Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2760,2,Mod(1,2760)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2760, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2760.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2760.a (trivial) |
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: | yes |
Analytic conductor: | \(22.0387109579\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.11491\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2760.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.58774 | −1.35604 | −0.678019 | − | 0.735044i | \(-0.737161\pi\) | ||||
−0.678019 | + | 0.735044i | \(0.737161\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.715853 | 0.198542 | 0.0992709 | − | 0.995060i | \(-0.468349\pi\) | ||||
0.0992709 | + | 0.995060i | \(0.468349\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.58774 | −0.385084 | −0.192542 | − | 0.981289i | \(-0.561673\pi\) | ||||
−0.192542 | + | 0.981289i | \(0.561673\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.58774 | −0.782909 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.58774 | 1.03762 | 0.518809 | − | 0.854890i | \(-0.326376\pi\) | ||||
0.518809 | + | 0.854890i | \(0.326376\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.87189 | 0.875017 | 0.437509 | − | 0.899214i | \(-0.355861\pi\) | ||||
0.437509 | + | 0.899214i | \(0.355861\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.58774 | −0.606439 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.15604 | 1.34084 | 0.670422 | − | 0.741980i | \(-0.266113\pi\) | ||||
0.670422 | + | 0.741980i | \(0.266113\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.715853 | 0.114628 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.30359 | 0.672108 | 0.336054 | − | 0.941843i | \(-0.390907\pi\) | ||||
0.336054 | + | 0.941843i | \(0.390907\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.45963 | 1.29008 | 0.645041 | − | 0.764148i | \(-0.276840\pi\) | ||||
0.645041 | + | 0.764148i | \(0.276840\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.17548 | −1.04665 | −0.523326 | − | 0.852133i | \(-0.675309\pi\) | ||||
−0.523326 | + | 0.852133i | \(0.675309\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.87189 | 0.838841 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.58774 | −0.222328 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.30359 | 1.14059 | 0.570293 | − | 0.821441i | \(-0.306830\pi\) | ||||
0.570293 | + | 0.821441i | \(0.306830\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.30359 | −0.299902 | −0.149951 | − | 0.988693i | \(-0.547912\pi\) | ||||
−0.149951 | + | 0.988693i | \(0.547912\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.45963 | 0.827071 | 0.413535 | − | 0.910488i | \(-0.364294\pi\) | ||||
0.413535 | + | 0.910488i | \(0.364294\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.58774 | −0.452013 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.715853 | 0.0887906 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.15604 | −0.752079 | −0.376040 | − | 0.926604i | \(-0.622714\pi\) | ||||
−0.376040 | + | 0.926604i | \(0.622714\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.01945 | −0.120986 | −0.0604930 | − | 0.998169i | \(-0.519267\pi\) | ||||
−0.0604930 | + | 0.998169i | \(0.519267\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.17548 | −0.605744 | −0.302872 | − | 0.953031i | \(-0.597946\pi\) | ||||
−0.302872 | + | 0.953031i | \(0.597946\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.89134 | 1.11286 | 0.556431 | − | 0.830894i | \(-0.312170\pi\) | ||||
0.556431 | + | 0.830894i | \(0.312170\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.01945 | 0.550956 | 0.275478 | − | 0.961307i | \(-0.411164\pi\) | ||||
0.275478 | + | 0.961307i | \(0.411164\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.58774 | −0.172215 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.58774 | 0.599069 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.7438 | 1.66884 | 0.834419 | − | 0.551131i | \(-0.185804\pi\) | ||||
0.834419 | + | 0.551131i | \(0.185804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.56829 | −0.269230 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.87189 | 0.505191 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.45963 | −0.655876 | −0.327938 | − | 0.944699i | \(-0.606354\pi\) | ||||
−0.327938 | + | 0.944699i | \(0.606354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.58774 | 0.556001 | 0.278001 | − | 0.960581i | \(-0.410328\pi\) | ||||
0.278001 | + | 0.960581i | \(0.410328\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.89134 | 0.580491 | 0.290245 | − | 0.956952i | \(-0.406263\pi\) | ||||
0.290245 | + | 0.956952i | \(0.406263\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.58774 | −0.350128 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.412259 | −0.0398545 | −0.0199273 | − | 0.999801i | \(-0.506343\pi\) | ||||
−0.0199273 | + | 0.999801i | \(0.506343\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.14756 | 0.205699 | 0.102849 | − | 0.994697i | \(-0.467204\pi\) | ||||
0.102849 | + | 0.994697i | \(0.467204\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.15604 | 0.774137 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.980553 | 0.0922427 | 0.0461213 | − | 0.998936i | \(-0.485314\pi\) | ||||
0.0461213 | + | 0.998936i | \(0.485314\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.715853 | 0.0661806 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.69641 | 0.522189 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.30359 | 0.388042 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.71585 | −0.240993 | −0.120496 | − | 0.992714i | \(-0.538449\pi\) | ||||
−0.120496 | + | 0.992714i | \(0.538449\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.45963 | 0.744829 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.56829 | −0.224393 | −0.112196 | − | 0.993686i | \(-0.535789\pi\) | ||||
−0.112196 | + | 0.993686i | \(0.535789\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.45963 | −0.551883 | −0.275942 | − | 0.961174i | \(-0.588990\pi\) | ||||
−0.275942 | + | 0.961174i | \(0.588990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.04737 | 0.682569 | 0.341285 | − | 0.939960i | \(-0.389138\pi\) | ||||
0.341285 | + | 0.939960i | \(0.389138\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.17548 | −0.604285 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.58774 | 0.464037 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.87189 | 0.484305 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.58774 | −0.128361 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.87189 | 0.391320 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.7632 | 1.01862 | 0.509308 | − | 0.860584i | \(-0.329901\pi\) | ||||
0.509308 | + | 0.860584i | \(0.329901\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.30359 | 0.658518 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.58774 | −0.282754 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.6072 | −1.30078 | −0.650388 | − | 0.759602i | \(-0.725394\pi\) | ||||
−0.650388 | + | 0.759602i | \(0.725394\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.1755 | −1.17431 | −0.587157 | − | 0.809473i | \(-0.699753\pi\) | ||||
−0.587157 | + | 0.809473i | \(0.699753\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4876 | −0.960581 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.1755 | 1.30583 | 0.652914 | − | 0.757432i | \(-0.273546\pi\) | ||||
0.652914 | + | 0.757432i | \(0.273546\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.58774 | −0.271208 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.30359 | −0.173149 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0668 | −1.11991 | −0.559954 | − | 0.828524i | \(-0.689181\pi\) | ||||
−0.559954 | + | 0.828524i | \(0.689181\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.45963 | 0.477510 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.15604 | 0.599644 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.58774 | −0.260970 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.60719 | 0.333364 | 0.166682 | − | 0.986011i | \(-0.446695\pi\) | ||||
0.166682 | + | 0.986011i | \(0.446695\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.6072 | −0.763522 | −0.381761 | − | 0.924261i | \(-0.624682\pi\) | ||||
−0.381761 | + | 0.924261i | \(0.624682\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.715853 | 0.0512633 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.78267 | −0.696986 | −0.348493 | − | 0.937311i | \(-0.613307\pi\) | ||||
−0.348493 | + | 0.937311i | \(0.613307\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.71585 | 0.192522 | 0.0962608 | − | 0.995356i | \(-0.469312\pi\) | ||||
0.0962608 | + | 0.995356i | \(0.469312\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.15604 | −0.434213 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.0474 | −1.40705 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.30359 | 0.300576 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.4791 | −0.927938 | −0.463969 | − | 0.885851i | \(-0.653575\pi\) | ||||
−0.463969 | + | 0.885851i | \(0.653575\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.01945 | −0.0698514 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.45963 | 0.576942 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.4791 | −1.18656 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.17548 | −0.349727 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.13659 | −0.0764553 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.14756 | −0.545601 | −0.272800 | − | 0.962071i | \(-0.587950\pi\) | ||||
−0.272800 | + | 0.962071i | \(0.587950\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.8106 | 1.24850 | 0.624252 | − | 0.781223i | \(-0.285404\pi\) | ||||
0.624252 | + | 0.781223i | \(0.285404\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.7717 | 1.76912 | 0.884562 | − | 0.466423i | \(-0.154457\pi\) | ||||
0.884562 | + | 0.466423i | \(0.154457\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.74378 | −0.245263 | −0.122632 | − | 0.992452i | \(-0.539133\pi\) | ||||
−0.122632 | + | 0.992452i | \(0.539133\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.17548 | −0.468077 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.89134 | 0.642511 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.6825 | −1.27315 | −0.636577 | − | 0.771213i | \(-0.719650\pi\) | ||||
−0.636577 | + | 0.771213i | \(0.719650\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.7438 | −1.01415 | −0.507073 | − | 0.861903i | \(-0.669273\pi\) | ||||
−0.507073 | + | 0.861903i | \(0.669273\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.87189 | 0.375141 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.01945 | 0.318095 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.6630 | 1.68296 | 0.841478 | − | 0.540291i | \(-0.181686\pi\) | ||||
0.841478 | + | 0.540291i | \(0.181686\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.58774 | −0.0994282 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.35097 | −0.520919 | −0.260459 | − | 0.965485i | \(-0.583874\pi\) | ||||
−0.260459 | + | 0.965485i | \(0.583874\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.2617 | −1.81824 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.58774 | 0.345873 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.12811 | −0.192888 | −0.0964438 | − | 0.995338i | \(-0.530747\pi\) | ||||
−0.0964438 | + | 0.995338i | \(0.530747\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.30359 | 0.510086 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.7438 | 0.963504 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.7632 | 1.75372 | 0.876862 | − | 0.480741i | \(-0.159632\pi\) | ||||
0.876862 | + | 0.480741i | \(0.159632\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.4402 | −0.937924 | −0.468962 | − | 0.883218i | \(-0.655372\pi\) | ||||
−0.468962 | + | 0.883218i | \(0.655372\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.56829 | −0.155440 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.2423 | 1.33641 | 0.668205 | − | 0.743977i | \(-0.267063\pi\) | ||||
0.668205 | + | 0.743977i | \(0.267063\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.87189 | 0.291672 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.0947 | 1.79530 | 0.897651 | − | 0.440707i | \(-0.145272\pi\) | ||||
0.897651 | + | 0.440707i | \(0.145272\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.8998 | −1.42070 | −0.710348 | − | 0.703850i | \(-0.751463\pi\) | ||||
−0.710348 | + | 0.703850i | \(0.751463\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.4402 | −0.911405 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.4791 | −0.851710 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.45963 | −0.378670 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.6546 | −0.622446 | −0.311223 | − | 0.950337i | \(-0.600739\pi\) | ||||
−0.311223 | + | 0.950337i | \(0.600739\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.30359 | −0.134120 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.715853 | 0.0413988 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.3510 | −1.74940 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.58774 | 0.321007 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.45963 | 0.369877 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.56829 | −0.374872 | −0.187436 | − | 0.982277i | \(-0.560018\pi\) | ||||
−0.187436 | + | 0.982277i | \(0.560018\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.89134 | 0.335146 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.8106 | 1.29347 | 0.646735 | − | 0.762715i | \(-0.276134\pi\) | ||||
0.646735 | + | 0.762715i | \(0.276134\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.7632 | 0.721420 | 0.360710 | − | 0.932678i | \(-0.382534\pi\) | ||||
0.360710 | + | 0.932678i | \(0.382534\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.58774 | −0.202146 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.2144 | 1.07919 | 0.539593 | − | 0.841926i | \(-0.318578\pi\) | ||||
0.539593 | + | 0.841926i | \(0.318578\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.412259 | −0.0230100 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.715853 | 0.0397084 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.14756 | 0.118760 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 25.7438 | 1.41930 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.2229 | 0.836724 | 0.418362 | − | 0.908280i | \(-0.362604\pi\) | ||||
0.418362 | + | 0.908280i | \(0.362604\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.15604 | 0.446948 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.15604 | −0.336340 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.2423 | 0.775828 | 0.387914 | − | 0.921696i | \(-0.373196\pi\) | ||||
0.387914 | + | 0.921696i | \(0.373196\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.980553 | 0.0532563 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.04737 | 0.218538 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.0000 | −0.644194 | −0.322097 | − | 0.946707i | \(-0.604388\pi\) | ||||
−0.322097 | + | 0.946707i | \(0.604388\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.4791 | −0.614461 | −0.307230 | − | 0.951635i | \(-0.599402\pi\) | ||||
−0.307230 | + | 0.951635i | \(0.599402\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.715853 | 0.0382094 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.7827 | 0.946476 | 0.473238 | − | 0.880935i | \(-0.343085\pi\) | ||||
0.473238 | + | 0.880935i | \(0.343085\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.01945 | −0.0541066 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.69641 | 0.301486 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.6072 | 1.08761 | 0.543803 | − | 0.839213i | \(-0.316984\pi\) | ||||
0.543803 | + | 0.839213i | \(0.316984\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.0000 | −0.577350 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.17548 | −0.270897 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.7632 | −0.561836 | −0.280918 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280918 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.30359 | 0.224036 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −29.7911 | −1.54668 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.5962 | −0.600429 | −0.300215 | − | 0.953872i | \(-0.597058\pi\) | ||||
−0.300215 | + | 0.953872i | \(0.597058\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.00000 | 0.206010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.919260 | 0.0472192 | 0.0236096 | − | 0.999721i | \(-0.492484\pi\) | ||||
0.0236096 | + | 0.999721i | \(0.492484\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.71585 | −0.139137 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.12811 | −0.159839 | −0.0799195 | − | 0.996801i | \(-0.525466\pi\) | ||||
−0.0799195 | + | 0.996801i | \(0.525466\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.45963 | 0.430027 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.4317 | 0.579610 | 0.289805 | − | 0.957086i | \(-0.406409\pi\) | ||||
0.289805 | + | 0.957086i | \(0.406409\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.58774 | −0.0802955 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.56829 | −0.129553 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.89134 | 0.497687 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.14756 | −0.107783 | −0.0538914 | − | 0.998547i | \(-0.517162\pi\) | ||||
−0.0538914 | + | 0.998547i | \(0.517162\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.6461 | −0.831266 | −0.415633 | − | 0.909532i | \(-0.636440\pi\) | ||||
−0.415633 | + | 0.909532i | \(0.636440\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.48755 | 0.173727 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.26470 | 0.111982 | 0.0559911 | − | 0.998431i | \(-0.482168\pi\) | ||||
0.0559911 | + | 0.998431i | \(0.482168\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.45963 | −0.318630 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.26470 | 0.406679 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.01945 | 0.246395 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.04737 | 0.394081 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.7827 | −0.575621 | −0.287811 | − | 0.957687i | \(-0.592927\pi\) | ||||
−0.287811 | + | 0.957687i | \(0.592927\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.4985 | −0.999037 | −0.499518 | − | 0.866303i | \(-0.666490\pi\) | ||||
−0.499518 | + | 0.866303i | \(0.666490\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.17548 | −0.348884 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.58774 | −0.0770168 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.1755 | −1.12154 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.9193 | −0.814972 | −0.407486 | − | 0.913211i | \(-0.633594\pi\) | ||||
−0.407486 | + | 0.913211i | \(0.633594\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.0753 | 0.820586 | 0.410293 | − | 0.911954i | \(-0.365426\pi\) | ||||
0.410293 | + | 0.911954i | \(0.365426\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.58774 | 0.267912 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.0558 | −1.05267 | −0.526334 | − | 0.850278i | \(-0.676434\pi\) | ||||
−0.526334 | + | 0.850278i | \(0.676434\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.87189 | 0.279614 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.8245 | −0.609311 | −0.304656 | − | 0.952463i | \(-0.598541\pi\) | ||||
−0.304656 | + | 0.952463i | \(0.598541\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.7438 | 0.746327 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.00000 | 0.283790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.5598 | 0.498349 | 0.249174 | − | 0.968459i | \(-0.419841\pi\) | ||||
0.249174 | + | 0.968459i | \(0.419841\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.56829 | −0.120404 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.72433 | −0.314551 | −0.157275 | − | 0.987555i | \(-0.550271\pi\) | ||||
−0.157275 | + | 0.987555i | \(0.550271\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.58774 | −0.0741094 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.81060 | 0.410350 | 0.205175 | − | 0.978725i | \(-0.434224\pi\) | ||||
0.205175 | + | 0.978725i | \(0.434224\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.1087 | −0.655685 | −0.327843 | − | 0.944732i | \(-0.606322\pi\) | ||||
−0.327843 | + | 0.944732i | \(0.606322\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.87189 | 0.225928 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.2757 | −0.521776 | −0.260888 | − | 0.965369i | \(-0.584015\pi\) | ||||
−0.260888 | + | 0.965369i | \(0.584015\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.0863 | 1.01985 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.7632 | 0.588098 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.30359 | 0.380195 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.9582 | −0.500691 | −0.250345 | − | 0.968157i | \(-0.580544\pi\) | ||||
−0.250345 | + | 0.968157i | \(0.580544\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.83852 | 0.266214 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.58774 | −0.163248 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.45963 | −0.293317 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.7717 | 1.12251 | 0.561256 | − | 0.827642i | \(-0.310318\pi\) | ||||
0.561256 | + | 0.827642i | \(0.310318\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.6072 | −0.751003 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.559817 | −0.0252642 | −0.0126321 | − | 0.999920i | \(-0.504021\pi\) | ||||
−0.0126321 | + | 0.999920i | \(0.504021\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.87189 | −0.399570 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.65751 | 0.164062 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.77419 | 0.258488 | 0.129244 | − | 0.991613i | \(-0.458745\pi\) | ||||
0.129244 | + | 0.991613i | \(0.458745\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.1755 | −0.677991 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.69641 | −0.253990 | −0.126995 | − | 0.991903i | \(-0.540533\pi\) | ||||
−0.126995 | + | 0.991903i | \(0.540533\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.58774 | 0.248651 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.4876 | −0.554592 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.3789 | −1.39084 | −0.695422 | − | 0.718601i | \(-0.744783\pi\) | ||||
−0.695422 | + | 0.718601i | \(0.744783\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.5683 | 0.821413 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.89134 | 0.259603 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.1755 | 0.753920 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.1755 | 0.577228 | 0.288614 | − | 0.957445i | \(-0.406806\pi\) | ||||
0.288614 | + | 0.957445i | \(0.406806\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.4596 | −1.06954 | −0.534772 | − | 0.844996i | \(-0.679603\pi\) | ||||
−0.534772 | + | 0.844996i | \(0.679603\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.58774 | −0.156582 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.73530 | −0.336955 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.30359 | −0.0999675 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.08074 | 0.133442 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.412259 | −0.0178235 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.8385 | −1.19687 | −0.598436 | − | 0.801171i | \(-0.704211\pi\) | ||||
−0.598436 | + | 0.801171i | \(0.704211\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.0668 | −0.646579 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.14756 | 0.0919913 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.13659 | 0.0485970 | 0.0242985 | − | 0.999705i | \(-0.492265\pi\) | ||||
0.0242985 | + | 0.999705i | \(0.492265\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.45963 | 0.275690 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −35.4876 | −1.50908 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.15604 | 0.346204 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.4791 | −0.486384 | −0.243192 | − | 0.969978i | \(-0.578195\pi\) | ||||
−0.243192 | + | 0.969978i | \(0.578195\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.05585 | 0.256135 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.5877 | −1.33126 | −0.665632 | − | 0.746280i | \(-0.731838\pi\) | ||||
−0.665632 | + | 0.746280i | \(0.731838\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.980553 | 0.0412522 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.58774 | −0.150671 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.0807 | 0.548373 | 0.274187 | − | 0.961677i | \(-0.411591\pi\) | ||||
0.274187 | + | 0.961677i | \(0.411591\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.5823 | −1.82386 | −0.911931 | − | 0.410343i | \(-0.865409\pi\) | ||||
−0.911931 | + | 0.410343i | \(0.865409\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.60719 | 0.192468 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.52645 | 0.313330 | 0.156665 | − | 0.987652i | \(-0.449926\pi\) | ||||
0.156665 | + | 0.987652i | \(0.449926\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.6072 | −0.440820 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.0085 | −0.747118 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.715853 | 0.0295969 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.95815 | 0.287194 | 0.143597 | − | 0.989636i | \(-0.454133\pi\) | ||||
0.143597 | + | 0.989636i | \(0.454133\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.78267 | −0.402405 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.00000 | 0.246390 | 0.123195 | − | 0.992382i | \(-0.460686\pi\) | ||||
0.123195 | + | 0.992382i | \(0.460686\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.69641 | 0.233530 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.71585 | 0.111152 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.5962 | 1.20927 | 0.604634 | − | 0.796503i | \(-0.293319\pi\) | ||||
0.604634 | + | 0.796503i | \(0.293319\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.7771 | −0.439609 | −0.219804 | − | 0.975544i | \(-0.570542\pi\) | ||||
−0.219804 | + | 0.975544i | \(0.570542\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.15604 | −0.250693 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.0000 | −0.447214 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.28415 | −0.214477 | −0.107238 | − | 0.994233i | \(-0.534201\pi\) | ||||
−0.107238 | + | 0.994233i | \(0.534201\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.0474 | −0.812360 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.13659 | −0.207804 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.9472 | −1.37111 | −0.685557 | − | 0.728019i | \(-0.740441\pi\) | ||||
−0.685557 | + | 0.728019i | \(0.740441\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.30359 | 0.173538 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.37041 | 0.0551707 | 0.0275854 | − | 0.999619i | \(-0.491218\pi\) | ||||
0.0275854 | + | 0.999619i | \(0.491218\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.35097 | 0.255267 | 0.127633 | − | 0.991821i | \(-0.459262\pi\) | ||||
0.127633 | + | 0.991821i | \(0.459262\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −56.4846 | −2.26301 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.9497 | −0.516337 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.57926 | 0.222107 | 0.111053 | − | 0.993814i | \(-0.464578\pi\) | ||||
0.111053 | + | 0.993814i | \(0.464578\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.4791 | −0.535745 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.71585 | −0.107775 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.20341 | 0.166545 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.01945 | −0.0403287 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.0947 | −1.03068 | −0.515340 | − | 0.856986i | \(-0.672334\pi\) | ||||
−0.515340 | + | 0.856986i | \(0.672334\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.0753 | −1.22549 | −0.612745 | − | 0.790281i | \(-0.709935\pi\) | ||||
−0.612745 | + | 0.790281i | \(0.709935\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.45963 | 0.333098 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.86341 | −0.112572 | −0.0562862 | − | 0.998415i | \(-0.517926\pi\) | ||||
−0.0562862 | + | 0.998415i | \(0.517926\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.4791 | −0.685059 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.2313 | 0.596048 | 0.298024 | − | 0.954558i | \(-0.403672\pi\) | ||||
0.298024 | + | 0.954558i | \(0.403672\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.56829 | −0.100352 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.17548 | −0.201915 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.7019 | 0.806433 | 0.403216 | − | 0.915105i | \(-0.367892\pi\) | ||||
0.403216 | + | 0.915105i | \(0.367892\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.9472 | 1.32039 | 0.660196 | − | 0.751093i | \(-0.270473\pi\) | ||||
0.660196 | + | 0.751093i | \(0.270473\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.13659 | −0.0441415 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.58774 | 0.216358 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.14756 | −0.315003 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.0558 | −1.69823 | −0.849114 | − | 0.528209i | \(-0.822864\pi\) | ||||
−0.849114 | + | 0.528209i | \(0.822864\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28.0085 | −1.07645 | −0.538227 | − | 0.842800i | \(-0.680906\pi\) | ||||
−0.538227 | + | 0.842800i | \(0.680906\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.1755 | 0.889393 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.8106 | 0.720824 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.90526 | −0.149430 | −0.0747152 | − | 0.997205i | \(-0.523805\pi\) | ||||
−0.0747152 | + | 0.997205i | \(0.523805\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.45963 | −0.246810 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.7717 | 1.02140 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.94415 | 0.226454 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 48.4068 | 1.84148 | 0.920741 | − | 0.390174i | \(-0.127585\pi\) | ||||
0.920741 | + | 0.390174i | \(0.127585\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.04737 | 0.305254 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.83299 | −0.258818 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.74378 | −0.141603 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.2144 | −0.725717 | −0.362858 | − | 0.931844i | \(-0.618199\pi\) | ||||
−0.362858 | + | 0.931844i | \(0.618199\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.17548 | −0.270244 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20.0474 | −0.753959 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.4596 | 0.543043 | 0.271521 | − | 0.962432i | \(-0.412473\pi\) | ||||
0.271521 | + | 0.962432i | \(0.412473\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.89134 | 0.370954 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.87189 | 0.182454 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19.6825 | −0.735056 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.2338 | 1.27671 | 0.638353 | − | 0.769744i | \(-0.279616\pi\) | ||||
0.638353 | + | 0.769744i | \(0.279616\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.1366 | −0.787168 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.7438 | −0.585517 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.58774 | 0.207524 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.4512 | 0.832667 | 0.416334 | − | 0.909212i | \(-0.363315\pi\) | ||||
0.416334 | + | 0.909212i | \(0.363315\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.4317 | −0.496790 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.27567 | −0.194861 | −0.0974306 | − | 0.995242i | \(-0.531062\pi\) | ||||
−0.0974306 | + | 0.995242i | \(0.531062\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.87189 | 0.216588 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.34544 | −0.123064 | −0.0615320 | − | 0.998105i | \(-0.519599\pi\) | ||||
−0.0615320 | + | 0.998105i | \(0.519599\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.1366 | −0.481935 | −0.240967 | − | 0.970533i | \(-0.577465\pi\) | ||||
−0.240967 | + | 0.970533i | \(0.577465\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00000 | 0.219823 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.01945 | 0.183652 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.47908 | 0.0540443 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.2453 | 0.410345 | 0.205173 | − | 0.978726i | \(-0.434224\pi\) | ||||
0.205173 | + | 0.978726i | \(0.434224\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.6630 | 0.971655 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.2926 | −0.628511 | −0.314256 | − | 0.949338i | \(-0.601755\pi\) | ||||
−0.314256 | + | 0.949338i | \(0.601755\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.6964 | −0.423994 | −0.211997 | − | 0.977270i | \(-0.567997\pi\) | ||||
−0.211997 | + | 0.977270i | \(0.567997\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.70488 | −0.278936 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.58774 | −0.0574049 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.64903 | −0.0595432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.5653 | −1.35464 | −0.677320 | − | 0.735688i | \(-0.736859\pi\) | ||||
−0.677320 | + | 0.735688i | \(0.736859\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.35097 | −0.300753 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.7827 | 1.21508 | 0.607539 | − | 0.794290i | \(-0.292157\pi\) | ||||
0.607539 | + | 0.794290i | \(0.292157\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.87189 | 0.175003 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −29.2617 | −1.04976 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.58774 | 0.199690 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.7632 | 0.455539 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.6406 | −1.37739 | −0.688695 | − | 0.725051i | \(-0.741816\pi\) | ||||
−0.688695 | + | 0.725051i | \(0.741816\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.12811 | −0.111364 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.51797 | −0.125085 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.62414 | 0.164208 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.30359 | 0.294498 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.7353 | −1.19497 | −0.597483 | − | 0.801882i | \(-0.703832\pi\) | ||||
−0.597483 | + | 0.801882i | \(0.703832\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.3928 | 0.403049 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.7438 | 0.556279 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.58774 | −0.126451 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.7632 | 1.01251 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.0474 | 1.33767 | 0.668837 | − | 0.743409i | \(-0.266792\pi\) | ||||
0.668837 | + | 0.743409i | \(0.266792\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.1421 | 0.847744 | 0.423872 | − | 0.905722i | \(-0.360671\pi\) | ||||
0.423872 | + | 0.905722i | \(0.360671\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.4402 | −0.541511 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.6072 | −0.581724 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.56829 | −0.0897435 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.18645 | −0.146108 | −0.0730541 | − | 0.997328i | \(-0.523275\pi\) | ||||
−0.0730541 | + | 0.997328i | \(0.523275\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.59622 | 0.334503 | 0.167252 | − | 0.985914i | \(-0.446511\pi\) | ||||
0.167252 | + | 0.985914i | \(0.446511\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.2897 | −1.26192 | −0.630958 | − | 0.775817i | \(-0.717338\pi\) | ||||
−0.630958 | + | 0.775817i | \(0.717338\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −49.9248 | −1.73396 | −0.866980 | − | 0.498343i | \(-0.833942\pi\) | ||||
−0.866980 | + | 0.498343i | \(0.833942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.2423 | 0.771577 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.32304 | −0.323024 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.1755 | −0.525169 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.87189 | 0.168397 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 49.3091 | 1.70234 | 0.851170 | − | 0.524890i | \(-0.175894\pi\) | ||||
0.851170 | + | 0.524890i | \(0.175894\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.22285 | 0.0766502 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30.0947 | 1.03652 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.4876 | −0.429585 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 39.4652 | 1.35604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.8998 | −0.820239 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.15604 | 0.279585 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.2982 | 0.968910 | 0.484455 | − | 0.874816i | \(-0.339018\pi\) | ||||
0.484455 | + | 0.874816i | \(0.339018\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.8634 | −0.712681 | −0.356340 | − | 0.934356i | \(-0.615976\pi\) | ||||
−0.356340 | + | 0.934356i | \(0.615976\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.77419 | −0.197013 | −0.0985065 | − | 0.995136i | \(-0.531407\pi\) | ||||
−0.0985065 | + | 0.995136i | \(0.531407\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.4402 | −0.526200 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.6072 | −0.429154 | −0.214577 | − | 0.976707i | \(-0.568837\pi\) | ||||
−0.214577 | + | 0.976707i | \(0.568837\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.1755 | 0.583984 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.4791 | −0.491735 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.40682 | −0.149319 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.45963 | −0.218625 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.58774 | −0.121288 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.16451 | 0.0730904 | 0.0365452 | − | 0.999332i | \(-0.488365\pi\) | ||||
0.0365452 | + | 0.999332i | \(0.488365\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.6546 | −0.359369 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.4288 | 1.09255 | 0.546276 | − | 0.837605i | \(-0.316045\pi\) | ||||
0.546276 | + | 0.837605i | \(0.316045\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.82452 | −0.162358 | −0.0811790 | − | 0.996700i | \(-0.525869\pi\) | ||||
−0.0811790 | + | 0.996700i | \(0.525869\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.30359 | −0.0774345 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −47.7996 | −1.60495 | −0.802477 | − | 0.596683i | \(-0.796485\pi\) | ||||
−0.802477 | + | 0.596683i | \(0.796485\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.74378 | 0.326796 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.715853 | 0.0239016 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27.2229 | 0.907933 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.1840 | −0.439221 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30.3510 | −1.01002 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.0668 | −0.500838 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.6266 | 0.718101 | 0.359050 | − | 0.933318i | \(-0.383101\pi\) | ||||
0.359050 | + | 0.933318i | \(0.383101\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.58774 | 0.185334 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.3510 | 1.53568 | 0.767838 | − | 0.640644i | \(-0.221333\pi\) | ||||
0.767838 | + | 0.640644i | \(0.221333\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.45963 | 0.213549 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.21438 | 0.304286 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.8106 | 1.67609 | 0.838043 | − | 0.545603i | \(-0.183700\pi\) | ||||
0.838043 | + | 0.545603i | \(0.183700\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.56829 | −0.216433 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.729774 | −0.0240208 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.15604 | 0.268169 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.89134 | 0.193497 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.91078 | 0.292353 | 0.146177 | − | 0.989259i | \(-0.453303\pi\) | ||||
0.146177 | + | 0.989259i | \(0.453303\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.8106 | 0.746785 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.81355 | 0.124583 | 0.0622916 | − | 0.998058i | \(-0.480159\pi\) | ||||
0.0622916 | + | 0.998058i | \(0.480159\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.7632 | 0.416512 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37.4876 | −1.22206 | −0.611030 | − | 0.791608i | \(-0.709244\pi\) | ||||
−0.611030 | + | 0.791608i | \(0.709244\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.30359 | 0.140144 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.58774 | −0.116709 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.6461 | 1.12585 | 0.562923 | − | 0.826509i | \(-0.309677\pi\) | ||||
0.562923 | + | 0.826509i | \(0.309677\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.70488 | −0.120266 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.2144 | 0.623069 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.3230 | 0.431576 | 0.215788 | − | 0.976440i | \(-0.430768\pi\) | ||||
0.215788 | + | 0.976440i | \(0.430768\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.60719 | 0.149085 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 23.1755 | 0.748375 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.26470 | −0.234345 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.412259 | −0.0132848 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.6072 | −0.341457 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.9332 | 0.737481 | 0.368741 | − | 0.929532i | \(-0.379789\pi\) | ||||
0.368741 | + | 0.929532i | \(0.379789\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.5653 | 1.26971 | 0.634856 | − | 0.772630i | \(-0.281059\pi\) | ||||
0.634856 | + | 0.772630i | \(0.281059\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.8719 | −0.925590 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.715853 | 0.0229256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.1142 | −1.50732 | −0.753658 | − | 0.657267i | \(-0.771713\pi\) | ||||
−0.753658 | + | 0.657267i | \(0.771713\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.14756 | 0.0685663 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −47.3006 | −1.50866 | −0.754328 | − | 0.656498i | \(-0.772037\pi\) | ||||
−0.754328 | + | 0.656498i | \(0.772037\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.78267 | −0.311702 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 25.7438 | 0.819433 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.45963 | 0.269001 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.3983 | −0.584442 | −0.292221 | − | 0.956351i | \(-0.594394\pi\) | ||||
−0.292221 | + | 0.956351i | \(0.594394\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.2229 | 0.483083 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.71585 | 0.0860983 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.4178 | −0.551627 | −0.275813 | − | 0.961211i | \(-0.588947\pi\) | ||||
−0.275813 | + | 0.961211i | \(0.588947\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.15604 | 0.258046 |
(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 | 2760.2.a.t.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 8280.2.a.bh.1.1 | 3 | |||
4.3 | odd | 2 | 5520.2.a.ca.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.t.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
5520.2.a.ca.1.3 | 3 | 4.3 | odd | 2 | |||
8280.2.a.bh.1.1 | 3 | 3.2 | odd | 2 |