Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6864,2,Mod(1,6864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6864, 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("6864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6864 = 2^{4} \cdot 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6864.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: | \(54.8093159474\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.2172244.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 8x^{3} + 16x^{2} + 5x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 3432) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.679950\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6864.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.05398 | −0.471354 | −0.235677 | − | 0.971831i | \(-0.575731\pi\) | ||||
−0.235677 | + | 0.971831i | \(0.575731\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.24902 | −1.60598 | −0.802990 | − | 0.595992i | \(-0.796759\pi\) | ||||
−0.802990 | + | 0.595992i | \(0.796759\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.05398 | −0.272137 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.55494 | −1.10474 | −0.552368 | − | 0.833600i | \(-0.686276\pi\) | ||||
−0.552368 | + | 0.833600i | \(0.686276\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.977426 | 0.224237 | 0.112118 | − | 0.993695i | \(-0.464236\pi\) | ||||
0.112118 | + | 0.993695i | \(0.464236\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.24902 | −0.927213 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82631 | 0.589327 | 0.294663 | − | 0.955601i | \(-0.404793\pi\) | ||||
0.294663 | + | 0.955601i | \(0.404793\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.88912 | −0.777825 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.75121 | 0.882277 | 0.441139 | − | 0.897439i | \(-0.354575\pi\) | ||||
0.441139 | + | 0.897439i | \(0.354575\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.28043 | 1.48721 | 0.743605 | − | 0.668619i | \(-0.233114\pi\) | ||||
0.743605 | + | 0.668619i | \(0.233114\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.47839 | 0.756986 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.14251 | −1.00982 | −0.504912 | − | 0.863171i | \(-0.668475\pi\) | ||||
−0.504912 | + | 0.863171i | \(0.668475\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.92368 | −1.08130 | −0.540648 | − | 0.841249i | \(-0.681821\pi\) | ||||
−0.540648 | + | 0.841249i | \(0.681821\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.56208 | −1.15321 | −0.576603 | − | 0.817024i | \(-0.695622\pi\) | ||||
−0.576603 | + | 0.817024i | \(0.695622\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.05398 | −0.157118 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.967375 | −0.141106 | −0.0705530 | − | 0.997508i | \(-0.522476\pi\) | ||||
−0.0705530 | + | 0.997508i | \(0.522476\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.0542 | 1.57917 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.55494 | −0.637820 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.76058 | −0.791277 | −0.395638 | − | 0.918406i | \(-0.629477\pi\) | ||||
−0.395638 | + | 0.918406i | \(0.629477\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.05398 | −0.142119 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.977426 | 0.129463 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.16364 | 0.672248 | 0.336124 | − | 0.941818i | \(-0.390884\pi\) | ||||
0.336124 | + | 0.941818i | \(0.390884\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.8023 | 1.63916 | 0.819582 | − | 0.572962i | \(-0.194206\pi\) | ||||
0.819582 | + | 0.572962i | \(0.194206\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.24902 | −0.535327 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.05398 | −0.130730 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.76942 | −1.07135 | −0.535677 | − | 0.844423i | \(-0.679944\pi\) | ||||
−0.535677 | + | 0.844423i | \(0.679944\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.82631 | 0.340248 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.74999 | −0.445042 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.141064 | 0.0165102 | 0.00825512 | − | 0.999966i | \(-0.497372\pi\) | ||||
0.00825512 | + | 0.999966i | \(0.497372\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.88912 | −0.449077 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.24902 | −0.484221 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.2704 | 1.38053 | 0.690263 | − | 0.723559i | \(-0.257495\pi\) | ||||
0.690263 | + | 0.723559i | \(0.257495\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.73747 | 0.959062 | 0.479531 | − | 0.877525i | \(-0.340807\pi\) | ||||
0.479531 | + | 0.877525i | \(0.340807\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.80082 | 0.520722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.75121 | 0.509383 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.5309 | −1.75227 | −0.876136 | − | 0.482063i | \(-0.839887\pi\) | ||||
−0.876136 | + | 0.482063i | \(0.839887\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.24902 | −0.445419 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.28043 | 0.858641 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.03019 | −0.105695 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.42271 | −0.753662 | −0.376831 | − | 0.926282i | \(-0.622986\pi\) | ||||
−0.376831 | + | 0.926282i | \(0.622986\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.2076 | 1.01569 | 0.507845 | − | 0.861448i | \(-0.330442\pi\) | ||||
0.507845 | + | 0.861448i | \(0.330442\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.27160 | 0.716492 | 0.358246 | − | 0.933627i | \(-0.383375\pi\) | ||||
0.358246 | + | 0.933627i | \(0.383375\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.47839 | 0.437046 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.9870 | 1.64220 | 0.821099 | − | 0.570785i | \(-0.193361\pi\) | ||||
0.821099 | + | 0.570785i | \(0.193361\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.3032 | 1.94470 | 0.972349 | − | 0.233534i | \(-0.0750289\pi\) | ||||
0.972349 | + | 0.233534i | \(0.0750289\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.14251 | −0.583022 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.72404 | −0.162184 | −0.0810919 | − | 0.996707i | \(-0.525841\pi\) | ||||
−0.0810919 | + | 0.996707i | \(0.525841\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.97888 | −0.277782 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.3541 | 1.77418 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.92368 | −0.624287 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.36897 | 0.837986 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.7382 | −1.04160 | −0.520800 | − | 0.853679i | \(-0.674366\pi\) | ||||
−0.520800 | + | 0.853679i | \(0.674366\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.56208 | −0.665804 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.61898 | 0.490932 | 0.245466 | − | 0.969405i | \(-0.421059\pi\) | ||||
0.245466 | + | 0.969405i | \(0.421059\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.15311 | −0.360120 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.05398 | −0.0907122 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.70315 | 0.316381 | 0.158191 | − | 0.987409i | \(-0.449434\pi\) | ||||
0.158191 | + | 0.987409i | \(0.449434\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.3501 | 1.72607 | 0.863036 | − | 0.505143i | \(-0.168560\pi\) | ||||
0.863036 | + | 0.505143i | \(0.168560\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.967375 | −0.0814676 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.00768 | −0.415865 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.0542 | 0.911736 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.30277 | −0.188651 | −0.0943253 | − | 0.995541i | \(-0.530069\pi\) | ||||
−0.0943253 | + | 0.995541i | \(0.530069\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.19528 | −0.666922 | −0.333461 | − | 0.942764i | \(-0.608217\pi\) | ||||
−0.333461 | + | 0.942764i | \(0.608217\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.55494 | −0.368245 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.72741 | −0.701003 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.9477 | −0.953530 | −0.476765 | − | 0.879031i | \(-0.658191\pi\) | ||||
−0.476765 | + | 0.879031i | \(0.658191\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.76058 | −0.456844 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.0091 | −0.946447 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.5822 | 1.61212 | 0.806062 | − | 0.591831i | \(-0.201595\pi\) | ||||
0.806062 | + | 0.591831i | \(0.201595\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.05398 | −0.0820523 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.9463 | 0.924429 | 0.462214 | − | 0.886768i | \(-0.347055\pi\) | ||||
0.462214 | + | 0.886768i | \(0.347055\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.977426 | 0.0747457 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.8879 | 1.43602 | 0.718010 | − | 0.696033i | \(-0.245053\pi\) | ||||
0.718010 | + | 0.696033i | \(0.245053\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.5250 | 1.24917 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.16364 | 0.388123 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.38247 | 0.626536 | 0.313268 | − | 0.949665i | \(-0.398576\pi\) | ||||
0.313268 | + | 0.949665i | \(0.398576\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.2721 | −0.763517 | −0.381759 | − | 0.924262i | \(-0.624681\pi\) | ||||
−0.381759 | + | 0.924262i | \(0.624681\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.8023 | 0.946371 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.47409 | 0.475985 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.55494 | −0.333091 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.24902 | −0.309071 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.2672 | 1.32177 | 0.660885 | − | 0.750487i | \(-0.270181\pi\) | ||||
0.660885 | + | 0.750487i | \(0.270181\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.13054 | 0.225341 | 0.112670 | − | 0.993632i | \(-0.464060\pi\) | ||||
0.112670 | + | 0.993632i | \(0.464060\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.05398 | −0.0754771 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.7380 | 1.05004 | 0.525020 | − | 0.851090i | \(-0.324058\pi\) | ||||
0.525020 | + | 0.851090i | \(0.324058\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.7859 | 1.75702 | 0.878511 | − | 0.477722i | \(-0.158537\pi\) | ||||
0.878511 | + | 0.477722i | \(0.158537\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.76942 | −0.618547 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.1880 | −1.41692 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.29742 | 0.509674 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.82631 | 0.196442 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.977426 | 0.0676100 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.46319 | 0.376101 | 0.188051 | − | 0.982159i | \(-0.439783\pi\) | ||||
0.188051 | + | 0.982159i | \(0.439783\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.74999 | −0.256945 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.97029 | 0.543569 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −35.1838 | −2.38843 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.141064 | 0.00953220 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.55494 | −0.306399 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.2765 | −1.69264 | −0.846321 | − | 0.532673i | \(-0.821187\pi\) | ||||
−0.846321 | + | 0.532673i | \(0.821187\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.88912 | −0.259275 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.869929 | −0.0577392 | −0.0288696 | − | 0.999583i | \(-0.509191\pi\) | ||||
−0.0288696 | + | 0.999583i | \(0.509191\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.3646 | −1.21357 | −0.606783 | − | 0.794867i | \(-0.707541\pi\) | ||||
−0.606783 | + | 0.794867i | \(0.707541\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.24902 | −0.279565 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.2407 | −1.52255 | −0.761273 | − | 0.648432i | \(-0.775425\pi\) | ||||
−0.761273 | + | 0.648432i | \(0.775425\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.01959 | 0.0665110 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.2704 | 0.797047 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.1838 | 1.43495 | 0.717475 | − | 0.696585i | \(-0.245298\pi\) | ||||
0.717475 | + | 0.696585i | \(0.245298\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.7567 | 1.46589 | 0.732943 | − | 0.680290i | \(-0.238146\pi\) | ||||
0.732943 | + | 0.680290i | \(0.238146\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.6509 | −0.744350 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.977426 | 0.0621921 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.73747 | 0.553714 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.3920 | −0.845297 | −0.422648 | − | 0.906294i | \(-0.638899\pi\) | ||||
−0.422648 | + | 0.906294i | \(0.638899\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.82631 | 0.177689 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.80082 | 0.300639 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.1612 | −1.07049 | −0.535243 | − | 0.844698i | \(-0.679780\pi\) | ||||
−0.535243 | + | 0.844698i | \(0.679780\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.0997 | 1.62176 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.75121 | 0.294092 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.2116 | 0.937985 | 0.468992 | − | 0.883202i | \(-0.344617\pi\) | ||||
0.468992 | + | 0.883202i | \(0.344617\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.07154 | 0.372972 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.5309 | −1.01168 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.36806 | 0.571181 | 0.285590 | − | 0.958352i | \(-0.407810\pi\) | ||||
0.285590 | + | 0.958352i | \(0.407810\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.4721 | 1.30434 | 0.652168 | − | 0.758074i | \(-0.273860\pi\) | ||||
0.652168 | + | 0.758074i | \(0.273860\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.24902 | −0.257163 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.88912 | −0.234523 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.4894 | 1.47143 | 0.735714 | − | 0.677292i | \(-0.236847\pi\) | ||||
0.735714 | + | 0.677292i | \(0.236847\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.28043 | 0.495736 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.6553 | 1.05323 | 0.526614 | − | 0.850105i | \(-0.323461\pi\) | ||||
0.526614 | + | 0.850105i | \(0.323461\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.9691 | −0.830374 | −0.415187 | − | 0.909736i | \(-0.636284\pi\) | ||||
−0.415187 | + | 0.909736i | \(0.636284\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.03019 | −0.0610231 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 29.4189 | 1.73654 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.74752 | 0.220442 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.42271 | −0.435127 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.06528 | 0.0622346 | 0.0311173 | − | 0.999516i | \(-0.490093\pi\) | ||||
0.0311173 | + | 0.999516i | \(0.490093\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.44237 | −0.316867 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.82631 | 0.163450 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.1315 | 1.85203 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.2076 | 0.586409 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.4933 | −0.772627 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.5349 | −1.00077 | −0.500385 | − | 0.865803i | \(-0.666808\pi\) | ||||
−0.500385 | + | 0.865803i | \(0.666808\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.27160 | 0.413667 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.55761 | 0.428553 | 0.214276 | − | 0.976773i | \(-0.431261\pi\) | ||||
0.214276 | + | 0.976773i | \(0.431261\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.2350 | −0.578519 | −0.289259 | − | 0.957251i | \(-0.593409\pi\) | ||||
−0.289259 | + | 0.957251i | \(0.593409\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.47839 | 0.252329 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.76319 | −0.211362 | −0.105681 | − | 0.994400i | \(-0.533702\pi\) | ||||
−0.105681 | + | 0.994400i | \(0.533702\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.75121 | 0.266017 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.9870 | 0.948124 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.45212 | −0.247723 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.88912 | −0.215730 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.3032 | 1.12277 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.11040 | 0.226614 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.5851 | 1.35132 | 0.675660 | − | 0.737213i | \(-0.263859\pi\) | ||||
0.675660 | + | 0.737213i | \(0.263859\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.14251 | −0.336608 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.24280 | 0.504988 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.4966 | 0.953100 | 0.476550 | − | 0.879147i | \(-0.341887\pi\) | ||||
0.476550 | + | 0.879147i | \(0.341887\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.72404 | −0.0936368 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.28043 | 0.448411 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.2265 | −0.930141 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.97888 | −0.160377 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.03602 | 0.162982 | 0.0814909 | − | 0.996674i | \(-0.474032\pi\) | ||||
0.0814909 | + | 0.996674i | \(0.474032\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.587880 | −0.0314685 | −0.0157343 | − | 0.999876i | \(-0.505009\pi\) | ||||
−0.0157343 | + | 0.999876i | \(0.505009\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.259864 | −0.0138312 | −0.00691558 | − | 0.999976i | \(-0.502201\pi\) | ||||
−0.00691558 | + | 0.999976i | \(0.502201\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.95242 | 0.209772 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.3541 | 1.02433 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.59640 | 0.348145 | 0.174072 | − | 0.984733i | \(-0.444307\pi\) | ||||
0.174072 | + | 0.984733i | \(0.444307\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0446 | −0.949718 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.148678 | −0.00778218 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.13108 | 0.267840 | 0.133920 | − | 0.990992i | \(-0.457243\pi\) | ||||
0.133920 | + | 0.990992i | \(0.457243\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.92368 | −0.360432 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.4769 | 1.27078 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.66849 | 0.138169 | 0.0690846 | − | 0.997611i | \(-0.477992\pi\) | ||||
0.0690846 | + | 0.997611i | \(0.477992\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.36897 | 0.483811 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.75121 | 0.244700 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.2900 | 0.888129 | 0.444065 | − | 0.895995i | \(-0.353536\pi\) | ||||
0.444065 | + | 0.895995i | \(0.353536\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.7382 | −0.601368 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.7826 | 1.36853 | 0.684264 | − | 0.729235i | \(-0.260124\pi\) | ||||
0.684264 | + | 0.729235i | \(0.260124\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.47839 | 0.228240 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.56208 | −0.384402 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.8661 | 1.31146 | 0.655732 | − | 0.754994i | \(-0.272360\pi\) | ||||
0.655732 | + | 0.754994i | \(0.272360\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.8737 | −0.651050 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.61898 | 0.283440 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.9327 | −0.650717 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.913162 | −0.0458303 | −0.0229151 | − | 0.999737i | \(-0.507295\pi\) | ||||
−0.0229151 | + | 0.999737i | \(0.507295\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.15311 | −0.207915 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.1048 | 0.554547 | 0.277274 | − | 0.960791i | \(-0.410569\pi\) | ||||
0.277274 | + | 0.960791i | \(0.410569\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.28043 | 0.412478 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.05398 | −0.0523727 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.14251 | −0.304473 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.25242 | 0.309162 | 0.154581 | − | 0.987980i | \(-0.450597\pi\) | ||||
0.154581 | + | 0.987980i | \(0.450597\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.70315 | 0.182663 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.9404 | −1.07962 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.20912 | −0.452058 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.3501 | 0.996548 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.7682 | −1.06345 | −0.531723 | − | 0.846918i | \(-0.678455\pi\) | ||||
−0.531723 | + | 0.846918i | \(0.678455\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.3099 | −1.86711 | −0.933556 | − | 0.358433i | \(-0.883311\pi\) | ||||
−0.933556 | + | 0.358433i | \(0.883311\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.967375 | −0.0470354 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.7147 | 0.859291 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −54.3972 | −2.63246 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.3906 | −1.56020 | −0.780099 | − | 0.625656i | \(-0.784831\pi\) | ||||
−0.780099 | + | 0.625656i | \(0.784831\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.2025 | 0.634471 | 0.317236 | − | 0.948347i | \(-0.397245\pi\) | ||||
0.317236 | + | 0.948347i | \(0.397245\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.00768 | −0.240100 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.76251 | 0.132149 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.2684 | −1.73100 | −0.865498 | − | 0.500912i | \(-0.832998\pi\) | ||||
−0.865498 | + | 0.500912i | \(0.832998\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.0542 | 0.526391 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.3416 | 1.15650 | 0.578251 | − | 0.815859i | \(-0.303735\pi\) | ||||
0.578251 | + | 0.815859i | \(0.303735\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.4233 | 0.825942 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.30277 | −0.108917 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.8932 | 1.64671 | 0.823356 | − | 0.567525i | \(-0.192099\pi\) | ||||
0.823356 | + | 0.567525i | \(0.192099\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.92368 | −0.326023 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.19528 | −0.385048 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.47839 | 0.209950 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.1410 | −1.03571 | −0.517856 | − | 0.855468i | \(-0.673270\pi\) | ||||
−0.517856 | + | 0.855468i | \(0.673270\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.55494 | −0.212607 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.8891 | −1.43865 | −0.719325 | − | 0.694673i | \(-0.755549\pi\) | ||||
−0.719325 | + | 0.694673i | \(0.755549\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.4244 | −0.623885 | −0.311943 | − | 0.950101i | \(-0.600980\pi\) | ||||
−0.311943 | + | 0.950101i | \(0.600980\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.72741 | −0.404724 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.4030 | −0.666493 | −0.333247 | − | 0.942840i | \(-0.608144\pi\) | ||||
−0.333247 | + | 0.942840i | \(0.608144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 37.2615 | 1.72057 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.9477 | −0.550521 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.56208 | −0.347705 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.80133 | −0.174417 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.76058 | −0.263759 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.4321 | −1.66463 | −0.832313 | − | 0.554306i | \(-0.812984\pi\) | ||||
−0.832313 | + | 0.554306i | \(0.812984\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.14251 | −0.280075 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.0091 | −0.546431 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.82340 | 0.355242 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.2709 | 0.737306 | 0.368653 | − | 0.929567i | \(-0.379819\pi\) | ||||
0.368653 | + | 0.929567i | \(0.379819\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.5822 | 0.930760 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −40.6615 | −1.83503 | −0.917513 | − | 0.397705i | \(-0.869807\pi\) | ||||
−0.917513 | + | 0.397705i | \(0.869807\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.6415 | −0.974683 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.05398 | −0.0473729 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.9338 | 0.714728 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.96515 | −0.356569 | −0.178285 | − | 0.983979i | \(-0.557055\pi\) | ||||
−0.178285 | + | 0.983979i | \(0.557055\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.9463 | 0.533719 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.6300 | 1.63325 | 0.816625 | − | 0.577169i | \(-0.195843\pi\) | ||||
0.816625 | + | 0.577169i | \(0.195843\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.7586 | −0.478750 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.2934 | −1.03246 | −0.516231 | − | 0.856449i | \(-0.672666\pi\) | ||||
−0.516231 | + | 0.856449i | \(0.672666\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.599383 | −0.0265151 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.977426 | 0.0431544 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.66412 | −0.337722 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.967375 | −0.0425451 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.8879 | 0.829087 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.85802 | −0.125212 | −0.0626060 | − | 0.998038i | \(-0.519941\pi\) | ||||
−0.0626060 | + | 0.998038i | \(0.519941\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.1624 | −1.14400 | −0.572001 | − | 0.820253i | \(-0.693833\pi\) | ||||
−0.572001 | + | 0.820253i | \(0.693833\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.5250 | 0.721210 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −37.7169 | −1.64297 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0120 | −0.652694 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.16364 | 0.224083 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.92368 | −0.299898 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.9040 | −0.774058 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.38247 | 0.361730 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.0542 | 0.476139 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.4318 | −1.78129 | −0.890646 | − | 0.454697i | \(-0.849747\pi\) | ||||
−0.890646 | + | 0.454697i | \(0.849747\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.2721 | −0.440817 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21.3992 | −0.916642 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.9239 | −0.680857 | −0.340429 | − | 0.940270i | \(-0.610572\pi\) | ||||
−0.340429 | + | 0.940270i | \(0.610572\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.8023 | 0.546388 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.64395 | 0.197839 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −52.1372 | −2.21710 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.47409 | 0.274810 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.6251 | 1.42474 | 0.712370 | − | 0.701804i | \(-0.247622\pi\) | ||||
0.712370 | + | 0.701804i | \(0.247622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.56208 | −0.319842 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.55494 | −0.192310 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.4510 | −0.651181 | −0.325590 | − | 0.945511i | \(-0.605563\pi\) | ||||
−0.325590 | + | 0.945511i | \(0.605563\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.81710 | 0.0764460 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.24902 | −0.178442 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.2238 | 0.638214 | 0.319107 | − | 0.947719i | \(-0.396617\pi\) | ||||
0.319107 | + | 0.947719i | \(0.396617\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.18083 | −0.0912651 | −0.0456325 | − | 0.998958i | \(-0.514530\pi\) | ||||
−0.0456325 | + | 0.998958i | \(0.514530\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.2672 | 0.763125 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.9919 | −0.458393 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.3464 | 0.638879 | 0.319440 | − | 0.947607i | \(-0.396505\pi\) | ||||
0.319440 | + | 0.947607i | \(0.396505\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.13054 | 0.130101 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −37.1257 | −1.54023 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.76058 | −0.238579 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.05398 | −0.0435767 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.8295 | 1.39629 | 0.698147 | − | 0.715954i | \(-0.254008\pi\) | ||||
0.698147 | + | 0.715954i | \(0.254008\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.09351 | 0.333487 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.7380 | 0.606241 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.689961 | 0.0283333 | 0.0141666 | − | 0.999900i | \(-0.495490\pi\) | ||||
0.0141666 | + | 0.999900i | \(0.495490\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.3988 | −0.836270 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.7859 | 1.01442 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.15034 | −0.169578 | −0.0847891 | − | 0.996399i | \(-0.527022\pi\) | ||||
−0.0847891 | + | 0.996399i | \(0.527022\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.88767 | 0.280954 | 0.140477 | − | 0.990084i | \(-0.455136\pi\) | ||||
0.140477 | + | 0.990084i | \(0.455136\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.76942 | −0.357118 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.05398 | −0.0428504 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.7382 | −0.476441 | −0.238220 | − | 0.971211i | \(-0.576564\pi\) | ||||
−0.238220 | + | 0.971211i | \(0.576564\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.1880 | −0.818059 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.967375 | −0.0391358 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.6477 | −0.591616 | −0.295808 | − | 0.955247i | \(-0.595589\pi\) | ||||
−0.295808 | + | 0.955247i | \(0.595589\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.29742 | 0.294260 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.9752 | −0.441844 | −0.220922 | − | 0.975291i | \(-0.570907\pi\) | ||||
−0.220922 | + | 0.975291i | \(0.570907\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.2138 | −1.29478 | −0.647391 | − | 0.762158i | \(-0.724140\pi\) | ||||
−0.647391 | + | 0.762158i | \(0.724140\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.82631 | 0.113416 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 70.2402 | 2.81412 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.57092 | 0.382837 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.977426 | 0.0390346 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.9788 | 1.11559 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.0712 | −1.79426 | −0.897128 | − | 0.441770i | \(-0.854351\pi\) | ||||
−0.897128 | + | 0.441770i | \(0.854351\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.46319 | 0.217142 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.3719 | 0.490963 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.0542 | 0.437984 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.74999 | −0.148347 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.1430 | 1.11158 | 0.555791 | − | 0.831322i | \(-0.312415\pi\) | ||||
0.555791 | + | 0.831322i | \(0.312415\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.10237 | 0.280090 | 0.140045 | − | 0.990145i | \(-0.455275\pi\) | ||||
0.140045 | + | 0.990145i | \(0.455275\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.97029 | 0.313830 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.2768 | 1.11167 | 0.555837 | − | 0.831291i | \(-0.312398\pi\) | ||||
0.555837 | + | 0.831291i | \(0.312398\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.16364 | 0.202690 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −35.1838 | −1.37896 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.1708 | 0.476279 | 0.238140 | − | 0.971231i | \(-0.423462\pi\) | ||||
0.238140 | + | 0.971231i | \(0.423462\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.92229 | −0.231403 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.141064 | 0.00550342 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.9183 | 1.24336 | 0.621681 | − | 0.783271i | \(-0.286450\pi\) | ||||
0.621681 | + | 0.783271i | \(0.286450\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.6021 | −1.30697 | −0.653485 | − | 0.756939i | \(-0.726694\pi\) | ||||
−0.653485 | + | 0.756939i | \(0.726694\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.55494 | −0.176899 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.37730 | 0.169744 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.4284 | 0.519949 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.2765 | −0.977247 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.8023 | 0.494226 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.3314 | 1.09210 | 0.546048 | − | 0.837754i | \(-0.316132\pi\) | ||||
0.546048 | + | 0.837754i | \(0.316132\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.88912 | −0.149692 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.74310 | 0.105426 | 0.0527129 | − | 0.998610i | \(-0.483213\pi\) | ||||
0.0527129 | + | 0.998610i | \(0.483213\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.5393 | 1.21037 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.869929 | −0.0333358 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.3066 | 0.891803 | 0.445901 | − | 0.895082i | \(-0.352883\pi\) | ||||
0.445901 | + | 0.895082i | \(0.352883\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.90304 | −0.149128 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.3646 | −0.700653 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.76058 | −0.219461 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.97295 | 0.379389 | 0.189694 | − | 0.981843i | \(-0.439250\pi\) | ||||
0.189694 | + | 0.981843i | \(0.439250\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.24902 | −0.161407 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.4486 | −0.813591 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.5370 | 1.19455 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.2407 | −0.879042 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.1096 | 0.495144 | 0.247572 | − | 0.968869i | \(-0.420367\pi\) | ||||
0.247572 | + | 0.968869i | \(0.420367\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.00386 | −0.226440 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.01959 | 0.0384001 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −43.3722 | −1.63118 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.7733 | 0.892826 | 0.446413 | − | 0.894827i | \(-0.352701\pi\) | ||||
0.446413 | + | 0.894827i | \(0.352701\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.2704 | 0.460175 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23.4031 | 0.876452 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.05398 | −0.0394166 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.1838 | 0.828468 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.1219 | 0.787712 | 0.393856 | − | 0.919172i | \(-0.371141\pi\) | ||||
0.393856 | + | 0.919172i | \(0.371141\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.8972 | −1.15067 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22.7567 | 0.846330 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.4780 | −0.686257 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.5157 | −0.390006 | −0.195003 | − | 0.980803i | \(-0.562472\pi\) | ||||
−0.195003 | + | 0.980803i | \(0.562472\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34.4449 | 1.27399 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −49.4643 | −1.82701 | −0.913503 | − | 0.406833i | \(-0.866633\pi\) | ||||
−0.913503 | + | 0.406833i | \(0.866633\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.6509 | −0.429751 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.76942 | −0.323026 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.74040 | 0.358306 | 0.179153 | − | 0.983821i | \(-0.442664\pi\) | ||||
0.179153 | + | 0.983821i | \(0.442664\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.977426 | 0.0359067 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.7182 | 0.503272 | 0.251636 | − | 0.967822i | \(-0.419031\pi\) | ||||
0.251636 | + | 0.967822i | \(0.419031\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.42708 | 0.0889213 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.73747 | 0.319687 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −72.1783 | −2.63734 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.6627 | −0.826972 | −0.413486 | − | 0.910510i | \(-0.635689\pi\) | ||||
−0.413486 | + | 0.910510i | \(0.635689\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.3920 | −0.488032 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.63766 | 0.314357 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.1376 | −0.768259 | −0.384130 | − | 0.923279i | \(-0.625498\pi\) | ||||
−0.384130 | + | 0.923279i | \(0.625498\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.82631 | 0.102589 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.32152 | 0.0841551 | 0.0420775 | − | 0.999114i | \(-0.486602\pi\) | ||||
0.0420775 | + | 0.999114i | \(0.486602\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −86.2690 | −3.12315 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.80082 | 0.173574 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.16364 | 0.186448 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.1170 | 0.436951 | 0.218476 | − | 0.975842i | \(-0.429892\pi\) | ||||
0.218476 | + | 0.975842i | \(0.429892\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.1612 | −0.618046 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40.2007 | −1.44592 | −0.722959 | − | 0.690890i | \(-0.757219\pi\) | ||||
−0.722959 | + | 0.690890i | \(0.757219\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.2036 | −1.15679 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 26.0997 | 0.936321 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.76738 | −0.242467 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.74999 | −0.134185 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.75121 | 0.169794 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.5926 | 0.449451 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.3882 | 1.08322 | 0.541611 | − | 0.840629i | \(-0.317815\pi\) | ||||
0.541611 | + | 0.840629i | \(0.317815\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.2116 | 0.541546 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.32548 | 0.260464 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.8023 | 0.454622 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.07154 | 0.215335 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.9490 | 1.20254 | 0.601268 | − | 0.799047i | \(-0.294662\pi\) | ||||
0.601268 | + | 0.799047i | \(0.294662\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.40634 | 0.155885 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.5309 | −0.584091 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.141064 | 0.00497803 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.6573 | 0.446112 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.36806 | 0.329771 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.60592 | 0.161936 | 0.0809678 | − | 0.996717i | \(-0.474199\pi\) | ||||
0.0809678 | + | 0.996717i | \(0.474199\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.5206 | −0.545003 | −0.272501 | − | 0.962155i | \(-0.587851\pi\) | ||||
−0.272501 | + | 0.962155i | \(0.587851\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.4721 | 0.753059 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.6933 | −0.759882 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.39138 | −0.258592 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.24902 | −0.148473 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.7361 | 0.549193 | 0.274597 | − | 0.961560i | \(-0.411456\pi\) | ||||
0.274597 | + | 0.961560i | \(0.411456\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.77401 | 0.166412 | 0.0832058 | − | 0.996532i | \(-0.473484\pi\) | ||||
0.0832058 | + | 0.996532i | \(0.473484\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.88912 | −0.135402 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.536827 | 0.0186673 | 0.00933365 | − | 0.999956i | \(-0.497029\pi\) | ||||
0.00933365 | + | 0.999956i | \(0.497029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.1757 | 0.909120 | 0.454560 | − | 0.890716i | \(-0.349796\pi\) | ||||
0.454560 | + | 0.890716i | \(0.349796\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.4894 | 0.849530 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −50.3513 | −1.74457 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.5911 | −0.435734 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.28043 | 0.286214 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.3887 | 0.703897 | 0.351949 | − | 0.936019i | \(-0.385519\pi\) | ||||
0.351949 | + | 0.936019i | \(0.385519\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.42603 | −0.221587 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.6553 | 0.608081 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.05398 | −0.0362580 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.24902 | −0.145998 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.9691 | −0.479417 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.3607 | −0.595116 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.4039 | −1.34916 | −0.674581 | − | 0.738201i | \(-0.735676\pi\) | ||||
−0.674581 | + | 0.738201i | \(0.735676\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.03019 | −0.0352317 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.72146 | 0.127123 | 0.0635614 | − | 0.997978i | \(-0.479754\pi\) | ||||
0.0635614 | + | 0.997978i | \(0.479754\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.8699 | −0.677952 | −0.338976 | − | 0.940795i | \(-0.610081\pi\) | ||||
−0.338976 | + | 0.940795i | \(0.610081\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29.4189 | 1.00259 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.6108 | −1.14413 | −0.572063 | − | 0.820210i | \(-0.693857\pi\) | ||||
−0.572063 | + | 0.820210i | \(0.693857\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.9075 | −0.676874 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.74752 | 0.127272 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.2704 | 0.416244 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.76942 | −0.297140 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.42271 | −0.251221 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −39.8090 | −1.34579 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.9946 | 1.78950 | 0.894750 | − | 0.446567i | \(-0.147354\pi\) | ||||
0.894750 | + | 0.446567i | \(0.147354\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.06528 | 0.0359311 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.6459 | 0.560816 | 0.280408 | − | 0.959881i | \(-0.409530\pi\) | ||||
0.280408 | + | 0.959881i | \(0.409530\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.1900 | 1.41981 | 0.709903 | − | 0.704299i | \(-0.248739\pi\) | ||||
0.709903 | + | 0.704299i | \(0.248739\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.44237 | −0.182943 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 55.4874 | 1.86308 | 0.931542 | − | 0.363633i | \(-0.118464\pi\) | ||||
0.931542 | + | 0.363633i | \(0.118464\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 49.8761 | 1.67279 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.945537 | −0.0316412 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.83497 | −0.295320 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.82631 | 0.0943678 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 39.3420 | 1.31213 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.2391 | 0.874152 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 32.1315 | 1.06927 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.8266 | 0.359887 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.47170 | −0.0488670 | −0.0244335 | − | 0.999701i | \(-0.507778\pi\) | ||||
−0.0244335 | + | 0.999701i | \(0.507778\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.2076 | 0.338564 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.3498 | 1.03866 | 0.519332 | − | 0.854573i | \(-0.326181\pi\) | ||||
0.519332 | + | 0.854573i | \(0.326181\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.73747 | 0.289168 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.4933 | −0.446076 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23.8752 | −0.788428 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.07327 | −0.101378 | −0.0506889 | − | 0.998714i | \(-0.516142\pi\) | ||||
−0.0506889 | + | 0.998714i | \(0.516142\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.5349 | −0.577795 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.74999 | −0.123432 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.8890 | 0.785466 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.27160 | 0.238831 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.13209 | 0.266805 | 0.133403 | − | 0.991062i | \(-0.457410\pi\) | ||||
0.133403 | + | 0.991062i | \(0.457410\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.8047 | 0.354109 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.55761 | 0.247425 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.80082 | 0.157004 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.7711 | 1.20126 | 0.600630 | − | 0.799527i | \(-0.294916\pi\) | ||||
0.600630 | + | 0.799527i | \(0.294916\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.2350 | −0.334008 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.5475 | 1.15881 | 0.579407 | − | 0.815038i | \(-0.303284\pi\) | ||||
0.579407 | + | 0.815038i | \(0.303284\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.5685 | −0.637237 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.47839 | 0.145682 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −55.7033 | −1.81012 | −0.905058 | − | 0.425289i | \(-0.860172\pi\) | ||||
−0.905058 | + | 0.425289i | \(0.860172\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.141064 | 0.00457912 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.76319 | −0.122030 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.19748 | 0.168363 | 0.0841815 | − | 0.996450i | \(-0.473172\pi\) | ||||
0.0841815 | + | 0.996450i | \(0.473172\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.2533 | −0.623023 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.75121 | 0.153585 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.7348 | −0.508102 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.5656 | 1.21179 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.9870 | 0.547400 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.29952 | −0.106215 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.7678 | −0.700004 | −0.350002 | − | 0.936749i | \(-0.613819\pi\) | ||||
−0.350002 | + | 0.936749i | \(0.613819\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.45212 | −0.143023 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.57482 | 0.243087 | 0.121544 | − | 0.992586i | \(-0.461216\pi\) | ||||
0.121544 | + | 0.992586i | \(0.461216\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −86.4680 | −2.77204 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.88912 | −0.124552 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.0642 | −0.577925 | −0.288962 | − | 0.957340i | \(-0.593310\pi\) | ||||
−0.288962 | + | 0.957340i | \(0.593310\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.5309 | −0.528330 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.3032 | 0.648232 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.91261 | −0.252373 | −0.126186 | − | 0.992007i | \(-0.540274\pi\) | ||||
−0.126186 | + | 0.992007i | \(0.540274\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.5336 | −0.494941 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.11040 | 0.130835 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.3728 | −0.679615 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.66751 | −0.243567 | −0.121783 | − | 0.992557i | \(-0.538861\pi\) | ||||
−0.121783 | + | 0.992557i | \(0.538861\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.5851 | 0.780185 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26.1238 | −0.828180 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.2163 | −1.27366 | −0.636831 | − | 0.771004i | \(-0.719755\pi\) | ||||
−0.636831 | + | 0.771004i | \(0.719755\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.14251 | −0.194341 |
(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 | 6864.2.a.cf.1.2 | 5 | ||
4.3 | odd | 2 | 3432.2.a.w.1.2 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3432.2.a.w.1.2 | ✓ | 5 | 4.3 | odd | 2 | ||
6864.2.a.cf.1.2 | 5 | 1.1 | even | 1 | trivial |