Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6525,2,Mod(1,6525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6525, 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("6525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6525 = 3^{2} \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6525.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: | \(52.1023873189\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 4x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 145) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.517638\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.517638 | 0.366025 | 0.183013 | − | 0.983111i | \(-0.441415\pi\) | ||||
0.183013 | + | 0.983111i | \(0.441415\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.73205 | −0.866025 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.44949 | 0.925820 | 0.462910 | − | 0.886405i | \(-0.346805\pi\) | ||||
0.462910 | + | 0.886405i | \(0.346805\pi\) | |||||||
\(8\) | −1.93185 | −0.683013 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.26795 | 0.382301 | 0.191151 | − | 0.981561i | \(-0.438778\pi\) | ||||
0.191151 | + | 0.981561i | \(0.438778\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.79315 | 0.497331 | 0.248665 | − | 0.968589i | \(-0.420008\pi\) | ||||
0.248665 | + | 0.968589i | \(0.420008\pi\) | |||||||
\(14\) | 1.26795 | 0.338874 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.46410 | 0.616025 | ||||||||
\(17\) | 1.41421 | 0.342997 | 0.171499 | − | 0.985184i | \(-0.445139\pi\) | ||||
0.171499 | + | 0.985184i | \(0.445139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.26795 | −0.749719 | −0.374859 | − | 0.927082i | \(-0.622309\pi\) | ||||
−0.374859 | + | 0.927082i | \(0.622309\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.656339 | 0.139932 | ||||||||
\(23\) | −6.31319 | −1.31639 | −0.658196 | − | 0.752847i | \(-0.728680\pi\) | ||||
−0.658196 | + | 0.752847i | \(0.728680\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.928203 | 0.182036 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.24264 | −0.801784 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.73205 | −1.56832 | −0.784161 | − | 0.620557i | \(-0.786907\pi\) | ||||
−0.784161 | + | 0.620557i | \(0.786907\pi\) | |||||||
\(32\) | 5.13922 | 0.908494 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.732051 | 0.125546 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.14162 | −1.50287 | −0.751437 | − | 0.659805i | \(-0.770639\pi\) | ||||
−0.751437 | + | 0.659805i | \(0.770639\pi\) | |||||||
\(38\) | −1.69161 | −0.274416 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.92820 | 1.08200 | 0.541002 | − | 0.841021i | \(-0.318045\pi\) | ||||
0.541002 | + | 0.841021i | \(0.318045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.14162 | −1.39408 | −0.697042 | − | 0.717030i | \(-0.745501\pi\) | ||||
−0.697042 | + | 0.717030i | \(0.745501\pi\) | |||||||
\(44\) | −2.19615 | −0.331082 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.26795 | −0.481833 | ||||||||
\(47\) | 1.41421 | 0.206284 | 0.103142 | − | 0.994667i | \(-0.467110\pi\) | ||||
0.103142 | + | 0.994667i | \(0.467110\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.10583 | −0.430701 | ||||||||
\(53\) | 5.93426 | 0.815133 | 0.407566 | − | 0.913176i | \(-0.366378\pi\) | ||||
0.407566 | + | 0.913176i | \(0.366378\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.73205 | −0.632347 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.517638 | −0.0679692 | ||||||||
\(59\) | 10.3923 | 1.35296 | 0.676481 | − | 0.736460i | \(-0.263504\pi\) | ||||
0.676481 | + | 0.736460i | \(0.263504\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.92820 | 0.374918 | 0.187459 | − | 0.982272i | \(-0.439975\pi\) | ||||
0.187459 | + | 0.982272i | \(0.439975\pi\) | |||||||
\(62\) | −4.52004 | −0.574046 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.26795 | −0.283494 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.24264 | −0.518321 | −0.259161 | − | 0.965834i | \(-0.583446\pi\) | ||||
−0.259161 | + | 0.965834i | \(0.583446\pi\) | |||||||
\(68\) | −2.44949 | −0.297044 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.46410 | −0.411113 | −0.205557 | − | 0.978645i | \(-0.565900\pi\) | ||||
−0.205557 | + | 0.978645i | \(0.565900\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.34847 | 0.860073 | 0.430037 | − | 0.902811i | \(-0.358501\pi\) | ||||
0.430037 | + | 0.902811i | \(0.358501\pi\) | |||||||
\(74\) | −4.73205 | −0.550090 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.66025 | 0.649276 | ||||||||
\(77\) | 3.10583 | 0.353942 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.19615 | −0.472104 | −0.236052 | − | 0.971740i | \(-0.575854\pi\) | ||||
−0.236052 | + | 0.971740i | \(0.575854\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.58630 | 0.396041 | ||||||||
\(83\) | 10.1769 | 1.11706 | 0.558530 | − | 0.829484i | \(-0.311366\pi\) | ||||
0.558530 | + | 0.829484i | \(0.311366\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.73205 | −0.510270 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.44949 | −0.261116 | ||||||||
\(89\) | −10.3923 | −1.10158 | −0.550791 | − | 0.834643i | \(-0.685674\pi\) | ||||
−0.550791 | + | 0.834643i | \(0.685674\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.39230 | 0.460439 | ||||||||
\(92\) | 10.9348 | 1.14003 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.732051 | 0.0755053 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.9348 | 1.11026 | 0.555129 | − | 0.831764i | \(-0.312669\pi\) | ||||
0.555129 | + | 0.831764i | \(0.312669\pi\) | |||||||
\(98\) | −0.517638 | −0.0522893 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.14162 | −0.900751 | −0.450375 | − | 0.892839i | \(-0.648710\pi\) | ||||
−0.450375 | + | 0.892839i | \(0.648710\pi\) | |||||||
\(104\) | −3.46410 | −0.339683 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.07180 | 0.298359 | ||||||||
\(107\) | −18.6622 | −1.80414 | −0.902070 | − | 0.431589i | \(-0.857953\pi\) | ||||
−0.902070 | + | 0.431589i | \(0.857953\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.8564 | 1.71033 | 0.855167 | − | 0.518353i | \(-0.173455\pi\) | ||||
0.855167 | + | 0.518353i | \(0.173455\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 6.03579 | 0.570329 | ||||||||
\(113\) | −13.0053 | −1.22344 | −0.611719 | − | 0.791075i | \(-0.709522\pi\) | ||||
−0.611719 | + | 0.791075i | \(0.709522\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.73205 | 0.160817 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.37945 | 0.495219 | ||||||||
\(119\) | 3.46410 | 0.317554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.39230 | −0.853846 | ||||||||
\(122\) | 1.51575 | 0.137230 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 15.1244 | 1.35821 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.24264 | −0.376473 | −0.188237 | − | 0.982124i | \(-0.560277\pi\) | ||||
−0.188237 | + | 0.982124i | \(0.560277\pi\) | |||||||
\(128\) | −11.4524 | −1.01226 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.73205 | 0.413441 | 0.206721 | − | 0.978400i | \(-0.433721\pi\) | ||||
0.206721 | + | 0.978400i | \(0.433721\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00481 | −0.694105 | ||||||||
\(134\) | −2.19615 | −0.189719 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.73205 | −0.234271 | ||||||||
\(137\) | 14.7985 | 1.26432 | 0.632159 | − | 0.774838i | \(-0.282169\pi\) | ||||
0.632159 | + | 0.774838i | \(0.282169\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.00000 | −0.678551 | −0.339276 | − | 0.940687i | \(-0.610182\pi\) | ||||
−0.339276 | + | 0.940687i | \(0.610182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.79315 | −0.150478 | ||||||||
\(143\) | 2.27362 | 0.190130 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.80385 | 0.314809 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 15.8338 | 1.30153 | ||||||||
\(149\) | 0.928203 | 0.0760414 | 0.0380207 | − | 0.999277i | \(-0.487895\pi\) | ||||
0.0380207 | + | 0.999277i | \(0.487895\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.7846 | −1.52867 | −0.764335 | − | 0.644819i | \(-0.776933\pi\) | ||||
−0.764335 | + | 0.644819i | \(0.776933\pi\) | |||||||
\(152\) | 6.31319 | 0.512068 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.60770 | 0.129552 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.9348 | −0.872690 | −0.436345 | − | 0.899780i | \(-0.643727\pi\) | ||||
−0.436345 | + | 0.899780i | \(0.643727\pi\) | |||||||
\(158\) | −2.17209 | −0.172802 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.4641 | −1.21874 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.0406 | −1.09974 | −0.549872 | − | 0.835249i | \(-0.685324\pi\) | ||||
−0.549872 | + | 0.835249i | \(0.685324\pi\) | |||||||
\(164\) | −12.0000 | −0.937043 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.26795 | 0.408872 | ||||||||
\(167\) | 11.2122 | 0.867624 | 0.433812 | − | 0.901003i | \(-0.357168\pi\) | ||||
0.433812 | + | 0.901003i | \(0.357168\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.78461 | −0.752662 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 15.8338 | 1.20731 | ||||||||
\(173\) | 4.62158 | 0.351372 | 0.175686 | − | 0.984446i | \(-0.443786\pi\) | ||||
0.175686 | + | 0.984446i | \(0.443786\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.12436 | 0.235507 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.37945 | −0.403207 | ||||||||
\(179\) | −2.53590 | −0.189542 | −0.0947710 | − | 0.995499i | \(-0.530212\pi\) | ||||
−0.0947710 | + | 0.995499i | \(0.530212\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | 2.27362 | 0.168532 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.1962 | 0.899112 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.79315 | 0.131128 | ||||||||
\(188\) | −2.44949 | −0.178647 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.1244 | −1.09436 | −0.547180 | − | 0.837015i | \(-0.684299\pi\) | ||||
−0.547180 | + | 0.837015i | \(0.684299\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.656339 | 0.0472443 | 0.0236222 | − | 0.999721i | \(-0.492480\pi\) | ||||
0.0236222 | + | 0.999721i | \(0.492480\pi\) | |||||||
\(194\) | 5.66025 | 0.406383 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.73205 | 0.123718 | ||||||||
\(197\) | −22.4243 | −1.59767 | −0.798834 | − | 0.601551i | \(-0.794550\pi\) | ||||
−0.798834 | + | 0.601551i | \(0.794550\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.0000 | −0.992434 | −0.496217 | − | 0.868199i | \(-0.665278\pi\) | ||||
−0.496217 | + | 0.868199i | \(0.665278\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.10583 | 0.218525 | ||||||||
\(203\) | −2.44949 | −0.171920 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.73205 | −0.329698 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.41851 | 0.306368 | ||||||||
\(209\) | −4.14359 | −0.286618 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.7321 | −1.01420 | −0.507098 | − | 0.861888i | \(-0.669282\pi\) | ||||
−0.507098 | + | 0.861888i | \(0.669282\pi\) | |||||||
\(212\) | −10.2784 | −0.705926 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.66025 | −0.660361 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.3891 | −1.45198 | ||||||||
\(218\) | 9.24316 | 0.626026 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.53590 | 0.170583 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.3533 | 1.02813 | 0.514066 | − | 0.857751i | \(-0.328139\pi\) | ||||
0.514066 | + | 0.857751i | \(0.328139\pi\) | |||||||
\(224\) | 12.5885 | 0.841102 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.73205 | −0.447809 | ||||||||
\(227\) | −20.4553 | −1.35767 | −0.678834 | − | 0.734292i | \(-0.737514\pi\) | ||||
−0.678834 | + | 0.734292i | \(0.737514\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.7846 | 1.24132 | 0.620661 | − | 0.784079i | \(-0.286864\pi\) | ||||
0.620661 | + | 0.784079i | \(0.286864\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.93185 | 0.126832 | ||||||||
\(233\) | −3.38323 | −0.221643 | −0.110821 | − | 0.993840i | \(-0.535348\pi\) | ||||
−0.110821 | + | 0.993840i | \(0.535348\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −18.0000 | −1.17170 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.79315 | 0.116233 | ||||||||
\(239\) | −10.3923 | −0.672222 | −0.336111 | − | 0.941822i | \(-0.609112\pi\) | ||||
−0.336111 | + | 0.941822i | \(0.609112\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.4641 | 0.738468 | 0.369234 | − | 0.929337i | \(-0.379620\pi\) | ||||
0.369234 | + | 0.929337i | \(0.379620\pi\) | |||||||
\(242\) | −4.86181 | −0.312529 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.07180 | −0.324689 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.85993 | −0.372858 | ||||||||
\(248\) | 16.8690 | 1.07118 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.1244 | −0.954641 | −0.477320 | − | 0.878729i | \(-0.658392\pi\) | ||||
−0.477320 | + | 0.878729i | \(0.658392\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.00481 | −0.503258 | ||||||||
\(254\) | −2.19615 | −0.137799 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.39230 | −0.0870191 | ||||||||
\(257\) | −9.52056 | −0.593876 | −0.296938 | − | 0.954897i | \(-0.595965\pi\) | ||||
−0.296938 | + | 0.954897i | \(0.595965\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.3923 | −1.39139 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.44949 | 0.151330 | ||||||||
\(263\) | 4.79744 | 0.295823 | 0.147912 | − | 0.989001i | \(-0.452745\pi\) | ||||
0.147912 | + | 0.989001i | \(0.452745\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.14359 | −0.254060 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.34847 | 0.448879 | ||||||||
\(269\) | 12.0000 | 0.731653 | 0.365826 | − | 0.930683i | \(-0.380786\pi\) | ||||
0.365826 | + | 0.930683i | \(0.380786\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.7321 | −1.62386 | −0.811928 | − | 0.583757i | \(-0.801582\pi\) | ||||
−0.811928 | + | 0.583757i | \(0.801582\pi\) | |||||||
\(272\) | 3.48477 | 0.211295 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.66025 | 0.462773 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.7637 | −1.12740 | −0.563701 | − | 0.825979i | \(-0.690623\pi\) | ||||
−0.563701 | + | 0.825979i | \(0.690623\pi\) | |||||||
\(278\) | −4.14110 | −0.248367 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.7846 | −1.95577 | −0.977883 | − | 0.209153i | \(-0.932929\pi\) | ||||
−0.977883 | + | 0.209153i | \(0.932929\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.4249 | 1.63024 | 0.815119 | − | 0.579293i | \(-0.196671\pi\) | ||||
0.815119 | + | 0.579293i | \(0.196671\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.17691 | 0.0695924 | ||||||||
\(287\) | 16.9706 | 1.00174 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0000 | −0.882353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12.7279 | −0.744845 | ||||||||
\(293\) | 30.7338 | 1.79549 | 0.897743 | − | 0.440520i | \(-0.145206\pi\) | ||||
0.897743 | + | 0.440520i | \(0.145206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 17.6603 | 1.02648 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.480473 | 0.0278331 | ||||||||
\(299\) | −11.3205 | −0.654682 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.3923 | −1.29067 | ||||||||
\(302\) | −9.72363 | −0.559532 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.05256 | −0.461846 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.4543 | −0.596658 | −0.298329 | − | 0.954463i | \(-0.596429\pi\) | ||||
−0.298329 | + | 0.954463i | \(0.596429\pi\) | |||||||
\(308\) | −5.37945 | −0.306523 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.58846 | 0.373597 | 0.186799 | − | 0.982398i | \(-0.440189\pi\) | ||||
0.186799 | + | 0.982398i | \(0.440189\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.6627 | 1.33749 | 0.668747 | − | 0.743490i | \(-0.266831\pi\) | ||||
0.668747 | + | 0.743490i | \(0.266831\pi\) | |||||||
\(314\) | −5.66025 | −0.319427 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.26795 | 0.408854 | ||||||||
\(317\) | −5.75839 | −0.323423 | −0.161712 | − | 0.986838i | \(-0.551701\pi\) | ||||
−0.161712 | + | 0.986838i | \(0.551701\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.26795 | −0.0709915 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.00481 | −0.446091 | ||||||||
\(323\) | −4.62158 | −0.257151 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.26795 | −0.402534 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −13.3843 | −0.739022 | ||||||||
\(329\) | 3.46410 | 0.190982 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.1962 | −1.00015 | −0.500075 | − | 0.865982i | \(-0.666694\pi\) | ||||
−0.500075 | + | 0.865982i | \(0.666694\pi\) | |||||||
\(332\) | −17.6269 | −0.967402 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.80385 | 0.317572 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.9053 | 1.52010 | 0.760050 | − | 0.649864i | \(-0.225174\pi\) | ||||
0.760050 | + | 0.649864i | \(0.225174\pi\) | |||||||
\(338\) | −5.06489 | −0.275494 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.0718 | −0.599571 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.5959 | −1.05808 | ||||||||
\(344\) | 17.6603 | 0.952177 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.39230 | 0.128611 | ||||||||
\(347\) | 21.4906 | 1.15368 | 0.576838 | − | 0.816859i | \(-0.304286\pi\) | ||||
0.576838 | + | 0.816859i | \(0.304286\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.7846 | −1.21963 | −0.609816 | − | 0.792543i | \(-0.708757\pi\) | ||||
−0.609816 | + | 0.792543i | \(0.708757\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.51626 | 0.347318 | ||||||||
\(353\) | −31.9449 | −1.70026 | −0.850128 | − | 0.526576i | \(-0.823475\pi\) | ||||
−0.850128 | + | 0.526576i | \(0.823475\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 18.0000 | 0.953998 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.31268 | −0.0693772 | ||||||||
\(359\) | 7.26795 | 0.383588 | 0.191794 | − | 0.981435i | \(-0.438570\pi\) | ||||
0.191794 | + | 0.981435i | \(0.438570\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.32051 | −0.437921 | ||||||||
\(362\) | −8.28221 | −0.435303 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.60770 | −0.398752 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.6365 | 1.75581 | 0.877906 | − | 0.478833i | \(-0.158940\pi\) | ||||
0.877906 | + | 0.478833i | \(0.158940\pi\) | |||||||
\(368\) | −15.5563 | −0.810931 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.5359 | 0.754666 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.5959 | 1.01464 | 0.507319 | − | 0.861758i | \(-0.330637\pi\) | ||||
0.507319 | + | 0.861758i | \(0.330637\pi\) | |||||||
\(374\) | 0.928203 | 0.0479962 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.73205 | −0.140895 | ||||||||
\(377\) | −1.79315 | −0.0923520 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.1962 | −0.831940 | −0.415970 | − | 0.909378i | \(-0.636558\pi\) | ||||
−0.415970 | + | 0.909378i | \(0.636558\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.82894 | −0.400564 | ||||||||
\(383\) | −0.933740 | −0.0477119 | −0.0238559 | − | 0.999715i | \(-0.507594\pi\) | ||||
−0.0238559 | + | 0.999715i | \(0.507594\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.339746 | 0.0172926 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.9396 | −0.961511 | ||||||||
\(389\) | 20.7846 | 1.05382 | 0.526911 | − | 0.849921i | \(-0.323350\pi\) | ||||
0.526911 | + | 0.849921i | \(0.323350\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.92820 | −0.451519 | ||||||||
\(392\) | 1.93185 | 0.0975732 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −11.6077 | −0.584787 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.89898 | −0.245873 | −0.122936 | − | 0.992415i | \(-0.539231\pi\) | ||||
−0.122936 | + | 0.992415i | \(0.539231\pi\) | |||||||
\(398\) | −7.24693 | −0.363256 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.8564 | −1.89046 | −0.945229 | − | 0.326407i | \(-0.894162\pi\) | ||||
−0.945229 | + | 0.326407i | \(0.894162\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.6579 | −0.779975 | ||||||||
\(404\) | −10.3923 | −0.517036 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.26795 | −0.0629273 | ||||||||
\(407\) | −11.5911 | −0.574550 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.07180 | 0.448571 | 0.224286 | − | 0.974523i | \(-0.427995\pi\) | ||||
0.224286 | + | 0.974523i | \(0.427995\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.8338 | 0.780073 | ||||||||
\(413\) | 25.4558 | 1.25260 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 9.21539 | 0.451822 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.14488 | −0.104910 | ||||||||
\(419\) | 6.00000 | 0.293119 | 0.146560 | − | 0.989202i | \(-0.453180\pi\) | ||||
0.146560 | + | 0.989202i | \(0.453180\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.46410 | 0.266304 | 0.133152 | − | 0.991096i | \(-0.457490\pi\) | ||||
0.133152 | + | 0.991096i | \(0.457490\pi\) | |||||||
\(422\) | −7.62587 | −0.371222 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.4641 | −0.556746 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.17260 | 0.347107 | ||||||||
\(428\) | 32.3238 | 1.56243 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.1769 | 1.79075 | 0.895374 | − | 0.445314i | \(-0.146908\pi\) | ||||
0.895374 | + | 0.445314i | \(0.146908\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.92996 | 0.140805 | 0.0704025 | − | 0.997519i | \(-0.477572\pi\) | ||||
0.0704025 | + | 0.997519i | \(0.477572\pi\) | |||||||
\(434\) | −11.0718 | −0.531463 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −30.9282 | −1.48119 | ||||||||
\(437\) | 20.6312 | 0.986924 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.07180 | −0.337518 | −0.168759 | − | 0.985657i | \(-0.553976\pi\) | ||||
−0.168759 | + | 0.985657i | \(0.553976\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.31268 | 0.0624377 | ||||||||
\(443\) | 18.1817 | 0.863839 | 0.431919 | − | 0.901912i | \(-0.357836\pi\) | ||||
0.431919 | + | 0.901912i | \(0.357836\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7.94744 | 0.376322 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.55532 | −0.262464 | ||||||||
\(449\) | 25.8564 | 1.22024 | 0.610120 | − | 0.792309i | \(-0.291121\pi\) | ||||
0.610120 | + | 0.792309i | \(0.291121\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.78461 | 0.413651 | ||||||||
\(452\) | 22.5259 | 1.05953 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.5885 | −0.496941 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.6627 | 1.10689 | 0.553447 | − | 0.832884i | \(-0.313312\pi\) | ||||
0.553447 | + | 0.832884i | \(0.313312\pi\) | |||||||
\(458\) | 9.72363 | 0.454355 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.9282 | −1.16102 | −0.580511 | − | 0.814252i | \(-0.697147\pi\) | ||||
−0.580511 | + | 0.814252i | \(0.697147\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.86800 | −0.319183 | −0.159591 | − | 0.987183i | \(-0.551018\pi\) | ||||
−0.159591 | + | 0.987183i | \(0.551018\pi\) | |||||||
\(464\) | −2.46410 | −0.114393 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.75129 | −0.0811269 | ||||||||
\(467\) | 21.0101 | 0.972233 | 0.486116 | − | 0.873894i | \(-0.338413\pi\) | ||||
0.486116 | + | 0.873894i | \(0.338413\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.3923 | −0.479872 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −20.0764 | −0.924091 | ||||||||
\(473\) | −11.5911 | −0.532960 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.00000 | −0.275010 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.37945 | −0.246050 | ||||||||
\(479\) | −5.66025 | −0.258624 | −0.129312 | − | 0.991604i | \(-0.541277\pi\) | ||||
−0.129312 | + | 0.991604i | \(0.541277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.3923 | −0.747425 | ||||||||
\(482\) | 5.93426 | 0.270298 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.2679 | 0.739452 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.9348 | 0.495502 | 0.247751 | − | 0.968824i | \(-0.420309\pi\) | ||||
0.247751 | + | 0.968824i | \(0.420309\pi\) | |||||||
\(488\) | −5.65685 | −0.256074 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.26795 | −0.327998 | −0.163999 | − | 0.986461i | \(-0.552439\pi\) | ||||
−0.163999 | + | 0.986461i | \(0.552439\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.41421 | −0.0636930 | ||||||||
\(494\) | −3.03332 | −0.136476 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.5167 | −0.966127 | ||||||||
\(497\) | −8.48528 | −0.380617 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.07180 | −0.0479802 | −0.0239901 | − | 0.999712i | \(-0.507637\pi\) | ||||
−0.0239901 | + | 0.999712i | \(0.507637\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.82894 | −0.349423 | ||||||||
\(503\) | −12.1731 | −0.542773 | −0.271386 | − | 0.962471i | \(-0.587482\pi\) | ||||
−0.271386 | + | 0.962471i | \(0.587482\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.14359 | −0.184205 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.34847 | 0.326036 | ||||||||
\(509\) | −33.4641 | −1.48327 | −0.741635 | − | 0.670804i | \(-0.765949\pi\) | ||||
−0.741635 | + | 0.670804i | \(0.765949\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.0000 | 0.796273 | ||||||||
\(512\) | 22.1841 | 0.980408 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.92820 | −0.217374 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.79315 | 0.0788627 | ||||||||
\(518\) | −11.5911 | −0.509284 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.39230 | −0.192430 | −0.0962152 | − | 0.995361i | \(-0.530674\pi\) | ||||
−0.0962152 | + | 0.995361i | \(0.530674\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.61729 | −0.0707190 | −0.0353595 | − | 0.999375i | \(-0.511258\pi\) | ||||
−0.0353595 | + | 0.999375i | \(0.511258\pi\) | |||||||
\(524\) | −8.19615 | −0.358051 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.48334 | 0.108279 | ||||||||
\(527\) | −12.3490 | −0.537930 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.8564 | 0.732887 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 13.8647 | 0.601112 | ||||||||
\(533\) | 12.4233 | 0.538113 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.19615 | 0.354020 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.21166 | 0.267804 | ||||||||
\(539\) | −1.26795 | −0.0546144 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.3923 | 1.82259 | 0.911294 | − | 0.411757i | \(-0.135085\pi\) | ||||
0.911294 | + | 0.411757i | \(0.135085\pi\) | |||||||
\(542\) | −13.8375 | −0.594373 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.26795 | 0.311611 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.44949 | 0.104733 | 0.0523663 | − | 0.998628i | \(-0.483324\pi\) | ||||
0.0523663 | + | 0.998628i | \(0.483324\pi\) | |||||||
\(548\) | −25.6317 | −1.09493 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.26795 | 0.139219 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.2784 | −0.437083 | ||||||||
\(554\) | −9.71281 | −0.412658 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.8564 | 0.587643 | ||||||||
\(557\) | −0.554803 | −0.0235078 | −0.0117539 | − | 0.999931i | \(-0.503741\pi\) | ||||
−0.0117539 | + | 0.999931i | \(0.503741\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.3923 | −0.693321 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.9706 | −0.715860 | ||||||||
\(563\) | 13.2827 | 0.559800 | 0.279900 | − | 0.960029i | \(-0.409699\pi\) | ||||
0.279900 | + | 0.960029i | \(0.409699\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.1962 | 0.596709 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.69213 | 0.280796 | ||||||||
\(569\) | −21.4641 | −0.899822 | −0.449911 | − | 0.893073i | \(-0.648544\pi\) | ||||
−0.449911 | + | 0.893073i | \(0.648544\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.3205 | −1.64551 | −0.822756 | − | 0.568395i | \(-0.807565\pi\) | ||||
−0.822756 | + | 0.568395i | \(0.807565\pi\) | |||||||
\(572\) | −3.93803 | −0.164657 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.78461 | 0.366663 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.14162 | −0.380571 | −0.190285 | − | 0.981729i | \(-0.560941\pi\) | ||||
−0.190285 | + | 0.981729i | \(0.560941\pi\) | |||||||
\(578\) | −7.76457 | −0.322964 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.9282 | 1.03420 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.52433 | 0.311626 | ||||||||
\(584\) | −14.1962 | −0.587441 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.9090 | 0.657193 | ||||||||
\(587\) | −15.5563 | −0.642079 | −0.321040 | − | 0.947066i | \(-0.604032\pi\) | ||||
−0.321040 | + | 0.947066i | \(0.604032\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.5359 | 1.17580 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −22.5259 | −0.925808 | ||||||||
\(593\) | 25.5302 | 1.04840 | 0.524199 | − | 0.851596i | \(-0.324365\pi\) | ||||
0.524199 | + | 0.851596i | \(0.324365\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.60770 | −0.0658538 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.85993 | −0.239630 | ||||||||
\(599\) | −1.26795 | −0.0518070 | −0.0259035 | − | 0.999664i | \(-0.508246\pi\) | ||||
−0.0259035 | + | 0.999664i | \(0.508246\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.7846 | 0.684659 | 0.342329 | − | 0.939580i | \(-0.388784\pi\) | ||||
0.342329 | + | 0.939580i | \(0.388784\pi\) | |||||||
\(602\) | −11.5911 | −0.472418 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 32.5359 | 1.32387 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.3142 | −0.662174 | −0.331087 | − | 0.943600i | \(-0.607415\pi\) | ||||
−0.331087 | + | 0.943600i | \(0.607415\pi\) | |||||||
\(608\) | −16.7947 | −0.681115 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.53590 | 0.102591 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.2832 | −0.738453 | −0.369227 | − | 0.929339i | \(-0.620377\pi\) | ||||
−0.369227 | + | 0.929339i | \(0.620377\pi\) | |||||||
\(614\) | −5.41154 | −0.218392 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.00000 | −0.241747 | ||||||||
\(617\) | −32.0464 | −1.29014 | −0.645071 | − | 0.764123i | \(-0.723172\pi\) | ||||
−0.645071 | + | 0.764123i | \(0.723172\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.8038 | −0.956757 | −0.478379 | − | 0.878154i | \(-0.658775\pi\) | ||||
−0.478379 | + | 0.878154i | \(0.658775\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.41044 | 0.136746 | ||||||||
\(623\) | −25.4558 | −1.01987 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12.2487 | 0.489557 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.9396 | 0.755771 | ||||||||
\(629\) | −12.9282 | −0.515481 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.6077 | 0.621333 | 0.310666 | − | 0.950519i | \(-0.399448\pi\) | ||||
0.310666 | + | 0.950519i | \(0.399448\pi\) | |||||||
\(632\) | 8.10634 | 0.322453 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.98076 | −0.118381 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.79315 | −0.0710472 | ||||||||
\(638\) | −0.656339 | −0.0259847 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.6410 | −1.36824 | −0.684119 | − | 0.729370i | \(-0.739813\pi\) | ||||
−0.684119 | + | 0.729370i | \(0.739813\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.4543 | 0.412277 | 0.206139 | − | 0.978523i | \(-0.433910\pi\) | ||||
0.206139 | + | 0.978523i | \(0.433910\pi\) | |||||||
\(644\) | 26.7846 | 1.05546 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.39230 | −0.0941240 | ||||||||
\(647\) | 14.3180 | 0.562899 | 0.281449 | − | 0.959576i | \(-0.409185\pi\) | ||||
0.281449 | + | 0.959576i | \(0.409185\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.1769 | 0.517239 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24.3190 | 0.952407 | ||||||||
\(653\) | −13.0053 | −0.508938 | −0.254469 | − | 0.967081i | \(-0.581901\pi\) | ||||
−0.254469 | + | 0.967081i | \(0.581901\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 17.0718 | 0.666542 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.79315 | 0.0699043 | ||||||||
\(659\) | −32.4449 | −1.26387 | −0.631936 | − | 0.775020i | \(-0.717740\pi\) | ||||
−0.631936 | + | 0.775020i | \(0.717740\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.784610 | −0.0305178 | −0.0152589 | − | 0.999884i | \(-0.504857\pi\) | ||||
−0.0152589 | + | 0.999884i | \(0.504857\pi\) | |||||||
\(662\) | −9.41902 | −0.366081 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19.6603 | −0.762966 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.31319 | 0.244448 | ||||||||
\(668\) | −19.4201 | −0.751384 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.71281 | 0.143332 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.3644 | −1.78722 | −0.893609 | − | 0.448846i | \(-0.851835\pi\) | ||||
−0.893609 | + | 0.448846i | \(0.851835\pi\) | |||||||
\(674\) | 14.4449 | 0.556395 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.9474 | 0.651825 | ||||||||
\(677\) | 32.2495 | 1.23945 | 0.619725 | − | 0.784819i | \(-0.287244\pi\) | ||||
0.619725 | + | 0.784819i | \(0.287244\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.7846 | 1.02790 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.73118 | −0.219458 | ||||||||
\(683\) | −21.9711 | −0.840700 | −0.420350 | − | 0.907362i | \(-0.638093\pi\) | ||||
−0.420350 | + | 0.907362i | \(0.638093\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10.1436 | −0.387284 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −22.5259 | −0.858791 | ||||||||
\(689\) | 10.6410 | 0.405390 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.7128 | 1.58683 | 0.793415 | − | 0.608681i | \(-0.208301\pi\) | ||||
0.793415 | + | 0.608681i | \(0.208301\pi\) | |||||||
\(692\) | −8.00481 | −0.304297 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.1244 | 0.422275 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.79796 | 0.371124 | ||||||||
\(698\) | −11.7942 | −0.446416 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.7128 | −1.04670 | −0.523349 | − | 0.852118i | \(-0.675318\pi\) | ||||
−0.523349 | + | 0.852118i | \(0.675318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29.8744 | 1.12673 | ||||||||
\(704\) | −2.87564 | −0.108380 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.5359 | −0.622337 | ||||||||
\(707\) | 14.6969 | 0.552735 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.3923 | 0.765849 | 0.382925 | − | 0.923780i | \(-0.374917\pi\) | ||||
0.382925 | + | 0.923780i | \(0.374917\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 20.0764 | 0.752395 | ||||||||
\(713\) | 55.1271 | 2.06453 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.39230 | 0.164148 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.76217 | 0.140403 | ||||||||
\(719\) | 19.8564 | 0.740519 | 0.370260 | − | 0.928928i | \(-0.379269\pi\) | ||||
0.370260 | + | 0.928928i | \(0.379269\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.3923 | −0.833933 | ||||||||
\(722\) | −4.30701 | −0.160290 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 27.7128 | 1.02994 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.6690 | 1.73086 | 0.865430 | − | 0.501031i | \(-0.167046\pi\) | ||||
0.865430 | + | 0.501031i | \(0.167046\pi\) | |||||||
\(728\) | −8.48528 | −0.314485 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.9282 | −0.478167 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.7279 | −0.470117 | −0.235058 | − | 0.971981i | \(-0.575528\pi\) | ||||
−0.235058 | + | 0.971981i | \(0.575528\pi\) | |||||||
\(734\) | 17.4115 | 0.642672 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −32.4449 | −1.19593 | ||||||||
\(737\) | −5.37945 | −0.198155 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.9808 | −0.698219 | −0.349109 | − | 0.937082i | \(-0.613516\pi\) | ||||
−0.349109 | + | 0.937082i | \(0.613516\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.52433 | 0.276227 | ||||||||
\(743\) | −9.89949 | −0.363177 | −0.181589 | − | 0.983375i | \(-0.558124\pi\) | ||||
−0.181589 | + | 0.983375i | \(0.558124\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.1436 | 0.371383 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.10583 | −0.113560 | ||||||||
\(749\) | −45.7128 | −1.67031 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.9090 | 1.82120 | 0.910602 | − | 0.413284i | \(-0.135618\pi\) | ||||
0.910602 | + | 0.413284i | \(0.135618\pi\) | |||||||
\(752\) | 3.48477 | 0.127076 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.928203 | −0.0338032 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.9348 | −0.397431 | −0.198716 | − | 0.980057i | \(-0.563677\pi\) | ||||
−0.198716 | + | 0.980057i | \(0.563677\pi\) | |||||||
\(758\) | −8.38375 | −0.304511 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.5692 | 1.28938 | 0.644692 | − | 0.764443i | \(-0.276986\pi\) | ||||
0.644692 | + | 0.764443i | \(0.276986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.7391 | 1.58346 | ||||||||
\(764\) | 26.1962 | 0.947744 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.483340 | −0.0174638 | ||||||||
\(767\) | 18.6350 | 0.672870 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.0718 | −0.687747 | −0.343873 | − | 0.939016i | \(-0.611739\pi\) | ||||
−0.343873 | + | 0.939016i | \(0.611739\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.13681 | −0.0409148 | ||||||||
\(773\) | −11.2122 | −0.403274 | −0.201637 | − | 0.979460i | \(-0.564626\pi\) | ||||
−0.201637 | + | 0.979460i | \(0.564626\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −21.1244 | −0.758320 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.7589 | 0.385725 | ||||||||
\(779\) | −22.6410 | −0.811199 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.39230 | −0.157169 | ||||||||
\(782\) | −4.62158 | −0.165267 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.46410 | −0.0880036 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.0779 | −1.25039 | −0.625197 | − | 0.780467i | \(-0.714981\pi\) | ||||
−0.625197 | + | 0.780467i | \(0.714981\pi\) | |||||||
\(788\) | 38.8401 | 1.38362 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.8564 | −1.13268 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.25071 | 0.186458 | ||||||||
\(794\) | −2.53590 | −0.0899957 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.2487 | 0.859473 | ||||||||
\(797\) | 29.0149 | 1.02776 | 0.513881 | − | 0.857862i | \(-0.328207\pi\) | ||||
0.513881 | + | 0.857862i | \(0.328207\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.00000 | 0.0707549 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.5959 | −0.691956 | ||||||||
\(803\) | 9.31749 | 0.328807 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.10512 | −0.285491 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.5911 | −0.407774 | ||||||||
\(809\) | −13.6077 | −0.478421 | −0.239211 | − | 0.970968i | \(-0.576889\pi\) | ||||
−0.239211 | + | 0.970968i | \(0.576889\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.7846 | −1.29168 | −0.645841 | − | 0.763472i | \(-0.723493\pi\) | ||||
−0.645841 | + | 0.763472i | \(0.723493\pi\) | |||||||
\(812\) | 4.24264 | 0.148888 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.00000 | −0.210300 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.8744 | 1.04517 | ||||||||
\(818\) | 4.69591 | 0.164189 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.21539 | −0.321619 | −0.160810 | − | 0.986985i | \(-0.551411\pi\) | ||||
−0.160810 | + | 0.986985i | \(0.551411\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.8091 | 1.42252 | 0.711258 | − | 0.702931i | \(-0.248126\pi\) | ||||
0.711258 | + | 0.702931i | \(0.248126\pi\) | |||||||
\(824\) | 17.6603 | 0.615224 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.1769 | 0.458483 | ||||||||
\(827\) | 3.68784 | 0.128239 | 0.0641193 | − | 0.997942i | \(-0.479576\pi\) | ||||
0.0641193 | + | 0.997942i | \(0.479576\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.7846 | −0.582954 | −0.291477 | − | 0.956578i | \(-0.594147\pi\) | ||||
−0.291477 | + | 0.956578i | \(0.594147\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.06678 | −0.140990 | ||||||||
\(833\) | −1.41421 | −0.0489996 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.17691 | 0.248219 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.10583 | 0.107289 | ||||||||
\(839\) | −40.9808 | −1.41481 | −0.707407 | − | 0.706807i | \(-0.750135\pi\) | ||||
−0.707407 | + | 0.706807i | \(0.750135\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 2.82843 | 0.0974740 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 25.5167 | 0.878320 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.0064 | −0.790508 | ||||||||
\(848\) | 14.6226 | 0.502142 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 57.7128 | 1.97837 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.3238 | −1.10675 | −0.553374 | − | 0.832933i | \(-0.686660\pi\) | ||||
−0.553374 | + | 0.832933i | \(0.686660\pi\) | |||||||
\(854\) | 3.71281 | 0.127050 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 36.0526 | 1.23225 | ||||||||
\(857\) | 33.2576 | 1.13606 | 0.568029 | − | 0.823009i | \(-0.307706\pi\) | ||||
0.568029 | + | 0.823009i | \(0.307706\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.7321 | −0.639129 | −0.319565 | − | 0.947564i | \(-0.603537\pi\) | ||||
−0.319565 | + | 0.947564i | \(0.603537\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.2442 | 0.655460 | ||||||||
\(863\) | 1.69161 | 0.0575832 | 0.0287916 | − | 0.999585i | \(-0.490834\pi\) | ||||
0.0287916 | + | 0.999585i | \(0.490834\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.51666 | 0.0515382 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 37.0470 | 1.25746 | ||||||||
\(869\) | −5.32051 | −0.180486 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.60770 | −0.257777 | ||||||||
\(872\) | −34.4959 | −1.16818 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 10.6795 | 0.361239 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.9754 | −0.843358 | −0.421679 | − | 0.906745i | \(-0.638559\pi\) | ||||
−0.421679 | + | 0.906745i | \(0.638559\pi\) | |||||||
\(878\) | −3.66063 | −0.123540 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50.5359 | 1.70260 | 0.851299 | − | 0.524681i | \(-0.175815\pi\) | ||||
0.851299 | + | 0.524681i | \(0.175815\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.48854 | −0.0500935 | −0.0250467 | − | 0.999686i | \(-0.507973\pi\) | ||||
−0.0250467 | + | 0.999686i | \(0.507973\pi\) | |||||||
\(884\) | −4.39230 | −0.147729 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.41154 | 0.316187 | ||||||||
\(887\) | 21.0101 | 0.705451 | 0.352726 | − | 0.935727i | \(-0.385255\pi\) | ||||
0.352726 | + | 0.935727i | \(0.385255\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.3923 | −0.348547 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −26.5927 | −0.890388 | ||||||||
\(893\) | −4.62158 | −0.154655 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −28.0526 | −0.937170 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.3843 | 0.446639 | ||||||||
\(899\) | 8.73205 | 0.291230 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.39230 | 0.279588 | ||||||||
\(902\) | 4.54725 | 0.151407 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 25.1244 | 0.835624 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.7081 | 1.51771 | 0.758856 | − | 0.651258i | \(-0.225758\pi\) | ||||
0.758856 | + | 0.651258i | \(0.225758\pi\) | |||||||
\(908\) | 35.4297 | 1.17577 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.80385 | 0.324816 | 0.162408 | − | 0.986724i | \(-0.448074\pi\) | ||||
0.162408 | + | 0.986724i | \(0.448074\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.9038 | 0.427053 | ||||||||
\(914\) | 12.2487 | 0.405151 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −32.5359 | −1.07502 | ||||||||
\(917\) | 11.5911 | 0.382772 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.9615 | 1.45016 | 0.725078 | − | 0.688666i | \(-0.241803\pi\) | ||||
0.725078 | + | 0.688666i | \(0.241803\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.9038 | −0.424964 | ||||||||
\(923\) | −6.21166 | −0.204459 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.55514 | −0.116829 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.13922 | −0.168703 | ||||||||
\(929\) | −55.8564 | −1.83259 | −0.916295 | − | 0.400505i | \(-0.868835\pi\) | ||||
−0.916295 | + | 0.400505i | \(0.868835\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.26795 | 0.107103 | ||||||||
\(932\) | 5.85993 | 0.191948 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.8756 | 0.355862 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.75410 | −0.0899724 | −0.0449862 | − | 0.998988i | \(-0.514324\pi\) | ||||
−0.0449862 | + | 0.998988i | \(0.514324\pi\) | |||||||
\(938\) | −5.37945 | −0.175645 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.85641 | 0.256112 | 0.128056 | − | 0.991767i | \(-0.459126\pi\) | ||||
0.128056 | + | 0.991767i | \(0.459126\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −43.7391 | −1.42434 | ||||||||
\(944\) | 25.6077 | 0.833459 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.00000 | −0.195077 | ||||||||
\(947\) | −27.9797 | −0.909217 | −0.454608 | − | 0.890691i | \(-0.650221\pi\) | ||||
−0.454608 | + | 0.890691i | \(0.650221\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.1769 | 0.427741 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.69213 | −0.216893 | ||||||||
\(953\) | −5.65685 | −0.183243 | −0.0916217 | − | 0.995794i | \(-0.529205\pi\) | ||||
−0.0916217 | + | 0.995794i | \(0.529205\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 18.0000 | 0.582162 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.92996 | −0.0946628 | ||||||||
\(959\) | 36.2487 | 1.17053 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45.2487 | 1.45964 | ||||||||
\(962\) | −8.48528 | −0.273576 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −19.8564 | −0.639532 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.96902 | 0.0633193 | 0.0316596 | − | 0.999499i | \(-0.489921\pi\) | ||||
0.0316596 | + | 0.999499i | \(0.489921\pi\) | |||||||
\(968\) | 18.1445 | 0.583188 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.5167 | 1.58907 | 0.794533 | − | 0.607221i | \(-0.207716\pi\) | ||||
0.794533 | + | 0.607221i | \(0.207716\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.5959 | −0.628216 | ||||||||
\(974\) | 5.66025 | 0.181366 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.21539 | 0.230959 | ||||||||
\(977\) | −22.9048 | −0.732790 | −0.366395 | − | 0.930459i | \(-0.619408\pi\) | ||||
−0.366395 | + | 0.930459i | \(0.619408\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.1769 | −0.421136 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.76217 | −0.120056 | ||||||||
\(983\) | 30.2533 | 0.964930 | 0.482465 | − | 0.875915i | \(-0.339742\pi\) | ||||
0.482465 | + | 0.875915i | \(0.339742\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.732051 | −0.0233132 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.1497 | 0.322905 | ||||||||
\(989\) | 57.7128 | 1.83516 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.7846 | 1.10497 | 0.552485 | − | 0.833523i | \(-0.313680\pi\) | ||||
0.552485 | + | 0.833523i | \(0.313680\pi\) | |||||||
\(992\) | −44.8759 | −1.42481 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.39230 | −0.139315 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.5927 | −0.842198 | −0.421099 | − | 0.907015i | \(-0.638355\pi\) | ||||
−0.421099 | + | 0.907015i | \(0.638355\pi\) | |||||||
\(998\) | −0.554803 | −0.0175620 | ||||||||
\(999\) | 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 | 6525.2.a.bj.1.3 | 4 | ||
3.2 | odd | 2 | 725.2.a.f.1.2 | 4 | |||
5.2 | odd | 4 | 1305.2.c.f.784.3 | 4 | |||
5.3 | odd | 4 | 1305.2.c.f.784.2 | 4 | |||
5.4 | even | 2 | inner | 6525.2.a.bj.1.2 | 4 | ||
15.2 | even | 4 | 145.2.b.b.59.2 | ✓ | 4 | ||
15.8 | even | 4 | 145.2.b.b.59.3 | yes | 4 | ||
15.14 | odd | 2 | 725.2.a.f.1.3 | 4 | |||
60.23 | odd | 4 | 2320.2.d.f.929.3 | 4 | |||
60.47 | odd | 4 | 2320.2.d.f.929.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
145.2.b.b.59.2 | ✓ | 4 | 15.2 | even | 4 | ||
145.2.b.b.59.3 | yes | 4 | 15.8 | even | 4 | ||
725.2.a.f.1.2 | 4 | 3.2 | odd | 2 | |||
725.2.a.f.1.3 | 4 | 15.14 | odd | 2 | |||
1305.2.c.f.784.2 | 4 | 5.3 | odd | 4 | |||
1305.2.c.f.784.3 | 4 | 5.2 | odd | 4 | |||
2320.2.d.f.929.1 | 4 | 60.47 | odd | 4 | |||
2320.2.d.f.929.3 | 4 | 60.23 | odd | 4 | |||
6525.2.a.bj.1.2 | 4 | 5.4 | even | 2 | inner | ||
6525.2.a.bj.1.3 | 4 | 1.1 | even | 1 | trivial |