Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9522,2,Mod(1,9522)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9522, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9522.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9522 = 2 \cdot 3^{2} \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9522.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: | \(76.0335528047\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.546984493056.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 20x^{6} + 129x^{4} - 320x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.75786\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9522.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.343645 | 0.153683 | 0.0768413 | − | 0.997043i | \(-0.475517\pi\) | ||||
0.0768413 | + | 0.997043i | \(0.475517\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.27550 | 0.860057 | 0.430028 | − | 0.902815i | \(-0.358504\pi\) | ||||
0.430028 | + | 0.902815i | \(0.358504\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.343645 | 0.108670 | ||||||||
\(11\) | −3.94128 | −1.18834 | −0.594170 | − | 0.804340i | \(-0.702519\pi\) | ||||
−0.594170 | + | 0.804340i | \(0.702519\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.39592 | 1.49656 | 0.748280 | − | 0.663383i | \(-0.230880\pi\) | ||||
0.748280 | + | 0.663383i | \(0.230880\pi\) | |||||||
\(14\) | 2.27550 | 0.608152 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.63099 | 1.85079 | 0.925393 | − | 0.379009i | \(-0.123735\pi\) | ||||
0.925393 | + | 0.379009i | \(0.123735\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.55099 | 1.04407 | 0.522035 | − | 0.852924i | \(-0.325173\pi\) | ||||
0.522035 | + | 0.852924i | \(0.325173\pi\) | |||||||
\(20\) | 0.343645 | 0.0768413 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.94128 | −0.840283 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.88191 | −0.976382 | ||||||||
\(26\) | 5.39592 | 1.05823 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.27550 | 0.430028 | ||||||||
\(29\) | 2.21804 | 0.411879 | 0.205940 | − | 0.978565i | \(-0.433975\pi\) | ||||
0.205940 | + | 0.978565i | \(0.433975\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.04015 | 0.366423 | 0.183211 | − | 0.983074i | \(-0.441351\pi\) | ||||
0.183211 | + | 0.983074i | \(0.441351\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.63099 | 1.30870 | ||||||||
\(35\) | 0.781962 | 0.132176 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.47584 | −1.22902 | −0.614510 | − | 0.788909i | \(-0.710646\pi\) | ||||
−0.614510 | + | 0.788909i | \(0.710646\pi\) | |||||||
\(38\) | 4.55099 | 0.738268 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.343645 | 0.0543350 | ||||||||
\(41\) | 1.09007 | 0.170240 | 0.0851198 | − | 0.996371i | \(-0.472873\pi\) | ||||
0.0851198 | + | 0.996371i | \(0.472873\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.22570 | −0.339416 | −0.169708 | − | 0.985494i | \(-0.554282\pi\) | ||||
−0.169708 | + | 0.985494i | \(0.554282\pi\) | |||||||
\(44\) | −3.94128 | −0.594170 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.2840 | 1.93767 | 0.968833 | − | 0.247714i | \(-0.0796794\pi\) | ||||
0.968833 | + | 0.247714i | \(0.0796794\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.82212 | −0.260302 | ||||||||
\(50\) | −4.88191 | −0.690406 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.39592 | 0.748280 | ||||||||
\(53\) | 5.62855 | 0.773141 | 0.386570 | − | 0.922260i | \(-0.373660\pi\) | ||||
0.386570 | + | 0.922260i | \(0.373660\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.35440 | −0.182627 | ||||||||
\(56\) | 2.27550 | 0.304076 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.21804 | 0.291243 | ||||||||
\(59\) | 8.39592 | 1.09306 | 0.546528 | − | 0.837441i | \(-0.315949\pi\) | ||||
0.546528 | + | 0.837441i | \(0.315949\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.48986 | −0.574868 | −0.287434 | − | 0.957800i | \(-0.592802\pi\) | ||||
−0.287434 | + | 0.957800i | \(0.592802\pi\) | |||||||
\(62\) | 2.04015 | 0.259100 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.85428 | 0.229995 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.17641 | −0.388061 | −0.194030 | − | 0.980996i | \(-0.562156\pi\) | ||||
−0.194030 | + | 0.980996i | \(0.562156\pi\) | |||||||
\(68\) | 7.63099 | 0.925393 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.781962 | 0.0934624 | ||||||||
\(71\) | 3.50787 | 0.416308 | 0.208154 | − | 0.978096i | \(-0.433255\pi\) | ||||
0.208154 | + | 0.978096i | \(0.433255\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.0977 | −1.41593 | −0.707964 | − | 0.706248i | \(-0.750386\pi\) | ||||
−0.707964 | + | 0.706248i | \(0.750386\pi\) | |||||||
\(74\) | −7.47584 | −0.869049 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.55099 | 0.522035 | ||||||||
\(77\) | −8.96836 | −1.02204 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.52246 | −0.846343 | −0.423172 | − | 0.906050i | \(-0.639083\pi\) | ||||
−0.423172 | + | 0.906050i | \(0.639083\pi\) | |||||||
\(80\) | 0.343645 | 0.0384206 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.09007 | 0.120378 | ||||||||
\(83\) | −5.31585 | −0.583491 | −0.291745 | − | 0.956496i | \(-0.594236\pi\) | ||||
−0.291745 | + | 0.956496i | \(0.594236\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.62235 | 0.284434 | ||||||||
\(86\) | −2.22570 | −0.240003 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.94128 | −0.420141 | ||||||||
\(89\) | −12.5911 | −1.33465 | −0.667327 | − | 0.744765i | \(-0.732561\pi\) | ||||
−0.667327 | + | 0.744765i | \(0.732561\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.2784 | 1.28713 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.2840 | 1.37014 | ||||||||
\(95\) | 1.56392 | 0.160455 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.1182 | −1.33195 | −0.665975 | − | 0.745974i | \(-0.731984\pi\) | ||||
−0.665975 | + | 0.745974i | \(0.731984\pi\) | |||||||
\(98\) | −1.82212 | −0.184062 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.88191 | −0.488191 | ||||||||
\(101\) | 12.1681 | 1.21077 | 0.605387 | − | 0.795931i | \(-0.293018\pi\) | ||||
0.605387 | + | 0.795931i | \(0.293018\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.764861 | −0.0753640 | −0.0376820 | − | 0.999290i | \(-0.511997\pi\) | ||||
−0.0376820 | + | 0.999290i | \(0.511997\pi\) | |||||||
\(104\) | 5.39592 | 0.529114 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.62855 | 0.546693 | ||||||||
\(107\) | 9.39319 | 0.908074 | 0.454037 | − | 0.890983i | \(-0.349983\pi\) | ||||
0.454037 | + | 0.890983i | \(0.349983\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.11843 | −0.490257 | −0.245128 | − | 0.969491i | \(-0.578830\pi\) | ||||
−0.245128 | + | 0.969491i | \(0.578830\pi\) | |||||||
\(110\) | −1.35440 | −0.129137 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.27550 | 0.215014 | ||||||||
\(113\) | 15.8262 | 1.48881 | 0.744403 | − | 0.667730i | \(-0.232734\pi\) | ||||
0.744403 | + | 0.667730i | \(0.232734\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.21804 | 0.205940 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.39592 | 0.772907 | ||||||||
\(119\) | 17.3643 | 1.59178 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.53365 | 0.412150 | ||||||||
\(122\) | −4.48986 | −0.406493 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.04015 | 0.183211 | ||||||||
\(125\) | −3.39587 | −0.303735 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 22.1561 | 1.96604 | 0.983019 | − | 0.183504i | \(-0.0587441\pi\) | ||||
0.983019 | + | 0.183504i | \(0.0587441\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.85428 | 0.162631 | ||||||||
\(131\) | −0.685756 | −0.0599148 | −0.0299574 | − | 0.999551i | \(-0.509537\pi\) | ||||
−0.0299574 | + | 0.999551i | \(0.509537\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.3558 | 0.897959 | ||||||||
\(134\) | −3.17641 | −0.274400 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.63099 | 0.654352 | ||||||||
\(137\) | 17.2833 | 1.47661 | 0.738304 | − | 0.674468i | \(-0.235627\pi\) | ||||
0.738304 | + | 0.674468i | \(0.235627\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.2279 | −0.952340 | −0.476170 | − | 0.879353i | \(-0.657975\pi\) | ||||
−0.476170 | + | 0.879353i | \(0.657975\pi\) | |||||||
\(140\) | 0.781962 | 0.0660879 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.50787 | 0.294374 | ||||||||
\(143\) | −21.2668 | −1.77842 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.762217 | 0.0632987 | ||||||||
\(146\) | −12.0977 | −1.00121 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.47584 | −0.614510 | ||||||||
\(149\) | 2.38836 | 0.195662 | 0.0978311 | − | 0.995203i | \(-0.468810\pi\) | ||||
0.0978311 | + | 0.995203i | \(0.468810\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.7616 | −1.20128 | −0.600640 | − | 0.799520i | \(-0.705087\pi\) | ||||
−0.600640 | + | 0.799520i | \(0.705087\pi\) | |||||||
\(152\) | 4.55099 | 0.369134 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.96836 | −0.722691 | ||||||||
\(155\) | 0.701088 | 0.0563128 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.0363 | −1.12022 | −0.560108 | − | 0.828420i | \(-0.689240\pi\) | ||||
−0.560108 | + | 0.828420i | \(0.689240\pi\) | |||||||
\(158\) | −7.52246 | −0.598455 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.343645 | 0.0271675 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.4361 | 0.817417 | 0.408708 | − | 0.912665i | \(-0.365979\pi\) | ||||
0.408708 | + | 0.912665i | \(0.365979\pi\) | |||||||
\(164\) | 1.09007 | 0.0851198 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.31585 | −0.412590 | ||||||||
\(167\) | −21.5837 | −1.67020 | −0.835098 | − | 0.550101i | \(-0.814589\pi\) | ||||
−0.835098 | + | 0.550101i | \(0.814589\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.1160 | 1.23969 | ||||||||
\(170\) | 2.62235 | 0.201125 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.22570 | −0.169708 | ||||||||
\(173\) | 10.6844 | 0.812319 | 0.406159 | − | 0.913802i | \(-0.366868\pi\) | ||||
0.406159 | + | 0.913802i | \(0.366868\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.1088 | −0.839744 | ||||||||
\(176\) | −3.94128 | −0.297085 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.5911 | −0.943742 | ||||||||
\(179\) | −10.1561 | −0.759104 | −0.379552 | − | 0.925170i | \(-0.623922\pi\) | ||||
−0.379552 | + | 0.925170i | \(0.623922\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0457 | 1.04401 | 0.522005 | − | 0.852943i | \(-0.325184\pi\) | ||||
0.522005 | + | 0.852943i | \(0.325184\pi\) | |||||||
\(182\) | 12.2784 | 0.910136 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.56903 | −0.188879 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −30.0758 | −2.19936 | ||||||||
\(188\) | 13.2840 | 0.968833 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.56392 | 0.113459 | ||||||||
\(191\) | −15.3239 | −1.10880 | −0.554398 | − | 0.832252i | \(-0.687052\pi\) | ||||
−0.554398 | + | 0.832252i | \(0.687052\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.52976 | 0.110114 | 0.0550572 | − | 0.998483i | \(-0.482466\pi\) | ||||
0.0550572 | + | 0.998483i | \(0.482466\pi\) | |||||||
\(194\) | −13.1182 | −0.941831 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.82212 | −0.130151 | ||||||||
\(197\) | 21.5724 | 1.53697 | 0.768486 | − | 0.639866i | \(-0.221010\pi\) | ||||
0.768486 | + | 0.639866i | \(0.221010\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.1817 | 1.57242 | 0.786210 | − | 0.617960i | \(-0.212041\pi\) | ||||
0.786210 | + | 0.617960i | \(0.212041\pi\) | |||||||
\(200\) | −4.88191 | −0.345203 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.1681 | 0.856146 | ||||||||
\(203\) | 5.04714 | 0.354240 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.374595 | 0.0261629 | ||||||||
\(206\) | −0.764861 | −0.0532904 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.39592 | 0.374140 | ||||||||
\(209\) | −17.9367 | −1.24071 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.13636 | −0.147073 | −0.0735366 | − | 0.997293i | \(-0.523429\pi\) | ||||
−0.0735366 | + | 0.997293i | \(0.523429\pi\) | |||||||
\(212\) | 5.62855 | 0.386570 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.39319 | 0.642105 | ||||||||
\(215\) | −0.764849 | −0.0521622 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.64236 | 0.315144 | ||||||||
\(218\) | −5.11843 | −0.346664 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.35440 | −0.0913135 | ||||||||
\(221\) | 41.1762 | 2.76981 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.1561 | 0.947964 | 0.473982 | − | 0.880535i | \(-0.342816\pi\) | ||||
0.473982 | + | 0.880535i | \(0.342816\pi\) | |||||||
\(224\) | 2.27550 | 0.152038 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.8262 | 1.05275 | ||||||||
\(227\) | −20.9207 | −1.38856 | −0.694278 | − | 0.719707i | \(-0.744276\pi\) | ||||
−0.694278 | + | 0.719707i | \(0.744276\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.599552 | 0.0396195 | 0.0198098 | − | 0.999804i | \(-0.493694\pi\) | ||||
0.0198098 | + | 0.999804i | \(0.493694\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.21804 | 0.145621 | ||||||||
\(233\) | 18.4981 | 1.21185 | 0.605926 | − | 0.795521i | \(-0.292803\pi\) | ||||
0.605926 | + | 0.795521i | \(0.292803\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.56497 | 0.297786 | ||||||||
\(236\) | 8.39592 | 0.546528 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 17.3643 | 1.12556 | ||||||||
\(239\) | −14.5164 | −0.938987 | −0.469493 | − | 0.882936i | \(-0.655563\pi\) | ||||
−0.469493 | + | 0.882936i | \(0.655563\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1157 | 0.780443 | 0.390222 | − | 0.920721i | \(-0.372398\pi\) | ||||
0.390222 | + | 0.920721i | \(0.372398\pi\) | |||||||
\(242\) | 4.53365 | 0.291434 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.48986 | −0.287434 | ||||||||
\(245\) | −0.626161 | −0.0400039 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.5568 | 1.56251 | ||||||||
\(248\) | 2.04015 | 0.129550 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.39587 | −0.214773 | ||||||||
\(251\) | −16.7349 | −1.05630 | −0.528149 | − | 0.849152i | \(-0.677114\pi\) | ||||
−0.528149 | + | 0.849152i | \(0.677114\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 22.1561 | 1.39020 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.2377 | 0.763365 | 0.381683 | − | 0.924293i | \(-0.375345\pi\) | ||||
0.381683 | + | 0.924293i | \(0.375345\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.0112 | −1.05703 | ||||||||
\(260\) | 1.85428 | 0.114998 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.685756 | −0.0423661 | ||||||||
\(263\) | −27.3336 | −1.68546 | −0.842730 | − | 0.538337i | \(-0.819053\pi\) | ||||
−0.842730 | + | 0.538337i | \(0.819053\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.93422 | 0.118818 | ||||||||
\(266\) | 10.3558 | 0.634953 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.17641 | −0.194030 | ||||||||
\(269\) | 25.4560 | 1.55208 | 0.776040 | − | 0.630684i | \(-0.217226\pi\) | ||||
0.776040 | + | 0.630684i | \(0.217226\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.1061 | 0.978375 | 0.489188 | − | 0.872179i | \(-0.337293\pi\) | ||||
0.489188 | + | 0.872179i | \(0.337293\pi\) | |||||||
\(272\) | 7.63099 | 0.462696 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.2833 | 1.04412 | ||||||||
\(275\) | 19.2409 | 1.16027 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.29972 | 0.498682 | 0.249341 | − | 0.968416i | \(-0.419786\pi\) | ||||
0.249341 | + | 0.968416i | \(0.419786\pi\) | |||||||
\(278\) | −11.2279 | −0.673406 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.781962 | 0.0467312 | ||||||||
\(281\) | −29.7692 | −1.77588 | −0.887942 | − | 0.459955i | \(-0.847865\pi\) | ||||
−0.887942 | + | 0.459955i | \(0.847865\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.0411 | 1.13188 | 0.565938 | − | 0.824448i | \(-0.308514\pi\) | ||||
0.565938 | + | 0.824448i | \(0.308514\pi\) | |||||||
\(284\) | 3.50787 | 0.208154 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −21.2668 | −1.25753 | ||||||||
\(287\) | 2.48044 | 0.146416 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.2319 | 2.42541 | ||||||||
\(290\) | 0.762217 | 0.0447589 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12.0977 | −0.707964 | ||||||||
\(293\) | −0.667667 | −0.0390056 | −0.0195028 | − | 0.999810i | \(-0.506208\pi\) | ||||
−0.0195028 | + | 0.999810i | \(0.506208\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.88521 | 0.167984 | ||||||||
\(296\) | −7.47584 | −0.434524 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.38836 | 0.138354 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.06456 | −0.291917 | ||||||||
\(302\) | −14.7616 | −0.849433 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.55099 | 0.261017 | ||||||||
\(305\) | −1.54292 | −0.0883472 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −31.3082 | −1.78685 | −0.893427 | − | 0.449208i | \(-0.851706\pi\) | ||||
−0.893427 | + | 0.449208i | \(0.851706\pi\) | |||||||
\(308\) | −8.96836 | −0.511020 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.701088 | 0.0398191 | ||||||||
\(311\) | 10.4361 | 0.591776 | 0.295888 | − | 0.955223i | \(-0.404385\pi\) | ||||
0.295888 | + | 0.955223i | \(0.404385\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.0889007 | −0.00502496 | −0.00251248 | − | 0.999997i | \(-0.500800\pi\) | ||||
−0.00251248 | + | 0.999997i | \(0.500800\pi\) | |||||||
\(314\) | −14.0363 | −0.792112 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.52246 | −0.423172 | ||||||||
\(317\) | 5.50924 | 0.309430 | 0.154715 | − | 0.987959i | \(-0.450554\pi\) | ||||
0.154715 | + | 0.987959i | \(0.450554\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.74190 | −0.489452 | ||||||||
\(320\) | 0.343645 | 0.0192103 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 34.7286 | 1.93235 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.3424 | −1.46121 | ||||||||
\(326\) | 10.4361 | 0.578001 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.09007 | 0.0601888 | ||||||||
\(329\) | 30.2276 | 1.66650 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.6640 | −0.751041 | −0.375521 | − | 0.926814i | \(-0.622536\pi\) | ||||
−0.375521 | + | 0.926814i | \(0.622536\pi\) | |||||||
\(332\) | −5.31585 | −0.291745 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −21.5837 | −1.18101 | ||||||||
\(335\) | −1.09156 | −0.0596382 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.71992 | −0.311584 | −0.155792 | − | 0.987790i | \(-0.549793\pi\) | ||||
−0.155792 | + | 0.987790i | \(0.549793\pi\) | |||||||
\(338\) | 16.1160 | 0.876593 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.62235 | 0.142217 | ||||||||
\(341\) | −8.04081 | −0.435434 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0747 | −1.08393 | ||||||||
\(344\) | −2.22570 | −0.120002 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.6844 | 0.574396 | ||||||||
\(347\) | 34.1303 | 1.83221 | 0.916106 | − | 0.400935i | \(-0.131315\pi\) | ||||
0.916106 | + | 0.400935i | \(0.131315\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.36702 | 0.394347 | 0.197174 | − | 0.980369i | \(-0.436824\pi\) | ||||
0.197174 | + | 0.980369i | \(0.436824\pi\) | |||||||
\(350\) | −11.1088 | −0.593788 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.94128 | −0.210071 | ||||||||
\(353\) | 6.03164 | 0.321032 | 0.160516 | − | 0.987033i | \(-0.448684\pi\) | ||||
0.160516 | + | 0.987033i | \(0.448684\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.20546 | 0.0639793 | ||||||||
\(356\) | −12.5911 | −0.667327 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.1561 | −0.536768 | ||||||||
\(359\) | 33.6448 | 1.77571 | 0.887853 | − | 0.460128i | \(-0.152196\pi\) | ||||
0.887853 | + | 0.460128i | \(0.152196\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.71153 | 0.0900808 | ||||||||
\(362\) | 14.0457 | 0.738226 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.2784 | 0.643563 | ||||||||
\(365\) | −4.15731 | −0.217604 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.35116 | −0.227129 | −0.113564 | − | 0.993531i | \(-0.536227\pi\) | ||||
−0.113564 | + | 0.993531i | \(0.536227\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.56903 | −0.133558 | ||||||||
\(371\) | 12.8077 | 0.664945 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.8123 | −1.44006 | −0.720032 | − | 0.693941i | \(-0.755873\pi\) | ||||
−0.720032 | + | 0.693941i | \(0.755873\pi\) | |||||||
\(374\) | −30.0758 | −1.55518 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.2840 | 0.685068 | ||||||||
\(377\) | 11.9684 | 0.616402 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 38.2513 | 1.96484 | 0.982420 | − | 0.186685i | \(-0.0597743\pi\) | ||||
0.982420 | + | 0.186685i | \(0.0597743\pi\) | |||||||
\(380\) | 1.56392 | 0.0802276 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15.3239 | −0.784037 | ||||||||
\(383\) | −28.1431 | −1.43805 | −0.719023 | − | 0.694987i | \(-0.755410\pi\) | ||||
−0.719023 | + | 0.694987i | \(0.755410\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.08193 | −0.157070 | ||||||||
\(386\) | 1.52976 | 0.0778626 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.1182 | −0.665975 | ||||||||
\(389\) | 13.1813 | 0.668316 | 0.334158 | − | 0.942517i | \(-0.391548\pi\) | ||||
0.334158 | + | 0.942517i | \(0.391548\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.82212 | −0.0920308 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 21.5724 | 1.08680 | ||||||||
\(395\) | −2.58505 | −0.130068 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.3484 | 1.32239 | 0.661194 | − | 0.750215i | \(-0.270050\pi\) | ||||
0.661194 | + | 0.750215i | \(0.270050\pi\) | |||||||
\(398\) | 22.1817 | 1.11187 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.88191 | −0.244095 | ||||||||
\(401\) | −22.0600 | −1.10162 | −0.550811 | − | 0.834630i | \(-0.685682\pi\) | ||||
−0.550811 | + | 0.834630i | \(0.685682\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.0085 | 0.548373 | ||||||||
\(404\) | 12.1681 | 0.605387 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.04714 | 0.250485 | ||||||||
\(407\) | 29.4643 | 1.46049 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.95535 | −0.195579 | −0.0977897 | − | 0.995207i | \(-0.531177\pi\) | ||||
−0.0977897 | + | 0.995207i | \(0.531177\pi\) | |||||||
\(410\) | 0.374595 | 0.0184999 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.764861 | −0.0376820 | ||||||||
\(413\) | 19.1049 | 0.940090 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.82676 | −0.0896724 | ||||||||
\(416\) | 5.39592 | 0.264557 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −17.9367 | −0.877313 | ||||||||
\(419\) | −17.0204 | −0.831499 | −0.415750 | − | 0.909479i | \(-0.636481\pi\) | ||||
−0.415750 | + | 0.909479i | \(0.636481\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.0964214 | 0.00469929 | 0.00234965 | − | 0.999997i | \(-0.499252\pi\) | ||||
0.00234965 | + | 0.999997i | \(0.499252\pi\) | |||||||
\(422\) | −2.13636 | −0.103996 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.62855 | 0.273346 | ||||||||
\(425\) | −37.2538 | −1.80707 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.2167 | −0.494419 | ||||||||
\(428\) | 9.39319 | 0.454037 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.764849 | −0.0368843 | ||||||||
\(431\) | −11.1725 | −0.538162 | −0.269081 | − | 0.963118i | \(-0.586720\pi\) | ||||
−0.269081 | + | 0.963118i | \(0.586720\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.2293 | −0.491591 | −0.245795 | − | 0.969322i | \(-0.579049\pi\) | ||||
−0.245795 | + | 0.969322i | \(0.579049\pi\) | |||||||
\(434\) | 4.64236 | 0.222841 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.11843 | −0.245128 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.8163 | −0.754869 | −0.377434 | − | 0.926036i | \(-0.623194\pi\) | ||||
−0.377434 | + | 0.926036i | \(0.623194\pi\) | |||||||
\(440\) | −1.35440 | −0.0645684 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 41.1762 | 1.95855 | ||||||||
\(443\) | −29.1805 | −1.38641 | −0.693204 | − | 0.720741i | \(-0.743802\pi\) | ||||
−0.693204 | + | 0.720741i | \(0.743802\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.32686 | −0.205113 | ||||||||
\(446\) | 14.1561 | 0.670312 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.27550 | 0.107507 | ||||||||
\(449\) | 13.0463 | 0.615693 | 0.307846 | − | 0.951436i | \(-0.400392\pi\) | ||||
0.307846 | + | 0.951436i | \(0.400392\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.29625 | −0.202302 | ||||||||
\(452\) | 15.8262 | 0.744403 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −20.9207 | −0.981857 | ||||||||
\(455\) | 4.21941 | 0.197809 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.2862 | 1.27639 | 0.638196 | − | 0.769874i | \(-0.279681\pi\) | ||||
0.638196 | + | 0.769874i | \(0.279681\pi\) | |||||||
\(458\) | 0.599552 | 0.0280152 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.1404 | 1.12433 | 0.562165 | − | 0.827025i | \(-0.309969\pi\) | ||||
0.562165 | + | 0.827025i | \(0.309969\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.2636 | 1.08115 | 0.540575 | − | 0.841296i | \(-0.318207\pi\) | ||||
0.540575 | + | 0.841296i | \(0.318207\pi\) | |||||||
\(464\) | 2.21804 | 0.102970 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.4981 | 0.856909 | ||||||||
\(467\) | 6.99900 | 0.323875 | 0.161938 | − | 0.986801i | \(-0.448226\pi\) | ||||
0.161938 | + | 0.986801i | \(0.448226\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.22792 | −0.333754 | ||||||||
\(470\) | 4.56497 | 0.210566 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.39592 | 0.386454 | ||||||||
\(473\) | 8.77208 | 0.403341 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.2175 | −1.01941 | ||||||||
\(476\) | 17.3643 | 0.795890 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14.5164 | −0.663964 | ||||||||
\(479\) | 0.0996001 | 0.00455084 | 0.00227542 | − | 0.999997i | \(-0.499276\pi\) | ||||
0.00227542 | + | 0.999997i | \(0.499276\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −40.3391 | −1.83930 | ||||||||
\(482\) | 12.1157 | 0.551857 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.53365 | 0.206075 | ||||||||
\(485\) | −4.50800 | −0.204698 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.1120 | −0.503531 | −0.251765 | − | 0.967788i | \(-0.581011\pi\) | ||||
−0.251765 | + | 0.967788i | \(0.581011\pi\) | |||||||
\(488\) | −4.48986 | −0.203247 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.626161 | −0.0282871 | ||||||||
\(491\) | −42.3941 | −1.91322 | −0.956609 | − | 0.291375i | \(-0.905887\pi\) | ||||
−0.956609 | + | 0.291375i | \(0.905887\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.9258 | 0.762300 | ||||||||
\(494\) | 24.5568 | 1.10486 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.04015 | 0.0916056 | ||||||||
\(497\) | 7.98215 | 0.358048 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.4849 | 0.558901 | 0.279450 | − | 0.960160i | \(-0.409848\pi\) | ||||
0.279450 | + | 0.960160i | \(0.409848\pi\) | |||||||
\(500\) | −3.39587 | −0.151868 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.7349 | −0.746915 | ||||||||
\(503\) | −28.8530 | −1.28649 | −0.643247 | − | 0.765659i | \(-0.722413\pi\) | ||||
−0.643247 | + | 0.765659i | \(0.722413\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.18151 | 0.186075 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 22.1561 | 0.983019 | ||||||||
\(509\) | 4.30108 | 0.190642 | 0.0953211 | − | 0.995447i | \(-0.469612\pi\) | ||||
0.0953211 | + | 0.995447i | \(0.469612\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.5283 | −1.21778 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.2377 | 0.539781 | ||||||||
\(515\) | −0.262841 | −0.0115821 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −52.3558 | −2.30260 | ||||||||
\(518\) | −17.0112 | −0.747431 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.85428 | 0.0813155 | ||||||||
\(521\) | −4.27910 | −0.187471 | −0.0937353 | − | 0.995597i | \(-0.529881\pi\) | ||||
−0.0937353 | + | 0.995597i | \(0.529881\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.9986 | −0.568388 | −0.284194 | − | 0.958767i | \(-0.591726\pi\) | ||||
−0.284194 | + | 0.958767i | \(0.591726\pi\) | |||||||
\(524\) | −0.685756 | −0.0299574 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −27.3336 | −1.19180 | ||||||||
\(527\) | 15.5684 | 0.678170 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 1.93422 | 0.0840172 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10.3558 | 0.448979 | ||||||||
\(533\) | 5.88191 | 0.254774 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.22792 | 0.139555 | ||||||||
\(536\) | −3.17641 | −0.137200 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 25.4560 | 1.09749 | ||||||||
\(539\) | 7.18146 | 0.309327 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.6710 | 1.23266 | 0.616332 | − | 0.787487i | \(-0.288618\pi\) | ||||
0.616332 | + | 0.787487i | \(0.288618\pi\) | |||||||
\(542\) | 16.1061 | 0.691816 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.63099 | 0.327176 | ||||||||
\(545\) | −1.75892 | −0.0753439 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.9637 | −1.45218 | −0.726092 | − | 0.687598i | \(-0.758665\pi\) | ||||
−0.726092 | + | 0.687598i | \(0.758665\pi\) | |||||||
\(548\) | 17.2833 | 0.738304 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 19.2409 | 0.820437 | ||||||||
\(551\) | 10.0943 | 0.430031 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.1173 | −0.727903 | ||||||||
\(554\) | 8.29972 | 0.352621 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.2279 | −0.476170 | ||||||||
\(557\) | 18.3963 | 0.779475 | 0.389738 | − | 0.920926i | \(-0.372566\pi\) | ||||
0.389738 | + | 0.920926i | \(0.372566\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.0097 | −0.507955 | ||||||||
\(560\) | 0.781962 | 0.0330439 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −29.7692 | −1.25574 | ||||||||
\(563\) | −25.7820 | −1.08658 | −0.543290 | − | 0.839545i | \(-0.682822\pi\) | ||||
−0.543290 | + | 0.839545i | \(0.682822\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.43860 | 0.228804 | ||||||||
\(566\) | 19.0411 | 0.800358 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.50787 | 0.147187 | ||||||||
\(569\) | −5.78221 | −0.242403 | −0.121201 | − | 0.992628i | \(-0.538675\pi\) | ||||
−0.121201 | + | 0.992628i | \(0.538675\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.2745 | −0.848462 | −0.424231 | − | 0.905554i | \(-0.639456\pi\) | ||||
−0.424231 | + | 0.905554i | \(0.639456\pi\) | |||||||
\(572\) | −21.2668 | −0.889210 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.48044 | 0.103532 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.2424 | −1.09249 | −0.546244 | − | 0.837626i | \(-0.683943\pi\) | ||||
−0.546244 | + | 0.837626i | \(0.683943\pi\) | |||||||
\(578\) | 41.2319 | 1.71502 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.762217 | 0.0316493 | ||||||||
\(581\) | −12.0962 | −0.501835 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.1837 | −0.918753 | ||||||||
\(584\) | −12.0977 | −0.500606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.667667 | −0.0275811 | ||||||||
\(587\) | 32.9237 | 1.35891 | 0.679453 | − | 0.733719i | \(-0.262217\pi\) | ||||
0.679453 | + | 0.733719i | \(0.262217\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.28473 | 0.382571 | ||||||||
\(590\) | 2.88521 | 0.118782 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.47584 | −0.307255 | ||||||||
\(593\) | −34.5877 | −1.42035 | −0.710173 | − | 0.704027i | \(-0.751383\pi\) | ||||
−0.710173 | + | 0.704027i | \(0.751383\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.96714 | 0.244629 | ||||||||
\(596\) | 2.38836 | 0.0978311 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.28397 | 0.0524616 | 0.0262308 | − | 0.999656i | \(-0.491650\pi\) | ||||
0.0262308 | + | 0.999656i | \(0.491650\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.4241 | 0.506788 | 0.253394 | − | 0.967363i | \(-0.418453\pi\) | ||||
0.253394 | + | 0.967363i | \(0.418453\pi\) | |||||||
\(602\) | −5.06456 | −0.206416 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.7616 | −0.600640 | ||||||||
\(605\) | 1.55796 | 0.0633403 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.0903 | −0.531321 | −0.265660 | − | 0.964067i | \(-0.585590\pi\) | ||||
−0.265660 | + | 0.964067i | \(0.585590\pi\) | |||||||
\(608\) | 4.55099 | 0.184567 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.54292 | −0.0624709 | ||||||||
\(611\) | 71.6793 | 2.89983 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.47582 | 0.342335 | 0.171168 | − | 0.985242i | \(-0.445246\pi\) | ||||
0.171168 | + | 0.985242i | \(0.445246\pi\) | |||||||
\(614\) | −31.3082 | −1.26350 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.96836 | −0.361345 | ||||||||
\(617\) | −18.4352 | −0.742173 | −0.371087 | − | 0.928598i | \(-0.621015\pi\) | ||||
−0.371087 | + | 0.928598i | \(0.621015\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.23967 | 0.0900199 | 0.0450100 | − | 0.998987i | \(-0.485668\pi\) | ||||
0.0450100 | + | 0.998987i | \(0.485668\pi\) | |||||||
\(620\) | 0.701088 | 0.0281564 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.4361 | 0.418449 | ||||||||
\(623\) | −28.6510 | −1.14788 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.2426 | 0.929703 | ||||||||
\(626\) | −0.0889007 | −0.00355318 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.0363 | −0.560108 | ||||||||
\(629\) | −57.0480 | −2.27465 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.6363 | 0.741901 | 0.370951 | − | 0.928653i | \(-0.379032\pi\) | ||||
0.370951 | + | 0.928653i | \(0.379032\pi\) | |||||||
\(632\) | −7.52246 | −0.299227 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.50924 | 0.218800 | ||||||||
\(635\) | 7.61383 | 0.302146 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.83200 | −0.389558 | ||||||||
\(638\) | −8.74190 | −0.346095 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.343645 | 0.0135837 | ||||||||
\(641\) | −10.2777 | −0.405943 | −0.202972 | − | 0.979185i | \(-0.565060\pi\) | ||||
−0.202972 | + | 0.979185i | \(0.565060\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.9391 | 0.549703 | 0.274852 | − | 0.961487i | \(-0.411371\pi\) | ||||
0.274852 | + | 0.961487i | \(0.411371\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 34.7286 | 1.36638 | ||||||||
\(647\) | −22.0153 | −0.865509 | −0.432755 | − | 0.901512i | \(-0.642458\pi\) | ||||
−0.432755 | + | 0.901512i | \(0.642458\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.0906 | −1.29892 | ||||||||
\(650\) | −26.3424 | −1.03323 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.4361 | 0.408708 | ||||||||
\(653\) | −33.6547 | −1.31701 | −0.658506 | − | 0.752576i | \(-0.728811\pi\) | ||||
−0.658506 | + | 0.752576i | \(0.728811\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.235656 | −0.00920786 | ||||||||
\(656\) | 1.09007 | 0.0425599 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 30.2276 | 1.17840 | ||||||||
\(659\) | 18.3540 | 0.714970 | 0.357485 | − | 0.933919i | \(-0.383634\pi\) | ||||
0.357485 | + | 0.933919i | \(0.383634\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.3013 | 0.867421 | 0.433710 | − | 0.901052i | \(-0.357204\pi\) | ||||
0.433710 | + | 0.901052i | \(0.357204\pi\) | |||||||
\(662\) | −13.6640 | −0.531066 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.31585 | −0.206295 | ||||||||
\(665\) | 3.55870 | 0.138001 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −21.5837 | −0.835098 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.09156 | −0.0421706 | ||||||||
\(671\) | 17.6958 | 0.683138 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.4847 | −1.13655 | −0.568277 | − | 0.822838i | \(-0.692390\pi\) | ||||
−0.568277 | + | 0.822838i | \(0.692390\pi\) | |||||||
\(674\) | −5.71992 | −0.220323 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.1160 | 0.619845 | ||||||||
\(677\) | −19.8135 | −0.761495 | −0.380747 | − | 0.924679i | \(-0.624333\pi\) | ||||
−0.380747 | + | 0.924679i | \(0.624333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.8504 | −1.14555 | ||||||||
\(680\) | 2.62235 | 0.100562 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.04081 | −0.307899 | ||||||||
\(683\) | −46.3953 | −1.77527 | −0.887633 | − | 0.460551i | \(-0.847652\pi\) | ||||
−0.887633 | + | 0.460551i | \(0.847652\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.93930 | 0.226929 | ||||||||
\(686\) | −20.0747 | −0.766455 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.22570 | −0.0848539 | ||||||||
\(689\) | 30.3712 | 1.15705 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.2997 | −0.772238 | −0.386119 | − | 0.922449i | \(-0.626185\pi\) | ||||
−0.386119 | + | 0.922449i | \(0.626185\pi\) | |||||||
\(692\) | 10.6844 | 0.406159 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 34.1303 | 1.29557 | ||||||||
\(695\) | −3.85841 | −0.146358 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.31827 | 0.315077 | ||||||||
\(698\) | 7.36702 | 0.278846 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11.1088 | −0.419872 | ||||||||
\(701\) | 18.8156 | 0.710656 | 0.355328 | − | 0.934742i | \(-0.384369\pi\) | ||||
0.355328 | + | 0.934742i | \(0.384369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −34.0225 | −1.28318 | ||||||||
\(704\) | −3.94128 | −0.148542 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.03164 | 0.227004 | ||||||||
\(707\) | 27.6885 | 1.04133 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.2990 | 1.13790 | 0.568951 | − | 0.822371i | \(-0.307349\pi\) | ||||
0.568951 | + | 0.822371i | \(0.307349\pi\) | |||||||
\(710\) | 1.20546 | 0.0452402 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.5911 | −0.471871 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.30823 | −0.273312 | ||||||||
\(716\) | −10.1561 | −0.379552 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 33.6448 | 1.25561 | ||||||||
\(719\) | 15.8004 | 0.589254 | 0.294627 | − | 0.955612i | \(-0.404805\pi\) | ||||
0.294627 | + | 0.955612i | \(0.404805\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.74044 | −0.0648173 | ||||||||
\(722\) | 1.71153 | 0.0636967 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.0457 | 0.522005 | ||||||||
\(725\) | −10.8283 | −0.402151 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.6309 | −1.21021 | −0.605107 | − | 0.796144i | \(-0.706870\pi\) | ||||
−0.605107 | + | 0.796144i | \(0.706870\pi\) | |||||||
\(728\) | 12.2784 | 0.455068 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.15731 | −0.153869 | ||||||||
\(731\) | −16.9843 | −0.628185 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.0266 | 1.88471 | 0.942355 | − | 0.334614i | \(-0.108606\pi\) | ||||
0.942355 | + | 0.334614i | \(0.108606\pi\) | |||||||
\(734\) | −4.35116 | −0.160604 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.5191 | 0.461148 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.9237 | −0.916833 | −0.458417 | − | 0.888737i | \(-0.651583\pi\) | ||||
−0.458417 | + | 0.888737i | \(0.651583\pi\) | |||||||
\(740\) | −2.56903 | −0.0944395 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.8077 | 0.470187 | ||||||||
\(743\) | −0.465432 | −0.0170750 | −0.00853752 | − | 0.999964i | \(-0.502718\pi\) | ||||
−0.00853752 | + | 0.999964i | \(0.502718\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.820748 | 0.0300699 | ||||||||
\(746\) | −27.8123 | −1.01828 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −30.0758 | −1.09968 | ||||||||
\(749\) | 21.3742 | 0.780995 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.2433 | −1.03061 | −0.515307 | − | 0.857006i | \(-0.672322\pi\) | ||||
−0.515307 | + | 0.857006i | \(0.672322\pi\) | |||||||
\(752\) | 13.2840 | 0.484417 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11.9684 | 0.435862 | ||||||||
\(755\) | −5.07273 | −0.184616 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.2042 | 1.38855 | 0.694277 | − | 0.719707i | \(-0.255724\pi\) | ||||
0.694277 | + | 0.719707i | \(0.255724\pi\) | |||||||
\(758\) | 38.2513 | 1.38935 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.56392 | 0.0567295 | ||||||||
\(761\) | 51.7670 | 1.87655 | 0.938275 | − | 0.345889i | \(-0.112423\pi\) | ||||
0.938275 | + | 0.345889i | \(0.112423\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.6470 | −0.421649 | ||||||||
\(764\) | −15.3239 | −0.554398 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −28.1431 | −1.01685 | ||||||||
\(767\) | 45.3037 | 1.63582 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.6546 | 1.46604 | 0.733021 | − | 0.680206i | \(-0.238110\pi\) | ||||
0.733021 | + | 0.680206i | \(0.238110\pi\) | |||||||
\(770\) | −3.08193 | −0.111065 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.52976 | 0.0550572 | ||||||||
\(773\) | −18.3489 | −0.659966 | −0.329983 | − | 0.943987i | \(-0.607043\pi\) | ||||
−0.329983 | + | 0.943987i | \(0.607043\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.95985 | −0.357768 | ||||||||
\(776\) | −13.1182 | −0.470916 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.1813 | 0.472571 | ||||||||
\(779\) | 4.96088 | 0.177742 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.8255 | −0.494715 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.82212 | −0.0650756 | ||||||||
\(785\) | −4.82349 | −0.172158 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.5743 | 1.12550 | 0.562750 | − | 0.826627i | \(-0.309743\pi\) | ||||
0.562750 | + | 0.826627i | \(0.309743\pi\) | |||||||
\(788\) | 21.5724 | 0.768486 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.58505 | −0.0919721 | ||||||||
\(791\) | 36.0125 | 1.28046 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.2270 | −0.860324 | ||||||||
\(794\) | 26.3484 | 0.935069 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.1817 | 0.786210 | ||||||||
\(797\) | 28.1590 | 0.997443 | 0.498722 | − | 0.866762i | \(-0.333803\pi\) | ||||
0.498722 | + | 0.866762i | \(0.333803\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 101.370 | 3.58621 | ||||||||
\(800\) | −4.88191 | −0.172602 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −22.0600 | −0.778965 | ||||||||
\(803\) | 47.6804 | 1.68260 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.0085 | 0.387758 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.1681 | 0.428073 | ||||||||
\(809\) | 28.2952 | 0.994807 | 0.497403 | − | 0.867519i | \(-0.334287\pi\) | ||||
0.497403 | + | 0.867519i | \(0.334287\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.5321 | −1.17747 | −0.588736 | − | 0.808325i | \(-0.700374\pi\) | ||||
−0.588736 | + | 0.808325i | \(0.700374\pi\) | |||||||
\(812\) | 5.04714 | 0.177120 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 29.4643 | 1.03272 | ||||||||
\(815\) | 3.58630 | 0.125623 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.1291 | −0.354373 | ||||||||
\(818\) | −3.95535 | −0.138296 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.374595 | 0.0130814 | ||||||||
\(821\) | −6.52389 | −0.227685 | −0.113843 | − | 0.993499i | \(-0.536316\pi\) | ||||
−0.113843 | + | 0.993499i | \(0.536316\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.4401 | 0.398777 | 0.199388 | − | 0.979921i | \(-0.436105\pi\) | ||||
0.199388 | + | 0.979921i | \(0.436105\pi\) | |||||||
\(824\) | −0.764861 | −0.0266452 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.1049 | 0.664744 | ||||||||
\(827\) | −0.603974 | −0.0210022 | −0.0105011 | − | 0.999945i | \(-0.503343\pi\) | ||||
−0.0105011 | + | 0.999945i | \(0.503343\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.3422 | −1.05383 | −0.526915 | − | 0.849918i | \(-0.676651\pi\) | ||||
−0.526915 | + | 0.849918i | \(0.676651\pi\) | |||||||
\(830\) | −1.82676 | −0.0634079 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.39592 | 0.187070 | ||||||||
\(833\) | −13.9045 | −0.481764 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.41712 | −0.256680 | ||||||||
\(836\) | −17.9367 | −0.620354 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −17.0204 | −0.587959 | ||||||||
\(839\) | 4.46537 | 0.154162 | 0.0770808 | − | 0.997025i | \(-0.475440\pi\) | ||||
0.0770808 | + | 0.997025i | \(0.475440\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.0803 | −0.830355 | ||||||||
\(842\) | 0.0964214 | 0.00332290 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.13636 | −0.0735366 | ||||||||
\(845\) | 5.53817 | 0.190519 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.3163 | 0.354472 | ||||||||
\(848\) | 5.62855 | 0.193285 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −37.2538 | −1.27779 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.7088 | −0.572098 | −0.286049 | − | 0.958215i | \(-0.592342\pi\) | ||||
−0.286049 | + | 0.958215i | \(0.592342\pi\) | |||||||
\(854\) | −10.2167 | −0.349607 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.39319 | 0.321052 | ||||||||
\(857\) | −34.1138 | −1.16531 | −0.582653 | − | 0.812721i | \(-0.697985\pi\) | ||||
−0.582653 | + | 0.812721i | \(0.697985\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.33279 | −0.250192 | −0.125096 | − | 0.992145i | \(-0.539924\pi\) | ||||
−0.125096 | + | 0.992145i | \(0.539924\pi\) | |||||||
\(860\) | −0.764849 | −0.0260811 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.1725 | −0.380538 | ||||||||
\(863\) | 4.93094 | 0.167851 | 0.0839256 | − | 0.996472i | \(-0.473254\pi\) | ||||
0.0839256 | + | 0.996472i | \(0.473254\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.67163 | 0.124839 | ||||||||
\(866\) | −10.2293 | −0.347607 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.64236 | 0.157572 | ||||||||
\(869\) | 29.6481 | 1.00574 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.1397 | −0.580756 | ||||||||
\(872\) | −5.11843 | −0.173332 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.72728 | −0.261230 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.5434 | −1.03138 | −0.515688 | − | 0.856776i | \(-0.672464\pi\) | ||||
−0.515688 | + | 0.856776i | \(0.672464\pi\) | |||||||
\(878\) | −15.8163 | −0.533773 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.35440 | −0.0456568 | ||||||||
\(881\) | −4.62398 | −0.155786 | −0.0778930 | − | 0.996962i | \(-0.524819\pi\) | ||||
−0.0778930 | + | 0.996962i | \(0.524819\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −58.8677 | −1.98105 | −0.990527 | − | 0.137317i | \(-0.956152\pi\) | ||||
−0.990527 | + | 0.137317i | \(0.956152\pi\) | |||||||
\(884\) | 41.1762 | 1.38491 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29.1805 | −0.980339 | ||||||||
\(887\) | −9.77610 | −0.328249 | −0.164125 | − | 0.986440i | \(-0.552480\pi\) | ||||
−0.164125 | + | 0.986440i | \(0.552480\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 50.4162 | 1.69090 | ||||||||
\(890\) | −4.32686 | −0.145037 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.1561 | 0.473982 | ||||||||
\(893\) | 60.4553 | 2.02306 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.49010 | −0.116661 | ||||||||
\(896\) | 2.27550 | 0.0760190 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.0463 | 0.435360 | ||||||||
\(899\) | 4.52514 | 0.150922 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.9514 | 1.43092 | ||||||||
\(902\) | −4.29625 | −0.143049 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.8262 | 0.526373 | ||||||||
\(905\) | 4.82674 | 0.160446 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.2122 | 1.43484 | 0.717419 | − | 0.696642i | \(-0.245323\pi\) | ||||
0.717419 | + | 0.696642i | \(0.245323\pi\) | |||||||
\(908\) | −20.9207 | −0.694278 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.21941 | 0.139872 | ||||||||
\(911\) | 22.5418 | 0.746843 | 0.373421 | − | 0.927662i | \(-0.378185\pi\) | ||||
0.373421 | + | 0.927662i | \(0.378185\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.9512 | 0.693385 | ||||||||
\(914\) | 27.2862 | 0.902546 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.599552 | 0.0198098 | ||||||||
\(917\) | −1.56044 | −0.0515301 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.8829 | 1.41457 | 0.707287 | − | 0.706926i | \(-0.249919\pi\) | ||||
0.707287 | + | 0.706926i | \(0.249919\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 24.1404 | 0.795021 | ||||||||
\(923\) | 18.9282 | 0.623029 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.4964 | 1.19999 | ||||||||
\(926\) | 23.2636 | 0.764489 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.21804 | 0.0728107 | ||||||||
\(929\) | −24.8632 | −0.815734 | −0.407867 | − | 0.913041i | \(-0.633727\pi\) | ||||
−0.407867 | + | 0.913041i | \(0.633727\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.29244 | −0.271774 | ||||||||
\(932\) | 18.4981 | 0.605926 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.99900 | 0.229014 | ||||||||
\(935\) | −10.3354 | −0.338004 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.7797 | −1.20154 | −0.600771 | − | 0.799422i | \(-0.705139\pi\) | ||||
−0.600771 | + | 0.799422i | \(0.705139\pi\) | |||||||
\(938\) | −7.22792 | −0.236000 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.56497 | 0.148893 | ||||||||
\(941\) | −33.6741 | −1.09774 | −0.548872 | − | 0.835907i | \(-0.684942\pi\) | ||||
−0.548872 | + | 0.835907i | \(0.684942\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 8.39592 | 0.273264 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.77208 | 0.285205 | ||||||||
\(947\) | −45.6580 | −1.48368 | −0.741842 | − | 0.670574i | \(-0.766048\pi\) | ||||
−0.741842 | + | 0.670574i | \(0.766048\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −65.2782 | −2.11902 | ||||||||
\(950\) | −22.2175 | −0.720832 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 17.3643 | 0.562780 | ||||||||
\(953\) | 16.3410 | 0.529337 | 0.264669 | − | 0.964339i | \(-0.414737\pi\) | ||||
0.264669 | + | 0.964339i | \(0.414737\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.26597 | −0.170403 | ||||||||
\(956\) | −14.5164 | −0.469493 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.0996001 | 0.00321793 | ||||||||
\(959\) | 39.3280 | 1.26997 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.8378 | −0.865735 | ||||||||
\(962\) | −40.3391 | −1.30058 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12.1157 | 0.390222 | ||||||||
\(965\) | 0.525693 | 0.0169227 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.2563 | 1.13377 | 0.566884 | − | 0.823798i | \(-0.308149\pi\) | ||||
0.566884 | + | 0.823798i | \(0.308149\pi\) | |||||||
\(968\) | 4.53365 | 0.145717 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.50800 | −0.144743 | ||||||||
\(971\) | 21.9679 | 0.704983 | 0.352492 | − | 0.935815i | \(-0.385334\pi\) | ||||
0.352492 | + | 0.935815i | \(0.385334\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.5491 | −0.819066 | ||||||||
\(974\) | −11.1120 | −0.356050 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.48986 | −0.143717 | ||||||||
\(977\) | 24.5459 | 0.785294 | 0.392647 | − | 0.919689i | \(-0.371559\pi\) | ||||
0.392647 | + | 0.919689i | \(0.371559\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 49.6250 | 1.58602 | ||||||||
\(980\) | −0.626161 | −0.0200020 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −42.3941 | −1.35285 | ||||||||
\(983\) | −12.7196 | −0.405693 | −0.202847 | − | 0.979211i | \(-0.565019\pi\) | ||||
−0.202847 | + | 0.979211i | \(0.565019\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.41325 | 0.236206 | ||||||||
\(986\) | 16.9258 | 0.539028 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 24.5568 | 0.781256 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.5606 | −1.70141 | −0.850704 | − | 0.525646i | \(-0.823824\pi\) | ||||
−0.850704 | + | 0.525646i | \(0.823824\pi\) | |||||||
\(992\) | 2.04015 | 0.0647750 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.98215 | 0.253178 | ||||||||
\(995\) | 7.62262 | 0.241653 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.1013 | −0.826637 | −0.413318 | − | 0.910587i | \(-0.635630\pi\) | ||||
−0.413318 | + | 0.910587i | \(0.635630\pi\) | |||||||
\(998\) | 12.4849 | 0.395202 | ||||||||
\(999\) | 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 | 9522.2.a.cf.1.5 | yes | 8 | |
3.2 | odd | 2 | 9522.2.a.cd.1.4 | ✓ | 8 | ||
23.22 | odd | 2 | inner | 9522.2.a.cf.1.4 | yes | 8 | |
69.68 | even | 2 | 9522.2.a.cd.1.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9522.2.a.cd.1.4 | ✓ | 8 | 3.2 | odd | 2 | ||
9522.2.a.cd.1.5 | yes | 8 | 69.68 | even | 2 | ||
9522.2.a.cf.1.4 | yes | 8 | 23.22 | odd | 2 | inner | |
9522.2.a.cf.1.5 | yes | 8 | 1.1 | even | 1 | trivial |