Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, 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("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3864) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-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 | ||||||||
\(5\) | 3.37228 | 1.50813 | 0.754065 | − | 0.656800i | \(-0.228090\pi\) | ||||
0.754065 | + | 0.656800i | \(0.228090\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.37228 | 0.715270 | 0.357635 | − | 0.933862i | \(-0.383583\pi\) | ||||
0.357635 | + | 0.933862i | \(0.383583\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.37228 | 1.49000 | 0.745001 | − | 0.667063i | \(-0.232449\pi\) | ||||
0.745001 | + | 0.667063i | \(0.232449\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.37228 | 0.870719 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.62772 | −0.373424 | −0.186712 | − | 0.982415i | \(-0.559783\pi\) | ||||
−0.186712 | + | 0.982415i | \(0.559783\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.37228 | 1.27446 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.37228 | 0.997608 | 0.498804 | − | 0.866715i | \(-0.333773\pi\) | ||||
0.498804 | + | 0.866715i | \(0.333773\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.37228 | 0.412961 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.37228 | −0.570020 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.62772 | −0.431994 | −0.215997 | − | 0.976394i | \(-0.569300\pi\) | ||||
−0.215997 | + | 0.976394i | \(0.569300\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.37228 | 0.860253 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.74456 | −0.897150 | −0.448575 | − | 0.893745i | \(-0.648068\pi\) | ||||
−0.448575 | + | 0.893745i | \(0.648068\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.37228 | −0.514268 | −0.257134 | − | 0.966376i | \(-0.582778\pi\) | ||||
−0.257134 | + | 0.966376i | \(0.582778\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.37228 | 0.502710 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.74456 | −0.546201 | −0.273100 | − | 0.961986i | \(-0.588049\pi\) | ||||
−0.273100 | + | 0.961986i | \(0.588049\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.11684 | 0.977574 | 0.488787 | − | 0.872403i | \(-0.337440\pi\) | ||||
0.488787 | + | 0.872403i | \(0.337440\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.00000 | 1.07872 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.62772 | −0.215597 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.62772 | −0.472289 | −0.236144 | − | 0.971718i | \(-0.575884\pi\) | ||||
−0.236144 | + | 0.971718i | \(0.575884\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.37228 | −1.07196 | −0.535980 | − | 0.844230i | \(-0.680058\pi\) | ||||
−0.535980 | + | 0.844230i | \(0.680058\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 18.1168 | 2.24712 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.25544 | −0.148993 | −0.0744965 | − | 0.997221i | \(-0.523735\pi\) | ||||
−0.0744965 | + | 0.997221i | \(0.523735\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.0000 | 1.40449 | 0.702247 | − | 0.711934i | \(-0.252180\pi\) | ||||
0.702247 | + | 0.711934i | \(0.252180\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.37228 | 0.735808 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.37228 | −0.270347 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.74456 | −0.983840 | −0.491920 | − | 0.870640i | \(-0.663705\pi\) | ||||
−0.491920 | + | 0.870640i | \(0.663705\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.74456 | 0.959840 | 0.479920 | − | 0.877312i | \(-0.340666\pi\) | ||||
0.479920 | + | 0.877312i | \(0.340666\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.4891 | 1.46310 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.37228 | 0.575969 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.48913 | −0.793846 | −0.396923 | − | 0.917852i | \(-0.629922\pi\) | ||||
−0.396923 | + | 0.917852i | \(0.629922\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.37228 | −0.563168 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.00000 | 0.622171 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.48913 | −0.563172 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.1168 | −1.23028 | −0.615140 | − | 0.788418i | \(-0.710900\pi\) | ||||
−0.615140 | + | 0.788418i | \(0.710900\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.37228 | 0.238423 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.11684 | −0.509145 | −0.254573 | − | 0.967054i | \(-0.581935\pi\) | ||||
−0.254573 | + | 0.967054i | \(0.581935\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.00000 | −0.689730 | −0.344865 | − | 0.938652i | \(-0.612075\pi\) | ||||
−0.344865 | + | 0.938652i | \(0.612075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.37228 | −0.329101 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.4891 | −1.69074 | −0.845369 | − | 0.534183i | \(-0.820619\pi\) | ||||
−0.845369 | + | 0.534183i | \(0.820619\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.62772 | 0.443255 | 0.221628 | − | 0.975131i | \(-0.428863\pi\) | ||||
0.221628 | + | 0.975131i | \(0.428863\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.62772 | −0.249412 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.3723 | −1.25796 | −0.628979 | − | 0.777422i | \(-0.716527\pi\) | ||||
−0.628979 | + | 0.777422i | \(0.716527\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.37228 | −0.314467 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.37228 | 0.496668 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.00000 | −0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.37228 | −0.488389 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.74456 | −0.517970 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.62772 | 0.413916 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | 0.0443678 | − | 0.999015i | \(-0.485873\pi\) | ||||
0.0443678 | + | 0.999015i | \(0.485873\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.37228 | −0.296913 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.1168 | 1.14602 | 0.573012 | − | 0.819547i | \(-0.305775\pi\) | ||||
0.573012 | + | 0.819547i | \(0.305775\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.62772 | 0.141141 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.37228 | 0.290240 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.48913 | −0.383532 | −0.191766 | − | 0.981441i | \(-0.561421\pi\) | ||||
−0.191766 | + | 0.981441i | \(0.561421\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.3723 | 0.964584 | 0.482292 | − | 0.876010i | \(-0.339804\pi\) | ||||
0.482292 | + | 0.876010i | \(0.339804\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.74456 | −0.315349 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.7446 | 1.06575 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.1168 | 1.50452 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.88316 | 0.400044 | 0.200022 | − | 0.979791i | \(-0.435899\pi\) | ||||
0.200022 | + | 0.979791i | \(0.435899\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.4891 | 1.50462 | 0.752312 | − | 0.658807i | \(-0.228939\pi\) | ||||
0.752312 | + | 0.658807i | \(0.228939\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.2337 | 1.62521 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.8614 | 1.26588 | 0.632939 | − | 0.774202i | \(-0.281848\pi\) | ||||
0.632939 | + | 0.774202i | \(0.281848\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.11684 | 0.564402 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.37228 | −0.185811 | −0.0929057 | − | 0.995675i | \(-0.529616\pi\) | ||||
−0.0929057 | + | 0.995675i | \(0.529616\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.00000 | 0.622799 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.1168 | −1.47931 | −0.739653 | − | 0.672989i | \(-0.765010\pi\) | ||||
−0.739653 | + | 0.672989i | \(0.765010\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.8614 | 1.22011 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.62772 | −0.124475 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.4891 | 1.17762 | 0.588808 | − | 0.808273i | \(-0.299597\pi\) | ||||
0.588808 | + | 0.808273i | \(0.299597\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.37228 | −0.481699 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.62772 | −0.272676 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.11684 | −0.158220 | −0.0791102 | − | 0.996866i | \(-0.525208\pi\) | ||||
−0.0791102 | + | 0.996866i | \(0.525208\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.37228 | −0.618897 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.86141 | −0.651504 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.48913 | 0.693914 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.8614 | −1.14769 | −0.573846 | − | 0.818964i | \(-0.694549\pi\) | ||||
−0.573846 | + | 0.818964i | \(0.694549\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.23369 | −0.520692 | −0.260346 | − | 0.965515i | \(-0.583837\pi\) | ||||
−0.260346 | + | 0.965515i | \(0.583837\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 18.1168 | 1.29737 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.8614 | −1.34382 | −0.671910 | − | 0.740633i | \(-0.734526\pi\) | ||||
−0.671910 | + | 0.740633i | \(0.734526\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.00000 | −0.0708881 | −0.0354441 | − | 0.999372i | \(-0.511285\pi\) | ||||
−0.0354441 | + | 0.999372i | \(0.511285\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.37228 | −0.377060 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.3723 | −1.35302 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.86141 | −0.267099 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.62772 | 0.387428 | 0.193714 | − | 0.981058i | \(-0.437947\pi\) | ||||
0.193714 | + | 0.981058i | \(0.437947\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.25544 | −0.0860212 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.3723 | −0.775583 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | −0.407307 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.0000 | 0.810885 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.4891 | 1.44551 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.0000 | −0.937509 | −0.468755 | − | 0.883328i | \(-0.655297\pi\) | ||||
−0.468755 | + | 0.883328i | \(0.655297\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.37228 | 0.424819 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.11684 | −0.538734 | −0.269367 | − | 0.963038i | \(-0.586814\pi\) | ||||
−0.269367 | + | 0.963038i | \(0.586814\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.3505 | 1.67521 | 0.837605 | − | 0.546276i | \(-0.183955\pi\) | ||||
0.837605 | + | 0.546276i | \(0.183955\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.37228 | −0.156085 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.7446 | 0.965948 | 0.482974 | − | 0.875635i | \(-0.339556\pi\) | ||||
0.482974 | + | 0.875635i | \(0.339556\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.6277 | −0.823742 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.74456 | −0.568020 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.4891 | −0.872539 | −0.436269 | − | 0.899816i | \(-0.643701\pi\) | ||||
−0.436269 | + | 0.899816i | \(0.643701\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.489125 | −0.0315073 | −0.0157537 | − | 0.999876i | \(-0.505015\pi\) | ||||
−0.0157537 | + | 0.999876i | \(0.505015\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.37228 | 0.215447 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.74456 | −0.556403 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.74456 | 0.554164 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.8614 | 1.19052 | 0.595261 | − | 0.803533i | \(-0.297049\pi\) | ||||
0.595261 | + | 0.803533i | \(0.297049\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.37228 | −0.149144 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.4891 | 0.844722 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.8832 | 0.678873 | 0.339436 | − | 0.940629i | \(-0.389764\pi\) | ||||
0.339436 | + | 0.940629i | \(0.389764\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.62772 | 0.163278 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.37228 | 0.332536 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.00000 | −0.0616626 | −0.0308313 | − | 0.999525i | \(-0.509815\pi\) | ||||
−0.0308313 | + | 0.999525i | \(0.509815\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.0000 | 1.47431 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.48913 | −0.458327 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.510875 | 0.0311486 | 0.0155743 | − | 0.999879i | \(-0.495042\pi\) | ||||
0.0155743 | + | 0.999879i | \(0.495042\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.48913 | 0.0904579 | 0.0452290 | − | 0.998977i | \(-0.485598\pi\) | ||||
0.0452290 | + | 0.998977i | \(0.485598\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.37228 | −0.325145 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.1168 | 0.911580 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.883156 | 0.0530637 | 0.0265319 | − | 0.999648i | \(-0.491554\pi\) | ||||
0.0265319 | + | 0.999648i | \(0.491554\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.3723 | 0.797723 | 0.398862 | − | 0.917011i | \(-0.369405\pi\) | ||||
0.398862 | + | 0.917011i | \(0.369405\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.25544 | −0.312403 | −0.156202 | − | 0.987725i | \(-0.549925\pi\) | ||||
−0.156202 | + | 0.987725i | \(0.549925\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.48913 | −0.325148 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.74456 | 0.339091 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.1168 | −0.710302 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.2337 | −0.714700 | −0.357350 | − | 0.933971i | \(-0.616320\pi\) | ||||
−0.357350 | + | 0.933971i | \(0.616320\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.2337 | −0.712273 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.37228 | 0.137654 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.37228 | −0.310687 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.37228 | 0.194375 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.11684 | −0.293955 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −28.2337 | −1.61666 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.6277 | 1.17729 | 0.588643 | − | 0.808393i | \(-0.299662\pi\) | ||||
0.588643 | + | 0.808393i | \(0.299662\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.00000 | −0.398216 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.3723 | −1.26862 | −0.634308 | − | 0.773081i | \(-0.718715\pi\) | ||||
−0.634308 | + | 0.773081i | \(0.718715\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.0951 | 1.81412 | 0.907061 | − | 0.420999i | \(-0.138320\pi\) | ||||
0.907061 | + | 0.420999i | \(0.138320\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.37228 | −0.190007 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.1168 | 1.57920 | 0.789600 | − | 0.613622i | \(-0.210288\pi\) | ||||
0.789600 | + | 0.613622i | \(0.210288\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.7446 | 0.713559 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.4891 | −0.976148 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.51087 | −0.362275 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 34.2337 | 1.89894 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.62772 | 0.255913 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.74456 | 0.206444 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.37228 | −0.130392 | −0.0651962 | − | 0.997872i | \(-0.520767\pi\) | ||||
−0.0651962 | + | 0.997872i | \(0.520767\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.62772 | −0.143998 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.4891 | 0.736990 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.2554 | −1.04891 | −0.524455 | − | 0.851438i | \(-0.675731\pi\) | ||||
−0.524455 | + | 0.851438i | \(0.675731\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.3723 | −0.726283 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.2337 | 0.770797 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.37228 | −0.181558 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.62772 | 0.355795 | 0.177897 | − | 0.984049i | \(-0.443071\pi\) | ||||
0.177897 | + | 0.984049i | \(0.443071\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.4891 | −1.68557 | −0.842787 | − | 0.538247i | \(-0.819087\pi\) | ||||
−0.842787 | + | 0.538247i | \(0.819087\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.37228 | 0.286751 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.1168 | 1.49651 | 0.748254 | − | 0.663412i | \(-0.230892\pi\) | ||||
0.748254 | + | 0.663412i | \(0.230892\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.23369 | −0.224701 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.00000 | −0.211702 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.8614 | 1.31213 | 0.656067 | − | 0.754702i | \(-0.272219\pi\) | ||||
0.656067 | + | 0.754702i | \(0.272219\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.3505 | −0.860554 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.37228 | −0.281972 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 40.4674 | 2.11816 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.51087 | −0.183266 | −0.0916331 | − | 0.995793i | \(-0.529209\pi\) | ||||
−0.0916331 | + | 0.995793i | \(0.529209\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.74456 | −0.299050 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.11684 | −0.369488 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.4891 | −1.00911 | −0.504554 | − | 0.863380i | \(-0.668343\pi\) | ||||
−0.504554 | + | 0.863380i | \(0.668343\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.62772 | 0.238974 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 28.8614 | 1.48644 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.8614 | −0.763379 | −0.381690 | − | 0.924291i | \(-0.624658\pi\) | ||||
−0.381690 | + | 0.924291i | \(0.624658\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.00000 | 0.0512316 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.2337 | −1.34048 | −0.670239 | − | 0.742145i | \(-0.733809\pi\) | ||||
−0.670239 | + | 0.742145i | \(0.733809\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | −0.407718 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.37228 | −0.171423 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.4891 | 0.988138 | 0.494069 | − | 0.869423i | \(-0.335509\pi\) | ||||
0.494069 | + | 0.869423i | \(0.335509\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.1168 | 0.661657 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −29.4891 | −1.48376 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.0000 | 0.702640 | 0.351320 | − | 0.936255i | \(-0.385733\pi\) | ||||
0.351320 | + | 0.936255i | \(0.385733\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.62772 | 0.0814879 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.1168 | 0.655024 | 0.327512 | − | 0.944847i | \(-0.393790\pi\) | ||||
0.327512 | + | 0.944847i | \(0.393790\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.2337 | 1.60567 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.37228 | 0.167570 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.23369 | −0.308992 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.2337 | −0.901598 | −0.450799 | − | 0.892626i | \(-0.648861\pi\) | ||||
−0.450799 | + | 0.892626i | \(0.648861\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.48913 | −0.221432 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.62772 | 0.178508 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.4891 | 1.44756 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.3723 | 0.556903 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.2554 | 1.13610 | 0.568051 | − | 0.822993i | \(-0.307698\pi\) | ||||
0.568051 | + | 0.822993i | \(0.307698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.6277 | 1.00533 | 0.502667 | − | 0.864480i | \(-0.332352\pi\) | ||||
0.502667 | + | 0.864480i | \(0.332352\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.74456 | −0.182067 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 25.4891 | 1.23640 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.37228 | 0.405163 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.7446 | 0.615313 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.5109 | −0.747133 | −0.373566 | − | 0.927603i | \(-0.621865\pi\) | ||||
−0.373566 | + | 0.927603i | \(0.621865\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.4891 | −1.36910 | −0.684550 | − | 0.728966i | \(-0.740001\pi\) | ||||
−0.684550 | + | 0.728966i | \(0.740001\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 18.1168 | 0.868636 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.62772 | 0.0778643 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.7446 | −0.894629 | −0.447315 | − | 0.894377i | \(-0.647620\pi\) | ||||
−0.447315 | + | 0.894377i | \(0.647620\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.3505 | −1.06191 | −0.530953 | − | 0.847401i | \(-0.678166\pi\) | ||||
−0.530953 | + | 0.847401i | \(0.678166\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.2554 | −1.19722 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.88316 | 0.230965 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.4674 | −1.81539 | −0.907694 | − | 0.419633i | \(-0.862159\pi\) | ||||
−0.907694 | + | 0.419633i | \(0.862159\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.6277 | −0.641704 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.4891 | 0.868695 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.1168 | −0.849331 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.2337 | −1.04005 | −0.520024 | − | 0.854152i | \(-0.674077\pi\) | ||||
−0.520024 | + | 0.854152i | \(0.674077\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.00000 | 0.186704 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.9783 | 0.604457 | 0.302229 | − | 0.953235i | \(-0.402269\pi\) | ||||
0.302229 | + | 0.953235i | \(0.402269\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.2337 | 1.17271 | 0.586354 | − | 0.810055i | \(-0.300563\pi\) | ||||
0.586354 | + | 0.810055i | \(0.300563\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20.2337 | 0.938315 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.8832 | −1.10518 | −0.552590 | − | 0.833453i | \(-0.686361\pi\) | ||||
−0.552590 | + | 0.833453i | \(0.686361\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.8614 | 0.730855 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.00000 | −0.367840 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.3723 | −0.475913 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.11684 | 0.325858 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.7228 | −1.17531 | −0.587653 | − | 0.809113i | \(-0.699948\pi\) | ||||
−0.587653 | + | 0.809113i | \(0.699948\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.1168 | −0.643673 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −40.8614 | −1.85542 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.627719 | 0.0284446 | 0.0142223 | − | 0.999899i | \(-0.495473\pi\) | ||||
0.0142223 | + | 0.999899i | \(0.495473\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.37228 | −0.107278 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.76631 | 0.260230 | 0.130115 | − | 0.991499i | \(-0.458465\pi\) | ||||
0.130115 | + | 0.991499i | \(0.458465\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.4891 | 0.967822 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.00000 | 0.359573 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.25544 | 0.0563141 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.7446 | 0.839122 | 0.419561 | − | 0.907727i | \(-0.362184\pi\) | ||||
0.419561 | + | 0.907727i | \(0.362184\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.1168 | −0.854078 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.2337 | 1.61558 | 0.807790 | − | 0.589470i | \(-0.200663\pi\) | ||||
0.807790 | + | 0.589470i | \(0.200663\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.2554 | −0.767857 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.8614 | 0.704430 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.1168 | 1.37923 | 0.689615 | − | 0.724176i | \(-0.257780\pi\) | ||||
0.689615 | + | 0.724176i | \(0.257780\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0000 | −0.530849 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.62772 | −0.0718655 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −23.6060 | −1.04020 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.88316 | −0.390681 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.4891 | 0.679897 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.4891 | −0.503348 | −0.251674 | − | 0.967812i | \(-0.580981\pi\) | ||||
−0.251674 | + | 0.967812i | \(0.580981\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 42.6060 | 1.86303 | 0.931514 | − | 0.363704i | \(-0.118488\pi\) | ||||
0.931514 | + | 0.363704i | \(0.118488\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.37228 | −0.278109 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.0000 | 1.04546 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.62772 | −0.157430 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.8614 | −1.33676 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −58.9783 | −2.54985 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.11684 | −0.0913486 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.37228 | 0.102181 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.0951 | −1.29389 | −0.646945 | − | 0.762537i | \(-0.723954\pi\) | ||||
−0.646945 | + | 0.762537i | \(0.723954\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.00000 | −0.257485 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.6060 | 0.668486 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.25544 | −0.395734 | −0.197867 | − | 0.980229i | \(-0.563401\pi\) | ||||
−0.197867 | + | 0.980229i | \(0.563401\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.37228 | −0.357320 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.74456 | −0.372531 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.74456 | 0.371857 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.86141 | −0.376146 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.2337 | −1.62001 | −0.810007 | − | 0.586421i | \(-0.800537\pi\) | ||||
−0.810007 | + | 0.586421i | \(0.800537\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.1168 | −0.766261 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.48913 | 0.400631 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.6277 | 0.700775 | 0.350387 | − | 0.936605i | \(-0.386050\pi\) | ||||
0.350387 | + | 0.936605i | \(0.386050\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −45.0951 | −1.89716 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.00000 | −0.0419222 | −0.0209611 | − | 0.999780i | \(-0.506673\pi\) | ||||
−0.0209611 | + | 0.999780i | \(0.506673\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.8614 | −0.662620 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.37228 | −0.265743 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.4891 | −1.47743 | −0.738716 | − | 0.674017i | \(-0.764567\pi\) | ||||
−0.738716 | + | 0.674017i | \(0.764567\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.23369 | −0.300622 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.74456 | −0.362786 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.8832 | 0.699229 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.1168 | 0.749039 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.3505 | 1.54162 | 0.770811 | − | 0.637064i | \(-0.219851\pi\) | ||||
0.770811 | + | 0.637064i | \(0.219851\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.76631 | −0.402414 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.8614 | −0.775855 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.8832 | 0.487983 | 0.243991 | − | 0.969777i | \(-0.421543\pi\) | ||||
0.243991 | + | 0.969777i | \(0.421543\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.4891 | −0.553000 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.00000 | −0.0409273 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.744563 | −0.0304220 | −0.0152110 | − | 0.999884i | \(-0.504842\pi\) | ||||
−0.0152110 | + | 0.999884i | \(0.504842\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.9783 | 1.26363 | 0.631815 | − | 0.775120i | \(-0.282310\pi\) | ||||
0.631815 | + | 0.775120i | \(0.282310\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000 | 0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18.1168 | −0.736554 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.25544 | −0.213312 | −0.106656 | − | 0.994296i | \(-0.534014\pi\) | ||||
−0.106656 | + | 0.994296i | \(0.534014\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.37228 | −0.217696 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.1168 | −0.813840 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.3505 | −1.30663 | −0.653313 | − | 0.757088i | \(-0.726621\pi\) | ||||
−0.653313 | + | 0.757088i | \(0.726621\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −19.3723 | −0.781166 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.9783 | 1.16662 | 0.583310 | − | 0.812249i | \(-0.301757\pi\) | ||||
0.583310 | + | 0.812249i | \(0.301757\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.7228 | 0.873114 | 0.436557 | − | 0.899677i | \(-0.356198\pi\) | ||||
0.436557 | + | 0.899677i | \(0.356198\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.48913 | 0.300045 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.2554 | −0.650217 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.86141 | −0.154210 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.5109 | −0.419096 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.7228 | 1.10363 | 0.551814 | − | 0.833967i | \(-0.313936\pi\) | ||||
0.551814 | + | 0.833967i | \(0.313936\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.62772 | 0.223682 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.37228 | 0.133825 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.37228 | 0.212858 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.25544 | −0.0496643 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.51087 | 0.375657 | 0.187828 | − | 0.982202i | \(-0.439855\pi\) | ||||
0.187828 | + | 0.982202i | \(0.439855\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.1168 | −0.675022 | −0.337511 | − | 0.941322i | \(-0.609585\pi\) | ||||
−0.337511 | + | 0.941322i | \(0.609585\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.3723 | −0.447783 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.4674 | 0.804656 | 0.402328 | − | 0.915496i | \(-0.368201\pi\) | ||||
0.402328 | + | 0.915496i | \(0.368201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.60597 | −0.337814 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.00000 | −0.235159 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.8832 | −1.01289 | −0.506443 | − | 0.862273i | \(-0.669040\pi\) | ||||
−0.506443 | + | 0.862273i | \(0.669040\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 44.2337 | 1.72835 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.0000 | 0.468165 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.0000 | −0.623272 | −0.311636 | − | 0.950202i | \(-0.600877\pi\) | ||||
−0.311636 | + | 0.950202i | \(0.600877\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.8832 | −0.734470 | −0.367235 | − | 0.930128i | \(-0.619695\pi\) | ||||
−0.367235 | + | 0.930128i | \(0.619695\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.4891 | 0.834568 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.48913 | 0.212859 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.37228 | −0.208016 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.0000 | −0.541271 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.8614 | −0.766741 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.7446 | 0.606908 | 0.303454 | − | 0.952846i | \(-0.401860\pi\) | ||||
0.303454 | + | 0.952846i | \(0.401860\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.37228 | 0.245269 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.7446 | 0.874145 | 0.437072 | − | 0.899426i | \(-0.356015\pi\) | ||||
0.437072 | + | 0.899426i | \(0.356015\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.1168 | 0.465002 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.11684 | −0.311038 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.9783 | 0.573127 | 0.286563 | − | 0.958061i | \(-0.407487\pi\) | ||||
0.286563 | + | 0.958061i | \(0.407487\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.1386 | −0.578416 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.3505 | 0.967183 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 38.2337 | 1.45659 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.6060 | 1.65885 | 0.829425 | − | 0.558619i | \(-0.188668\pi\) | ||||
0.829425 | + | 0.558619i | \(0.188668\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.37228 | −0.0901155 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 38.3505 | 1.45472 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.9783 | −0.870363 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.7446 | 0.557691 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.35053 | −0.353165 | −0.176582 | − | 0.984286i | \(-0.556504\pi\) | ||||
−0.176582 | + | 0.984286i | \(0.556504\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.27719 | 0.161317 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.6277 | −0.475587 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.11684 | 0.192439 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.4891 | −0.731929 | −0.365965 | − | 0.930629i | \(-0.619261\pi\) | ||||
−0.365965 | + | 0.930629i | \(0.619261\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.74456 | −0.327947 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.00000 | −0.224702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 42.9783 | 1.60730 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.4891 | −0.503761 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.37228 | 0.125765 | 0.0628824 | − | 0.998021i | \(-0.479971\pi\) | ||||
0.0628824 | + | 0.998021i | \(0.479971\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.00000 | 0.260694 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.489125 | −0.0181908 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 34.2337 | 1.27141 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.3505 | −1.23690 | −0.618451 | − | 0.785823i | \(-0.712240\pi\) | ||||
−0.618451 | + | 0.785823i | \(0.712240\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.4891 | −0.498913 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −45.2119 | −1.66994 | −0.834971 | − | 0.550295i | \(-0.814515\pi\) | ||||
−0.834971 | + | 0.550295i | \(0.814515\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.37228 | 0.124388 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.48913 | 0.349536 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.2554 | 0.487609 | 0.243805 | − | 0.969824i | \(-0.421604\pi\) | ||||
0.243805 | + | 0.969824i | \(0.421604\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.74456 | −0.321240 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.6277 | −0.499953 | −0.249976 | − | 0.968252i | \(-0.580423\pi\) | ||||
−0.249976 | + | 0.968252i | \(0.580423\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.4674 | 0.603318 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.74456 | 0.319947 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.4891 | 0.639039 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.9783 | 0.838488 | 0.419244 | − | 0.907874i | \(-0.362295\pi\) | ||||
0.419244 | + | 0.907874i | \(0.362295\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.8614 | 0.687348 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 62.3505 | 2.26917 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.2337 | −0.735406 | −0.367703 | − | 0.929943i | \(-0.619856\pi\) | ||||
−0.367703 | + | 0.929943i | \(0.619856\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.37228 | −0.0861084 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.0951 | 1.01845 | 0.509223 | − | 0.860634i | \(-0.329933\pi\) | ||||
0.509223 | + | 0.860634i | \(0.329933\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.62772 | −0.167535 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.4891 | 0.487700 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.4891 | −0.703712 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.3505 | 0.733859 | 0.366929 | − | 0.930249i | \(-0.380409\pi\) | ||||
0.366929 | + | 0.930249i | \(0.380409\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.8832 | 0.391947 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.6277 | −1.02967 | −0.514834 | − | 0.857290i | \(-0.672146\pi\) | ||||
−0.514834 | + | 0.857290i | \(0.672146\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38.2337 | 1.37339 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.62772 | 0.0942689 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.35053 | 0.335018 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.97825 | −0.106570 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.37228 | 0.191990 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 53.4891 | 1.90911 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.8397 | −0.956730 | −0.478365 | − | 0.878161i | \(-0.658770\pi\) | ||||
−0.478365 | + | 0.878161i | \(0.658770\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.00000 | −0.0356009 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.3723 | 0.475464 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −44.9783 | −1.59722 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 24.0000 | 0.851192 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.6060 | 1.04870 | 0.524349 | − | 0.851504i | \(-0.324309\pi\) | ||||
0.524349 | + | 0.851504i | \(0.324309\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.9783 | −0.529892 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.48913 | −0.264615 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.4674 | 1.00459 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.37228 | 0.118857 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.510875 | 0.0179836 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.2554 | 0.817618 | 0.408809 | − | 0.912620i | \(-0.365944\pi\) | ||||
0.408809 | + | 0.912620i | \(0.365944\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.8614 | −0.381396 | −0.190698 | − | 0.981649i | \(-0.561075\pi\) | ||||
−0.190698 | + | 0.981649i | \(0.561075\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.48913 | 0.0522259 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.00000 | −0.280228 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.48913 | 0.192040 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.37228 | −0.187723 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.2337 | −1.54377 | −0.771883 | − | 0.635764i | \(-0.780685\pi\) | ||||
−0.771883 | + | 0.635764i | \(0.780685\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 55.2337 | 1.92533 | 0.962663 | − | 0.270704i | \(-0.0872564\pi\) | ||||
0.962663 | + | 0.270704i | \(0.0872564\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.1168 | 0.526301 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.6060 | 1.06427 | 0.532137 | − | 0.846658i | \(-0.321389\pi\) | ||||
0.532137 | + | 0.846658i | \(0.321389\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.4674 | −0.919250 | −0.459625 | − | 0.888113i | \(-0.652016\pi\) | ||||
−0.459625 | + | 0.888113i | \(0.652016\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.883156 | 0.0306363 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.00000 | 0.138592 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −64.4674 | −2.23099 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.00000 | 0.207390 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.0000 | 1.45000 | 0.725001 | − | 0.688748i | \(-0.241839\pi\) | ||||
0.725001 | + | 0.688748i | \(0.241839\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.138593 | −0.00477908 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.3723 | 0.460566 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 53.4891 | 1.84008 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.37228 | 0.184594 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.25544 | −0.180366 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.62772 | 0.0900770 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.3505 | 0.491353 | 0.245676 | − | 0.969352i | \(-0.420990\pi\) | ||||
0.245676 | + | 0.969352i | \(0.420990\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.48913 | −0.187724 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.25544 | −0.145363 | −0.0726815 | − | 0.997355i | \(-0.523156\pi\) | ||||
−0.0726815 | + | 0.997355i | \(0.523156\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.1168 | −0.618139 | −0.309069 | − | 0.951039i | \(-0.600018\pi\) | ||||
−0.309069 | + | 0.951039i | \(0.600018\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.74456 | 0.195774 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.7228 | −1.07986 | −0.539929 | − | 0.841711i | \(-0.681549\pi\) | ||||
−0.539929 | + | 0.841711i | \(0.681549\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 52.2337 | 1.77600 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.7446 | −0.703711 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.4891 | 0.728131 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.1168 | −0.410093 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.62772 | −0.156445 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.35053 | 0.0456042 | 0.0228021 | − | 0.999740i | \(-0.492741\pi\) | ||||
0.0228021 | + | 0.999740i | \(0.492741\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.2337 | −0.412632 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.4891 | −0.791369 | −0.395684 | − | 0.918387i | \(-0.629493\pi\) | ||||
−0.395684 | + | 0.918387i | \(0.629493\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.7228 | −0.865642 | −0.432821 | − | 0.901480i | \(-0.642482\pi\) | ||||
−0.432821 | + | 0.901480i | \(0.642482\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.2337 | −0.411231 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45.9565 | 1.54307 | 0.771534 | − | 0.636188i | \(-0.219490\pi\) | ||||
0.771534 | + | 0.636188i | \(0.219490\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.37228 | 0.0794744 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.09509 | 0.203965 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.13859 | −0.238617 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.37228 | −0.179375 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.2337 | 1.07505 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.4674 | 0.948386 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.37228 | 0.112222 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.2337 | −0.672591 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.86141 | 0.161420 | 0.0807102 | − | 0.996738i | \(-0.474281\pi\) | ||||
0.0807102 | + | 0.996738i | \(0.474281\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.11684 | −0.169715 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.1168 | −1.13034 | −0.565171 | − | 0.824974i | \(-0.691190\pi\) | ||||
−0.565171 | + | 0.824974i | \(0.691190\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.7446 | 0.686545 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −28.2337 | −0.933377 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.1168 | −0.433156 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.2337 | 1.52511 | 0.762554 | − | 0.646924i | \(-0.223945\pi\) | ||||
0.762554 | + | 0.646924i | \(0.223945\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.6277 | 0.679706 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.74456 | −0.222000 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.7446 | −0.550558 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.00000 | −0.229910 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.11684 | −0.266305 | −0.133153 | − | 0.991096i | \(-0.542510\pi\) | ||||
−0.133153 | + | 0.991096i | \(0.542510\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.62772 | −0.0533463 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.3723 | −0.732436 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 32.0000 | 1.04651 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.2554 | −1.05374 | −0.526870 | − | 0.849946i | \(-0.676634\pi\) | ||||
−0.526870 | + | 0.849946i | \(0.676634\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.0951 | 1.04738 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.09509 | −0.296492 | −0.148246 | − | 0.988951i | \(-0.547363\pi\) | ||||
−0.148246 | + | 0.988951i | \(0.547363\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.74456 | 0.187069 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.37228 | −0.109700 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.0951 | 1.33541 | 0.667706 | − | 0.744425i | \(-0.267277\pi\) | ||||
0.667706 | + | 0.744425i | \(0.267277\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 64.4674 | 2.09270 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.1168 | 0.911751 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.62772 | −0.117513 | −0.0587567 | − | 0.998272i | \(-0.518714\pi\) | ||||
−0.0587567 | + | 0.998272i | \(0.518714\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −53.4891 | −1.73087 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.7446 | 0.411973 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.48913 | 0.144961 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.4891 | −0.563579 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −24.3940 | −0.785272 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.00000 | −0.128631 | −0.0643157 | − | 0.997930i | \(-0.520486\pi\) | ||||
−0.0643157 | + | 0.997930i | \(0.520486\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.51087 | −0.209159 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 62.2337 | 1.99717 | 0.998587 | − | 0.0531405i | \(-0.0169231\pi\) | ||||
0.998587 | + | 0.0531405i | \(0.0169231\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.3723 | −0.364579 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 34.2337 | 1.09636 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.5109 | 0.496237 | 0.248118 | − | 0.968730i | \(-0.420188\pi\) | ||||
0.248118 | + | 0.968730i | \(0.420188\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.7663 | −0.567814 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.62772 | 0.147752 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.4891 | −0.621607 | −0.310803 | − | 0.950474i | \(-0.600598\pi\) | ||||
−0.310803 | + | 0.950474i | \(0.600598\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −63.6060 | −2.02665 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.74456 | 0.119191 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.37228 | 0.107232 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.3505 | −1.82180 | −0.910900 | − | 0.412628i | \(-0.864611\pi\) | ||||
−0.910900 | + | 0.412628i | \(0.864611\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.37228 | −0.0752821 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.37228 | −0.106909 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.23369 | 0.134082 | 0.0670411 | − | 0.997750i | \(-0.478644\pi\) | ||||
0.0670411 | + | 0.997750i | \(0.478644\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.62772 | −0.0831373 |
(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 | 7728.2.a.bj.1.2 | 2 | ||
4.3 | odd | 2 | 3864.2.a.i.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.i.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
7728.2.a.bj.1.2 | 2 | 1.1 | even | 1 | trivial |