 14.5948i | −1.12938 | − | 1.12938i | −0.990278 | − | 0.139100i | \(-0.955579\pi\) |
−0.139100 | − | 0.990278i | \(-0.544421\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.71707 | − | 5.71707i | 0.439775 | − | 0.439775i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.96193 | + | 3.29794i | 0.608864 | + | 0.252200i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.74788 | + | 6.63397i | 0.208918 | + | 0.504372i | 0.993253 | − | 0.115965i | \(-0.0369960\pi\) |
−0.784336 | + | 0.620337i | \(0.786996\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.5886i | 1.02720i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 11.4675i | − | 0.861950i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.333419 | + | 0.804946i | 0.0249209 | + | 0.0601645i | 0.935850 | − | 0.352398i | \(-0.114634\pi\) |
−0.910929 | + | 0.412563i | \(0.864634\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.9365 | + | 6.60110i | 1.18455 | + | 0.490656i | 0.885976 | − | 0.463731i | \(-0.153490\pi\) |
0.298572 | + | 0.954387i | \(0.403490\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.118553 | − | 0.118553i | 0.00876367 | − | 0.00876367i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.75787 | − | 1.75787i | −0.129242 | − | 0.129242i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.52423 | + | 10.9225i | −0.330844 | + | 0.798729i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.6955 | − | 6.08709i | 1.06894 | − | 0.442770i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.7629 | 1.57471 | 0.787356 | − | 0.616499i | \(-0.211449\pi\) | ||||
0.787356 | + | 0.616499i | \(0.211449\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.640834 | 0.0461283 | 0.0230641 | − | 0.999734i | \(-0.492658\pi\) | ||||
0.0230641 | + | 0.999734i | \(0.492658\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.82553 | + | 0.756158i | −0.130729 | + | 0.0541496i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.91794 | + | 19.1156i | −0.564130 | + | 1.36193i | 0.342306 | + | 0.939588i | \(0.388792\pi\) |
−0.906436 | + | 0.422342i | \(0.861208\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.96053 | + | 7.96053i | 0.564307 | + | 0.564307i | 0.930528 | − | 0.366221i | \(-0.119349\pi\) |
−0.366221 | + | 0.930528i | \(0.619349\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.98831 | − | 5.98831i | 0.422383 | − | 0.422383i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −32.2449 | − | 13.3563i | −2.26315 | − | 0.937427i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.713791 | − | 1.72324i | −0.0498533 | − | 0.120356i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.77964i | 0.610227i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 7.95278i | − | 0.550105i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.27691 | + | 5.49696i | 0.156749 | + | 0.378426i | 0.982671 | − | 0.185359i | \(-0.0593447\pi\) |
−0.825922 | + | 0.563785i | \(0.809345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.64564 | − | 3.99536i | −0.660909 | − | 0.273757i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.95379 | + | 7.95379i | −0.542444 | + | 0.542444i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.6909 | − | 17.6909i | −1.20094 | − | 1.20094i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.94794 | − | 7.11696i | 0.199203 | − | 0.480920i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.3095 | − | 5.09878i | 0.828030 | − | 0.342981i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.3054 | 1.02493 | 0.512464 | − | 0.858709i | \(-0.328733\pi\) | ||||
0.512464 | + | 0.858709i | \(0.328733\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.70815 | −0.580543 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.1228 | − | 6.67827i | 1.07011 | − | 0.443252i | 0.223078 | − | 0.974801i | \(-0.428390\pi\) |
0.847028 | + | 0.531548i | \(0.178390\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.84666 | − | 14.1151i | 0.386358 | − | 0.932752i | −0.604346 | − | 0.796722i | \(-0.706566\pi\) |
0.990705 | − | 0.136030i | \(-0.0434343\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.31152 | − | 4.31152i | −0.283677 | − | 0.283677i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.21582 | + | 8.21582i | −0.538236 | + | 0.538236i | −0.923011 | − | 0.384774i | \(-0.874279\pi\) |
0.384774 | + | 0.923011i | \(0.374279\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.94413 | + | 1.21950i | 0.192054 | + | 0.0795512i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.642242 | − | 1.55051i | −0.0417181 | − | 0.100716i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.21394i | 0.272577i | 0.990669 | + | 0.136289i | \(0.0435175\pi\) | ||||
−0.990669 | + | 0.136289i | \(0.956483\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 20.9382i | − | 1.34875i | −0.738391 | − | 0.674373i | \(-0.764414\pi\) | ||
0.738391 | − | 0.674373i | \(-0.235586\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.18133 | + | 14.9230i | 0.396532 | + | 0.957314i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.59165 | − | 1.48771i | −0.229462 | − | 0.0950463i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.33762 | + | 6.33762i | −0.403253 | + | 0.403253i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.41662 | − | 3.41662i | −0.216519 | − | 0.216519i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.98106 | + | 16.8538i | −0.440641 | + | 1.06380i | 0.535084 | + | 0.844799i | \(0.320280\pi\) |
−0.975724 | + | 0.219002i | \(0.929720\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.48528 | − | 3.10051i | 0.470596 | − | 0.194927i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.35662 | 0.335444 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.7839 | 0.984570 | 0.492285 | − | 0.870434i | \(-0.336162\pi\) | ||||
0.492285 | + | 0.870434i | \(0.336162\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.98753 | + | 3.30854i | −0.496321 | + | 0.205583i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.55926 | − | 20.6639i | 0.529805 | − | 1.27906i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.7140 | − | 15.7140i | −0.968967 | − | 0.968967i | 0.0305653 | − | 0.999533i | \(-0.490269\pi\) |
−0.999533 | + | 0.0305653i | \(0.990269\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.87832 | − | 5.87832i | 0.361102 | − | 0.361102i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.76943 | − | 3.21820i | −0.475481 | − | 0.196951i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.62542 | − | 8.75253i | −0.221045 | − | 0.533651i | 0.773987 | − | 0.633201i | \(-0.218260\pi\) |
−0.995033 | + | 0.0995505i | \(0.968260\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 6.69345i | − | 0.406598i | −0.979117 | − | 0.203299i | \(-0.934834\pi\) | ||
0.979117 | − | 0.203299i | \(-0.0651664\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.87175i | 0.415897i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.07526 | + | 7.42433i | 0.185445 | + | 0.447704i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.3643 | + | 9.67781i | 1.40382 | + | 0.581483i | 0.950741 | − | 0.309985i | \(-0.100324\pi\) |
0.453083 | + | 0.891468i | \(0.350324\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.3371 | − | 11.3371i | 0.678731 | − | 0.678731i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.6559 | + | 13.6559i | 0.814640 | + | 0.814640i | 0.985326 | − | 0.170685i | \(-0.0545982\pi\) |
−0.170685 | + | 0.985326i | \(0.554598\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.28083 | − | 12.7490i | 0.313913 | − | 0.757852i | −0.685640 | − | 0.727941i | \(-0.740478\pi\) |
0.999553 | − | 0.0299113i | \(-0.00952250\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.32905 | + | 1.37894i | −0.197196 | + | 0.0816812i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.48672 | −0.382899 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −19.1197 | −1.12469 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.753231 | + | 0.311998i | −0.0441552 | + | 0.0182897i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.15402 | + | 14.8571i | −0.359521 | + | 0.867962i | 0.635846 | + | 0.771816i | \(0.280651\pi\) |
−0.995367 | + | 0.0961455i | \(0.969349\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.32298 | − | 8.32298i | −0.484582 | − | 0.484582i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.65153 | − | 6.65153i | 0.385961 | − | 0.385961i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.43587 | − | 3.49425i | −0.487859 | − | 0.202078i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.9700 | + | 36.1409i | 0.862859 | + | 2.08313i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 0.00171456i | − | 9.84990e-5i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 0.172088i | − | 0.00985375i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.65468 | + | 6.40896i | 0.151511 | + | 0.365779i | 0.981352 | − | 0.192221i | \(-0.0615690\pi\) |
−0.829841 | + | 0.558000i | \(0.811569\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.8737 | + | 4.50402i | 0.618582 | + | 0.256225i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.7524 | + | 21.7524i | −1.23347 | + | 1.23347i | −0.270841 | + | 0.962624i | \(0.587302\pi\) |
−0.962624 | + | 0.270841i | \(0.912698\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.78658 | + | 2.78658i | 0.157507 | + | 0.157507i | 0.781461 | − | 0.623954i | \(-0.214475\pi\) |
−0.623954 | + | 0.781461i | \(0.714475\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.59534 | − | 6.26569i | 0.146231 | − | 0.353032i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.91065 | + | 1.61984i | −0.219644 | + | 0.0909794i | −0.489792 | − | 0.871839i | \(-0.662927\pi\) |
0.270148 | + | 0.962819i | \(0.412927\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.6401 | −1.15563 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.10442 | −0.173272 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.4478 | − | 9.29819i | 1.24903 | − | 0.517365i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.46580 | − | 8.36719i | 0.192248 | − | 0.464128i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.50033 | + | 5.50033i | 0.304169 | + | 0.304169i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.83647 | − | 7.83647i | 0.432039 | − | 0.432039i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.9631 | + | 6.19790i | 0.822444 | + | 0.340668i | 0.753907 | − | 0.656981i | \(-0.228167\pi\) |
0.0685372 | + | 0.997649i | \(0.478167\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.12025 | − | 5.11874i | −0.116189 | − | 0.280505i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 8.69248i | − | 0.474921i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.16071i | 0.117702i | 0.998267 | + | 0.0588508i | \(0.0187436\pi\) | ||||
−0.998267 | + | 0.0588508i | \(0.981256\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.50881 | − | 6.05680i | −0.136260 | − | 0.328960i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.6693 | − | 5.66201i | −0.740235 | − | 0.306615i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.90451 | − | 6.90451i | 0.372809 | − | 0.372809i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.59575 | − | 2.59575i | −0.139751 | − | 0.139751i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.36433 | + | 8.12222i | −0.180607 | + | 0.436024i | −0.988092 | − | 0.153864i | \(-0.950828\pi\) |
0.807485 | + | 0.589888i | \(0.200828\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.8014 | − | 6.13095i | 0.792302 | − | 0.328182i | 0.0504332 | − | 0.998727i | \(-0.483940\pi\) |
0.741869 | + | 0.670545i | \(0.233940\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.6013 | −0.565855 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.59235 | −0.137977 | −0.0689885 | − | 0.997617i | \(-0.521977\pi\) | ||||
−0.0689885 | + | 0.997617i | \(0.521977\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.90047 | + | 4.10091i | −0.525463 | + | 0.217654i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.12893 | − | 17.2108i | 0.377303 | − | 0.910890i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.94678 | − | 4.94678i | −0.261081 | − | 0.261081i | 0.564412 | − | 0.825493i | \(-0.309103\pi\) |
−0.825493 | + | 0.564412i | \(0.809103\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.87768 | − | 1.87768i | 0.0988255 | − | 0.0988255i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.13870 | + | 2.54273i | 0.322198 | + | 0.133459i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.02582 | − | 7.30499i | −0.158379 | − | 0.382360i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 19.5663i | − | 1.02135i | −0.859774 | − | 0.510675i | \(-0.829395\pi\) | ||
0.859774 | − | 0.510675i | \(-0.170605\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 4.15696i | − | 0.216403i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.0637 | − | 26.7102i | −0.574401 | − | 1.38673i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.3665 | − | 8.43606i | −1.05454 | − | 0.436803i | −0.213026 | − | 0.977046i | \(-0.568332\pi\) |
−0.841509 | + | 0.540244i | \(0.818332\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.72580 | − | 5.72580i | 0.295679 | − | 0.295679i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.4482 | + | 16.4482i | 0.847128 | + | 0.847128i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.60971 | + | 3.88618i | −0.0826851 | + | 0.199620i | −0.959815 | − | 0.280634i | \(-0.909455\pi\) |
0.877130 | + | 0.480253i | \(0.159455\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.945468 | − | 0.391626i | 0.0484378 | − | 0.0200636i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.6568 | 1.05552 | 0.527758 | − | 0.849395i | \(-0.323033\pi\) | ||||
0.527758 | + | 0.849395i | \(0.323033\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.25850 | −0.318963 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −23.1606 | + | 9.59343i | −1.17732 | + | 0.487661i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.58576 | + | 15.8994i | −0.333911 | + | 0.806133i | 0.664363 | + | 0.747410i | \(0.268703\pi\) |
−0.998274 | + | 0.0587232i | \(0.981297\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.5032 | + | 17.5032i | 0.885175 | + | 0.885175i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.1679 | + | 12.1679i | −0.613791 | + | 0.613791i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.59147 | − | 0.659210i | −0.0800757 | − | 0.0331685i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.38205 | − | 17.8218i | −0.370494 | − | 0.894452i | −0.993667 | − | 0.112368i | \(-0.964157\pi\) |
0.623172 | − | 0.782084i | \(-0.285843\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.5314i | 0.627354i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 0.119032i | − | 0.00594418i | −0.999996 | − | 0.00297209i | \(-0.999054\pi\) | ||
0.999996 | − | 0.00297209i | \(-0.000946048\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.38106 | + | 15.4052i | 0.317863 | + | 0.767390i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.71334 | + | 0.709687i | 0.0851363 | + | 0.0352646i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.61534 | + | 3.61534i | −0.179206 | + | 0.179206i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.5505 | − | 10.5505i | −0.521689 | − | 0.521689i | 0.396392 | − | 0.918081i | \(-0.370262\pi\) |
−0.918081 | + | 0.396392i | \(0.870262\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.94107 | + | 7.10038i | −0.145073 | + | 0.350236i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −37.8184 | + | 15.6649i | −1.86092 | + | 0.770819i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.95948 | −0.243451 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.5159 | 0.612907 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.44401 | + | 3.49762i | −0.412517 | + | 0.170870i | −0.579283 | − | 0.815126i | \(-0.696667\pi\) |
0.166766 | + | 0.985996i | \(0.446667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.4476 | + | 25.2227i | −0.509184 | + | 1.22928i | 0.435171 | + | 0.900348i | \(0.356688\pi\) |
−0.944354 | + | 0.328930i | \(0.893312\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.02193 | + | 5.02193i | 0.244175 | + | 0.244175i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.3607 | + | 17.3607i | −0.842117 | + | 0.842117i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.552918 | − | 0.229026i | −0.0267576 | − | 0.0110834i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.55515 | + | 3.75447i | 0.0750836 | + | 0.181268i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.31726i | 0.159787i | 0.996803 | + | 0.0798934i | \(0.0254580\pi\) | ||||
−0.996803 | + | 0.0798934i | \(0.974542\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.3224i | 1.07275i | 0.843981 | + | 0.536374i | \(0.180206\pi\) | ||||
−0.843981 | + | 0.536374i | \(0.819794\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.57881 | + | 8.64000i | 0.171591 | + | 0.414256i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.3837 | − | 6.37216i | −0.735904 | − | 0.304822i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.1260 | − | 21.1260i | 1.00829 | − | 1.00829i | 0.00832228 | − | 0.999965i | \(-0.497351\pi\) |
0.999965 | − | 0.00832228i | \(-0.00264909\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.12644 | − | 6.12644i | −0.291735 | − | 0.291735i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.0916028 | + | 0.221149i | −0.00435218 | + | 0.0105071i | −0.926041 | − | 0.377424i | \(-0.876810\pi\) |
0.921689 | + | 0.387931i | \(0.126810\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.97469 | + | 3.30323i | −0.378037 | + | 0.156588i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.7620 | −0.792817 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.5081 | 1.01503 | 0.507515 | − | 0.861643i | \(-0.330564\pi\) | ||||
0.507515 | + | 0.861643i | \(0.330564\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.54411 | + | 1.46802i | −0.166886 | + | 0.0691263i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.31127 | + | 10.4083i | −0.202561 | + | 0.489026i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.98743 | + | 4.98743i | 0.233814 | + | 0.233814i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.73721 | + | 9.73721i | −0.455487 | + | 0.455487i | −0.897171 | − | 0.441683i | \(-0.854381\pi\) |
0.441683 | + | 0.897171i | \(0.354381\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 26.5516 | + | 10.9981i | 1.23932 | + | 0.513345i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.3049 | + | 27.2925i | 0.526523 | + | 1.27114i | 0.933787 | + | 0.357828i | \(0.116483\pi\) |
−0.407265 | + | 0.913310i | \(0.633517\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.6338i | 1.84194i | 0.389635 | + | 0.920969i | \(0.372601\pi\) | ||||
−0.389635 | + | 0.920969i | \(0.627399\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.70374i | 0.310878i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.16422 | − | 19.7102i | −0.377795 | − | 0.912077i | −0.992379 | − | 0.123226i | \(-0.960676\pi\) |
0.614584 | − | 0.788852i | \(-0.289324\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.9289 | − | 11.5685i | −1.28964 | − | 0.534185i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.89997 | + | 3.89997i | −0.179701 | + | 0.179701i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.3582 | + | 16.3582i | 0.752150 | + | 0.752150i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.32027 | − | 15.2585i | 0.289994 | − | 0.700107i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.1170 | − | 7.09010i | 0.783734 | − | 0.324633i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.07863 | 0.140666 | 0.0703331 | − | 0.997524i | \(-0.477594\pi\) | ||||
0.0703331 | + | 0.997524i | \(0.477594\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.76217 | 0.262732 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.7947 | + | 4.88554i | −0.536679 | + | 0.222300i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.320241 | + | 0.773131i | −0.0145414 | + | 0.0351061i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.0643 | + | 21.0643i | 0.954517 | + | 0.954517i | 0.999010 | − | 0.0444931i | \(-0.0141673\pi\) |
−0.0444931 | + | 0.999010i | \(0.514167\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.10858 | + | 5.10858i | −0.231018 | + | 0.231018i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.0818 | + | 6.66130i | 0.725761 | + | 0.300620i | 0.714809 | − | 0.699320i | \(-0.246514\pi\) |
0.0109525 | + | 0.999940i | \(0.496514\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.1319 | − | 58.2596i | −1.08685 | − | 2.62388i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 4.01070i | − | 0.180268i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 37.2679i | 1.67169i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.69930 | − | 18.5877i | −0.344668 | − | 0.832102i | −0.997231 | − | 0.0743674i | \(-0.976306\pi\) |
0.652563 | − | 0.757734i | \(-0.273694\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.7695 | + | 7.36036i | 0.793882 | + | 0.328837i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.0921 | − | 11.0921i | 0.494572 | − | 0.494572i | −0.415172 | − | 0.909743i | \(-0.636278\pi\) |
0.909743 | + | 0.415172i | \(0.136278\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.00124441 | − | 0.00124441i | −5.53755e−5 | − | 5.53755e-5i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.88320 | + | 6.96067i | −0.128048 | + | 0.309134i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −33.5605 | + | 13.9012i | −1.48754 | + | 0.616160i | −0.970780 | − | 0.239970i | \(-0.922862\pi\) |
−0.516761 | + | 0.856130i | \(0.672862\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.4978 | −1.21643 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.3326 | −0.853556 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.1609 | − | 4.62301i | 0.491810 | − | 0.203714i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.50808 | − | 6.05505i | 0.110305 | − | 0.266301i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.73141 | − | 4.73141i | −0.207686 | − | 0.207686i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.27400 | − | 5.27400i | 0.231058 | − | 0.231058i | −0.582076 | − | 0.813134i | \(-0.697759\pi\) |
0.813134 | + | 0.582076i | \(0.197759\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.67885 | + | 2.35226i | 0.248319 | + | 0.102857i | 0.503371 | − | 0.864070i | \(-0.332093\pi\) |
−0.255053 | + | 0.966927i | \(0.582093\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.84576 | − | 11.6987i | −0.211486 | − | 0.510573i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 45.2034i | − | 1.96909i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.03631i | 0.262448i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.0387 | − | 24.2356i | −0.435643 | − | 1.05174i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.99420 | + | 1.65445i | 0.173008 | + | 0.0716622i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.25315 | + | 2.25315i | −0.0974122 | + | 0.0974122i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.574094 | − | 0.574094i | −0.0247740 | − | 0.0247740i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.05970 | + | 7.38678i | −0.131791 | + | 0.318171i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.5140 | + | 8.08295i | −0.838971 | + | 0.347513i | −0.760448 | − | 0.649399i | \(-0.775020\pi\) |
−0.0785232 | + | 0.996912i | \(0.525020\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.0740 | −0.689801 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.98414 | 0.342003 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.60625 | + | 1.49376i | −0.154192 | + | 0.0638684i | −0.458445 | − | 0.888723i | \(-0.651593\pi\) |
0.304253 | + | 0.952591i | \(0.401593\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.146770 | − | 0.354333i | 0.00626397 | − | 0.0151226i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29.9952 | + | 29.9952i | 1.27784 | + | 1.27784i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.23607 | + | 4.23607i | −0.180136 | + | 0.180136i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.14025 | + | 0.886522i | 0.0908487 | + | 0.0376308i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.31781 | + | 17.6668i | 0.310066 | + | 0.748565i | 0.999702 | + | 0.0244089i | \(0.00777037\pi\) |
−0.689636 | + | 0.724156i | \(0.742230\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 26.0719i | − | 1.10272i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 11.0167i | − | 0.465125i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.12618 | − | 2.71884i | −0.0474628 | − | 0.114585i | 0.898370 | − | 0.439240i | \(-0.144752\pi\) |
−0.945833 | + | 0.324654i | \(0.894752\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.21682 | − | 2.57509i | −0.261543 | − | 0.108335i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.56044 | − | 4.56044i | 0.191520 | − | 0.191520i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.4042 | + | 10.4042i | 0.436169 | + | 0.436169i | 0.890720 | − | 0.454552i | \(-0.150201\pi\) |
−0.454552 | + | 0.890720i | \(0.650201\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.6556 | − | 37.7960i | 0.655167 | − | 1.58171i | −0.150013 | − | 0.988684i | \(-0.547932\pi\) |
0.805181 | − | 0.593030i | \(-0.202068\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.7361 | + | 7.76076i | −0.782713 | + | 0.324210i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.8256 | 0.701675 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.1981 | −1.25716 | −0.628582 | − | 0.777744i | \(-0.716364\pi\) | ||||
−0.628582 | + | 0.777744i | \(0.716364\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.551706 | + | 0.228524i | −0.0229281 | + | 0.00949714i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.60040 | + | 15.9348i | −0.273831 | + | 0.661086i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0897 | − | 12.0897i | −0.500702 | − | 0.500702i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.19615 | + | 3.19615i | −0.132145 | + | 0.132145i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.0997 | + | 8.32558i | 0.829605 | + | 0.343634i | 0.756746 | − | 0.653709i | \(-0.226788\pi\) |
0.0728586 | + | 0.997342i | \(0.476788\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.6366 | + | 28.0932i | 0.479476 | + | 1.15756i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 19.2806i | − | 0.793096i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 38.2715i | 1.57162i | 0.618468 | + | 0.785810i | \(0.287754\pi\) | ||||
−0.618468 | + | 0.785810i | \(0.712246\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.31727 | − | 17.6655i | −0.299979 | − | 0.724213i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.69213 | − | 4.01461i | −0.396672 | − | 0.164307i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.76223 | + | 2.76223i | −0.112862 | + | 0.112862i | −0.761282 | − | 0.648421i | \(-0.775430\pi\) |
0.648421 | + | 0.761282i | \(0.275430\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.7961 | + | 20.7961i | 0.848289 | + | 0.848289i | 0.989920 | − | 0.141630i | \(-0.0452344\pi\) |
−0.141630 | + | 0.989920i | \(0.545234\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.41359 | − | 17.8980i | 0.301905 | − | 0.728862i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.30088 | − | 2.60991i | 0.256167 | − | 0.106108i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.7402 | −0.760642 | −0.380321 | − | 0.924855i | \(-0.624187\pi\) | ||||
−0.380321 | + | 0.924855i | \(0.624187\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 32.5232 | 1.31790 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.82401 | + | 2.82660i | −0.276070 | + | 0.114352i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.19497 | − | 14.9560i | 0.250212 | − | 0.604066i | −0.748009 | − | 0.663689i | \(-0.768990\pi\) |
0.998221 | + | 0.0596229i | \(0.0189898\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.22903 | + | 1.22903i | 0.0495593 | + | 0.0495593i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.7897 | − | 25.7897i | 1.03825 | − | 1.03825i | 0.0390142 | − | 0.999239i | \(-0.487578\pi\) |
0.999239 | − | 0.0390142i | \(-0.0124218\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.34111 | + | 2.21236i | 0.214677 | + | 0.0889222i | 0.487431 | − | 0.873162i | \(-0.337934\pi\) |
−0.272753 | + | 0.962084i | \(0.587934\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.53709 | − | 18.1962i | −0.302453 | − | 0.730186i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 30.0188i | 1.20268i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.1144i | 0.484576i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.83600 | + | 6.84670i | 0.113259 | + | 0.273431i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.4317 | − | 5.97782i | −0.575431 | − | 0.238351i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.43699 | − | 5.43699i | 0.216443 | − | 0.216443i | −0.590555 | − | 0.806998i | \(-0.701091\pi\) |
0.806998 | + | 0.590555i | \(0.201091\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.92048 | − | 3.92048i | −0.155825 | − | 0.155825i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.401972 | − | 0.970446i | 0.0159518 | − | 0.0385110i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.32486 | − | 3.44827i | 0.329843 | − | 0.136625i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.8828 | −0.944789 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.1732 | 0.441315 | 0.220658 | − | 0.975351i | \(-0.429180\pi\) | ||||
0.220658 | + | 0.975351i | \(0.429180\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.7957 | + | 14.8270i | −1.41164 | + | 0.584722i | −0.952746 | − | 0.303768i | \(-0.901755\pi\) |
−0.458897 | + | 0.888490i | \(0.651755\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.01121 | − | 9.68392i | 0.157941 | − | 0.381304i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.05035 | + | 3.05035i | 0.119922 | + | 0.119922i | 0.764521 | − | 0.644599i | \(-0.222976\pi\) |
−0.644599 | + | 0.764521i | \(0.722976\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.1175 | + | 17.1175i | −0.671920 | + | 0.671920i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.5391 | + | 8.92177i | 0.844182 | + | 0.349672i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.45384 | − | 15.5810i | −0.252558 | − | 0.609730i | 0.745851 | − | 0.666113i | \(-0.232043\pi\) |
−0.998409 | + | 0.0563832i | \(0.982043\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.6627i | 0.690138i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 17.6217i | − | 0.687490i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.0504 | + | 38.7490i | 0.625233 | + | 1.50945i | 0.845483 | + | 0.534003i | \(0.179313\pi\) |
−0.220250 | + | 0.975444i | \(0.570687\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.6719 | + | 9.39102i | 0.881836 | + | 0.365268i | 0.777208 | − | 0.629243i | \(-0.216635\pi\) |
0.104627 | + | 0.994512i | \(0.466635\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.77927 | + | 8.77927i | −0.340959 | + | 0.340959i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.09513 | + | 9.09513i | 0.352694 | + | 0.352694i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.5379 | + | 39.9260i | −0.640349 | + | 1.54594i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.1767 | + | 5.45798i | −0.509442 | + | 0.211018i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.353926 | −0.0136632 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.5003 | −0.751680 | −0.375840 | − | 0.926685i | \(-0.622646\pi\) | ||||
−0.375840 | + | 0.926685i | \(0.622646\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.0480 | − | 7.47572i | 0.694668 | − | 0.287741i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.44466 | + | 15.5588i | −0.247688 | + | 0.597972i | −0.998007 | − | 0.0631039i | \(-0.979900\pi\) |
0.750319 | + | 0.661076i | \(0.229900\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.05787 | + | 2.05787i | 0.0789736 | + | 0.0789736i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.4989 | + | 11.4989i | −0.440639 | + | 0.440639i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −45.3415 | − | 18.7811i | −1.73495 | − | 0.718638i | −0.999141 | − | 0.0414451i | \(-0.986804\pi\) |
−0.735805 | − | 0.677193i | \(-0.763196\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.01878 | + | 7.28797i | 0.115341 | + | 0.278459i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.2369i | 0.543171i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.2686i | 0.734076i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.36470 | − | 8.12311i | −0.127999 | − | 0.309018i | 0.846868 | − | 0.531803i | \(-0.178485\pi\) |
−0.974868 | + | 0.222785i | \(0.928485\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.8864 | − | 5.33770i | −0.489512 | − | 0.202763i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.08390 | − | 9.08390i | 0.344572 | − | 0.344572i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.28737 | − | 8.28737i | −0.313906 | − | 0.313906i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.14336 | − | 10.0029i | 0.156716 | − | 0.378346i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.6052 | − | 10.6060i | 0.967094 | − | 0.400584i | 0.157465 | − | 0.987525i | \(-0.449668\pi\) |
0.809630 | + | 0.586941i | \(0.199668\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.5079 | 0.396315 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.96953 | −0.111839 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.00565442 | + | 0.00234214i | −0.000212656 | + | 8.80851e-5i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.52863 | + | 20.5899i | −0.320299 | + | 0.773271i | 0.678937 | + | 0.734197i | \(0.262441\pi\) |
−0.999236 | + | 0.0390744i | \(0.987559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.71465 | − | 2.71465i | −0.101807 | − | 0.101807i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.9050 | + | 21.9050i | −0.820350 | + | 0.820350i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.85367 | + | 1.59624i | 0.144119 | + | 0.0596960i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.50271 | − | 3.62786i | −0.0561197 | − | 0.135485i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 33.6036i | − | 1.25320i | −0.779340 | − | 0.626601i | \(-0.784445\pi\) | ||
0.779340 | − | 0.626601i | \(-0.215555\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 42.0126i | − | 1.56463i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.46664 | + | 18.0261i | 0.277687 | + | 0.670396i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −39.6009 | − | 16.4032i | −1.47074 | − | 0.609200i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.49728 | + | 6.49728i | −0.240971 | + | 0.240971i | −0.817252 | − | 0.576281i | \(-0.804503\pi\) |
0.576281 | + | 0.817252i | \(0.304503\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.53021 | − | 6.53021i | −0.241860 | − | 0.241860i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.0476 | + | 65.2988i | −1.00039 | + | 2.41516i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.3970 | − | 5.96344i | 0.531766 | − | 0.220265i | −0.100611 | − | 0.994926i | \(-0.532080\pi\) |
0.632376 | + | 0.774661i | \(0.282080\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.62264 | 0.133623 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.8774 | −0.658523 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.18771 | − | 3.80567i | 0.337975 | − | 0.139994i | −0.207240 | − | 0.978290i | \(-0.566448\pi\) |
0.545215 | + | 0.838296i | \(0.316448\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.19615 | − | 7.71619i | 0.117414 | − | 0.283461i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.28243 | − | 3.28243i | −0.120421 | − | 0.120421i | 0.644328 | − | 0.764749i | \(-0.277137\pi\) |
−0.764749 | + | 0.644328i | \(0.777137\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.1657 | + | 12.1657i | −0.445716 | + | 0.445716i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.2117 | − | 4.22981i | −0.373625 | − | 0.154761i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.24072 | + | 10.2380i | 0.154952 | + | 0.374088i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 5.40568i | − | 0.197256i | −0.995124 | − | 0.0986280i | \(-0.968555\pi\) | ||
0.995124 | − | 0.0986280i | \(-0.0314454\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 16.9992i | − | 0.619485i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.42517 | + | 10.6833i | 0.161048 | + | 0.388805i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.532954 | + | 0.220757i | 0.0193705 | + | 0.00802354i | 0.392348 | − | 0.919817i | \(-0.371663\pi\) |
−0.372977 | + | 0.927841i | \(0.621663\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.33857 | + | 5.33857i | −0.193778 | + | 0.193778i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.74202 | − | 3.74202i | −0.135648 | − | 0.135648i | 0.636022 | − | 0.771671i | \(-0.280579\pi\) |
−0.771671 | + | 0.636022i | \(0.780579\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.6258 | − | 25.6530i | 0.384680 | − | 0.928701i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.3208 | − | 4.68921i | 0.409303 | − | 0.169539i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.2820 | 0.985097 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.7699 | 1.57838 | 0.789192 | − | 0.614146i | \(-0.210499\pi\) | ||||
0.789192 | + | 0.614146i | \(0.210499\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.5886 | + | 5.62859i | −0.489382 | + | 0.202709i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.2653 | − | 44.0963i | 0.656956 | − | 1.58603i | −0.145525 | − | 0.989355i | \(-0.546487\pi\) |
0.802481 | − | 0.596678i | \(-0.203513\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.7267 | − | 21.7267i | −0.780445 | − | 0.780445i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.69677 | − | 5.69677i | 0.204371 | − | 0.204371i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.28386 | + | 3.01707i | 0.260971 | + | 0.108098i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.43415 | + | 20.3618i | 0.301798 | + | 0.728604i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 50.1746i | 1.79309i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.66110i | 0.202053i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.8193 | − | 35.7769i | −0.528250 | − | 1.27531i | −0.932668 | − | 0.360735i | \(-0.882526\pi\) |
0.404418 | − | 0.914574i | \(-0.367474\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 19.1322 | + | 7.92480i | 0.681123 | + | 0.282130i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.5475 | + | 16.5475i | −0.588361 | + | 0.588361i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.282046 | + | 0.282046i | 0.0100157 | + | 0.0100157i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.96452 | + | 7.15698i | −0.105141 | + | 0.253832i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.2186 | + | 10.8601i | −0.928709 | + | 0.384684i | −0.795188 | − | 0.606362i | \(-0.792628\pi\) |
−0.133520 | + | 0.991046i | \(0.542628\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.0236 | 0.708383 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.2373 | −0.679715 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.0238 | + | 6.22307i | −0.530179 | + | 0.219607i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.01461 | + | 12.1063i | −0.176742 | + | 0.426693i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.24238 | + | 6.24238i | 0.219742 | + | 0.219742i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.1908 | − | 36.1908i | 1.27240 | − | 1.27240i | 0.327575 | − | 0.944825i | \(-0.393769\pi\) |
0.944825 | − | 0.327575i | \(-0.106231\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.52316 | − | 1.87355i | −0.158829 | − | 0.0657893i | 0.301852 | − | 0.953355i | \(-0.402395\pi\) |
−0.460682 | + | 0.887565i | \(0.652395\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.38691 | + | 5.76252i | 0.0837127 | + | 0.202100i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.41550i | 0.259754i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 47.5449i | − | 1.66339i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.01557 | + | 14.5229i | 0.210201 | + | 0.507470i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.3794 | + | 11.3409i | 0.955549 | + | 0.395801i | 0.805314 | − | 0.592849i | \(-0.201997\pi\) |
0.150235 | + | 0.988650i | \(0.451997\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.6023 | − | 17.6023i | 0.613576 | − | 0.613576i | −0.330300 | − | 0.943876i | \(-0.607150\pi\) |
0.943876 | + | 0.330300i | \(0.107150\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.29510 | − | 5.29510i | −0.184352 | − | 0.184352i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.09145 | − | 21.9487i | 0.316141 | − | 0.763231i | −0.683311 | − | 0.730127i | \(-0.739461\pi\) |
0.999452 | − | 0.0331040i | \(-0.0105393\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.0340 | − | 19.0679i | 1.59883 | − | 0.662256i | 0.607578 | − | 0.794260i | \(-0.292141\pi\) |
0.991249 | + | 0.132004i | \(0.0421412\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.5659 | −0.817492 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.4275 | −0.846363 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.2389 | − | 7.55482i | 0.631185 | − | 0.261445i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.7639 | + | 33.2291i | −0.475751 | + | 1.14856i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.6558 | − | 32.6558i | −1.12740 | − | 1.12740i | −0.990598 | − | 0.136807i | \(-0.956316\pi\) |
−0.136807 | − | 0.990598i | \(-0.543684\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57.3415 | − | 57.3415i | 1.97729 | − | 1.97729i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.6263 | − | 6.88685i | −0.572641 | − | 0.237196i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.95938 | + | 7.14456i | 0.101806 | + | 0.245780i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 23.7181i | − | 0.814964i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.8591i | 0.441322i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.09667 | + | 9.89024i | 0.140432 | + | 0.339033i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.254393 | − | 0.105373i | −0.00871025 | − | 0.00360790i | 0.378324 | − | 0.925673i | \(-0.376501\pi\) |
−0.387034 | + | 0.922065i | \(0.626501\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.82854 | + | 5.82854i | −0.199332 | + | 0.199332i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.7107 | − | 15.7107i | −0.536666 | − | 0.536666i | 0.385882 | − | 0.922548i | \(-0.373897\pi\) |
−0.922548 | + | 0.385882i | \(0.873897\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.205658 | + | 0.496502i | −0.00701695 | + | 0.0169404i | −0.927349 | − | 0.374197i | \(-0.877918\pi\) |
0.920332 | + | 0.391138i | \(0.127918\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.58454 | − | 2.31319i | 0.190321 | − | 0.0788334i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.3841 | 0.387520 | 0.193760 | − | 0.981049i | \(-0.437932\pi\) | ||||
0.193760 | + | 0.981049i | \(0.437932\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.86800 | −0.233519 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.4605 | − | 6.81817i | 0.559028 | − | 0.231557i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.35577 | + | 3.27311i | −0.0459912 | + | 0.111033i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.2466 | + | 14.2466i | 0.482728 | + | 0.482728i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.31877 | + | 1.31877i | −0.0446334 | + | 0.0446334i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26.7046 | − | 11.0614i | −0.902779 | − | 0.373943i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.76098 | + | 4.25139i | 0.0594642 | + | 0.143559i | 0.950819 | − | 0.309747i | \(-0.100244\pi\) |
−0.891355 | + | 0.453306i | \(0.850244\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 14.9853i | − | 0.505442i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 41.1185i | − | 1.38532i | −0.721266 | − | 0.692658i | \(-0.756439\pi\) | ||
0.721266 | − | 0.692658i | \(-0.243561\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.9313 | + | 28.8046i | 0.401519 | + | 0.969353i | 0.987298 | + | 0.158881i | \(0.0507888\pi\) |
−0.585779 | + | 0.810471i | \(0.699211\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.1334 | + | 4.19740i | 0.340631 | + | 0.141094i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.97107 | − | 8.97107i | 0.301219 | − | 0.301219i | −0.540272 | − | 0.841491i | \(-0.681679\pi\) |
0.841491 | + | 0.540272i | \(0.181679\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.58307 | − | 2.58307i | −0.0866333 | − | 0.0866333i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.45958 | − | 3.52374i | 0.0488977 | − | 0.118050i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.4443 | + | 5.15461i | −0.416434 | + | 0.172492i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.833341 | −0.0278555 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.50867 | 0.284096 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 72.9112 | − | 30.2008i | 2.43172 | − | 1.00725i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.9898 | − | 48.2596i | 0.665956 | − | 1.60776i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25.7760 | − | 25.7760i | −0.857771 | − | 0.857771i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.6663 | + | 11.6663i | −0.387801 | + | 0.387801i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.90281 | + | 2.44502i | 0.196000 | + | 0.0811857i | 0.478524 | − | 0.878074i | \(-0.341172\pi\) |
−0.282525 | + | 0.959260i | \(0.591172\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.00150094 | − | 0.00362358i | −4.97830e−5 | − | 0.000120187i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.93353i | − | 0.0971921i | −0.998819 | − | 0.0485961i | \(-0.984525\pi\) | ||
0.998819 | − | 0.0485961i | \(-0.0154747\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.1999i | 0.337568i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.0613674 | + | 0.148154i | 0.00202874 | + | 0.00489782i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 56.7500 | + | 23.5066i | 1.87405 | + | 0.776257i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31.0406 | + | 31.0406i | −1.02393 | + | 1.02393i | −0.0242270 | + | 0.999706i | \(0.507712\pi\) |
−0.999706 | + | 0.0242270i | \(0.992288\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.57093 | − | 4.57093i | −0.150617 | − | 0.150617i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.50524 | − | 22.9477i | 0.312869 | − | 0.755332i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.80971 | + | 4.06332i | −0.322541 | + | 0.133601i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.9234 | 0.884282 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.7583 | −0.385776 | −0.192888 | − | 0.981221i | \(-0.561785\pi\) | ||||
−0.192888 | + | 0.981221i | \(0.561785\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.1813 | − | 6.28830i | 0.497547 | − | 0.206091i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.9700 | − | 26.4840i | 0.359143 | − | 0.867048i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.99579 | − | 7.99579i | −0.261490 | − | 0.261490i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.46723 | + | 1.46723i | −0.0479325 | + | 0.0479325i | −0.730667 | − | 0.682734i | \(-0.760791\pi\) |
0.682734 | + | 0.730667i | \(0.260791\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.39273 | − | 1.40531i | −0.110718 | − | 0.0458607i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.87108 | + | 9.34561i | 0.126194 | + | 0.304658i | 0.974332 | − | 0.225117i | \(-0.0722764\pi\) |
−0.848138 | + | 0.529775i | \(0.822276\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.03193i | 0.261556i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 15.2139i | 0.494909i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.6842 | − | 33.0365i | −0.444676 | − | 1.07354i | −0.974289 | − | 0.225303i | \(-0.927663\pi\) |
0.529613 | − | 0.848240i | \(-0.322337\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.9318 | + | 7.01337i | 0.549628 | + | 0.227664i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.78911 | − | 2.78911i | 0.0904430 | − | 0.0904430i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.2740 | − | 11.2740i | −0.365201 | − | 0.365201i | 0.500523 | − | 0.865723i | \(-0.333141\pi\) |
−0.865723 | + | 0.500523i | \(0.833141\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.96579 | + | 19.2311i | −0.257767 | + | 0.622305i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.7695 | − | 7.36036i | 0.574406 | − | 0.237927i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27.4338 | 0.885883 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.5715 | 0.824886 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.56093 | + | 2.71763i | −0.211423 | + | 0.0875743i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.234562 | + | 0.566282i | −0.00755080 | + | 0.0182293i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.1865 | − | 25.1865i | −0.809944 | − | 0.809944i | 0.174681 | − | 0.984625i | \(-0.444111\pi\) |
−0.984625 | + | 0.174681i | \(0.944111\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.0100 | + | 16.0100i | −0.514314 | + | 0.514314i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.05357 | − | 2.92168i | −0.226360 | − | 0.0937613i | 0.266621 | − | 0.963801i | \(-0.414093\pi\) |
−0.492981 | + | 0.870040i | \(0.664093\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.0971 | − | 41.2759i | −0.548106 | − | 1.32325i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.43939i | 0.270277i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 21.0511i | − | 0.673484i | −0.941597 | − | 0.336742i | \(-0.890675\pi\) | ||
0.941597 | − | 0.336742i | \(-0.109325\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.79359 | + | 16.4012i | 0.217124 | + | 0.524184i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.4395 | + | 6.80946i | 0.524873 | + | 0.217409i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.6221 | + | 23.6221i | −0.753429 | + | 0.753429i | −0.975117 | − | 0.221689i | \(-0.928843\pi\) |
0.221689 | + | 0.975117i | \(0.428843\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.9936 | − | 13.9936i | −0.445873 | − | 0.445873i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.95205 | + | 9.54108i | −0.125795 | + | 0.303696i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 44.7500 | − | 18.5361i | 1.42297 | − | 0.589412i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.0358 | 0.858822 | 0.429411 | − | 0.903109i | \(-0.358721\pi\) | ||||
0.429411 | + | 0.903109i | \(0.358721\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.0922 | −0.478936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.94819 | + | 4.12067i | −0.315379 | + | 0.130634i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.4320 | − | 32.4278i | 0.425397 | − | 1.02700i | −0.555333 | − | 0.831628i | \(-0.687409\pi\) |
0.980729 | − | 0.195371i | \(-0.0625910\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.78861 | + | 8.78861i | 0.278059 | + | 0.278059i |
(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 | 1024.2.g.f.385.2 | yes | 16 | |
4.3 | odd | 2 | inner | 1024.2.g.f.385.3 | yes | 16 | |
8.3 | odd | 2 | 1024.2.g.a.385.2 | ✓ | 16 | ||
8.5 | even | 2 | 1024.2.g.a.385.3 | yes | 16 | ||
16.3 | odd | 4 | 1024.2.g.d.897.3 | yes | 16 | ||
16.5 | even | 4 | 1024.2.g.g.897.3 | yes | 16 | ||
16.11 | odd | 4 | 1024.2.g.g.897.2 | yes | 16 | ||
16.13 | even | 4 | 1024.2.g.d.897.2 | yes | 16 | ||
32.3 | odd | 8 | inner | 1024.2.g.f.641.3 | yes | 16 | |
32.5 | even | 8 | 1024.2.g.g.129.3 | yes | 16 | ||
32.11 | odd | 8 | 1024.2.g.d.129.3 | yes | 16 | ||
32.13 | even | 8 | 1024.2.g.a.641.3 | yes | 16 | ||
32.19 | odd | 8 | 1024.2.g.a.641.2 | yes | 16 | ||
32.21 | even | 8 | 1024.2.g.d.129.2 | yes | 16 | ||
32.27 | odd | 8 | 1024.2.g.g.129.2 | yes | 16 | ||
32.29 | even | 8 | inner | 1024.2.g.f.641.2 | yes | 16 | |
64.3 | odd | 16 | 4096.2.a.s.1.1 | 8 | |||
64.29 | even | 16 | 4096.2.a.s.1.2 | 8 | |||
64.35 | odd | 16 | 4096.2.a.i.1.8 | 8 | |||
64.61 | even | 16 | 4096.2.a.i.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1024.2.g.a.385.2 | ✓ | 16 | 8.3 | odd | 2 | ||
1024.2.g.a.385.3 | yes | 16 | 8.5 | even | 2 | ||
1024.2.g.a.641.2 | yes | 16 | 32.19 | odd | 8 | ||
1024.2.g.a.641.3 | yes | 16 | 32.13 | even | 8 | ||
1024.2.g.d.129.2 | yes | 16 | 32.21 | even | 8 | ||
1024.2.g.d.129.3 | yes | 16 | 32.11 | odd | 8 | ||
1024.2.g.d.897.2 | yes | 16 | 16.13 | even | 4 | ||
1024.2.g.d.897.3 | yes | 16 | 16.3 | odd | 4 | ||
1024.2.g.f.385.2 | yes | 16 | 1.1 | even | 1 | trivial | |
1024.2.g.f.385.3 | yes | 16 | 4.3 | odd | 2 | inner | |
1024.2.g.f.641.2 | yes | 16 | 32.29 | even | 8 | inner | |
1024.2.g.f.641.3 | yes | 16 | 32.3 | odd | 8 | inner | |
1024.2.g.g.129.2 | yes | 16 | 32.27 | odd | 8 | ||
1024.2.g.g.129.3 | yes | 16 | 32.5 | even | 8 | ||
1024.2.g.g.897.2 | yes | 16 | 16.11 | odd | 4 | ||
1024.2.g.g.897.3 | yes | 16 | 16.5 | even | 4 | ||
4096.2.a.i.1.7 | 8 | 64.61 | even | 16 | |||
4096.2.a.i.1.8 | 8 | 64.35 | odd | 16 | |||
4096.2.a.s.1.1 | 8 | 64.3 | odd | 16 | |||
4096.2.a.s.1.2 | 8 | 64.29 | even | 16 |