Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5184,2,Mod(1,5184)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5184, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5184.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5184 = 2^{6} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5184.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: | \(41.3944484078\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 288) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5184.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.44949 | 0.547856 | 0.273928 | − | 0.961750i | \(-0.411677\pi\) | ||||
0.273928 | + | 0.961750i | \(0.411677\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.44949 | −1.04006 | −0.520030 | − | 0.854148i | \(-0.674079\pi\) | ||||
−0.520030 | + | 0.854148i | \(0.674079\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.89898 | 1.08138 | 0.540691 | − | 0.841221i | \(-0.318163\pi\) | ||||
0.540691 | + | 0.841221i | \(0.318163\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.89898 | −1.18818 | −0.594089 | − | 0.804400i | \(-0.702487\pi\) | ||||
−0.594089 | + | 0.804400i | \(0.702487\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.550510 | 0.114789 | 0.0573947 | − | 0.998352i | \(-0.481721\pi\) | ||||
0.0573947 | + | 0.998352i | \(0.481721\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.89898 | −1.83819 | −0.919097 | − | 0.394031i | \(-0.871080\pi\) | ||||
−0.919097 | + | 0.394031i | \(0.871080\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.44949 | −1.33797 | −0.668984 | − | 0.743277i | \(-0.733271\pi\) | ||||
−0.668984 | + | 0.743277i | \(0.733271\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.44949 | 0.245008 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.89898 | −1.46298 | −0.731492 | − | 0.681850i | \(-0.761175\pi\) | ||||
−0.731492 | + | 0.681850i | \(0.761175\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.10102 | −0.328124 | −0.164062 | − | 0.986450i | \(-0.552460\pi\) | ||||
−0.164062 | + | 0.986450i | \(0.552460\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.3485 | 1.88312 | 0.941562 | − | 0.336840i | \(-0.109358\pi\) | ||||
0.941562 | + | 0.336840i | \(0.109358\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.34847 | −1.21775 | −0.608875 | − | 0.793266i | \(-0.708379\pi\) | ||||
−0.608875 | + | 0.793266i | \(0.708379\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.89898 | −0.699854 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.898979 | 0.123484 | 0.0617422 | − | 0.998092i | \(-0.480334\pi\) | ||||
0.0617422 | + | 0.998092i | \(0.480334\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.44949 | −0.465129 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.348469 | −0.0453668 | −0.0226834 | − | 0.999743i | \(-0.507221\pi\) | ||||
−0.0226834 | + | 0.999743i | \(0.507221\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.89898 | −0.243139 | −0.121570 | − | 0.992583i | \(-0.538793\pi\) | ||||
−0.121570 | + | 0.992583i | \(0.538793\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.89898 | 0.483609 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.34847 | −0.286911 | −0.143456 | − | 0.989657i | \(-0.545821\pi\) | ||||
−0.143456 | + | 0.989657i | \(0.545821\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.7980 | 1.40016 | 0.700080 | − | 0.714064i | \(-0.253148\pi\) | ||||
0.700080 | + | 0.714064i | \(0.253148\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.89898 | 0.573382 | 0.286691 | − | 0.958023i | \(-0.407445\pi\) | ||||
0.286691 | + | 0.958023i | \(0.407445\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.00000 | −0.569803 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.55051 | −0.962008 | −0.481004 | − | 0.876719i | \(-0.659728\pi\) | ||||
−0.481004 | + | 0.876719i | \(0.659728\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.44949 | −0.598159 | −0.299080 | − | 0.954228i | \(-0.596680\pi\) | ||||
−0.299080 | + | 0.954228i | \(0.596680\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.89898 | −0.531369 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.10102 | −0.328708 | −0.164354 | − | 0.986401i | \(-0.552554\pi\) | ||||
−0.164354 | + | 0.986401i | \(0.552554\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.65153 | 0.592441 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.89898 | 0.598951 | 0.299475 | − | 0.954104i | \(-0.403188\pi\) | ||||
0.299475 | + | 0.954104i | \(0.403188\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.79796 | 0.676422 | 0.338211 | − | 0.941070i | \(-0.390178\pi\) | ||||
0.338211 | + | 0.941070i | \(0.390178\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.4495 | −1.71935 | −0.859675 | − | 0.510842i | \(-0.829334\pi\) | ||||
−0.859675 | + | 0.510842i | \(0.829334\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.7980 | 1.33390 | 0.666950 | − | 0.745103i | \(-0.267600\pi\) | ||||
0.666950 | + | 0.745103i | \(0.267600\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.89898 | 0.852368 | 0.426184 | − | 0.904637i | \(-0.359858\pi\) | ||||
0.426184 | + | 0.904637i | \(0.359858\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.7980 | −1.01579 | −0.507893 | − | 0.861420i | \(-0.669576\pi\) | ||||
−0.507893 | + | 0.861420i | \(0.669576\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.550510 | 0.0513353 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.10102 | −0.650949 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.898979 | 0.0817254 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.2474 | 0.982694 | 0.491347 | − | 0.870964i | \(-0.336505\pi\) | ||||
0.491347 | + | 0.870964i | \(0.336505\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.79796 | 0.502747 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.8990 | −1.70008 | −0.850042 | − | 0.526714i | \(-0.823424\pi\) | ||||
−0.850042 | + | 0.526714i | \(0.823424\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.44949 | 0.122944 | 0.0614721 | − | 0.998109i | \(-0.480420\pi\) | ||||
0.0614721 | + | 0.998109i | \(0.480420\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.4495 | −1.12470 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.89898 | −0.822066 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.8990 | −1.13865 | −0.569324 | − | 0.822113i | \(-0.692795\pi\) | ||||
−0.569324 | + | 0.822113i | \(0.692795\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.24745 | 0.752547 | 0.376273 | − | 0.926509i | \(-0.377205\pi\) | ||||
0.376273 | + | 0.926509i | \(0.377205\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.44949 | −0.598357 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.79796 | −0.702154 | −0.351077 | − | 0.936347i | \(-0.614184\pi\) | ||||
−0.351077 | + | 0.936347i | \(0.614184\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.797959 | 0.0628880 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.7980 | 1.08074 | 0.540370 | − | 0.841428i | \(-0.318284\pi\) | ||||
0.540370 | + | 0.841428i | \(0.318284\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.44949 | −0.731223 | −0.365612 | − | 0.930767i | \(-0.619140\pi\) | ||||
−0.365612 | + | 0.930767i | \(0.619140\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.20204 | 0.169388 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.00000 | −0.228086 | −0.114043 | − | 0.993476i | \(-0.536380\pi\) | ||||
−0.114043 | + | 0.993476i | \(0.536380\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.79796 | −0.438285 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.6969 | 1.38973 | 0.694866 | − | 0.719139i | \(-0.255464\pi\) | ||||
0.694866 | + | 0.719139i | \(0.255464\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.89898 | −0.654266 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.8990 | 1.23578 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.4495 | 1.26260 | 0.631300 | − | 0.775538i | \(-0.282522\pi\) | ||||
0.631300 | + | 0.775538i | \(0.282522\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.8990 | 1.00047 | 0.500235 | − | 0.865890i | \(-0.333247\pi\) | ||||
0.500235 | + | 0.865890i | \(0.333247\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.5959 | −1.53865 | −0.769323 | − | 0.638860i | \(-0.779406\pi\) | ||||
−0.769323 | + | 0.638860i | \(0.779406\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.7980 | −0.836335 | −0.418168 | − | 0.908370i | \(-0.637328\pi\) | ||||
−0.418168 | + | 0.908370i | \(0.637328\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.3485 | −1.00707 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.10102 | −0.146742 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.7980 | −0.954425 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.4495 | 1.06359 | 0.531793 | − | 0.846874i | \(-0.321518\pi\) | ||||
0.531793 | + | 0.846874i | \(0.321518\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.3485 | 0.842159 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.7980 | −0.733013 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.1010 | −1.28487 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.1464 | −1.21517 | −0.607587 | − | 0.794253i | \(-0.707863\pi\) | ||||
−0.607587 | + | 0.794253i | \(0.707863\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.3485 | 1.48332 | 0.741660 | − | 0.670776i | \(-0.234039\pi\) | ||||
0.741660 | + | 0.670776i | \(0.234039\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.00000 | 0.0660819 | 0.0330409 | − | 0.999454i | \(-0.489481\pi\) | ||||
0.0330409 | + | 0.999454i | \(0.489481\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.34847 | −0.544594 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.1464 | 1.30316 | 0.651582 | − | 0.758578i | \(-0.274106\pi\) | ||||
0.651582 | + | 0.758578i | \(0.274106\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.00000 | 0.450910 | 0.225455 | − | 0.974254i | \(-0.427613\pi\) | ||||
0.225455 | + | 0.974254i | \(0.427613\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.89898 | −0.312984 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.5959 | 0.992344 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.20204 | 0.138992 | 0.0694958 | − | 0.997582i | \(-0.477861\pi\) | ||||
0.0694958 | + | 0.997582i | \(0.477861\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.89898 | −0.119388 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.79796 | 0.548802 | 0.274401 | − | 0.961615i | \(-0.411521\pi\) | ||||
0.274401 | + | 0.961615i | \(0.411521\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.8990 | −0.801504 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.550510 | −0.0339459 | −0.0169730 | − | 0.999856i | \(-0.505403\pi\) | ||||
−0.0169730 | + | 0.999856i | \(0.505403\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.898979 | 0.0552239 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.8990 | −1.03035 | −0.515174 | − | 0.857085i | \(-0.672273\pi\) | ||||
−0.515174 | + | 0.857085i | \(0.672273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.3939 | 1.78555 | 0.892775 | − | 0.450502i | \(-0.148755\pi\) | ||||
0.892775 | + | 0.450502i | \(0.148755\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.7980 | 0.832048 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.79796 | −0.288281 | −0.144141 | − | 0.989557i | \(-0.546042\pi\) | ||||
−0.144141 | + | 0.989557i | \(0.546042\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.8990 | −1.18707 | −0.593537 | − | 0.804807i | \(-0.702269\pi\) | ||||
−0.593537 | + | 0.804807i | \(0.702269\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.44949 | 0.0861632 | 0.0430816 | − | 0.999072i | \(-0.486282\pi\) | ||||
0.0430816 | + | 0.999072i | \(0.486282\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.04541 | −0.179765 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.00000 | 0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.7980 | 1.09819 | 0.549094 | − | 0.835760i | \(-0.314973\pi\) | ||||
0.549094 | + | 0.835760i | \(0.314973\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.348469 | −0.0202887 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.14643 | 0.124131 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.8990 | 1.03168 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.89898 | −0.108735 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.20204 | −0.125677 | −0.0628386 | − | 0.998024i | \(-0.520015\pi\) | ||||
−0.0628386 | + | 0.998024i | \(0.520015\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.24745 | −0.524375 | −0.262187 | − | 0.965017i | \(-0.584444\pi\) | ||||
−0.262187 | + | 0.965017i | \(0.584444\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.0000 | −0.960897 | −0.480448 | − | 0.877023i | \(-0.659526\pi\) | ||||
−0.480448 | + | 0.877023i | \(0.659526\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.1010 | −0.904323 | −0.452162 | − | 0.891936i | \(-0.649347\pi\) | ||||
−0.452162 | + | 0.891936i | \(0.649347\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.1464 | 1.91183 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.5959 | −1.09035 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.5959 | −0.865106 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.1010 | −0.667151 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.2474 | −0.728146 | −0.364073 | − | 0.931370i | \(-0.618614\pi\) | ||||
−0.364073 | + | 0.931370i | \(0.618614\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.34847 | −0.128311 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.79796 | 0.479255 | 0.239628 | − | 0.970865i | \(-0.422975\pi\) | ||||
0.239628 | + | 0.970865i | \(0.422975\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.6969 | 1.39157 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.2474 | −0.931275 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.1464 | −1.51098 | −0.755490 | − | 0.655161i | \(-0.772601\pi\) | ||||
−0.755490 | + | 0.655161i | \(0.772601\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.79796 | −0.256829 | −0.128414 | − | 0.991721i | \(-0.540989\pi\) | ||||
−0.128414 | + | 0.991721i | \(0.540989\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.6969 | 0.835464 | 0.417732 | − | 0.908570i | \(-0.362825\pi\) | ||||
0.417732 | + | 0.908570i | \(0.362825\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.7980 | 0.626171 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.7980 | −0.939340 | −0.469670 | − | 0.882842i | \(-0.655627\pi\) | ||||
−0.469670 | + | 0.882842i | \(0.655627\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.89898 | 0.256424 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.3485 | −0.540186 | −0.270093 | − | 0.962834i | \(-0.587054\pi\) | ||||
−0.270093 | + | 0.962834i | \(0.587054\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.30306 | 0.0676516 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.30306 | −0.119248 | −0.0596240 | − | 0.998221i | \(-0.518990\pi\) | ||||
−0.0596240 | + | 0.998221i | \(0.518990\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −38.5959 | −1.98779 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.0000 | −1.33553 | −0.667765 | − | 0.744372i | \(-0.732749\pi\) | ||||
−0.667765 | + | 0.744372i | \(0.732749\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.4495 | −1.70919 | −0.854595 | − | 0.519296i | \(-0.826194\pi\) | ||||
−0.854595 | + | 0.519296i | \(0.826194\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.00000 | −0.254824 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.7980 | −0.648882 | −0.324441 | − | 0.945906i | \(-0.605176\pi\) | ||||
−0.324441 | + | 0.945906i | \(0.605176\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.69694 | −0.136390 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.55051 | −0.430223 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.6969 | −0.938372 | −0.469186 | − | 0.883099i | \(-0.655453\pi\) | ||||
−0.469186 | + | 0.883099i | \(0.655453\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.6969 | 0.783868 | 0.391934 | − | 0.919993i | \(-0.371806\pi\) | ||||
0.391934 | + | 0.919993i | \(0.371806\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.0454 | −1.44685 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 30.6969 | 1.52159 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.5959 | −0.622828 | −0.311414 | − | 0.950274i | \(-0.600803\pi\) | ||||
−0.311414 | + | 0.950274i | \(0.600803\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.505103 | −0.0248545 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.44949 | −0.267505 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.75255 | −0.329884 | −0.164942 | − | 0.986303i | \(-0.552744\pi\) | ||||
−0.164942 | + | 0.986303i | \(0.552744\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.89898 | −0.482447 | −0.241223 | − | 0.970470i | \(-0.577549\pi\) | ||||
−0.241223 | + | 0.970470i | \(0.577549\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 19.5959 | 0.950542 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.75255 | −0.133205 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.7980 | −1.62799 | −0.813995 | − | 0.580872i | \(-0.802712\pi\) | ||||
−0.813995 | + | 0.580872i | \(0.802712\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 40.4949 | 1.94606 | 0.973030 | − | 0.230677i | \(-0.0740942\pi\) | ||||
0.973030 | + | 0.230677i | \(0.0740942\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.20204 | 0.105338 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.6515 | 1.03337 | 0.516686 | − | 0.856175i | \(-0.327166\pi\) | ||||
0.516686 | + | 0.856175i | \(0.327166\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.5505 | 0.881361 | 0.440681 | − | 0.897664i | \(-0.354737\pi\) | ||||
0.440681 | + | 0.897664i | \(0.354737\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.10102 | −0.147002 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.8990 | 0.986284 | 0.493142 | − | 0.869949i | \(-0.335848\pi\) | ||||
0.493142 | + | 0.869949i | \(0.335848\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.24745 | 0.341269 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.65153 | 0.264948 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.4949 | 0.818377 | 0.409188 | − | 0.912450i | \(-0.365812\pi\) | ||||
0.409188 | + | 0.912450i | \(0.365812\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.30306 | −0.293563 | −0.146781 | − | 0.989169i | \(-0.546891\pi\) | ||||
−0.146781 | + | 0.989169i | \(0.546891\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.75255 | 0.313818 | 0.156909 | − | 0.987613i | \(-0.449847\pi\) | ||||
0.156909 | + | 0.987613i | \(0.449847\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.404082 | 0.0186987 | 0.00934934 | − | 0.999956i | \(-0.497024\pi\) | ||||
0.00934934 | + | 0.999956i | \(0.497024\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.40408 | −0.157186 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −42.5959 | −1.95856 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.0000 | −0.734130 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.0454 | 0.870207 | 0.435103 | − | 0.900380i | \(-0.356712\pi\) | ||||
0.435103 | + | 0.900380i | \(0.356712\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.6969 | −1.58204 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.89898 | 0.267859 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.79796 | −0.0814733 | −0.0407366 | − | 0.999170i | \(-0.512970\pi\) | ||||
−0.0407366 | + | 0.999170i | \(0.512970\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.2474 | 1.59070 | 0.795348 | − | 0.606154i | \(-0.207288\pi\) | ||||
0.795348 | + | 0.606154i | \(0.207288\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 48.4949 | 2.18410 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.1010 | 0.767086 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.3485 | −0.731858 | −0.365929 | − | 0.930643i | \(-0.619249\pi\) | ||||
−0.365929 | + | 0.930643i | \(0.619249\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.2020 | 0.900764 | 0.450382 | − | 0.892836i | \(-0.351288\pi\) | ||||
0.450382 | + | 0.892836i | \(0.351288\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.79796 | 0.302505 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −33.4949 | −1.48464 | −0.742318 | − | 0.670048i | \(-0.766273\pi\) | ||||
−0.742318 | + | 0.670048i | \(0.766273\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.10102 | 0.314131 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.4495 | −0.768916 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28.7980 | 1.26653 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.0000 | −0.788594 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.5959 | −1.11923 | −0.559616 | − | 0.828752i | \(-0.689051\pi\) | ||||
−0.559616 | + | 0.828752i | \(0.689051\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 36.4949 | 1.58974 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6969 | −0.986823 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.19184 | −0.354828 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.7980 | 0.596538 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.8990 | 0.727891 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.59592 | 0.412561 | 0.206280 | − | 0.978493i | \(-0.433864\pi\) | ||||
0.206280 | + | 0.978493i | \(0.433864\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.89898 | 0.381190 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.4495 | −0.489545 | −0.244772 | − | 0.969581i | \(-0.578713\pi\) | ||||
−0.244772 | + | 0.969581i | \(0.578713\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.5959 | −1.68684 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.3939 | −0.527041 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.6969 | −0.453244 | −0.226622 | − | 0.973983i | \(-0.572768\pi\) | ||||
−0.226622 | + | 0.973983i | \(0.572768\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.1464 | 2.03638 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.3485 | −0.436136 | −0.218068 | − | 0.975934i | \(-0.569975\pi\) | ||||
−0.218068 | + | 0.975934i | \(0.569975\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.7980 | −0.454274 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.00000 | −0.0419222 | −0.0209611 | − | 0.999780i | \(-0.506673\pi\) | ||||
−0.0209611 | + | 0.999780i | \(0.506673\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.3485 | −0.767860 | −0.383930 | − | 0.923362i | \(-0.625430\pi\) | ||||
−0.383930 | + | 0.923362i | \(0.625430\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.20204 | −0.0918315 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.8990 | −1.20308 | −0.601540 | − | 0.798843i | \(-0.705446\pi\) | ||||
−0.601540 | + | 0.798843i | \(0.705446\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.89898 | −0.327705 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.10102 | −0.128431 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.9444 | 0.988291 | 0.494145 | − | 0.869379i | \(-0.335481\pi\) | ||||
0.494145 | + | 0.869379i | \(0.335481\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.7980 | −1.22780 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.1010 | 0.784385 | 0.392192 | − | 0.919883i | \(-0.371717\pi\) | ||||
0.392192 | + | 0.919883i | \(0.371717\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.10102 | −0.291113 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.4495 | −1.36671 | −0.683355 | − | 0.730087i | \(-0.739480\pi\) | ||||
−0.683355 | + | 0.730087i | \(0.739480\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.6969 | 1.61927 | 0.809636 | − | 0.586932i | \(-0.199665\pi\) | ||||
0.809636 | + | 0.586932i | \(0.199665\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.898979 | 0.0365487 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.9444 | 1.13423 | 0.567114 | − | 0.823639i | \(-0.308060\pi\) | ||||
0.567114 | + | 0.823639i | \(0.308060\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.5505 | −1.31685 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.69694 | −0.108928 | −0.0544642 | − | 0.998516i | \(-0.517345\pi\) | ||||
−0.0544642 | + | 0.998516i | \(0.517345\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.69694 | −0.229350 | −0.114675 | − | 0.993403i | \(-0.536583\pi\) | ||||
−0.114675 | + | 0.993403i | \(0.536583\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.14643 | 0.327433 | 0.163716 | − | 0.986507i | \(-0.447652\pi\) | ||||
0.163716 | + | 0.986507i | \(0.447652\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.49490 | −0.180084 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 43.5959 | 1.73828 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.7980 | 1.02700 | 0.513500 | − | 0.858089i | \(-0.328349\pi\) | ||||
0.513500 | + | 0.858089i | \(0.328349\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.00000 | −0.317470 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.1010 | −0.756810 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.5959 | −0.497509 | −0.248754 | − | 0.968567i | \(-0.580021\pi\) | ||||
−0.248754 | + | 0.968567i | \(0.580021\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.3485 | −0.408104 | −0.204052 | − | 0.978960i | \(-0.565411\pi\) | ||||
−0.204052 | + | 0.978960i | \(0.565411\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.79796 | 0.385198 | 0.192599 | − | 0.981278i | \(-0.438308\pi\) | ||||
0.192599 | + | 0.981278i | \(0.438308\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.20204 | 0.0471842 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.0000 | 0.665261 | 0.332631 | − | 0.943057i | \(-0.392064\pi\) | ||||
0.332631 | + | 0.943057i | \(0.392064\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.2474 | 0.439474 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.3485 | 0.870573 | 0.435286 | − | 0.900292i | \(-0.356647\pi\) | ||||
0.435286 | + | 0.900292i | \(0.356647\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.3939 | −1.10439 | −0.552197 | − | 0.833714i | \(-0.686210\pi\) | ||||
−0.552197 | + | 0.833714i | \(0.686210\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.79796 | 0.224835 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.44949 | −0.211005 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.55051 | 0.252880 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41.2929 | −1.59172 | −0.795861 | − | 0.605479i | \(-0.792982\pi\) | ||||
−0.795861 | + | 0.605479i | \(0.792982\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.3939 | 1.32186 | 0.660932 | − | 0.750446i | \(-0.270161\pi\) | ||||
0.660932 | + | 0.750446i | \(0.270161\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.55051 | 0.328138 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.3939 | 1.58389 | 0.791946 | − | 0.610591i | \(-0.209068\pi\) | ||||
0.791946 | + | 0.610591i | \(0.209068\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.8990 | −0.760301 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.50510 | 0.133534 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.9444 | 0.606553 | 0.303277 | − | 0.952903i | \(-0.401919\pi\) | ||||
0.303277 | + | 0.952903i | \(0.401919\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.44949 | 0.0549823 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.2929 | 0.389870 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.4949 | −1.37839 | −0.689197 | − | 0.724574i | \(-0.742036\pi\) | ||||
−0.689197 | + | 0.724574i | \(0.742036\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −35.5959 | −1.34253 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.85357 | 0.370582 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.00000 | 0.187779 | 0.0938895 | − | 0.995583i | \(-0.470070\pi\) | ||||
0.0938895 | + | 0.995583i | \(0.470070\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.10102 | −0.153584 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.4495 | −0.502982 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.1918 | 1.75996 | 0.879979 | − | 0.475012i | \(-0.157556\pi\) | ||||
0.879979 | + | 0.475012i | \(0.157556\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.2929 | −0.941955 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 39.5959 | 1.47056 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.4495 | 0.869693 | 0.434847 | − | 0.900504i | \(-0.356803\pi\) | ||||
0.434847 | + | 0.900504i | \(0.356803\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −60.4949 | −2.23748 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.10102 | 0.0776030 | 0.0388015 | − | 0.999247i | \(-0.487646\pi\) | ||||
0.0388015 | + | 0.999247i | \(0.487646\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.10102 | 0.298405 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.0000 | −0.514998 | −0.257499 | − | 0.966279i | \(-0.582898\pi\) | ||||
−0.257499 | + | 0.966279i | \(0.582898\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.5505 | 1.12079 | 0.560395 | − | 0.828226i | \(-0.310649\pi\) | ||||
0.560395 | + | 0.828226i | \(0.310649\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.8990 | −0.509219 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.0000 | 0.730784 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.6413 | −1.48302 | −0.741512 | − | 0.670940i | \(-0.765891\pi\) | ||||
−0.741512 | + | 0.670940i | \(0.765891\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.24745 | 0.336549 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.0000 | 1.52652 | 0.763258 | − | 0.646094i | \(-0.223599\pi\) | ||||
0.763258 | + | 0.646094i | \(0.223599\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.2929 | 1.56936 | 0.784682 | − | 0.619898i | \(-0.212826\pi\) | ||||
0.784682 | + | 0.619898i | \(0.212826\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.8990 | 0.466974 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.35867 | −0.0490589 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.59592 | 0.0936112 | 0.0468056 | − | 0.998904i | \(-0.485096\pi\) | ||||
0.0468056 | + | 0.998904i | \(0.485096\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.4949 | −0.449410 | −0.224705 | − | 0.974427i | \(-0.572142\pi\) | ||||
−0.224705 | + | 0.974427i | \(0.572142\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.7980 | 1.07037 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.40408 | −0.301107 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −40.6969 | −1.45625 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.79796 | −0.314013 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.24745 | 0.115759 | 0.0578795 | − | 0.998324i | \(-0.481566\pi\) | ||||
0.0578795 | + | 0.998324i | \(0.481566\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.6515 | −0.556504 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.40408 | −0.262927 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.3031 | −0.648328 | −0.324164 | − | 0.946001i | \(-0.605083\pi\) | ||||
−0.324164 | + | 0.946001i | \(0.605083\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.8990 | 1.44690 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.8990 | −0.596352 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.797959 | 0.0281244 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.4949 | 0.579930 | 0.289965 | − | 0.957037i | \(-0.406356\pi\) | ||||
0.289965 | + | 0.957037i | \(0.406356\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.5959 | 1.67132 | 0.835659 | − | 0.549248i | \(-0.185086\pi\) | ||||
0.835659 | + | 0.549248i | \(0.185086\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.7980 | 0.483321 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 49.3939 | 1.72807 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 53.2929 | 1.85993 | 0.929967 | − | 0.367644i | \(-0.119835\pi\) | ||||
0.929967 | + | 0.367644i | \(0.119835\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.4495 | −0.538535 | −0.269268 | − | 0.963065i | \(-0.586782\pi\) | ||||
−0.269268 | + | 0.963065i | \(0.586782\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.0000 | −0.973655 | −0.486828 | − | 0.873498i | \(-0.661846\pi\) | ||||
−0.486828 | + | 0.873498i | \(0.661846\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.8990 | 1.14263 | 0.571314 | − | 0.820731i | \(-0.306434\pi\) | ||||
0.571314 | + | 0.820731i | \(0.306434\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.0000 | 0.831551 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.44949 | −0.327013 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.6515 | 0.540351 | 0.270175 | − | 0.962811i | \(-0.412918\pi\) | ||||
0.270175 | + | 0.962811i | \(0.412918\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 68.9898 | 2.37896 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.20204 | 0.0757525 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.30306 | 0.0447737 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.89898 | −0.167935 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.89898 | −0.0650198 | −0.0325099 | − | 0.999471i | \(-0.510350\pi\) | ||||
−0.0325099 | + | 0.999471i | \(0.510350\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.1010 | −0.618319 | −0.309160 | − | 0.951010i | \(-0.600048\pi\) | ||||
−0.309160 | + | 0.951010i | \(0.600048\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.5505 | −0.564696 | −0.282348 | − | 0.959312i | \(-0.591113\pi\) | ||||
−0.282348 | + | 0.959312i | \(0.591113\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.79796 | −0.0612032 | −0.0306016 | − | 0.999532i | \(-0.509742\pi\) | ||||
−0.0306016 | + | 0.999532i | \(0.509742\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.00000 | −0.102003 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29.4949 | 1.00055 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.15663 | −0.310261 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.0454 | −0.441015 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.1010 | 0.611228 | 0.305614 | − | 0.952155i | \(-0.401138\pi\) | ||||
0.305614 | + | 0.952155i | \(0.401138\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.4949 | 0.825254 | 0.412627 | − | 0.910900i | \(-0.364611\pi\) | ||||
0.412627 | + | 0.910900i | \(0.364611\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.404082 | 0.0135984 | 0.00679922 | − | 0.999977i | \(-0.497836\pi\) | ||||
0.00679922 | + | 0.999977i | \(0.497836\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.8434 | −0.968465 | −0.484233 | − | 0.874939i | \(-0.660901\pi\) | ||||
−0.484233 | + | 0.874939i | \(0.660901\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.5959 | −0.388915 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.3939 | −1.11748 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0000 | −0.401116 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 73.7423 | 2.45944 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.40408 | −0.146721 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.6969 | 0.621507 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.752551 | 0.0249881 | 0.0124940 | − | 0.999922i | \(-0.496023\pi\) | ||||
0.0124940 | + | 0.999922i | \(0.496023\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.5403 | −1.64134 | −0.820672 | − | 0.571400i | \(-0.806401\pi\) | ||||
−0.820672 | + | 0.571400i | \(0.806401\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.7980 | 0.622122 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.3031 | 0.538375 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.79796 | −0.323205 | −0.161602 | − | 0.986856i | \(-0.551666\pi\) | ||||
−0.161602 | + | 0.986856i | \(0.551666\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 46.0000 | 1.51411 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.5959 | 1.17039 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.3031 | 0.600504 | 0.300252 | − | 0.953860i | \(-0.402929\pi\) | ||||
0.300252 | + | 0.953860i | \(0.402929\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.5959 | −0.642230 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.8990 | 0.552656 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.50510 | 0.245181 | 0.122591 | − | 0.992457i | \(-0.460880\pi\) | ||||
0.122591 | + | 0.992457i | \(0.460880\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.00000 | −0.228193 | −0.114097 | − | 0.993470i | \(-0.536397\pi\) | ||||
−0.114097 | + | 0.993470i | \(0.536397\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.15663 | −0.0376652 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.2474 | −1.47034 | −0.735172 | − | 0.677880i | \(-0.762899\pi\) | ||||
−0.735172 | + | 0.677880i | \(0.762899\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.1010 | 0.620045 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.8990 | 1.71357 | 0.856783 | − | 0.515677i | \(-0.172460\pi\) | ||||
0.856783 | + | 0.515677i | \(0.172460\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.4495 | 0.564652 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.8434 | −0.931401 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.4949 | 0.790158 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.8990 | 0.447424 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.24745 | −0.297378 | −0.148689 | − | 0.988884i | \(-0.547505\pi\) | ||||
−0.148689 | + | 0.988884i | \(0.547505\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.0000 | −0.320915 | −0.160458 | − | 0.987043i | \(-0.551297\pi\) | ||||
−0.160458 | + | 0.987043i | \(0.551297\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.10102 | 0.0673556 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.7980 | 1.04930 | 0.524650 | − | 0.851318i | \(-0.324196\pi\) | ||||
0.524650 | + | 0.851318i | \(0.324196\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.6969 | 0.341876 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34.3485 | −1.09555 | −0.547773 | − | 0.836627i | \(-0.684524\pi\) | ||||
−0.547773 | + | 0.836627i | \(0.684524\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.5959 | −0.688103 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.79796 | 0.216163 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.3939 | −1.18786 | −0.593928 | − | 0.804518i | \(-0.702424\pi\) | ||||
−0.593928 | + | 0.804518i | \(0.702424\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.7980 | −0.374020 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.3939 | 0.835902 | 0.417951 | − | 0.908469i | \(-0.362748\pi\) | ||||
0.417951 | + | 0.908469i | \(0.362748\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5184.2.a.bu.1.2 | 2 | ||
3.2 | odd | 2 | 5184.2.a.bj.1.2 | 2 | |||
4.3 | odd | 2 | 5184.2.a.by.1.1 | 2 | |||
8.3 | odd | 2 | 2592.2.a.n.1.1 | 2 | |||
8.5 | even | 2 | 2592.2.a.j.1.2 | 2 | |||
9.2 | odd | 6 | 1728.2.i.m.577.1 | 4 | |||
9.4 | even | 3 | 576.2.i.m.385.1 | 4 | |||
9.5 | odd | 6 | 1728.2.i.m.1153.1 | 4 | |||
9.7 | even | 3 | 576.2.i.m.193.2 | 4 | |||
12.11 | even | 2 | 5184.2.a.bn.1.1 | 2 | |||
24.5 | odd | 2 | 2592.2.a.o.1.2 | 2 | |||
24.11 | even | 2 | 2592.2.a.s.1.1 | 2 | |||
36.7 | odd | 6 | 576.2.i.i.193.1 | 4 | |||
36.11 | even | 6 | 1728.2.i.k.577.2 | 4 | |||
36.23 | even | 6 | 1728.2.i.k.1153.2 | 4 | |||
36.31 | odd | 6 | 576.2.i.i.385.2 | 4 | |||
72.5 | odd | 6 | 864.2.i.e.289.1 | 4 | |||
72.11 | even | 6 | 864.2.i.c.577.2 | 4 | |||
72.13 | even | 6 | 288.2.i.c.97.2 | ✓ | 4 | ||
72.29 | odd | 6 | 864.2.i.e.577.1 | 4 | |||
72.43 | odd | 6 | 288.2.i.e.193.2 | yes | 4 | ||
72.59 | even | 6 | 864.2.i.c.289.2 | 4 | |||
72.61 | even | 6 | 288.2.i.c.193.1 | yes | 4 | ||
72.67 | odd | 6 | 288.2.i.e.97.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.i.c.97.2 | ✓ | 4 | 72.13 | even | 6 | ||
288.2.i.c.193.1 | yes | 4 | 72.61 | even | 6 | ||
288.2.i.e.97.1 | yes | 4 | 72.67 | odd | 6 | ||
288.2.i.e.193.2 | yes | 4 | 72.43 | odd | 6 | ||
576.2.i.i.193.1 | 4 | 36.7 | odd | 6 | |||
576.2.i.i.385.2 | 4 | 36.31 | odd | 6 | |||
576.2.i.m.193.2 | 4 | 9.7 | even | 3 | |||
576.2.i.m.385.1 | 4 | 9.4 | even | 3 | |||
864.2.i.c.289.2 | 4 | 72.59 | even | 6 | |||
864.2.i.c.577.2 | 4 | 72.11 | even | 6 | |||
864.2.i.e.289.1 | 4 | 72.5 | odd | 6 | |||
864.2.i.e.577.1 | 4 | 72.29 | odd | 6 | |||
1728.2.i.k.577.2 | 4 | 36.11 | even | 6 | |||
1728.2.i.k.1153.2 | 4 | 36.23 | even | 6 | |||
1728.2.i.m.577.1 | 4 | 9.2 | odd | 6 | |||
1728.2.i.m.1153.1 | 4 | 9.5 | odd | 6 | |||
2592.2.a.j.1.2 | 2 | 8.5 | even | 2 | |||
2592.2.a.n.1.1 | 2 | 8.3 | odd | 2 | |||
2592.2.a.o.1.2 | 2 | 24.5 | odd | 2 | |||
2592.2.a.s.1.1 | 2 | 24.11 | even | 2 | |||
5184.2.a.bj.1.2 | 2 | 3.2 | odd | 2 | |||
5184.2.a.bn.1.1 | 2 | 12.11 | even | 2 | |||
5184.2.a.bu.1.2 | 2 | 1.1 | even | 1 | trivial | ||
5184.2.a.by.1.1 | 2 | 4.3 | odd | 2 |