Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6160,2,Mod(1,6160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6160.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6160 = 2^{4} \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6160.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: | \(49.1878476451\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.549616.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 7x^{3} + 4x^{2} + 4x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 3080) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.718866\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6160.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.33189 | −1.34632 | −0.673160 | − | 0.739497i | \(-0.735063\pi\) | ||||
−0.673160 | + | 0.739497i | \(0.735063\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.43773 | 0.812578 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.04175 | 0.288930 | 0.144465 | − | 0.989510i | \(-0.453854\pi\) | ||||
0.144465 | + | 0.989510i | \(0.453854\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.33189 | 0.602093 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.88368 | 1.66954 | 0.834769 | − | 0.550601i | \(-0.185601\pi\) | ||||
0.834769 | + | 0.550601i | \(0.185601\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.55179 | 1.50308 | 0.751541 | − | 0.659686i | \(-0.229311\pi\) | ||||
0.751541 | + | 0.659686i | \(0.229311\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.33189 | −0.508861 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.836442 | 0.174410 | 0.0872051 | − | 0.996190i | \(-0.472206\pi\) | ||||
0.0872051 | + | 0.996190i | \(0.472206\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.31115 | 0.252331 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.55179 | 1.58803 | 0.794013 | − | 0.607900i | \(-0.207988\pi\) | ||||
0.794013 | + | 0.607900i | \(0.207988\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.19278 | −0.573440 | −0.286720 | − | 0.958014i | \(-0.592565\pi\) | ||||
−0.286720 | + | 0.958014i | \(0.592565\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.33189 | 0.405931 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.50023 | 1.23303 | 0.616515 | − | 0.787343i | \(-0.288544\pi\) | ||||
0.616515 | + | 0.787343i | \(0.288544\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.42926 | −0.388993 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.72012 | −1.20568 | −0.602840 | − | 0.797862i | \(-0.705964\pi\) | ||||
−0.602840 | + | 0.797862i | \(0.705964\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.8739 | −1.65825 | −0.829125 | − | 0.559063i | \(-0.811161\pi\) | ||||
−0.829125 | + | 0.559063i | \(0.811161\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.43773 | −0.363396 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.5475 | −1.97610 | −0.988051 | − | 0.154129i | \(-0.950743\pi\) | ||||
−0.988051 | + | 0.154129i | \(0.950743\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.0520 | −2.24773 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.85241 | 0.529169 | 0.264585 | − | 0.964362i | \(-0.414765\pi\) | ||||
0.264585 | + | 0.964362i | \(0.414765\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15.2781 | −2.02363 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.16834 | 0.933238 | 0.466619 | − | 0.884458i | \(-0.345472\pi\) | ||||
0.466619 | + | 0.884458i | \(0.345472\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.29287 | 0.293572 | 0.146786 | − | 0.989168i | \(-0.453107\pi\) | ||||
0.146786 | + | 0.989168i | \(0.453107\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.43773 | 0.307125 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.04175 | −0.129214 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0771 | 1.23111 | 0.615556 | − | 0.788093i | \(-0.288932\pi\) | ||||
0.615556 | + | 0.788093i | \(0.288932\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.95050 | −0.234812 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.89143 | −0.461828 | −0.230914 | − | 0.972974i | \(-0.574172\pi\) | ||||
−0.230914 | + | 0.972974i | \(0.574172\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.547006 | 0.0640223 | 0.0320111 | − | 0.999488i | \(-0.489809\pi\) | ||||
0.0320111 | + | 0.999488i | \(0.489809\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.33189 | −0.269264 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.83644 | −0.994177 | −0.497089 | − | 0.867700i | \(-0.665598\pi\) | ||||
−0.497089 | + | 0.867700i | \(0.665598\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.3707 | −1.15230 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.89143 | 0.866197 | 0.433099 | − | 0.901347i | \(-0.357420\pi\) | ||||
0.433099 | + | 0.901347i | \(0.357420\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.88368 | −0.746640 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −19.9419 | −2.13799 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.67288 | 0.813324 | 0.406662 | − | 0.913579i | \(-0.366693\pi\) | ||||
0.406662 | + | 0.913579i | \(0.366693\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.04175 | 0.109205 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.44522 | 0.772034 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.55179 | −0.672199 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.52672 | −0.662688 | −0.331344 | − | 0.943510i | \(-0.607502\pi\) | ||||
−0.331344 | + | 0.943510i | \(0.607502\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.43773 | −0.245001 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.8572 | 1.17983 | 0.589917 | − | 0.807464i | \(-0.299160\pi\) | ||||
0.589917 | + | 0.807464i | \(0.299160\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.3449 | −1.61051 | −0.805255 | − | 0.592929i | \(-0.797972\pi\) | ||||
−0.805255 | + | 0.592929i | \(0.797972\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.33189 | 0.227570 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.796799 | −0.0770295 | −0.0385147 | − | 0.999258i | \(-0.512263\pi\) | ||||
−0.0385147 | + | 0.999258i | \(0.512263\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.9044 | −1.14024 | −0.570119 | − | 0.821562i | \(-0.693103\pi\) | ||||
−0.570119 | + | 0.821562i | \(0.693103\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.4898 | −1.66005 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.6478 | 1.28388 | 0.641940 | − | 0.766755i | \(-0.278130\pi\) | ||||
0.641940 | + | 0.766755i | \(0.278130\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.836442 | −0.0779987 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.53951 | 0.234778 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.88368 | 0.631026 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.0025 | 1.62323 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.2286 | 1.88373 | 0.941865 | − | 0.335990i | \(-0.109071\pi\) | ||||
0.941865 | + | 0.335990i | \(0.109071\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 25.3567 | 2.23254 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.91306 | 0.341886 | 0.170943 | − | 0.985281i | \(-0.445319\pi\) | ||||
0.170943 | + | 0.985281i | \(0.445319\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.55179 | 0.568112 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.31115 | −0.112846 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.0606495 | 0.00518164 | 0.00259082 | − | 0.999997i | \(-0.499175\pi\) | ||||
0.00259082 | + | 0.999997i | \(0.499175\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.5272 | 1.31700 | 0.658499 | − | 0.752581i | \(-0.271192\pi\) | ||||
0.658499 | + | 0.752581i | \(0.271192\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 31.5913 | 2.66047 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.04175 | −0.0871157 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.55179 | −0.710187 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.33189 | −0.192331 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.8885 | −0.892017 | −0.446009 | − | 0.895029i | \(-0.647155\pi\) | ||||
−0.446009 | + | 0.895029i | \(0.647155\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.0645 | −1.55145 | −0.775725 | − | 0.631071i | \(-0.782616\pi\) | ||||
−0.775725 | + | 0.631071i | \(0.782616\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.7806 | 1.35663 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.19278 | 0.256450 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.58028 | 0.365546 | 0.182773 | − | 0.983155i | \(-0.441493\pi\) | ||||
0.182773 | + | 0.983155i | \(0.441493\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.98341 | −0.712431 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.836442 | 0.0659209 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.94845 | −0.544244 | −0.272122 | − | 0.962263i | \(-0.587725\pi\) | ||||
−0.272122 | + | 0.962263i | \(0.587725\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.33189 | −0.181538 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.9713 | 0.848985 | 0.424492 | − | 0.905431i | \(-0.360453\pi\) | ||||
0.424492 | + | 0.905431i | \(0.360453\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.9148 | −0.916519 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.9715 | 1.22137 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.34443 | 0.558386 | 0.279193 | − | 0.960235i | \(-0.409933\pi\) | ||||
0.279193 | + | 0.960235i | \(0.409933\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.7158 | −1.25644 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23.8264 | −1.78087 | −0.890435 | − | 0.455110i | \(-0.849600\pi\) | ||||
−0.890435 | + | 0.455110i | \(0.849600\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.31115 | 0.246116 | 0.123058 | − | 0.992399i | \(-0.460730\pi\) | ||||
0.123058 | + | 0.992399i | \(0.460730\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.34674 | −0.395242 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.50023 | −0.551428 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.88368 | −0.503385 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.31115 | 0.0953720 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.60535 | −0.333231 | −0.166616 | − | 0.986022i | \(-0.553284\pi\) | ||||
−0.166616 | + | 0.986022i | \(0.553284\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.76531 | 0.630941 | 0.315470 | − | 0.948935i | \(-0.397838\pi\) | ||||
0.315470 | + | 0.948935i | \(0.397838\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.42926 | 0.173963 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.19615 | −0.227717 | −0.113858 | − | 0.993497i | \(-0.536321\pi\) | ||||
−0.113858 | + | 0.993497i | \(0.536321\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.84809 | 0.627225 | 0.313612 | − | 0.949551i | \(-0.398461\pi\) | ||||
0.313612 | + | 0.949551i | \(0.398461\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −23.4987 | −1.65747 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.55179 | 0.600218 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.72012 | 0.539197 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.03902 | 0.141722 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.55179 | −0.453196 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0041 | −0.688711 | −0.344355 | − | 0.938839i | \(-0.611902\pi\) | ||||
−0.344355 | + | 0.938839i | \(0.611902\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.07441 | 0.621768 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.8739 | 0.741592 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.19278 | −0.216740 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.27556 | −0.0861944 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.17109 | 0.482380 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.77465 | −0.386699 | −0.193350 | − | 0.981130i | \(-0.561935\pi\) | ||||
−0.193350 | + | 0.981130i | \(0.561935\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.43773 | 0.162516 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.1775 | 0.741878 | 0.370939 | − | 0.928657i | \(-0.379036\pi\) | ||||
0.370939 | + | 0.928657i | \(0.379036\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.2370 | −0.940810 | −0.470405 | − | 0.882451i | \(-0.655892\pi\) | ||||
−0.470405 | + | 0.882451i | \(0.655892\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.33189 | 0.153427 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.3832 | −1.20433 | −0.602163 | − | 0.798373i | \(-0.705694\pi\) | ||||
−0.602163 | + | 0.798373i | \(0.705694\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.5475 | 0.883739 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.6057 | 1.33848 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.4186 | 1.25609 | 0.628043 | − | 0.778179i | \(-0.283856\pi\) | ||||
0.628043 | + | 0.778179i | \(0.283856\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.0067 | 1.41757 | 0.708787 | − | 0.705422i | \(-0.249243\pi\) | ||||
0.708787 | + | 0.705422i | \(0.249243\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.2498 | 1.29903 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.82534 | 0.434286 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.4020 | −1.16618 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.72855 | 0.424703 | 0.212351 | − | 0.977193i | \(-0.431888\pi\) | ||||
0.212351 | + | 0.977193i | \(0.431888\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.836442 | −0.0525867 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.0520 | 1.00522 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.00890 | −0.125311 | −0.0626557 | − | 0.998035i | \(-0.519957\pi\) | ||||
−0.0626557 | + | 0.998035i | \(0.519957\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.50023 | 0.466042 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.8470 | 1.29039 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 29.4946 | 1.81871 | 0.909357 | − | 0.416016i | \(-0.136574\pi\) | ||||
0.909357 | + | 0.416016i | \(0.136574\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.85241 | −0.236652 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.8924 | −1.09499 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.1987 | −1.53639 | −0.768195 | − | 0.640216i | \(-0.778845\pi\) | ||||
−0.768195 | + | 0.640216i | \(0.778845\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.2231 | 1.16772 | 0.583860 | − | 0.811854i | \(-0.301542\pi\) | ||||
0.583860 | + | 0.811854i | \(0.301542\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.42926 | −0.147025 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.9690 | 1.13974 | 0.569868 | − | 0.821737i | \(-0.306994\pi\) | ||||
0.569868 | + | 0.821737i | \(0.306994\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.78314 | −0.465965 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.6679 | −0.994323 | −0.497161 | − | 0.867658i | \(-0.665624\pi\) | ||||
−0.497161 | + | 0.867658i | \(0.665624\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.52329 | −0.387769 | −0.193885 | − | 0.981024i | \(-0.562109\pi\) | ||||
−0.193885 | + | 0.981024i | \(0.562109\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.2781 | 0.904995 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.72012 | −0.455704 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.3851 | 1.78736 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.2196 | 0.892191 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.1868 | 1.64669 | 0.823346 | − | 0.567540i | \(-0.192105\pi\) | ||||
0.823346 | + | 0.567540i | \(0.192105\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.16834 | −0.417357 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.31115 | −0.0760805 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.871366 | 0.0503924 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.8739 | −0.626760 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −27.6497 | −1.58843 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.29287 | −0.131289 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.7728 | 1.35679 | 0.678393 | − | 0.734699i | \(-0.262677\pi\) | ||||
0.678393 | + | 0.734699i | \(0.262677\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 38.1146 | 2.16826 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.08058 | −0.458207 | −0.229104 | − | 0.973402i | \(-0.573579\pi\) | ||||
−0.229104 | + | 0.973402i | \(0.573579\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.44322 | 0.477239 | 0.238619 | − | 0.971113i | \(-0.423305\pi\) | ||||
0.238619 | + | 0.971113i | \(0.423305\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.43773 | −0.137351 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.01663 | −0.169431 | −0.0847154 | − | 0.996405i | \(-0.526998\pi\) | ||||
−0.0847154 | + | 0.996405i | \(0.526998\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.55179 | −0.478808 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.85805 | 0.103706 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 45.1004 | 2.50945 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.04175 | 0.0577860 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 27.7599 | 1.53512 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.5475 | −0.746896 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.3315 | −1.55724 | −0.778621 | − | 0.627495i | \(-0.784080\pi\) | ||||
−0.778621 | + | 0.627495i | \(0.784080\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 18.2836 | 1.00193 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.0771 | −0.550570 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.8778 | −1.73650 | −0.868248 | − | 0.496131i | \(-0.834754\pi\) | ||||
−0.868248 | + | 0.496131i | \(0.834754\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −31.8253 | −1.72851 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.19278 | 0.172899 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.95050 | 0.105011 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.1376 | 1.40314 | 0.701569 | − | 0.712602i | \(-0.252483\pi\) | ||||
0.701569 | + | 0.712602i | \(0.252483\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.51364 | 0.295139 | 0.147569 | − | 0.989052i | \(-0.452855\pi\) | ||||
0.147569 | + | 0.989052i | \(0.452855\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.36589 | 0.0729059 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.2115 | 0.596727 | 0.298363 | − | 0.954452i | \(-0.403559\pi\) | ||||
0.298363 | + | 0.954452i | \(0.403559\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.89143 | 0.206536 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −16.0520 | −0.849563 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.7238 | 1.46321 | 0.731603 | − | 0.681731i | \(-0.238772\pi\) | ||||
0.731603 | + | 0.681731i | \(0.238772\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.9259 | 1.25926 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.33189 | −0.122393 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.547006 | −0.0286316 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.3900 | 1.32535 | 0.662674 | − | 0.748908i | \(-0.269421\pi\) | ||||
0.662674 | + | 0.748908i | \(0.269421\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −18.8196 | −0.979709 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.85241 | 0.200007 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.9184 | 1.44556 | 0.722780 | − | 0.691079i | \(-0.242864\pi\) | ||||
0.722780 | + | 0.691079i | \(0.242864\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.33189 | 0.120419 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.90885 | 0.458829 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0666 | −0.619817 | −0.309909 | − | 0.950766i | \(-0.600298\pi\) | ||||
−0.309909 | + | 0.950766i | \(0.600298\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −49.5028 | −2.53610 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.1022 | 0.771688 | 0.385844 | − | 0.922564i | \(-0.373910\pi\) | ||||
0.385844 | + | 0.922564i | \(0.373910\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.00000 | 0.0509647 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −26.5076 | −1.34746 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.2140 | −1.63332 | −0.816658 | − | 0.577122i | \(-0.804176\pi\) | ||||
−0.816658 | + | 0.577122i | \(0.804176\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.75780 | 0.291185 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.12484 | −0.460287 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.83644 | 0.444610 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.6017 | −0.582273 | −0.291137 | − | 0.956681i | \(-0.594033\pi\) | ||||
−0.291137 | + | 0.956681i | \(0.594033\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.2781 | −0.764860 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.7475 | 0.586640 | 0.293320 | − | 0.956014i | \(-0.405240\pi\) | ||||
0.293320 | + | 0.956014i | \(0.405240\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.32609 | −0.165684 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.3707 | 0.515322 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.50023 | −0.371773 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.74394 | 0.0862325 | 0.0431163 | − | 0.999070i | \(-0.486271\pi\) | ||||
0.0431163 | + | 0.999070i | \(0.486271\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.141428 | −0.00697615 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.16834 | 0.352731 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.89143 | −0.387375 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −36.2078 | −1.77310 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.3213 | 1.33473 | 0.667365 | − | 0.744730i | \(-0.267422\pi\) | ||||
0.667365 | + | 0.744730i | \(0.267422\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.4667 | −1.38738 | −0.693692 | − | 0.720272i | \(-0.744017\pi\) | ||||
−0.693692 | + | 0.720272i | \(0.744017\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −33.0251 | −1.60574 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.88368 | 0.333908 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.29287 | 0.110960 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.42926 | 0.117286 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.3287 | 1.41271 | 0.706357 | − | 0.707856i | \(-0.250338\pi\) | ||||
0.706357 | + | 0.707856i | \(0.250338\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.3561 | 1.12242 | 0.561211 | − | 0.827673i | \(-0.310336\pi\) | ||||
0.561211 | + | 0.827673i | \(0.310336\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 19.9419 | 0.956139 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.48019 | 0.262153 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.9699 | −1.28721 | −0.643603 | − | 0.765360i | \(-0.722561\pi\) | ||||
−0.643603 | + | 0.765360i | \(0.722561\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.43773 | 0.116083 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −33.0539 | −1.57044 | −0.785219 | − | 0.619218i | \(-0.787450\pi\) | ||||
−0.785219 | + | 0.619218i | \(0.787450\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.67288 | −0.363730 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 25.3907 | 1.20094 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.0715 | 1.84390 | 0.921948 | − | 0.387313i | \(-0.126597\pi\) | ||||
0.921948 | + | 0.387313i | \(0.126597\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.72012 | 0.363526 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 44.4565 | 2.08875 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.04175 | −0.0488381 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.1465 | 1.22308 | 0.611541 | − | 0.791213i | \(-0.290550\pi\) | ||||
0.611541 | + | 0.791213i | \(0.290550\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.02553 | 0.421275 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.45708 | 0.300736 | 0.150368 | − | 0.988630i | \(-0.451954\pi\) | ||||
0.150368 | + | 0.988630i | \(0.451954\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.83644 | 0.410664 | 0.205332 | − | 0.978692i | \(-0.434173\pi\) | ||||
0.205332 | + | 0.978692i | \(0.434173\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.44522 | −0.345264 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.64714 | −0.261319 | −0.130659 | − | 0.991427i | \(-0.541709\pi\) | ||||
−0.130659 | + | 0.991427i | \(0.541709\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.0771 | 0.465316 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.6807 | −0.492142 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.8739 | 0.499981 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.55179 | 0.300617 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.39114 | 0.429991 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.44388 | −0.111664 | −0.0558319 | − | 0.998440i | \(-0.517781\pi\) | ||||
−0.0558319 | + | 0.998440i | \(0.517781\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.81339 | 0.356260 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.95050 | −0.0887506 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.52672 | 0.296363 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.21778 | 0.0551830 | 0.0275915 | − | 0.999619i | \(-0.491216\pi\) | ||||
0.0275915 | + | 0.999619i | \(0.491216\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.2030 | 0.732727 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.2057 | 1.31804 | 0.659018 | − | 0.752127i | \(-0.270972\pi\) | ||||
0.659018 | + | 0.752127i | \(0.270972\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 58.8678 | 2.65127 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.43773 | 0.109568 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.89143 | −0.174555 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.18677 | −0.142659 | −0.0713297 | − | 0.997453i | \(-0.522724\pi\) | ||||
−0.0713297 | + | 0.997453i | \(0.522724\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −25.5839 | −1.14301 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.9238 | 0.932947 | 0.466474 | − | 0.884535i | \(-0.345524\pi\) | ||||
0.466474 | + | 0.884535i | \(0.345524\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.8572 | −0.527638 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27.7839 | 1.23393 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.46121 | 0.242064 | 0.121032 | − | 0.992649i | \(-0.461380\pi\) | ||||
0.121032 | + | 0.992649i | \(0.461380\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.547006 | 0.0241981 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.59036 | 0.379274 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.3449 | 0.720242 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.5475 | 0.595817 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.1264 | −0.751767 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.7965 | 0.867301 | 0.433651 | − | 0.901081i | \(-0.357225\pi\) | ||||
0.433651 | + | 0.901081i | \(0.357225\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.94748 | 0.391246 | 0.195623 | − | 0.980679i | \(-0.437327\pi\) | ||||
0.195623 | + | 0.980679i | \(0.437327\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.33189 | −0.101772 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.9781 | −0.957380 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3004 | −0.969581 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.4745 | 0.758328 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.04246 | −0.348358 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.796799 | 0.0344486 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 55.5607 | 2.39762 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.5687 | −0.841323 | −0.420662 | − | 0.907218i | \(-0.638202\pi\) | ||||
−0.420662 | + | 0.907218i | \(0.638202\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.72125 | −0.331351 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.9044 | 0.509930 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.8550 | −1.78959 | −0.894795 | − | 0.446478i | \(-0.852678\pi\) | ||||
−0.894795 | + | 0.446478i | \(0.852678\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.58941 | 0.238550 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 56.0295 | 2.38694 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.83644 | −0.375764 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.4898 | 0.742399 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.180622 | −0.00765319 | −0.00382660 | − | 0.999993i | \(-0.501218\pi\) | ||||
−0.00382660 | + | 0.999993i | \(0.501218\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.3279 | −0.479119 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.0520 | 0.677717 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 46.6716 | 1.96697 | 0.983486 | − | 0.180982i | \(-0.0579275\pi\) | ||||
0.983486 | + | 0.180982i | \(0.0579275\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.6478 | −0.574168 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.3707 | −0.435527 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.9845 | −0.670105 | −0.335052 | − | 0.942199i | \(-0.608754\pi\) | ||||
−0.335052 | + | 0.942199i | \(0.608754\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.1792 | −0.593382 | −0.296691 | − | 0.954974i | \(-0.595883\pi\) | ||||
−0.296691 | + | 0.954974i | \(0.595883\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.7392 | 0.448636 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.836442 | 0.0348821 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.8794 | −0.577805 | −0.288903 | − | 0.957358i | \(-0.593290\pi\) | ||||
−0.288903 | + | 0.957358i | \(0.593290\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.4398 | −0.849448 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.89143 | 0.327392 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.85241 | −0.159550 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.53951 | −0.104996 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.86428 | −0.242045 | −0.121022 | − | 0.992650i | \(-0.538617\pi\) | ||||
−0.121022 | + | 0.992650i | \(0.538617\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.9184 | −0.861928 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.45310 | 0.306579 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.07763 | 0.0853180 | 0.0426590 | − | 0.999090i | \(-0.486417\pi\) | ||||
0.0426590 | + | 0.999090i | \(0.486417\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.88368 | −0.282203 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.6328 | −0.844445 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.4106 | −1.16083 | −0.580413 | − | 0.814322i | \(-0.697109\pi\) | ||||
−0.580413 | + | 0.814322i | \(0.697109\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.1513 | −1.22990 | −0.614948 | − | 0.788568i | \(-0.710823\pi\) | ||||
−0.614948 | + | 0.788568i | \(0.710823\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.5652 | 1.00037 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.7804 | −1.04639 | −0.523197 | − | 0.852212i | \(-0.675261\pi\) | ||||
−0.523197 | + | 0.852212i | \(0.675261\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −19.9419 | −0.808085 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.1131 | −0.570955 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.5967 | −0.468388 | −0.234194 | − | 0.972190i | \(-0.575245\pi\) | ||||
−0.234194 | + | 0.972190i | \(0.575245\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.0025 | −0.725931 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.35907 | −0.0547140 | −0.0273570 | − | 0.999626i | \(-0.508709\pi\) | ||||
−0.0273570 | + | 0.999626i | \(0.508709\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.5703 | −0.545437 | −0.272719 | − | 0.962094i | \(-0.587923\pi\) | ||||
−0.272719 | + | 0.962094i | \(0.587923\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.09670 | 0.0440091 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.67288 | 0.307408 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15.2781 | 0.610148 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 51.6292 | 2.05859 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.2889 | −1.36502 | −0.682510 | − | 0.730877i | \(-0.739111\pi\) | ||||
−0.682510 | + | 0.730877i | \(0.739111\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.3285 | 0.927225 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.2286 | −0.842430 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.04175 | 0.0412757 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.48627 | −0.375271 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.1720 | 1.07323 | 0.536615 | − | 0.843827i | \(-0.319703\pi\) | ||||
0.536615 | + | 0.843827i | \(0.319703\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 46.7251 | 1.84266 | 0.921330 | − | 0.388782i | \(-0.127104\pi\) | ||||
0.921330 | + | 0.388782i | \(0.127104\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −25.3567 | −0.998421 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.8896 | 1.17508 | 0.587541 | − | 0.809195i | \(-0.300096\pi\) | ||||
0.587541 | + | 0.809195i | \(0.300096\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.16834 | −0.281382 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.44522 | 0.291801 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.4473 | −0.565367 | −0.282684 | − | 0.959213i | \(-0.591225\pi\) | ||||
−0.282684 | + | 0.959213i | \(0.591225\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.91306 | −0.152896 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.33346 | 0.0520230 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.3339 | 0.831050 | 0.415525 | − | 0.909582i | \(-0.363598\pi\) | ||||
0.415525 | + | 0.909582i | \(0.363598\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 49.5315 | 1.92655 | 0.963277 | − | 0.268510i | \(-0.0865311\pi\) | ||||
0.963277 | + | 0.268510i | \(0.0865311\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.7222 | −0.649438 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.55179 | −0.254067 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.15308 | 0.276968 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.4659 | 0.520621 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.29287 | −0.0885153 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.9586 | −1.00063 | −0.500316 | − | 0.865843i | \(-0.666783\pi\) | ||||
−0.500316 | + | 0.865843i | \(0.666783\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.31115 | 0.0504661 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.6670 | −1.29393 | −0.646964 | − | 0.762520i | \(-0.723962\pi\) | ||||
−0.646964 | + | 0.762520i | \(0.723962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.52672 | −0.250473 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.0648 | −0.998805 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.68024 | −0.140820 | −0.0704102 | − | 0.997518i | \(-0.522431\pi\) | ||||
−0.0704102 | + | 0.997518i | \(0.522431\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.0606495 | −0.00231730 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 33.1993 | 1.26663 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.01326 | 0.152893 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.2473 | 1.11262 | 0.556310 | − | 0.830975i | \(-0.312217\pi\) | ||||
0.556310 | + | 0.830975i | \(0.312217\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.43773 | −0.0926018 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.5272 | −0.588980 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −53.1429 | −2.01293 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 42.8678 | 1.62141 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.75847 | −0.141955 | −0.0709776 | − | 0.997478i | \(-0.522612\pi\) | ||||
−0.0709776 | + | 0.997478i | \(0.522612\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49.1399 | 1.85335 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −31.5913 | −1.18980 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.8572 | 0.445935 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.05700 | −0.0772521 | −0.0386261 | − | 0.999254i | \(-0.512298\pi\) | ||||
−0.0386261 | + | 0.999254i | \(0.512298\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21.5409 | −0.807846 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.67058 | −0.100014 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.04175 | 0.0389593 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −45.2822 | −1.69109 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.7851 | −1.07350 | −0.536752 | − | 0.843740i | \(-0.680349\pi\) | ||||
−0.536752 | + | 0.843740i | \(0.680349\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.3449 | −0.608715 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −51.3172 | −1.90851 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.55179 | 0.317605 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.4508 | 0.461773 | 0.230887 | − | 0.972981i | \(-0.425837\pi\) | ||||
0.230887 | + | 0.972981i | \(0.425837\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.1085 | −0.596612 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −74.8523 | −2.76851 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.81849 | 0.104103 | 0.0520516 | − | 0.998644i | \(-0.483424\pi\) | ||||
0.0520516 | + | 0.998644i | \(0.483424\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.33189 | 0.0860132 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.0771 | −0.371194 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.5526 | 1.60211 | 0.801054 | − | 0.598592i | \(-0.204273\pi\) | ||||
0.801054 | + | 0.598592i | \(0.204273\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.9160 | −0.584688 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.0849172 | 0.00311531 | 0.00155766 | − | 0.999999i | \(-0.499504\pi\) | ||||
0.00155766 | + | 0.999999i | \(0.499504\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.8885 | 0.398922 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.2372 | 0.703852 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.796799 | −0.0291144 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −52.0412 | −1.89901 | −0.949505 | − | 0.313753i | \(-0.898414\pi\) | ||||
−0.949505 | + | 0.313753i | \(0.898414\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.6903 | −0.571786 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.0645 | 0.693830 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0869 | 0.366616 | 0.183308 | − | 0.983056i | \(-0.441319\pi\) | ||||
0.183308 | + | 0.983056i | \(0.441319\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.95050 | 0.0707985 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −47.9897 | −1.73963 | −0.869813 | − | 0.493381i | \(-0.835761\pi\) | ||||
−0.869813 | + | 0.493381i | \(0.835761\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.9044 | −0.430969 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.7806 | −0.606703 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.46763 | 0.269641 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.8164 | 0.678538 | 0.339269 | − | 0.940689i | \(-0.389820\pi\) | ||||
0.339269 | + | 0.940689i | \(0.389820\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.68453 | 0.168709 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.3610 | −0.768300 | −0.384150 | − | 0.923271i | \(-0.625506\pi\) | ||||
−0.384150 | + | 0.923271i | \(0.625506\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.19278 | −0.114688 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.4898 | −0.627441 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −50.5806 | −1.81224 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.89143 | 0.139246 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.2127 | 0.400708 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.58028 | −0.163477 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.66333 | 0.344460 | 0.172230 | − | 0.985057i | \(-0.444903\pi\) | ||||
0.172230 | + | 0.985057i | \(0.444903\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −68.7783 | −2.44857 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.6478 | 0.485261 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.38861 | 0.0848219 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.98341 | 0.318609 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.48127 | −0.158735 | −0.0793675 | − | 0.996845i | \(-0.525290\pi\) | ||||
−0.0793675 | + | 0.996845i | \(0.525290\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −93.2565 | −3.29918 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.7044 | 0.660889 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.547006 | −0.0193034 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.836442 | −0.0294807 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 58.7606 | 2.06847 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 51.6638 | 1.81640 | 0.908202 | − | 0.418533i | \(-0.137456\pi\) | ||||
0.908202 | + | 0.418533i | \(0.137456\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.85243 | 0.170392 | 0.0851959 | − | 0.996364i | \(-0.472848\pi\) | ||||
0.0851959 | + | 0.996364i | \(0.472848\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −44.8263 | −1.57213 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.94845 | 0.243393 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −71.2433 | −2.49249 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.53951 | 0.0887378 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.6135 | −0.475113 | −0.237557 | − | 0.971374i | \(-0.576347\pi\) | ||||
−0.237557 | + | 0.971374i | \(0.576347\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.4114 | 1.47837 | 0.739185 | − | 0.673503i | \(-0.235211\pi\) | ||||
0.739185 | + | 0.673503i | \(0.235211\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.33189 | 0.0811862 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.0844 | 1.56774 | 0.783869 | − | 0.620926i | \(-0.213243\pi\) | ||||
0.783869 | + | 0.620926i | \(0.213243\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.2139 | −1.57034 | −0.785171 | − | 0.619279i | \(-0.787425\pi\) | ||||
−0.785171 | + | 0.619279i | \(0.787425\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −44.2337 | −1.53445 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.88368 | 0.238505 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.9713 | −0.379678 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.18621 | −0.144696 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.935511 | −0.0322974 | −0.0161487 | − | 0.999870i | \(-0.505141\pi\) | ||||
−0.0161487 | + | 0.999870i | \(0.505141\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 44.1330 | 1.52183 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 38.8678 | 1.33868 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.9148 | 0.409880 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.2116 | 0.522061 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.27351 | 0.215053 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.48591 | 0.222073 | 0.111037 | − | 0.993816i | \(-0.464583\pi\) | ||||
0.111037 | + | 0.993816i | \(0.464583\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.9715 | −0.546214 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.14560 | −0.175770 | −0.0878852 | − | 0.996131i | \(-0.528011\pi\) | ||||
−0.0878852 | + | 0.996131i | \(0.528011\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.1437 | −0.687295 | −0.343648 | − | 0.939099i | \(-0.611663\pi\) | ||||
−0.343648 | + | 0.939099i | \(0.611663\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.0025 | 0.613524 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.3580 | −1.13552 | −0.567759 | − | 0.823195i | \(-0.692190\pi\) | ||||
−0.567759 | + | 0.823195i | \(0.692190\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.34443 | −0.249718 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −70.8547 | −2.40635 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.83644 | 0.299756 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.4978 | 0.355705 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15.9104 | −0.538486 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.50003 | −0.0844201 | −0.0422100 | − | 0.999109i | \(-0.513440\pi\) | ||||
−0.0422100 | + | 0.999109i | \(0.513440\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −65.7287 | −2.21697 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.5154 | 0.927018 | 0.463509 | − | 0.886092i | \(-0.346590\pi\) | ||||
0.463509 | + | 0.886092i | \(0.346590\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.9181 | 1.74718 | 0.873591 | − | 0.486661i | \(-0.161785\pi\) | ||||
0.873591 | + | 0.486661i | \(0.161785\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.7158 | 0.561896 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.9590 | 0.569427 | 0.284713 | − | 0.958613i | \(-0.408102\pi\) | ||||
0.284713 | + | 0.958613i | \(0.408102\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.2286 | 0.711983 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.3707 | 0.347430 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −88.7601 | −2.97024 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.8264 | 0.796430 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.03193 | −0.0678443 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.3040 | −0.910638 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.5188 | 0.883468 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.3567 | 0.843819 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.31115 | −0.110066 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.8809 | −0.859361 | −0.429681 | − | 0.902981i | \(-0.641374\pi\) | ||||
−0.429681 | + | 0.902981i | \(0.641374\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 28.9047 | 0.958707 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.86397 | −0.227414 | −0.113707 | − | 0.993514i | \(-0.536272\pi\) | ||||
−0.113707 | + | 0.993514i | \(0.536272\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.89143 | −0.261168 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.34674 | 0.176758 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.91306 | 0.129221 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.4400 | 0.476333 | 0.238167 | − | 0.971224i | \(-0.423454\pi\) | ||||
0.238167 | + | 0.971224i | \(0.423454\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −55.4357 | −1.82667 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.05391 | −0.133436 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.50023 | 0.246606 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −39.8445 | −1.30866 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −47.7350 | −1.56614 | −0.783068 | − | 0.621936i | \(-0.786346\pi\) | ||||
−0.783068 | + | 0.621936i | \(0.786346\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.55179 | 0.214726 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.8431 | 0.616894 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.88368 | 0.225120 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.2026 | 0.823332 | 0.411666 | − | 0.911335i | \(-0.364947\pi\) | ||||
0.411666 | + | 0.911335i | \(0.364947\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.6887 | −0.642516 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.6447 | 1.06419 | 0.532094 | − | 0.846685i | \(-0.321405\pi\) | ||||
0.532094 | + | 0.846685i | \(0.321405\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.45744 | −0.210283 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.31115 | −0.0426517 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54.3257 | 1.76535 | 0.882674 | − | 0.469985i | \(-0.155741\pi\) | ||||
0.882674 | + | 0.469985i | \(0.155741\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.569845 | 0.0184980 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.03446 | 0.228108 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.5837 | −0.634378 | −0.317189 | − | 0.948362i | \(-0.602739\pi\) | ||||
−0.317189 | + | 0.948362i | \(0.602739\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.60535 | 0.149026 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19.9419 | 0.644629 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.0606495 | 0.00195848 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.8062 | −0.671167 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.94238 | −0.0625924 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.76531 | −0.282165 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.8637 | −1.34625 | −0.673123 | − | 0.739530i | \(-0.735048\pi\) | ||||
−0.673123 | + | 0.739530i | \(0.735048\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −105.169 | −3.37853 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.6310 | −0.469531 | −0.234765 | − | 0.972052i | \(-0.575432\pi\) | ||||
−0.234765 | + | 0.972052i | \(0.575432\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.5272 | 0.497779 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.42926 | −0.0777985 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.9335 | −1.11762 | −0.558810 | − | 0.829295i | \(-0.688742\pi\) | ||||
−0.558810 | + | 0.829295i | \(0.688742\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.67288 | −0.245226 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.0198 | −0.926531 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.0654 | 1.37357 | 0.686786 | − | 0.726860i | \(-0.259021\pi\) | ||||
0.686786 | + | 0.726860i | \(0.259021\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.19615 | 0.101838 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 31.5913 | 1.00556 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.09537 | −0.289216 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.8418 | −1.36091 | −0.680457 | − | 0.732788i | \(-0.738219\pi\) | ||||
−0.680457 | + | 0.732788i | \(0.738219\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 66.0661 | 2.09654 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.84809 | −0.280503 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.0734 | −1.14246 | −0.571228 | − | 0.820791i | \(-0.693533\pi\) | ||||
−0.571228 | + | 0.820791i | \(0.693533\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.83392 | 0.311131 |
(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 | 6160.2.a.by.1.1 | 5 | ||
4.3 | odd | 2 | 3080.2.a.r.1.5 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3080.2.a.r.1.5 | ✓ | 5 | 4.3 | odd | 2 | ||
6160.2.a.by.1.1 | 5 | 1.1 | even | 1 | trivial |