Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2925,2,Mod(2224,2925)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2925, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2925.2224");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2925.c (of order \(2\), degree \(1\), not 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: | \(23.3562425912\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 585) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2224.4 | ||
Root | \(2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2925.2224 |
Dual form | 2925.2.c.p.2224.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2925\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(2251\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.56155i | 1.81129i | 0.424035 | + | 0.905646i | \(0.360613\pi\) | ||||
−0.424035 | + | 0.905646i | \(0.639387\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.56155 | −2.28078 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 0.438447i | − 0.165717i | −0.996561 | − | 0.0828587i | \(-0.973595\pi\) | ||||
0.996561 | − | 0.0828587i | \(-0.0264050\pi\) | |||||||
\(8\) | − 6.56155i | − 2.31986i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.56155 | −0.470826 | −0.235413 | − | 0.971895i | \(-0.575644\pi\) | ||||
−0.235413 | + | 0.971895i | \(0.575644\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 1.12311 | 0.300163 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.68466 | 1.92116 | ||||||||
\(17\) | 1.56155i | 0.378732i | 0.981907 | + | 0.189366i | \(0.0606433\pi\) | ||||
−0.981907 | + | 0.189366i | \(0.939357\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.12311 | 1.17532 | 0.587661 | − | 0.809108i | \(-0.300049\pi\) | ||||
0.587661 | + | 0.809108i | \(0.300049\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 4.00000i | − 0.852803i | ||||||||
\(23\) | − 2.43845i | − 0.508451i | −0.967145 | − | 0.254226i | \(-0.918179\pi\) | ||||
0.967145 | − | 0.254226i | \(-0.0818206\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.56155 | −0.502362 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.00000i | 0.377964i | ||||||||
\(29\) | 7.12311 | 1.32273 | 0.661364 | − | 0.750065i | \(-0.269978\pi\) | ||||
0.661364 | + | 0.750065i | \(0.269978\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 6.56155i | 1.15993i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 10.6847i | − 1.75655i | −0.478159 | − | 0.878274i | \(-0.658696\pi\) | ||||
0.478159 | − | 0.878274i | \(-0.341304\pi\) | |||||||
\(38\) | 13.1231i | 2.12885i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.56155 | 0.556221 | 0.278111 | − | 0.960549i | \(-0.410292\pi\) | ||||
0.278111 | + | 0.960549i | \(0.410292\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 3.12311i | − 0.476269i | −0.971232 | − | 0.238135i | \(-0.923464\pi\) | ||||
0.971232 | − | 0.238135i | \(-0.0765359\pi\) | |||||||
\(44\) | 7.12311 | 1.07385 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.24621 | 0.920954 | ||||||||
\(47\) | 11.1231i | 1.62247i | 0.584719 | + | 0.811236i | \(0.301205\pi\) | ||||
−0.584719 | + | 0.811236i | \(0.698795\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.80776 | 0.972538 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 4.56155i | − 0.632574i | ||||||||
\(53\) | 4.68466i | 0.643487i | 0.946827 | + | 0.321744i | \(0.104269\pi\) | ||||
−0.946827 | + | 0.321744i | \(0.895731\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.87689 | −0.384441 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 18.2462i | 2.39584i | ||||||||
\(59\) | −12.0000 | −1.56227 | −0.781133 | − | 0.624364i | \(-0.785358\pi\) | ||||
−0.781133 | + | 0.624364i | \(0.785358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.68466 | −0.855883 | −0.427941 | − | 0.903806i | \(-0.640761\pi\) | ||||
−0.427941 | + | 0.903806i | \(0.640761\pi\) | |||||||
\(62\) | 15.3693i | 1.95191i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.43845 | −0.179806 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 11.3693i | − 1.38898i | −0.719501 | − | 0.694492i | \(-0.755629\pi\) | ||||
0.719501 | − | 0.694492i | \(-0.244371\pi\) | |||||||
\(68\) | − 7.12311i | − 0.863803i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.4384 | 1.23882 | 0.619408 | − | 0.785069i | \(-0.287373\pi\) | ||||
0.619408 | + | 0.785069i | \(0.287373\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000i | 0.702247i | 0.936329 | + | 0.351123i | \(0.114200\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | 27.3693 | 3.18162 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −23.3693 | −2.68064 | ||||||||
\(77\) | 0.684658i | 0.0780241i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.68466 | −0.527065 | −0.263533 | − | 0.964650i | \(-0.584888\pi\) | ||||
−0.263533 | + | 0.964650i | \(0.584888\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.12311i | 1.00748i | ||||||||
\(83\) | 16.4924i | 1.81028i | 0.425115 | + | 0.905139i | \(0.360234\pi\) | ||||
−0.425115 | + | 0.905139i | \(0.639766\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.2462i | 1.09225i | ||||||||
\(89\) | −10.6847 | −1.13257 | −0.566286 | − | 0.824209i | \(-0.691620\pi\) | ||||
−0.566286 | + | 0.824209i | \(0.691620\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.438447 | 0.0459618 | ||||||||
\(92\) | 11.1231i | 1.15966i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −28.4924 | −2.93877 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.9309i | 1.71907i | 0.511077 | + | 0.859535i | \(0.329247\pi\) | ||||
−0.511077 | + | 0.859535i | \(0.670753\pi\) | |||||||
\(98\) | 17.4384i | 1.76155i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.2462 | 1.01954 | 0.509768 | − | 0.860312i | \(-0.329731\pi\) | ||||
0.509768 | + | 0.860312i | \(0.329731\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.1231i | 1.49012i | 0.666995 | + | 0.745062i | \(0.267580\pi\) | ||||
−0.666995 | + | 0.745062i | \(0.732420\pi\) | |||||||
\(104\) | 6.56155 | 0.643413 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0000 | −1.16554 | ||||||||
\(107\) | 10.9309i | 1.05673i | 0.849018 | + | 0.528364i | \(0.177194\pi\) | ||||
−0.849018 | + | 0.528364i | \(0.822806\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 3.36932i | − 0.318371i | ||||||||
\(113\) | 4.87689i | 0.458780i | 0.973335 | + | 0.229390i | \(0.0736731\pi\) | ||||
−0.973335 | + | 0.229390i | \(0.926327\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −32.4924 | −3.01685 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 30.7386i | − 2.82972i | ||||||||
\(119\) | 0.684658 | 0.0627625 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.56155 | −0.778323 | ||||||||
\(122\) | − 17.1231i | − 1.55025i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −27.3693 | −2.45784 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.75379i | 0.155624i | 0.996968 | + | 0.0778118i | \(0.0247933\pi\) | ||||
−0.996968 | + | 0.0778118i | \(0.975207\pi\) | |||||||
\(128\) | 9.43845i | 0.834249i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2.24621i | − 0.194771i | ||||||||
\(134\) | 29.1231 | 2.51585 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.2462 | 0.878605 | ||||||||
\(137\) | 1.12311i | 0.0959534i | 0.998848 | + | 0.0479767i | \(0.0152773\pi\) | ||||
−0.998848 | + | 0.0479767i | \(0.984723\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.31534 | −0.281204 | −0.140602 | − | 0.990066i | \(-0.544904\pi\) | ||||
−0.140602 | + | 0.990066i | \(0.544904\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 26.7386i | 2.24386i | ||||||||
\(143\) | − 1.56155i | − 0.130584i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −15.3693 | −1.27197 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 48.7386i | 4.00629i | ||||||||
\(149\) | 17.8078 | 1.45887 | 0.729434 | − | 0.684051i | \(-0.239783\pi\) | ||||
0.729434 | + | 0.684051i | \(0.239783\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3693 | 0.925222 | 0.462611 | − | 0.886561i | \(-0.346913\pi\) | ||||
0.462611 | + | 0.886561i | \(0.346913\pi\) | |||||||
\(152\) | − 33.6155i | − 2.72658i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.75379 | −0.141324 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.36932i | 0.268901i | 0.990920 | + | 0.134450i | \(0.0429269\pi\) | ||||
−0.990920 | + | 0.134450i | \(0.957073\pi\) | |||||||
\(158\) | − 12.0000i | − 0.954669i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.06913 | −0.0842593 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 16.0540i | − 1.25744i | −0.777630 | − | 0.628722i | \(-0.783578\pi\) | ||||
0.777630 | − | 0.628722i | \(-0.216422\pi\) | |||||||
\(164\) | −16.2462 | −1.26862 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −42.2462 | −3.27894 | ||||||||
\(167\) | 4.87689i | 0.377385i | 0.982036 | + | 0.188693i | \(0.0604250\pi\) | ||||
−0.982036 | + | 0.188693i | \(0.939575\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 14.2462i | 1.08626i | ||||||||
\(173\) | − 12.8769i | − 0.979012i | −0.872000 | − | 0.489506i | \(-0.837177\pi\) | ||||
0.872000 | − | 0.489506i | \(-0.162823\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.0000 | −0.904534 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 27.3693i | − 2.05142i | ||||||||
\(179\) | 4.87689 | 0.364516 | 0.182258 | − | 0.983251i | \(-0.441659\pi\) | ||||
0.182258 | + | 0.983251i | \(0.441659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.3153 | 0.989722 | 0.494861 | − | 0.868972i | \(-0.335219\pi\) | ||||
0.494861 | + | 0.868972i | \(0.335219\pi\) | |||||||
\(182\) | 1.12311i | 0.0832501i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.0000 | −1.17954 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2.43845i | − 0.178317i | ||||||||
\(188\) | − 50.7386i | − 3.70050i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.6155 | 1.41933 | 0.709665 | − | 0.704539i | \(-0.248846\pi\) | ||||
0.709665 | + | 0.704539i | \(0.248846\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 19.5616i | − 1.40807i | −0.710165 | − | 0.704036i | \(-0.751379\pi\) | ||||
0.710165 | − | 0.704036i | \(-0.248621\pi\) | |||||||
\(194\) | −43.3693 | −3.11374 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −31.0540 | −2.21814 | ||||||||
\(197\) | − 3.36932i | − 0.240054i | −0.992771 | − | 0.120027i | \(-0.961702\pi\) | ||||
0.992771 | − | 0.120027i | \(-0.0382981\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 26.2462i | 1.84668i | ||||||||
\(203\) | − 3.12311i | − 0.219199i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −38.7386 | −2.69905 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.68466i | 0.532835i | ||||||||
\(209\) | −8.00000 | −0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.24621 | 0.430007 | 0.215003 | − | 0.976613i | \(-0.431024\pi\) | ||||
0.215003 | + | 0.976613i | \(0.431024\pi\) | |||||||
\(212\) | − 21.3693i | − 1.46765i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −28.0000 | −1.91404 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 2.63068i | − 0.178582i | ||||||||
\(218\) | 5.12311i | 0.346980i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.56155 | −0.105041 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.3693i | 1.02921i | 0.857429 | + | 0.514603i | \(0.172061\pi\) | ||||
−0.857429 | + | 0.514603i | \(0.827939\pi\) | |||||||
\(224\) | 2.87689 | 0.192221 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.4924 | −0.830984 | ||||||||
\(227\) | 5.75379i | 0.381892i | 0.981601 | + | 0.190946i | \(0.0611556\pi\) | ||||
−0.981601 | + | 0.190946i | \(0.938844\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.1231 | −1.13153 | −0.565763 | − | 0.824568i | \(-0.691418\pi\) | ||||
−0.565763 | + | 0.824568i | \(0.691418\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 46.7386i | − 3.06854i | ||||||||
\(233\) | 27.8078i | 1.82175i | 0.412685 | + | 0.910874i | \(0.364591\pi\) | ||||
−0.412685 | + | 0.910874i | \(0.635409\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 54.7386 | 3.56318 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.75379i | 0.113681i | ||||||||
\(239\) | −22.9309 | −1.48327 | −0.741637 | − | 0.670801i | \(-0.765950\pi\) | ||||
−0.741637 | + | 0.670801i | \(0.765950\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.7386 | 1.59356 | 0.796778 | − | 0.604272i | \(-0.206536\pi\) | ||||
0.796778 | + | 0.604272i | \(0.206536\pi\) | |||||||
\(242\) | − 21.9309i | − 1.40977i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 30.4924 | 1.95208 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.12311i | 0.325975i | ||||||||
\(248\) | − 39.3693i | − 2.49995i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.2462 | 1.65665 | 0.828323 | − | 0.560251i | \(-0.189295\pi\) | ||||
0.828323 | + | 0.560251i | \(0.189295\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.80776i | 0.239392i | ||||||||
\(254\) | −4.49242 | −0.281880 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −27.0540 | −1.69087 | ||||||||
\(257\) | − 12.8769i | − 0.803239i | −0.915807 | − | 0.401619i | \(-0.868448\pi\) | ||||
0.915807 | − | 0.401619i | \(-0.131552\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.68466 | −0.291091 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.24621i | 0.138507i | 0.997599 | + | 0.0692537i | \(0.0220618\pi\) | ||||
−0.997599 | + | 0.0692537i | \(0.977938\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.75379 | 0.352787 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 51.8617i | 3.16796i | ||||||||
\(269\) | 0.876894 | 0.0534652 | 0.0267326 | − | 0.999643i | \(-0.491490\pi\) | ||||
0.0267326 | + | 0.999643i | \(0.491490\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.3693 | −1.17660 | −0.588301 | − | 0.808642i | \(-0.700203\pi\) | ||||
−0.588301 | + | 0.808642i | \(0.700203\pi\) | |||||||
\(272\) | 12.0000i | 0.727607i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.87689 | −0.173800 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 12.2462i | − 0.735804i | −0.929865 | − | 0.367902i | \(-0.880076\pi\) | ||||
0.929865 | − | 0.367902i | \(-0.119924\pi\) | |||||||
\(278\) | − 8.49242i | − 0.509342i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.24621 | 0.253308 | 0.126654 | − | 0.991947i | \(-0.459576\pi\) | ||||
0.126654 | + | 0.991947i | \(0.459576\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000i | 0.237775i | 0.992908 | + | 0.118888i | \(0.0379328\pi\) | ||||
−0.992908 | + | 0.118888i | \(0.962067\pi\) | |||||||
\(284\) | −47.6155 | −2.82546 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | − 1.56155i | − 0.0921755i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.5616 | 0.856562 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 27.3693i | − 1.60167i | ||||||||
\(293\) | 20.2462i | 1.18280i | 0.806380 | + | 0.591398i | \(0.201424\pi\) | ||||
−0.806380 | + | 0.591398i | \(0.798576\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −70.1080 | −4.07494 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 45.6155i | 2.64244i | ||||||||
\(299\) | 2.43845 | 0.141019 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.36932 | −0.0789261 | ||||||||
\(302\) | 29.1231i | 1.67585i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 39.3693 | 2.25799 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.56155i | 0.431561i | 0.976442 | + | 0.215780i | \(0.0692295\pi\) | ||||
−0.976442 | + | 0.215780i | \(0.930770\pi\) | |||||||
\(308\) | − 3.12311i | − 0.177955i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.63068 | 0.149172 | 0.0745862 | − | 0.997215i | \(-0.476236\pi\) | ||||
0.0745862 | + | 0.997215i | \(0.476236\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 29.1231i | − 1.64614i | −0.567943 | − | 0.823068i | \(-0.692261\pi\) | ||||
0.567943 | − | 0.823068i | \(-0.307739\pi\) | |||||||
\(314\) | −8.63068 | −0.487058 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 21.3693 | 1.20212 | ||||||||
\(317\) | 1.50758i | 0.0846740i | 0.999103 | + | 0.0423370i | \(0.0134803\pi\) | ||||
−0.999103 | + | 0.0423370i | \(0.986520\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.1231 | −0.622774 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 2.73863i | − 0.152618i | ||||||||
\(323\) | 8.00000i | 0.445132i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 41.1231 | 2.27760 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 23.3693i | − 1.29035i | ||||||||
\(329\) | 4.87689 | 0.268872 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.1231 | 1.60075 | 0.800375 | − | 0.599499i | \(-0.204634\pi\) | ||||
0.800375 | + | 0.599499i | \(0.204634\pi\) | |||||||
\(332\) | − 75.2311i | − 4.12884i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.4924 | −0.683555 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 30.4924i | − 1.66103i | −0.556998 | − | 0.830514i | \(-0.688047\pi\) | ||||
0.556998 | − | 0.830514i | \(-0.311953\pi\) | |||||||
\(338\) | − 2.56155i | − 0.139330i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.36932 | −0.507377 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 6.05398i | − 0.326884i | ||||||||
\(344\) | −20.4924 | −1.10488 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 32.9848 | 1.77328 | ||||||||
\(347\) | − 26.0540i | − 1.39865i | −0.714804 | − | 0.699325i | \(-0.753484\pi\) | ||||
0.714804 | − | 0.699325i | \(-0.246516\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.3693 | 1.25093 | 0.625465 | − | 0.780252i | \(-0.284909\pi\) | ||||
0.625465 | + | 0.780252i | \(0.284909\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 10.2462i | − 0.546125i | ||||||||
\(353\) | 22.4924i | 1.19715i | 0.801066 | + | 0.598575i | \(0.204266\pi\) | ||||
−0.801066 | + | 0.598575i | \(0.795734\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 48.7386 | 2.58314 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.4924i | 0.660245i | ||||||||
\(359\) | 14.2462 | 0.751886 | 0.375943 | − | 0.926643i | \(-0.377319\pi\) | ||||
0.375943 | + | 0.926643i | \(0.377319\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.24621 | 0.381380 | ||||||||
\(362\) | 34.1080i | 1.79267i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.00000 | −0.104828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 1.75379i | − 0.0915470i | −0.998952 | − | 0.0457735i | \(-0.985425\pi\) | ||||
0.998952 | − | 0.0457735i | \(-0.0145753\pi\) | |||||||
\(368\) | − 18.7386i | − 0.976819i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.05398 | 0.106637 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 12.2462i | − 0.634085i | −0.948411 | − | 0.317042i | \(-0.897310\pi\) | ||||
0.948411 | − | 0.317042i | \(-0.102690\pi\) | |||||||
\(374\) | 6.24621 | 0.322984 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 72.9848 | 3.76391 | ||||||||
\(377\) | 7.12311i | 0.366859i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.4924 | 1.56629 | 0.783145 | − | 0.621839i | \(-0.213614\pi\) | ||||
0.783145 | + | 0.621839i | \(0.213614\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 50.2462i | 2.57082i | ||||||||
\(383\) | − 3.50758i | − 0.179229i | −0.995977 | − | 0.0896144i | \(-0.971437\pi\) | ||||
0.995977 | − | 0.0896144i | \(-0.0285635\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 50.1080 | 2.55043 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 77.2311i | − 3.92081i | ||||||||
\(389\) | −37.8617 | −1.91967 | −0.959833 | − | 0.280571i | \(-0.909476\pi\) | ||||
−0.959833 | + | 0.280571i | \(0.909476\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.80776 | 0.192567 | ||||||||
\(392\) | − 44.6695i | − 2.25615i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.63068 | 0.434808 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 4.43845i | − 0.222759i | −0.993778 | − | 0.111380i | \(-0.964473\pi\) | ||||
0.993778 | − | 0.111380i | \(-0.0355270\pi\) | |||||||
\(398\) | 20.4924i | 1.02719i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.75379 | 0.187455 | 0.0937276 | − | 0.995598i | \(-0.470122\pi\) | ||||
0.0937276 | + | 0.995598i | \(0.470122\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.00000i | 0.298881i | ||||||||
\(404\) | −46.7386 | −2.32533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.00000 | 0.397033 | ||||||||
\(407\) | 16.6847i | 0.827028i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.87689 | 0.340041 | 0.170020 | − | 0.985441i | \(-0.445617\pi\) | ||||
0.170020 | + | 0.985441i | \(0.445617\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 68.9848i | − 3.39864i | ||||||||
\(413\) | 5.26137i | 0.258895i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.56155 | −0.321707 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 20.4924i | − 1.00232i | ||||||||
\(419\) | −7.61553 | −0.372043 | −0.186021 | − | 0.982546i | \(-0.559559\pi\) | ||||
−0.186021 | + | 0.982546i | \(0.559559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 39.3693 | 1.91874 | 0.959372 | − | 0.282146i | \(-0.0910462\pi\) | ||||
0.959372 | + | 0.282146i | \(0.0910462\pi\) | |||||||
\(422\) | 16.0000i | 0.778868i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 30.7386 | 1.49280 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.93087i | 0.141835i | ||||||||
\(428\) | − 49.8617i | − 2.41016i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.50758 | −0.168954 | −0.0844770 | − | 0.996425i | \(-0.526922\pi\) | ||||
−0.0844770 | + | 0.996425i | \(0.526922\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.61553i | 0.462093i | 0.972943 | + | 0.231046i | \(0.0742149\pi\) | ||||
−0.972943 | + | 0.231046i | \(0.925785\pi\) | |||||||
\(434\) | 6.73863 | 0.323465 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.12311 | −0.436918 | ||||||||
\(437\) | − 12.4924i | − 0.597594i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.0540 | −1.05258 | −0.526289 | − | 0.850306i | \(-0.676417\pi\) | ||||
−0.526289 | + | 0.850306i | \(0.676417\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 4.00000i | − 0.190261i | ||||||||
\(443\) | 7.80776i | 0.370958i | 0.982648 | + | 0.185479i | \(0.0593837\pi\) | ||||
−0.982648 | + | 0.185479i | \(0.940616\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −39.3693 | −1.86419 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.630683i | 0.0297970i | ||||||||
\(449\) | 35.1771 | 1.66011 | 0.830055 | − | 0.557682i | \(-0.188309\pi\) | ||||
0.830055 | + | 0.557682i | \(0.188309\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.56155 | −0.261883 | ||||||||
\(452\) | − 22.2462i | − 1.04637i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −14.7386 | −0.691718 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 13.3153i | − 0.622865i | −0.950268 | − | 0.311433i | \(-0.899191\pi\) | ||||
0.950268 | − | 0.311433i | \(-0.100809\pi\) | |||||||
\(458\) | − 43.8617i | − 2.04952i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.05398 | 0.375111 | 0.187556 | − | 0.982254i | \(-0.439944\pi\) | ||||
0.187556 | + | 0.982254i | \(0.439944\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.9309i | 1.34453i | 0.740310 | + | 0.672266i | \(0.234679\pi\) | ||||
−0.740310 | + | 0.672266i | \(0.765321\pi\) | |||||||
\(464\) | 54.7386 | 2.54118 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −71.2311 | −3.29971 | ||||||||
\(467\) | 6.93087i | 0.320722i | 0.987058 | + | 0.160361i | \(0.0512659\pi\) | ||||
−0.987058 | + | 0.160361i | \(0.948734\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.98485 | −0.230179 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 78.7386i | 3.62424i | ||||||||
\(473\) | 4.87689i | 0.224240i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.12311 | −0.143147 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 58.7386i | − 2.68664i | ||||||||
\(479\) | −26.0540 | −1.19044 | −0.595218 | − | 0.803564i | \(-0.702934\pi\) | ||||
−0.595218 | + | 0.803564i | \(0.702934\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.6847 | 0.487178 | ||||||||
\(482\) | 63.3693i | 2.88639i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 39.0540 | 1.77518 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 32.0540i | − 1.45250i | −0.687428 | − | 0.726252i | \(-0.741260\pi\) | ||||
0.687428 | − | 0.726252i | \(-0.258740\pi\) | |||||||
\(488\) | 43.8617i | 1.98553i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.6155 | −1.24627 | −0.623136 | − | 0.782114i | \(-0.714142\pi\) | ||||
−0.623136 | + | 0.782114i | \(0.714142\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.1231i | 0.500959i | ||||||||
\(494\) | −13.1231 | −0.590436 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 46.1080 | 2.07031 | ||||||||
\(497\) | − 4.57671i | − 0.205293i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.9848 | −1.56614 | −0.783068 | − | 0.621936i | \(-0.786347\pi\) | ||||
−0.783068 | + | 0.621936i | \(0.786347\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 67.2311i | 3.00067i | ||||||||
\(503\) | − 13.7538i | − 0.613251i | −0.951830 | − | 0.306626i | \(-0.900800\pi\) | ||||
0.951830 | − | 0.306626i | \(-0.0991999\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.75379 | −0.433609 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 8.00000i | − 0.354943i | ||||||||
\(509\) | 23.5616 | 1.04435 | 0.522174 | − | 0.852839i | \(-0.325121\pi\) | ||||
0.522174 | + | 0.852839i | \(0.325121\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.63068 | 0.116375 | ||||||||
\(512\) | − 50.4233i | − 2.22842i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 32.9848 | 1.45490 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 17.3693i | − 0.763902i | ||||||||
\(518\) | − 12.0000i | − 0.527250i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.8617 | −1.13302 | −0.566512 | − | 0.824054i | \(-0.691707\pi\) | ||||
−0.566512 | + | 0.824054i | \(0.691707\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.7386i | 1.34411i | 0.740503 | + | 0.672053i | \(0.234587\pi\) | ||||
−0.740503 | + | 0.672053i | \(0.765413\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.75379 | −0.250877 | ||||||||
\(527\) | 9.36932i | 0.408134i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.0540 | 0.741477 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10.2462i | 0.444230i | ||||||||
\(533\) | 3.56155i | 0.154268i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −74.6004 | −3.22225 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.24621i | 0.0968410i | ||||||||
\(539\) | −10.6307 | −0.457896 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.8769 | 0.811581 | 0.405791 | − | 0.913966i | \(-0.366996\pi\) | ||||
0.405791 | + | 0.913966i | \(0.366996\pi\) | |||||||
\(542\) | − 49.6155i | − 2.13117i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10.2462 | −0.439303 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 5.36932i | − 0.229575i | −0.993390 | − | 0.114788i | \(-0.963381\pi\) | ||||
0.993390 | − | 0.114788i | \(-0.0366188\pi\) | |||||||
\(548\) | − 5.12311i | − 0.218848i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.4924 | 1.55463 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.05398i | 0.0873439i | ||||||||
\(554\) | 31.3693 | 1.33275 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.1231 | 0.641363 | ||||||||
\(557\) | 6.49242i | 0.275093i | 0.990495 | + | 0.137546i | \(0.0439216\pi\) | ||||
−0.990495 | + | 0.137546i | \(0.956078\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.12311 | 0.132093 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.8769i | 0.458814i | ||||||||
\(563\) | 19.3153i | 0.814045i | 0.913418 | + | 0.407022i | \(0.133433\pi\) | ||||
−0.913418 | + | 0.407022i | \(0.866567\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.2462 | −0.430680 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 68.4924i | − 2.87388i | ||||||||
\(569\) | 32.8769 | 1.37827 | 0.689136 | − | 0.724632i | \(-0.257990\pi\) | ||||
0.689136 | + | 0.724632i | \(0.257990\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.0540 | −0.922930 | −0.461465 | − | 0.887158i | \(-0.652676\pi\) | ||||
−0.461465 | + | 0.887158i | \(0.652676\pi\) | |||||||
\(572\) | 7.12311i | 0.297832i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.00000 | 0.166957 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.4384i | 1.01739i | 0.860948 | + | 0.508693i | \(0.169871\pi\) | ||||
−0.860948 | + | 0.508693i | \(0.830129\pi\) | |||||||
\(578\) | 37.3002i | 1.55148i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.23106 | 0.299995 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 7.31534i | − 0.302970i | ||||||||
\(584\) | 39.3693 | 1.62911 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −51.8617 | −2.14239 | ||||||||
\(587\) | − 32.4924i | − 1.34111i | −0.741862 | − | 0.670553i | \(-0.766057\pi\) | ||||
0.741862 | − | 0.670553i | \(-0.233943\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.7386 | 1.26656 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 82.1080i | − 3.37462i | ||||||||
\(593\) | − 24.2462i | − 0.995673i | −0.867271 | − | 0.497836i | \(-0.834128\pi\) | ||||
0.867271 | − | 0.497836i | \(-0.165872\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −81.2311 | −3.32735 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.24621i | 0.255427i | ||||||||
\(599\) | 9.36932 | 0.382820 | 0.191410 | − | 0.981510i | \(-0.438694\pi\) | ||||
0.191410 | + | 0.981510i | \(0.438694\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.5464 | −1.16443 | −0.582216 | − | 0.813034i | \(-0.697814\pi\) | ||||
−0.582216 | + | 0.813034i | \(0.697814\pi\) | |||||||
\(602\) | − 3.50758i | − 0.142958i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −51.8617 | −2.11022 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 24.0000i | − 0.974130i | −0.873366 | − | 0.487065i | \(-0.838067\pi\) | ||||
0.873366 | − | 0.487065i | \(-0.161933\pi\) | |||||||
\(608\) | 33.6155i | 1.36329i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.1231 | −0.449993 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.5464i | 1.31454i | 0.753657 | + | 0.657268i | \(0.228288\pi\) | ||||
−0.753657 | + | 0.657268i | \(0.771712\pi\) | |||||||
\(614\) | −19.3693 | −0.781682 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.49242 | 0.181005 | ||||||||
\(617\) | 0.738634i | 0.0297363i | 0.999889 | + | 0.0148681i | \(0.00473285\pi\) | ||||
−0.999889 | + | 0.0148681i | \(0.995267\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.63068 | 0.346896 | 0.173448 | − | 0.984843i | \(-0.444509\pi\) | ||||
0.173448 | + | 0.984843i | \(0.444509\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.73863i | 0.270195i | ||||||||
\(623\) | 4.68466i | 0.187687i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 74.6004 | 2.98163 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 15.3693i | − 0.613303i | ||||||||
\(629\) | 16.6847 | 0.665261 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.7386 | −1.30330 | −0.651652 | − | 0.758518i | \(-0.725924\pi\) | ||||
−0.651652 | + | 0.758518i | \(0.725924\pi\) | |||||||
\(632\) | 30.7386i | 1.22272i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.86174 | −0.153369 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.80776i | 0.269733i | ||||||||
\(638\) | − 28.4924i | − 1.12803i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.9848 | −1.30282 | −0.651412 | − | 0.758725i | \(-0.725823\pi\) | ||||
−0.651412 | + | 0.758725i | \(0.725823\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.6847i | 0.421362i | 0.977555 | + | 0.210681i | \(0.0675681\pi\) | ||||
−0.977555 | + | 0.210681i | \(0.932432\pi\) | |||||||
\(644\) | 4.87689 | 0.192177 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20.4924 | −0.806264 | ||||||||
\(647\) | 31.8078i | 1.25049i | 0.780428 | + | 0.625246i | \(0.215001\pi\) | ||||
−0.780428 | + | 0.625246i | \(0.784999\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.7386 | 0.735556 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 73.2311i | 2.86795i | ||||||||
\(653\) | 33.3693i | 1.30584i | 0.757426 | + | 0.652921i | \(0.226457\pi\) | ||||
−0.757426 | + | 0.652921i | \(0.773543\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 27.3693 | 1.06859 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.4924i | 0.487005i | ||||||||
\(659\) | −0.876894 | −0.0341590 | −0.0170795 | − | 0.999854i | \(-0.505437\pi\) | ||||
−0.0170795 | + | 0.999854i | \(0.505437\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.49242 | 0.252526 | 0.126263 | − | 0.991997i | \(-0.459702\pi\) | ||||
0.126263 | + | 0.991997i | \(0.459702\pi\) | |||||||
\(662\) | 74.6004i | 2.89943i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 108.216 | 4.19959 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 17.3693i | − 0.672543i | ||||||||
\(668\) | − 22.2462i | − 0.860732i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.4384 | 0.402972 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 16.7386i | − 0.645227i | −0.946531 | − | 0.322613i | \(-0.895439\pi\) | ||||
0.946531 | − | 0.322613i | \(-0.104561\pi\) | |||||||
\(674\) | 78.1080 | 3.00861 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.56155 | 0.175444 | ||||||||
\(677\) | − 14.4384i | − 0.554915i | −0.960738 | − | 0.277457i | \(-0.910508\pi\) | ||||
0.960738 | − | 0.277457i | \(-0.0894917\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.42329 | 0.284880 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 24.0000i | − 0.919007i | ||||||||
\(683\) | − 32.4924i | − 1.24329i | −0.783300 | − | 0.621644i | \(-0.786465\pi\) | ||||
0.783300 | − | 0.621644i | \(-0.213535\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 15.5076 | 0.592082 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 24.0000i | − 0.914991i | ||||||||
\(689\) | −4.68466 | −0.178471 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.6155 | −0.822293 | −0.411147 | − | 0.911569i | \(-0.634872\pi\) | ||||
−0.411147 | + | 0.911569i | \(0.634872\pi\) | |||||||
\(692\) | 58.7386i | 2.23291i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 66.7386 | 2.53336 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.56155i | 0.210659i | ||||||||
\(698\) | 59.8617i | 2.26580i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.9848 | −1.85013 | −0.925066 | − | 0.379806i | \(-0.875991\pi\) | ||||
−0.925066 | + | 0.379806i | \(0.875991\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 54.7386i | − 2.06451i | ||||||||
\(704\) | 2.24621 | 0.0846573 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −57.6155 | −2.16839 | ||||||||
\(707\) | − 4.49242i | − 0.168955i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.12311 | −0.342625 | −0.171313 | − | 0.985217i | \(-0.554801\pi\) | ||||
−0.171313 | + | 0.985217i | \(0.554801\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 70.1080i | 2.62741i | ||||||||
\(713\) | − 14.6307i | − 0.547923i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −22.2462 | −0.831380 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 36.4924i | 1.36189i | ||||||||
\(719\) | −36.0000 | −1.34257 | −0.671287 | − | 0.741198i | \(-0.734258\pi\) | ||||
−0.671287 | + | 0.741198i | \(0.734258\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.63068 | 0.246940 | ||||||||
\(722\) | 18.5616i | 0.690789i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −60.7386 | −2.25733 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.8769i | 0.477578i | 0.971072 | + | 0.238789i | \(0.0767504\pi\) | ||||
−0.971072 | + | 0.238789i | \(0.923250\pi\) | |||||||
\(728\) | − 2.87689i | − 0.106625i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.87689 | 0.180378 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.4384i | 0.607168i | 0.952805 | + | 0.303584i | \(0.0981833\pi\) | ||||
−0.952805 | + | 0.303584i | \(0.901817\pi\) | |||||||
\(734\) | 4.49242 | 0.165818 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.0000 | 0.589768 | ||||||||
\(737\) | 17.7538i | 0.653969i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −48.7386 | −1.79288 | −0.896440 | − | 0.443166i | \(-0.853855\pi\) | ||||
−0.896440 | + | 0.443166i | \(0.853855\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.26137i | 0.193151i | ||||||||
\(743\) | − 18.7386i | − 0.687454i | −0.939070 | − | 0.343727i | \(-0.888311\pi\) | ||||
0.939070 | − | 0.343727i | \(-0.111689\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 31.3693 | 1.14851 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.1231i | 0.406701i | ||||||||
\(749\) | 4.79261 | 0.175118 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.0540 | 0.512837 | 0.256418 | − | 0.966566i | \(-0.417458\pi\) | ||||
0.256418 | + | 0.966566i | \(0.417458\pi\) | |||||||
\(752\) | 85.4773i | 3.11704i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −18.2462 | −0.664488 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 14.4924i | − 0.526736i | −0.964695 | − | 0.263368i | \(-0.915167\pi\) | ||||
0.964695 | − | 0.263368i | \(-0.0848334\pi\) | |||||||
\(758\) | 78.1080i | 2.83701i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.2311 | 1.63962 | 0.819812 | − | 0.572632i | \(-0.194078\pi\) | ||||
0.819812 | + | 0.572632i | \(0.194078\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 0.876894i | − 0.0317457i | ||||||||
\(764\) | −89.4773 | −3.23717 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.98485 | 0.324636 | ||||||||
\(767\) | − 12.0000i | − 0.433295i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.0000 | 1.08183 | 0.540914 | − | 0.841078i | \(-0.318079\pi\) | ||||
0.540914 | + | 0.841078i | \(0.318079\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 89.2311i | 3.21150i | ||||||||
\(773\) | 9.12311i | 0.328135i | 0.986449 | + | 0.164068i | \(0.0524615\pi\) | ||||
−0.986449 | + | 0.164068i | \(0.947538\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 111.093 | 3.98800 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 96.9848i | − 3.47708i | ||||||||
\(779\) | 18.2462 | 0.653738 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.3002 | −0.583267 | ||||||||
\(782\) | 9.75379i | 0.348795i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 52.3153 | 1.86841 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.3693i | 0.405272i | 0.979254 | + | 0.202636i | \(0.0649509\pi\) | ||||
−0.979254 | + | 0.202636i | \(0.935049\pi\) | |||||||
\(788\) | 15.3693i | 0.547509i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.13826 | 0.0760278 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 6.68466i | − 0.237379i | ||||||||
\(794\) | 11.3693 | 0.403482 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −36.4924 | −1.29344 | ||||||||
\(797\) | 4.68466i | 0.165939i | 0.996552 | + | 0.0829696i | \(0.0264404\pi\) | ||||
−0.996552 | + | 0.0829696i | \(0.973560\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.3693 | −0.614482 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.61553i | 0.339536i | ||||||||
\(803\) | − 9.36932i | − 0.330636i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −15.3693 | −0.541361 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 67.2311i | − 2.36518i | ||||||||
\(809\) | −7.50758 | −0.263952 | −0.131976 | − | 0.991253i | \(-0.542132\pi\) | ||||
−0.131976 | + | 0.991253i | \(0.542132\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.24621 | 0.149105 | 0.0745523 | − | 0.997217i | \(-0.476247\pi\) | ||||
0.0745523 | + | 0.997217i | \(0.476247\pi\) | |||||||
\(812\) | 14.2462i | 0.499944i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −42.7386 | −1.49799 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 16.0000i | − 0.559769i | ||||||||
\(818\) | 17.6155i | 0.615912i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.5464 | 1.69428 | 0.847140 | − | 0.531369i | \(-0.178322\pi\) | ||||
0.847140 | + | 0.531369i | \(0.178322\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.7538i | 1.03715i | 0.855032 | + | 0.518576i | \(0.173538\pi\) | ||||
−0.855032 | + | 0.518576i | \(0.826462\pi\) | |||||||
\(824\) | 99.2311 | 3.45688 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.4773 | −0.468934 | ||||||||
\(827\) | 7.12311i | 0.247695i | 0.992301 | + | 0.123847i | \(0.0395233\pi\) | ||||
−0.992301 | + | 0.123847i | \(0.960477\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.738634 | −0.0256538 | −0.0128269 | − | 0.999918i | \(-0.504083\pi\) | ||||
−0.0128269 | + | 0.999918i | \(0.504083\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 1.43845i | − 0.0498692i | ||||||||
\(833\) | 10.6307i | 0.368331i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 36.4924 | 1.26212 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 19.5076i | − 0.673878i | ||||||||
\(839\) | 44.7926 | 1.54641 | 0.773206 | − | 0.634155i | \(-0.218652\pi\) | ||||
0.773206 | + | 0.634155i | \(0.218652\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.7386 | 0.749608 | ||||||||
\(842\) | 100.847i | 3.47540i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −28.4924 | −0.980750 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.75379i | 0.128982i | ||||||||
\(848\) | 36.0000i | 1.23625i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.0540 | −0.893119 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 41.4233i | − 1.41831i | −0.705054 | − | 0.709153i | \(-0.749077\pi\) | ||||
0.705054 | − | 0.709153i | \(-0.250923\pi\) | |||||||
\(854\) | −7.50758 | −0.256904 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 71.7235 | 2.45146 | ||||||||
\(857\) | 2.43845i | 0.0832958i | 0.999132 | + | 0.0416479i | \(0.0132608\pi\) | ||||
−0.999132 | + | 0.0416479i | \(0.986739\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.80776 | −0.129919 | −0.0649596 | − | 0.997888i | \(-0.520692\pi\) | ||||
−0.0649596 | + | 0.997888i | \(0.520692\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 8.98485i | − 0.306025i | ||||||||
\(863\) | 9.36932i | 0.318935i | 0.987203 | + | 0.159468i | \(0.0509778\pi\) | ||||
−0.987203 | + | 0.159468i | \(0.949022\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −24.6307 | −0.836985 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.0000i | 0.407307i | ||||||||
\(869\) | 7.31534 | 0.248156 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.3693 | 0.385235 | ||||||||
\(872\) | − 13.1231i | − 0.444404i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 32.0000 | 1.08242 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.9848i | 1.58657i | 0.608853 | + | 0.793283i | \(0.291630\pi\) | ||||
−0.608853 | + | 0.793283i | \(0.708370\pi\) | |||||||
\(878\) | − 56.4924i | − 1.90653i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.3693 | −0.719951 | −0.359975 | − | 0.932962i | \(-0.617215\pi\) | ||||
−0.359975 | + | 0.932962i | \(0.617215\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 56.1080i | 1.88818i | 0.329684 | + | 0.944091i | \(0.393058\pi\) | ||||
−0.329684 | + | 0.944091i | \(0.606942\pi\) | |||||||
\(884\) | 7.12311 | 0.239576 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.0000 | −0.671913 | ||||||||
\(887\) | 5.56155i | 0.186739i | 0.995632 | + | 0.0933693i | \(0.0297637\pi\) | ||||
−0.995632 | + | 0.0933693i | \(0.970236\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.768944 | 0.0257895 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 70.1080i | − 2.34739i | ||||||||
\(893\) | 56.9848i | 1.90693i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.13826 | 0.138250 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 90.1080i | 3.00694i | ||||||||
\(899\) | 42.7386 | 1.42541 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.31534 | −0.243709 | ||||||||
\(902\) | − 14.2462i | − 0.474347i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 32.0000 | 1.06430 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 2.63068i | − 0.0873504i | −0.999046 | − | 0.0436752i | \(-0.986093\pi\) | ||||
0.999046 | − | 0.0436752i | \(-0.0139067\pi\) | |||||||
\(908\) | − 26.2462i | − 0.871011i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 25.7538i | − 0.852326i | ||||||||
\(914\) | 34.1080 | 1.12819 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 78.1080 | 2.58076 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.94602 | −0.0641934 | −0.0320967 | − | 0.999485i | \(-0.510218\pi\) | ||||
−0.0320967 | + | 0.999485i | \(0.510218\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.6307i | 0.679435i | ||||||||
\(923\) | 10.4384i | 0.343586i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −74.1080 | −2.43534 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 46.7386i | 1.53427i | ||||||||
\(929\) | −39.6695 | −1.30151 | −0.650757 | − | 0.759286i | \(-0.725548\pi\) | ||||
−0.650757 | + | 0.759286i | \(0.725548\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.8769 | 1.14304 | ||||||||
\(932\) | − 126.847i | − 4.15500i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17.7538 | −0.580922 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 27.3693i | − 0.894117i | −0.894505 | − | 0.447058i | \(-0.852472\pi\) | ||||
0.894505 | − | 0.447058i | \(-0.147528\pi\) | |||||||
\(938\) | − 12.7689i | − 0.416921i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.8078 | −1.36289 | −0.681447 | − | 0.731867i | \(-0.738649\pi\) | ||||
−0.681447 | + | 0.731867i | \(0.738649\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 8.68466i | − 0.282811i | ||||||||
\(944\) | −92.2159 | −3.00137 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.4924 | −0.406164 | ||||||||
\(947\) | 60.6004i | 1.96925i | 0.174688 | + | 0.984624i | \(0.444108\pi\) | ||||
−0.174688 | + | 0.984624i | \(0.555892\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.00000 | −0.194768 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 4.49242i | − 0.145600i | ||||||||
\(953\) | − 29.5616i | − 0.957593i | −0.877926 | − | 0.478796i | \(-0.841073\pi\) | ||||
0.877926 | − | 0.478796i | \(-0.158927\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 104.600 | 3.38302 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 66.7386i | − 2.15623i | ||||||||
\(959\) | 0.492423 | 0.0159012 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 27.3693i | 0.882422i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −112.847 | −3.63454 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 7.36932i | − 0.236981i | −0.992955 | − | 0.118491i | \(-0.962194\pi\) | ||||
0.992955 | − | 0.118491i | \(-0.0378056\pi\) | |||||||
\(968\) | 56.1771i | 1.80560i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.4924 | −0.785999 | −0.393000 | − | 0.919539i | \(-0.628563\pi\) | ||||
−0.393000 | + | 0.919539i | \(0.628563\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.45360i | 0.0466003i | ||||||||
\(974\) | 82.1080 | 2.63091 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −51.3693 | −1.64429 | ||||||||
\(977\) | − 43.4773i | − 1.39096i | −0.718545 | − | 0.695481i | \(-0.755192\pi\) | ||||
0.718545 | − | 0.695481i | \(-0.244808\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.6847 | 0.533244 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 70.7386i | − 2.25736i | ||||||||
\(983\) | − 42.7386i | − 1.36315i | −0.731748 | − | 0.681575i | \(-0.761295\pi\) | ||||
0.731748 | − | 0.681575i | \(-0.238705\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −28.4924 | −0.907384 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 23.3693i | − 0.743477i | ||||||||
\(989\) | −7.61553 | −0.242160 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.0540 | 0.319375 | 0.159688 | − | 0.987168i | \(-0.448951\pi\) | ||||
0.159688 | + | 0.987168i | \(0.448951\pi\) | |||||||
\(992\) | 39.3693i | 1.24998i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 11.7235 | 0.371846 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.2462i | 0.894566i | 0.894392 | + | 0.447283i | \(0.147608\pi\) | ||||
−0.894392 | + | 0.447283i | \(0.852392\pi\) | |||||||
\(998\) | − 89.6155i | − 2.83673i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2925.2.c.p.2224.4 | 4 | ||
3.2 | odd | 2 | 2925.2.c.o.2224.1 | 4 | |||
5.2 | odd | 4 | 2925.2.a.x.1.1 | 2 | |||
5.3 | odd | 4 | 585.2.a.l.1.2 | yes | 2 | ||
5.4 | even | 2 | inner | 2925.2.c.p.2224.1 | 4 | ||
15.2 | even | 4 | 2925.2.a.bc.1.2 | 2 | |||
15.8 | even | 4 | 585.2.a.j.1.1 | ✓ | 2 | ||
15.14 | odd | 2 | 2925.2.c.o.2224.4 | 4 | |||
20.3 | even | 4 | 9360.2.a.cw.1.1 | 2 | |||
60.23 | odd | 4 | 9360.2.a.cl.1.1 | 2 | |||
65.38 | odd | 4 | 7605.2.a.bd.1.1 | 2 | |||
195.38 | even | 4 | 7605.2.a.bi.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.a.j.1.1 | ✓ | 2 | 15.8 | even | 4 | ||
585.2.a.l.1.2 | yes | 2 | 5.3 | odd | 4 | ||
2925.2.a.x.1.1 | 2 | 5.2 | odd | 4 | |||
2925.2.a.bc.1.2 | 2 | 15.2 | even | 4 | |||
2925.2.c.o.2224.1 | 4 | 3.2 | odd | 2 | |||
2925.2.c.o.2224.4 | 4 | 15.14 | odd | 2 | |||
2925.2.c.p.2224.1 | 4 | 5.4 | even | 2 | inner | ||
2925.2.c.p.2224.4 | 4 | 1.1 | even | 1 | trivial | ||
7605.2.a.bd.1.1 | 2 | 65.38 | odd | 4 | |||
7605.2.a.bi.1.2 | 2 | 195.38 | even | 4 | |||
9360.2.a.cl.1.1 | 2 | 60.23 | odd | 4 | |||
9360.2.a.cw.1.1 | 2 | 20.3 | even | 4 |