Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7920,2,Mod(1,7920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7920, 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("7920.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7920 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7920.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: | \(63.2415184009\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7920.1 |
$q$-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 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.07838 | −0.407588 | −0.203794 | − | 0.979014i | \(-0.565327\pi\) | ||||
−0.203794 | + | 0.979014i | \(0.565327\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.34017 | −1.20375 | −0.601874 | − | 0.798591i | \(-0.705579\pi\) | ||||
−0.601874 | + | 0.798591i | \(0.705579\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.75872 | −1.88177 | −0.940883 | − | 0.338730i | \(-0.890003\pi\) | ||||
−0.940883 | + | 0.338730i | \(0.890003\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.26180 | −1.20714 | −0.603569 | − | 0.797311i | \(-0.706255\pi\) | ||||
−0.603569 | + | 0.797311i | \(0.706255\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.15676 | −0.449715 | −0.224857 | − | 0.974392i | \(-0.572192\pi\) | ||||
−0.224857 | + | 0.974392i | \(0.572192\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.41855 | −0.263418 | −0.131709 | − | 0.991288i | \(-0.542046\pi\) | ||||
−0.131709 | + | 0.991288i | \(0.542046\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.68035 | 0.840615 | 0.420307 | − | 0.907382i | \(-0.361922\pi\) | ||||
0.420307 | + | 0.907382i | \(0.361922\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.07838 | 0.182279 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.41855 | 1.47093 | 0.735465 | − | 0.677562i | \(-0.236964\pi\) | ||||
0.735465 | + | 0.677562i | \(0.236964\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.60197 | −1.15929 | −0.579645 | − | 0.814869i | \(-0.696809\pi\) | ||||
−0.579645 | + | 0.814869i | \(0.696809\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.68035 | 0.682699 | 0.341349 | − | 0.939937i | \(-0.389116\pi\) | ||||
0.341349 | + | 0.939937i | \(0.389116\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.83710 | −0.833872 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.156755 | −0.0215320 | −0.0107660 | − | 0.999942i | \(-0.503427\pi\) | ||||
−0.0107660 | + | 0.999942i | \(0.503427\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.15676 | 0.801541 | 0.400771 | − | 0.916178i | \(-0.368742\pi\) | ||||
0.400771 | + | 0.916178i | \(0.368742\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.15676 | −0.532218 | −0.266109 | − | 0.963943i | \(-0.585738\pi\) | ||||
−0.266109 | + | 0.963943i | \(0.585738\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.34017 | 0.538332 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.68035 | 1.06047 | 0.530237 | − | 0.847850i | \(-0.322103\pi\) | ||||
0.530237 | + | 0.847850i | \(0.322103\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.68035 | −0.555455 | −0.277727 | − | 0.960660i | \(-0.589581\pi\) | ||||
−0.277727 | + | 0.960660i | \(0.589581\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.4969 | −1.22857 | −0.614286 | − | 0.789083i | \(-0.710556\pi\) | ||||
−0.614286 | + | 0.789083i | \(0.710556\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.07838 | −0.122893 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.09890 | 0.911197 | 0.455599 | − | 0.890185i | \(-0.349425\pi\) | ||||
0.455599 | + | 0.890185i | \(0.349425\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.0205 | −1.20966 | −0.604830 | − | 0.796355i | \(-0.706759\pi\) | ||||
−0.604830 | + | 0.796355i | \(0.706759\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.75872 | 0.841552 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.8371 | 1.36073 | 0.680365 | − | 0.732873i | \(-0.261821\pi\) | ||||
0.680365 | + | 0.732873i | \(0.261821\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.68035 | 0.490634 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.26180 | 0.539849 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.6803 | 1.49056 | 0.745282 | − | 0.666750i | \(-0.232315\pi\) | ||||
0.745282 | + | 0.666750i | \(0.232315\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.5753 | 1.54980 | 0.774900 | − | 0.632083i | \(-0.217800\pi\) | ||||
0.774900 | + | 0.632083i | \(0.217800\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.83710 | −0.673680 | −0.336840 | − | 0.941562i | \(-0.609358\pi\) | ||||
−0.336840 | + | 0.941562i | \(0.609358\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.34017 | 0.612928 | 0.306464 | − | 0.951882i | \(-0.400854\pi\) | ||||
0.306464 | + | 0.951882i | \(0.400854\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.31351 | 0.221594 | 0.110797 | − | 0.993843i | \(-0.464660\pi\) | ||||
0.110797 | + | 0.993843i | \(0.464660\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.15676 | 0.201118 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.36683 | 0.766987 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.24128 | 0.198881 | 0.0994406 | − | 0.995044i | \(-0.468295\pi\) | ||||
0.0994406 | + | 0.995044i | \(0.468295\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.68035 | 0.758405 | 0.379203 | − | 0.925314i | \(-0.376198\pi\) | ||||
0.379203 | + | 0.925314i | \(0.376198\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.67420 | 0.492016 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.3607 | 1.31235 | 0.656176 | − | 0.754608i | \(-0.272173\pi\) | ||||
0.656176 | + | 0.754608i | \(0.272173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.58145 | −0.727869 | −0.363935 | − | 0.931425i | \(-0.618567\pi\) | ||||
−0.363935 | + | 0.931425i | \(0.618567\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.34017 | −0.362943 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.41855 | 0.117804 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.0989 | 1.48272 | 0.741360 | − | 0.671108i | \(-0.234181\pi\) | ||||
0.741360 | + | 0.671108i | \(0.234181\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.9360 | −1.86651 | −0.933253 | − | 0.359221i | \(-0.883042\pi\) | ||||
−0.933253 | + | 0.359221i | \(0.883042\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.68035 | −0.375934 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.9939 | −0.877405 | −0.438703 | − | 0.898632i | \(-0.644562\pi\) | ||||
−0.438703 | + | 0.898632i | \(0.644562\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.32580 | 0.183298 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.52359 | 0.510967 | 0.255484 | − | 0.966813i | \(-0.417765\pi\) | ||||
0.255484 | + | 0.966813i | \(0.417765\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.97334 | 0.152701 | 0.0763507 | − | 0.997081i | \(-0.475673\pi\) | ||||
0.0763507 | + | 0.997081i | \(0.475673\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.83710 | 0.449008 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.75872 | −0.285770 | −0.142885 | − | 0.989739i | \(-0.545638\pi\) | ||||
−0.142885 | + | 0.989739i | \(0.545638\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.07838 | −0.0815177 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.1506 | 1.13241 | 0.566205 | − | 0.824264i | \(-0.308411\pi\) | ||||
0.566205 | + | 0.824264i | \(0.308411\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.83710 | 0.359539 | 0.179769 | − | 0.983709i | \(-0.442465\pi\) | ||||
0.179769 | + | 0.983709i | \(0.442465\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.00000 | 0.147043 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.75872 | −0.567374 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.52359 | 0.182601 | 0.0913003 | − | 0.995823i | \(-0.470898\pi\) | ||||
0.0913003 | + | 0.995823i | \(0.470898\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.0266620 | 0.00191917 | 0.000959586 | − | 1.00000i | \(-0.499695\pi\) | ||||
0.000959586 | 1.00000i | \(0.499695\pi\) | ||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.1194 | −1.50470 | −0.752348 | − | 0.658766i | \(-0.771079\pi\) | ||||
−0.752348 | + | 0.658766i | \(0.771079\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.5236 | −0.745998 | −0.372999 | − | 0.927832i | \(-0.621670\pi\) | ||||
−0.372999 | + | 0.927832i | \(0.621670\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.52973 | 0.107366 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.41855 | −0.657820 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.26180 | −0.363966 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.57531 | −0.659191 | −0.329596 | − | 0.944122i | \(-0.606912\pi\) | ||||
−0.329596 | + | 0.944122i | \(0.606912\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.60197 | 0.518450 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.04718 | −0.342625 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33.6742 | 2.26517 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.15676 | 0.144427 | 0.0722135 | − | 0.997389i | \(-0.476994\pi\) | ||||
0.0722135 | + | 0.997389i | \(0.476994\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.65983 | 0.641145 | 0.320573 | − | 0.947224i | \(-0.396125\pi\) | ||||
0.320573 | + | 0.947224i | \(0.396125\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.36069 | −0.222081 | −0.111040 | − | 0.993816i | \(-0.535418\pi\) | ||||
−0.111040 | + | 0.993816i | \(0.535418\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.39803 | 0.157100 | 0.0785501 | − | 0.996910i | \(-0.474971\pi\) | ||||
0.0785501 | + | 0.996910i | \(0.474971\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.68035 | −0.305312 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.20394 | −0.465984 | −0.232992 | − | 0.972479i | \(-0.574852\pi\) | ||||
−0.232992 | + | 0.972479i | \(0.574852\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.20394 | −0.335215 | −0.167608 | − | 0.985854i | \(-0.553604\pi\) | ||||
−0.167608 | + | 0.985854i | \(0.553604\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.83710 | 0.372919 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.8371 | 1.45309 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.3197 | 0.966968 | 0.483484 | − | 0.875353i | \(-0.339371\pi\) | ||||
0.483484 | + | 0.875353i | \(0.339371\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.15676 | −0.135594 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.15676 | −0.259291 | −0.129646 | − | 0.991560i | \(-0.541384\pi\) | ||||
−0.129646 | + | 0.991560i | \(0.541384\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.15676 | 0.134014 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.7070 | −1.15352 | −0.576762 | − | 0.816912i | \(-0.695684\pi\) | ||||
−0.576762 | + | 0.816912i | \(0.695684\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.156755 | 0.00962941 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.3607 | −1.42433 | −0.712163 | − | 0.702014i | \(-0.752284\pi\) | ||||
−0.712163 | + | 0.702014i | \(0.752284\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.57531 | 0.338676 | 0.169338 | − | 0.985558i | \(-0.445837\pi\) | ||||
0.169338 | + | 0.985558i | \(0.445837\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.0144 | −1.56305 | −0.781526 | − | 0.623872i | \(-0.785558\pi\) | ||||
−0.781526 | + | 0.623872i | \(0.785558\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.41855 | 0.561864 | 0.280932 | − | 0.959728i | \(-0.409357\pi\) | ||||
0.280932 | + | 0.959728i | \(0.409357\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.2413 | −0.846556 | −0.423278 | − | 0.906000i | \(-0.639121\pi\) | ||||
−0.423278 | + | 0.906000i | \(0.639121\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.1568 | −0.599534 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 43.1978 | 2.54105 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.7587 | 0.920634 | 0.460317 | − | 0.887754i | \(-0.347736\pi\) | ||||
0.460317 | + | 0.887754i | \(0.347736\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.15676 | −0.358460 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.36069 | 0.541343 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.19779 | 0.472513 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.15676 | 0.238015 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.9216 | 1.07991 | 0.539957 | − | 0.841693i | \(-0.318440\pi\) | ||||
0.539957 | + | 0.841693i | \(0.318440\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.8781 | −1.18389 | −0.591945 | − | 0.805978i | \(-0.701640\pi\) | ||||
−0.591945 | + | 0.805978i | \(0.701640\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.31351 | 0.356861 | 0.178430 | − | 0.983953i | \(-0.442898\pi\) | ||||
0.178430 | + | 0.983953i | \(0.442898\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −31.3607 | −1.76139 | −0.880696 | − | 0.473682i | \(-0.842925\pi\) | ||||
−0.880696 | + | 0.473682i | \(0.842925\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.41855 | −0.0794236 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 40.8248 | 2.27155 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.34017 | −0.240749 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.04718 | −0.278260 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.2039 | −1.05554 | −0.527772 | − | 0.849386i | \(-0.676972\pi\) | ||||
−0.527772 | + | 0.849386i | \(0.676972\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.68035 | −0.474258 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.5031 | 0.735559 | 0.367780 | − | 0.929913i | \(-0.380118\pi\) | ||||
0.367780 | + | 0.929913i | \(0.380118\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.68035 | 0.253455 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.8432 | 0.747465 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.34017 | 0.340358 | 0.170179 | − | 0.985413i | \(-0.445565\pi\) | ||||
0.170179 | + | 0.985413i | \(0.445565\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.1568 | 0.864851 | 0.432426 | − | 0.901670i | \(-0.357658\pi\) | ||||
0.432426 | + | 0.901670i | \(0.357658\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.2039 | 0.702775 | 0.351387 | − | 0.936230i | \(-0.385710\pi\) | ||||
0.351387 | + | 0.936230i | \(0.385710\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.68035 | 0.248407 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.31965 | 0.175205 | 0.0876023 | − | 0.996156i | \(-0.472080\pi\) | ||||
0.0876023 | + | 0.996156i | \(0.472080\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.68649 | 0.457184 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.4969 | 0.549434 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 36.1445 | 1.88673 | 0.943363 | − | 0.331762i | \(-0.107643\pi\) | ||||
0.943363 | + | 0.331762i | \(0.107643\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.169042 | 0.00877620 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.81044 | −0.145519 | −0.0727595 | − | 0.997350i | \(-0.523181\pi\) | ||||
−0.0727595 | + | 0.997350i | \(0.523181\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.15676 | 0.317089 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.5585 | 1.71476 | 0.857379 | − | 0.514685i | \(-0.172091\pi\) | ||||
0.857379 | + | 0.514685i | \(0.172091\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.07838 | 0.0549592 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.8371 | −0.650867 | −0.325433 | − | 0.945565i | \(-0.605510\pi\) | ||||
−0.325433 | + | 0.945565i | \(0.605510\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.7337 | 0.846258 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.09890 | −0.407500 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.31965 | −0.266986 | −0.133493 | − | 0.991050i | \(-0.542619\pi\) | ||||
−0.133493 | + | 0.991050i | \(0.542619\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.00000 | −0.0998752 | −0.0499376 | − | 0.998752i | \(-0.515902\pi\) | ||||
−0.0499376 | + | 0.998752i | \(0.515902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.3135 | −1.01189 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.00000 | −0.0991363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.1978 | 1.29540 | 0.647699 | − | 0.761897i | \(-0.275732\pi\) | ||||
0.647699 | + | 0.761897i | \(0.275732\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.63931 | −0.326699 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.0205 | 0.540976 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.83710 | −0.138601 | −0.0693007 | − | 0.997596i | \(-0.522077\pi\) | ||||
−0.0693007 | + | 0.997596i | \(0.522077\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.4764 | 0.559326 | 0.279663 | − | 0.960098i | \(-0.409777\pi\) | ||||
0.279663 | + | 0.960098i | \(0.409777\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.75872 | −0.376353 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.48255 | 0.216926 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.5708 | 1.13536 | 0.567682 | − | 0.823248i | \(-0.307840\pi\) | ||||
0.567682 | + | 0.823248i | \(0.307840\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.9939 | −0.720559 | −0.360279 | − | 0.932844i | \(-0.617319\pi\) | ||||
−0.360279 | + | 0.932844i | \(0.617319\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.3484 | 0.542868 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.77924 | −0.228101 | −0.114050 | − | 0.993475i | \(-0.536383\pi\) | ||||
−0.114050 | + | 0.993475i | \(0.536383\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.1978 | 0.959626 | 0.479813 | − | 0.877371i | \(-0.340704\pi\) | ||||
0.479813 | + | 0.877371i | \(0.340704\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.8371 | −0.608537 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.5708 | 1.01799 | 0.508994 | − | 0.860770i | \(-0.330018\pi\) | ||||
0.508994 | + | 0.860770i | \(0.330018\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.41855 | 0.443502 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.68035 | −0.219418 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.1711 | 1.31779 | 0.658895 | − | 0.752235i | \(-0.271024\pi\) | ||||
0.658895 | + | 0.752235i | \(0.271024\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.47187 | 0.0685520 | 0.0342760 | − | 0.999412i | \(-0.489087\pi\) | ||||
0.0342760 | + | 0.999412i | \(0.489087\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.2039 | 1.07838 | 0.539189 | − | 0.842185i | \(-0.318731\pi\) | ||||
0.539189 | + | 0.842185i | \(0.318731\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.1568 | 0.655097 | 0.327548 | − | 0.944834i | \(-0.393778\pi\) | ||||
0.327548 | + | 0.944834i | \(0.393778\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.36069 | −0.432237 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.60197 | −0.349539 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.26180 | −0.241428 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.8432 | −0.632514 | −0.316257 | − | 0.948674i | \(-0.602426\pi\) | ||||
−0.316257 | + | 0.948674i | \(0.602426\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.68035 | 0.395790 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.6803 | −0.666600 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.9939 | 1.85761 | 0.928804 | − | 0.370570i | \(-0.120838\pi\) | ||||
0.928804 | + | 0.370570i | \(0.120838\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.8371 | 1.57218 | 0.786088 | − | 0.618114i | \(-0.212103\pi\) | ||||
0.786088 | + | 0.618114i | \(0.212103\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.0061 | 0.495692 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.04718 | 0.226397 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.1506 | −0.678235 | −0.339117 | − | 0.940744i | \(-0.610128\pi\) | ||||
−0.339117 | + | 0.940744i | \(0.610128\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.65368 | −0.296673 | −0.148337 | − | 0.988937i | \(-0.547392\pi\) | ||||
−0.148337 | + | 0.988937i | \(0.547392\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.5753 | −0.693092 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −41.3484 | −1.83274 | −0.916368 | − | 0.400337i | \(-0.868893\pi\) | ||||
−0.916368 | + | 0.400337i | \(0.868893\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.3197 | 0.500752 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.83710 | 0.301279 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.68035 | 0.205841 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.67420 | −0.336213 | −0.168106 | − | 0.985769i | \(-0.553765\pi\) | ||||
−0.168106 | + | 0.985769i | \(0.553765\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.2351 | −1.01600 | −0.508001 | − | 0.861357i | \(-0.669615\pi\) | ||||
−0.508001 | + | 0.861357i | \(0.669615\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −36.3135 | −1.58184 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.3484 | −0.797757 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −40.8781 | −1.77063 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.34017 | −0.274110 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.83710 | −0.251422 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0000 | −0.773880 | −0.386940 | − | 0.922105i | \(-0.626468\pi\) | ||||
−0.386940 | + | 0.922105i | \(0.626468\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.31351 | −0.0990999 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.0661 | 0.986235 | 0.493117 | − | 0.869963i | \(-0.335857\pi\) | ||||
0.493117 | + | 0.869963i | \(0.335857\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.46412 | 0.317982 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.73367 | −0.371393 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.5958 | −0.448960 | −0.224480 | − | 0.974479i | \(-0.572068\pi\) | ||||
−0.224480 | + | 0.974479i | \(0.572068\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.9939 | 1.39549 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.2122 | −1.52616 | −0.763080 | − | 0.646303i | \(-0.776314\pi\) | ||||
−0.763080 | + | 0.646303i | \(0.776314\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.00000 | −0.252422 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.5753 | 1.15602 | 0.578008 | − | 0.816031i | \(-0.303830\pi\) | ||||
0.578008 | + | 0.816031i | \(0.303830\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.9299 | 1.16883 | 0.584414 | − | 0.811456i | \(-0.301324\pi\) | ||||
0.584414 | + | 0.811456i | \(0.301324\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.15676 | −0.0899429 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 41.4017 | 1.72358 | 0.861788 | − | 0.507268i | \(-0.169345\pi\) | ||||
0.861788 | + | 0.507268i | \(0.169345\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.8843 | 0.493043 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.156755 | −0.00649215 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.48255 | 0.350112 | 0.175056 | − | 0.984558i | \(-0.443989\pi\) | ||||
0.175056 | + | 0.984558i | \(0.443989\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.6270 | −1.01474 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.56093 | −0.310490 | −0.155245 | − | 0.987876i | \(-0.549617\pi\) | ||||
−0.155245 | + | 0.987876i | \(0.549617\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.36683 | −0.343007 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.67420 | 0.231842 | 0.115921 | − | 0.993258i | \(-0.463018\pi\) | ||||
0.115921 | + | 0.993258i | \(0.463018\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.31965 | −0.0538298 | −0.0269149 | − | 0.999638i | \(-0.508568\pi\) | ||||
−0.0269149 | + | 0.999638i | \(0.508568\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.24128 | 0.0909706 | 0.0454853 | − | 0.998965i | \(-0.485517\pi\) | ||||
0.0454853 | + | 0.998965i | \(0.485517\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.3135 | −0.821797 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.8638 | 1.73125 | 0.865626 | − | 0.500692i | \(-0.166921\pi\) | ||||
0.865626 | + | 0.500692i | \(0.166921\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.3607 | −0.457364 | −0.228682 | − | 0.973501i | \(-0.573442\pi\) | ||||
−0.228682 | + | 0.973501i | \(0.573442\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 45.1917 | 1.81641 | 0.908203 | − | 0.418530i | \(-0.137455\pi\) | ||||
0.908203 | + | 0.418530i | \(0.137455\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.8432 | −0.554618 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.5174 | 0.618721 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.78992 | 0.389731 | 0.194865 | − | 0.980830i | \(-0.437573\pi\) | ||||
0.194865 | + | 0.980830i | \(0.437573\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.24128 | −0.0889423 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.3340 | 1.00377 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.210079 | −0.00829764 | −0.00414882 | − | 0.999991i | \(-0.501321\pi\) | ||||
−0.00414882 | + | 0.999991i | \(0.501321\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.5236 | −0.572754 | −0.286377 | − | 0.958117i | \(-0.592451\pi\) | ||||
−0.286377 | + | 0.958117i | \(0.592451\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.4641 | 0.607957 | 0.303979 | − | 0.952679i | \(-0.401685\pi\) | ||||
0.303979 | + | 0.952679i | \(0.401685\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.15676 | 0.241674 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.8310 | 0.697779 | 0.348890 | − | 0.937164i | \(-0.386559\pi\) | ||||
0.348890 | + | 0.937164i | \(0.386559\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.68035 | −0.339169 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.3135 | −1.25876 | −0.629378 | − | 0.777099i | \(-0.716690\pi\) | ||||
−0.629378 | + | 0.777099i | \(0.716690\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.68649 | −0.221179 | −0.110589 | − | 0.993866i | \(-0.535274\pi\) | ||||
−0.110589 | + | 0.993866i | \(0.535274\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.67420 | −0.220036 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.05947 | 0.118463 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.15676 | −0.160470 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.0205 | −0.810281 | −0.405141 | − | 0.914254i | \(-0.632777\pi\) | ||||
−0.405141 | + | 0.914254i | \(0.632777\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.7526 | −1.41252 | −0.706258 | − | 0.707954i | \(-0.749618\pi\) | ||||
−0.706258 | + | 0.707954i | \(0.749618\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.8310 | −0.607536 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.3074 | −0.662248 | −0.331124 | − | 0.943587i | \(-0.607428\pi\) | ||||
−0.331124 | + | 0.943587i | \(0.607428\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.3607 | −0.586902 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.680346 | 0.0259191 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.6742 | −0.672358 | −0.336179 | − | 0.941798i | \(-0.609135\pi\) | ||||
−0.336179 | + | 0.941798i | \(0.609135\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.58145 | 0.325513 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −73.0759 | −2.76795 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.1050 | 0.646048 | 0.323024 | − | 0.946391i | \(-0.395300\pi\) | ||||
0.323024 | + | 0.946391i | \(0.395300\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.5236 | 0.396905 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.7961 | −0.631681 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.1506 | 0.944551 | 0.472276 | − | 0.881451i | \(-0.343433\pi\) | ||||
0.472276 | + | 0.881451i | \(0.343433\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.0944 | −0.378037 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.34017 | 0.162313 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.78992 | −0.0667528 | −0.0333764 | − | 0.999443i | \(-0.510626\pi\) | ||||
−0.0333764 | + | 0.999443i | \(0.510626\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.37298 | 0.274584 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.41855 | −0.0526837 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.9877 | −0.963831 | −0.481915 | − | 0.876218i | \(-0.660059\pi\) | ||||
−0.481915 | + | 0.876218i | \(0.660059\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 58.9816 | 2.18151 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.0205 | −1.51513 | −0.757564 | − | 0.652761i | \(-0.773610\pi\) | ||||
−0.757564 | + | 0.652761i | \(0.773610\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.68035 | 0.319745 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.6163 | 1.75160 | 0.875798 | − | 0.482678i | \(-0.160336\pi\) | ||||
0.875798 | + | 0.482678i | \(0.160336\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.550252 | 0.0201868 | 0.0100934 | − | 0.999949i | \(-0.496787\pi\) | ||||
0.0100934 | + | 0.999949i | \(0.496787\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0989 | −0.663092 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.83710 | −0.249822 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.5585 | −1.51649 | −0.758245 | − | 0.651969i | \(-0.773943\pi\) | ||||
−0.758245 | + | 0.651969i | \(0.773943\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.9360 | 0.834726 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.31965 | 0.0479636 | 0.0239818 | − | 0.999712i | \(-0.492366\pi\) | ||||
0.0239818 | + | 0.999712i | \(0.492366\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.21461 | 0.0802797 | 0.0401399 | − | 0.999194i | \(-0.487220\pi\) | ||||
0.0401399 | + | 0.999194i | \(0.487220\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.49484 | −0.0903192 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.7214 | −0.964853 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.3668 | −0.518081 | −0.259041 | − | 0.965866i | \(-0.583406\pi\) | ||||
−0.259041 | + | 0.965866i | \(0.583406\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40.1568 | −1.44434 | −0.722169 | − | 0.691717i | \(-0.756855\pi\) | ||||
−0.722169 | + | 0.691717i | \(0.756855\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.68035 | 0.168123 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −49.5585 | −1.77562 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.68035 | −0.167476 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.9939 | 0.392388 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −49.5897 | −1.76768 | −0.883841 | − | 0.467788i | \(-0.845051\pi\) | ||||
−0.883841 | + | 0.467788i | \(0.845051\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.47027 | −0.230056 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.0410 | 0.640656 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.7091 | 1.65452 | 0.827261 | − | 0.561818i | \(-0.189898\pi\) | ||||
0.827261 | + | 0.561818i | \(0.189898\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.3135 | −1.28468 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.4969 | −0.370429 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.32580 | −0.0819736 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.5814 | 0.653289 | 0.326644 | − | 0.945147i | \(-0.394082\pi\) | ||||
0.326644 | + | 0.945147i | \(0.394082\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.3028 | −0.958732 | −0.479366 | − | 0.877615i | \(-0.659133\pi\) | ||||
−0.479366 | + | 0.877615i | \(0.659133\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.52359 | −0.228511 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40.0000 | 1.39942 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.2085 | 1.08918 | 0.544592 | − | 0.838701i | \(-0.316685\pi\) | ||||
0.544592 | + | 0.838701i | \(0.316685\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.1855 | 1.74936 | 0.874678 | − | 0.484704i | \(-0.161073\pi\) | ||||
0.874678 | + | 0.484704i | \(0.161073\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.3874 | 0.952352 | 0.476176 | − | 0.879350i | \(-0.342023\pi\) | ||||
0.476176 | + | 0.879350i | \(0.342023\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.1978 | −0.909887 | −0.454943 | − | 0.890520i | \(-0.650341\pi\) | ||||
−0.454943 | + | 0.890520i | \(0.650341\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 45.2885 | 1.56915 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.97334 | −0.0682902 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.20394 | 0.248708 | 0.124354 | − | 0.992238i | \(-0.460314\pi\) | ||||
0.124354 | + | 0.992238i | \(0.460314\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.9877 | −0.930611 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.83710 | −0.200802 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.07838 | −0.0370535 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.31351 | 0.147865 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.8043 | 1.36287 | 0.681437 | − | 0.731877i | \(-0.261356\pi\) | ||||
0.681437 | + | 0.731877i | \(0.261356\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.9504 | 1.26220 | 0.631100 | − | 0.775701i | \(-0.282604\pi\) | ||||
0.631100 | + | 0.775701i | \(0.282604\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −57.5052 | −1.96205 | −0.981025 | − | 0.193879i | \(-0.937893\pi\) | ||||
−0.981025 | + | 0.193879i | \(0.937893\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.89657 | −0.0645599 | −0.0322800 | − | 0.999479i | \(-0.510277\pi\) | ||||
−0.0322800 | + | 0.999479i | \(0.510277\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.75872 | 0.127800 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.09890 | 0.274736 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.6742 | −1.27654 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.07838 | 0.0364558 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.5380 | 1.09873 | 0.549365 | − | 0.835583i | \(-0.314870\pi\) | ||||
0.549365 | + | 0.835583i | \(0.314870\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.1978 | −0.613099 | −0.306550 | − | 0.951855i | \(-0.599175\pi\) | ||||
−0.306550 | + | 0.951855i | \(0.599175\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.3956 | −1.22481 | −0.612405 | − | 0.790545i | \(-0.709798\pi\) | ||||
−0.612405 | + | 0.790545i | \(0.709798\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.8699 | 0.935780 | 0.467890 | − | 0.883787i | \(-0.345014\pi\) | ||||
0.467890 | + | 0.883787i | \(0.345014\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.41694 | −0.0810616 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −24.6270 | −0.824112 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.1506 | −0.506429 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.63931 | −0.221433 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.21622 | 0.0405182 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.83710 | −0.160791 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.9376 | 0.927653 | 0.463826 | − | 0.885926i | \(-0.346476\pi\) | ||||
0.463826 | + | 0.885926i | \(0.346476\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.8843 | −0.393744 | −0.196872 | − | 0.980429i | \(-0.563078\pi\) | ||||
−0.196872 | + | 0.980429i | \(0.563078\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.0205 | −0.364726 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.36069 | −0.309117 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.6041 | 1.50434 | 0.752170 | − | 0.658970i | \(-0.229007\pi\) | ||||
0.752170 | + | 0.658970i | \(0.229007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.3135 | 0.668627 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.00000 | −0.0657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.1506 | 0.825165 | 0.412582 | − | 0.910920i | \(-0.364627\pi\) | ||||
0.412582 | + | 0.910920i | \(0.364627\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.7136 | 1.00660 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.75872 | 0.253737 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.33403 | 0.174255 | 0.0871276 | − | 0.996197i | \(-0.472231\pi\) | ||||
0.0871276 | + | 0.996197i | \(0.472231\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −56.8203 | −1.85229 | −0.926144 | − | 0.377170i | \(-0.876897\pi\) | ||||
−0.926144 | + | 0.377170i | \(0.876897\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.3135 | −0.661499 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.9939 | −0.682209 | −0.341104 | − | 0.940025i | \(-0.610801\pi\) | ||||
−0.341104 | + | 0.940025i | \(0.610801\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.5585 | 1.47889 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.2351 | 0.817446 | 0.408723 | − | 0.912658i | \(-0.365974\pi\) | ||||
0.408723 | + | 0.912658i | \(0.365974\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.52359 | −0.0816615 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.5646 | −0.534900 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.09436 | −0.293367 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.0266620 | −0.000858280 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.1317 | −0.422287 | −0.211144 | − | 0.977455i | \(-0.567719\pi\) | ||||
−0.211144 | + | 0.977455i | \(0.567719\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.94053 | 0.286915 | 0.143458 | − | 0.989656i | \(-0.454178\pi\) | ||||
0.143458 | + | 0.989656i | \(0.454178\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.25404 | 0.296671 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −50.3956 | −1.61230 | −0.806149 | − | 0.591713i | \(-0.798452\pi\) | ||||
−0.806149 | + | 0.591713i | \(0.798452\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.8371 | 0.410276 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.1978 | −1.02695 | −0.513475 | − | 0.858105i | \(-0.671642\pi\) | ||||
−0.513475 | + | 0.858105i | \(0.671642\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.1194 | 0.672921 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.3956 | 0.521349 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.7747 | 1.48585 | 0.742924 | − | 0.669376i | \(-0.233438\pi\) | ||||
0.742924 | + | 0.669376i | \(0.233438\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.5236 | 0.333620 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.2122 | 1.21019 | 0.605096 | − | 0.796153i | \(-0.293135\pi\) | ||||
0.605096 | + | 0.796153i | \(0.293135\pi\) | |||||||
\(998\) | 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 | 7920.2.a.cj.1.2 | 3 | ||
3.2 | odd | 2 | 2640.2.a.be.1.2 | 3 | |||
4.3 | odd | 2 | 495.2.a.e.1.3 | 3 | |||
12.11 | even | 2 | 165.2.a.c.1.1 | ✓ | 3 | ||
20.3 | even | 4 | 2475.2.c.r.199.1 | 6 | |||
20.7 | even | 4 | 2475.2.c.r.199.6 | 6 | |||
20.19 | odd | 2 | 2475.2.a.bb.1.1 | 3 | |||
44.43 | even | 2 | 5445.2.a.z.1.1 | 3 | |||
60.23 | odd | 4 | 825.2.c.g.199.6 | 6 | |||
60.47 | odd | 4 | 825.2.c.g.199.1 | 6 | |||
60.59 | even | 2 | 825.2.a.k.1.3 | 3 | |||
84.83 | odd | 2 | 8085.2.a.bk.1.1 | 3 | |||
132.131 | odd | 2 | 1815.2.a.m.1.3 | 3 | |||
660.659 | odd | 2 | 9075.2.a.cf.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.a.c.1.1 | ✓ | 3 | 12.11 | even | 2 | ||
495.2.a.e.1.3 | 3 | 4.3 | odd | 2 | |||
825.2.a.k.1.3 | 3 | 60.59 | even | 2 | |||
825.2.c.g.199.1 | 6 | 60.47 | odd | 4 | |||
825.2.c.g.199.6 | 6 | 60.23 | odd | 4 | |||
1815.2.a.m.1.3 | 3 | 132.131 | odd | 2 | |||
2475.2.a.bb.1.1 | 3 | 20.19 | odd | 2 | |||
2475.2.c.r.199.1 | 6 | 20.3 | even | 4 | |||
2475.2.c.r.199.6 | 6 | 20.7 | even | 4 | |||
2640.2.a.be.1.2 | 3 | 3.2 | odd | 2 | |||
5445.2.a.z.1.1 | 3 | 44.43 | even | 2 | |||
7920.2.a.cj.1.2 | 3 | 1.1 | even | 1 | trivial | ||
8085.2.a.bk.1.1 | 3 | 84.83 | odd | 2 | |||
9075.2.a.cf.1.1 | 3 | 660.659 | odd | 2 |