Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5148,2,Mod(1,5148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5148, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5148.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5148 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5148.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: | \(41.1069869606\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.815952.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 6x^{3} + 6x^{2} + 9x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.63081\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5148.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.47267 | 0.658597 | 0.329298 | − | 0.944226i | \(-0.393188\pi\) | ||||
0.329298 | + | 0.944226i | \(0.393188\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.87430 | −1.46435 | −0.732174 | − | 0.681117i | \(-0.761494\pi\) | ||||
−0.732174 | + | 0.681117i | \(0.761494\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.358587 | −0.0869700 | −0.0434850 | − | 0.999054i | \(-0.513846\pi\) | ||||
−0.0434850 | + | 0.999054i | \(0.513846\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.61547 | −0.370615 | −0.185307 | − | 0.982681i | \(-0.559328\pi\) | ||||
−0.185307 | + | 0.982681i | \(0.559328\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.63731 | 0.758432 | 0.379216 | − | 0.925308i | \(-0.376194\pi\) | ||||
0.379216 | + | 0.925308i | \(0.376194\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.83125 | −0.566251 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.34418 | 0.806695 | 0.403347 | − | 0.915047i | \(-0.367847\pi\) | ||||
0.403347 | + | 0.915047i | \(0.367847\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.59501 | 0.645682 | 0.322841 | − | 0.946453i | \(-0.395362\pi\) | ||||
0.322841 | + | 0.946453i | \(0.395362\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.70556 | −0.964415 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.44115 | 0.565722 | 0.282861 | − | 0.959161i | \(-0.408716\pi\) | ||||
0.282861 | + | 0.959161i | \(0.408716\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.93919 | 1.23989 | 0.619947 | − | 0.784644i | \(-0.287154\pi\) | ||||
0.619947 | + | 0.784644i | \(0.287154\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.36881 | −1.12373 | −0.561866 | − | 0.827228i | \(-0.689916\pi\) | ||||
−0.561866 | + | 0.827228i | \(0.689916\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.30745 | −0.920036 | −0.460018 | − | 0.887910i | \(-0.652157\pi\) | ||||
−0.460018 | + | 0.887910i | \(0.652157\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.01022 | 1.14432 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.25883 | −0.859716 | −0.429858 | − | 0.902896i | \(-0.641436\pi\) | ||||
−0.429858 | + | 0.902896i | \(0.641436\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.47267 | 0.198574 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.46578 | 0.581395 | 0.290697 | − | 0.956815i | \(-0.406113\pi\) | ||||
0.290697 | + | 0.956815i | \(0.406113\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.64810 | −1.23531 | −0.617657 | − | 0.786448i | \(-0.711918\pi\) | ||||
−0.617657 | + | 0.786448i | \(0.711918\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.47267 | −0.182662 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.79173 | 0.341065 | 0.170532 | − | 0.985352i | \(-0.445451\pi\) | ||||
0.170532 | + | 0.985352i | \(0.445451\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.3865 | −1.47001 | −0.735003 | − | 0.678064i | \(-0.762819\pi\) | ||||
−0.735003 | + | 0.678064i | \(0.762819\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.76497 | −0.908821 | −0.454410 | − | 0.890792i | \(-0.650150\pi\) | ||||
−0.454410 | + | 0.890792i | \(0.650150\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.87430 | −0.441518 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.90024 | 0.213794 | 0.106897 | − | 0.994270i | \(-0.465908\pi\) | ||||
0.106897 | + | 0.994270i | \(0.465908\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.2958 | −1.23988 | −0.619939 | − | 0.784650i | \(-0.712843\pi\) | ||||
−0.619939 | + | 0.784650i | \(0.712843\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.528079 | −0.0572782 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.919392 | 0.0974554 | 0.0487277 | − | 0.998812i | \(-0.484483\pi\) | ||||
0.0487277 | + | 0.998812i | \(0.484483\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.87430 | 0.406137 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.37905 | −0.244086 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.07651 | −0.109303 | −0.0546513 | − | 0.998506i | \(-0.517405\pi\) | ||||
−0.0546513 | + | 0.998506i | \(0.517405\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.58675 | 0.257391 | 0.128695 | − | 0.991684i | \(-0.458921\pi\) | ||||
0.128695 | + | 0.991684i | \(0.458921\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.20695 | −0.611589 | −0.305794 | − | 0.952098i | \(-0.598922\pi\) | ||||
−0.305794 | + | 0.952098i | \(0.598922\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.38396 | −0.907181 | −0.453591 | − | 0.891210i | \(-0.649857\pi\) | ||||
−0.453591 | + | 0.891210i | \(0.649857\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.49313 | 0.143016 | 0.0715081 | − | 0.997440i | \(-0.477219\pi\) | ||||
0.0715081 | + | 0.997440i | \(0.477219\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.105819 | 0.00995466 | 0.00497733 | − | 0.999988i | \(-0.498416\pi\) | ||||
0.00497733 | + | 0.999988i | \(0.498416\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.35655 | 0.499501 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.38927 | 0.127354 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.5328 | −1.03153 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.56212 | −0.316087 | −0.158044 | − | 0.987432i | \(-0.550519\pi\) | ||||
−0.158044 | + | 0.987432i | \(0.550519\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.4630 | −1.35101 | −0.675504 | − | 0.737356i | \(-0.736074\pi\) | ||||
−0.675504 | + | 0.737356i | \(0.736074\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.25883 | 0.542709 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.28126 | −0.536644 | −0.268322 | − | 0.963329i | \(-0.586469\pi\) | ||||
−0.268322 | + | 0.963329i | \(0.586469\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.66604 | −0.226130 | −0.113065 | − | 0.993588i | \(-0.536067\pi\) | ||||
−0.113065 | + | 0.993588i | \(0.536067\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.39753 | 0.531286 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.55058 | −0.127029 | −0.0635144 | − | 0.997981i | \(-0.520231\pi\) | ||||
−0.0635144 | + | 0.997981i | \(0.520231\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.36686 | −0.518128 | −0.259064 | − | 0.965860i | \(-0.583414\pi\) | ||||
−0.259064 | + | 0.965860i | \(0.583414\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.29425 | 0.425244 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.68362 | −0.613220 | −0.306610 | − | 0.951835i | \(-0.599195\pi\) | ||||
−0.306610 | + | 0.951835i | \(0.599195\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.0920 | −1.11061 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.71244 | 0.212455 | 0.106227 | − | 0.994342i | \(-0.466123\pi\) | ||||
0.106227 | + | 0.994342i | \(0.466123\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.0409 | −1.16390 | −0.581950 | − | 0.813225i | \(-0.697710\pi\) | ||||
−0.581950 | + | 0.813225i | \(0.697710\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.644199 | 0.0489775 | 0.0244888 | − | 0.999700i | \(-0.492204\pi\) | ||||
0.0244888 | + | 0.999700i | \(0.492204\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.9691 | 0.829188 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.1515 | −1.65568 | −0.827839 | − | 0.560966i | \(-0.810430\pi\) | ||||
−0.827839 | + | 0.560966i | \(0.810430\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.3312 | 1.21389 | 0.606946 | − | 0.794743i | \(-0.292394\pi\) | ||||
0.606946 | + | 0.794743i | \(0.292394\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.06767 | 0.372583 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.358587 | −0.0262225 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.25326 | −0.307755 | −0.153878 | − | 0.988090i | \(-0.549176\pi\) | ||||
−0.153878 | + | 0.988090i | \(0.549176\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.50408 | −0.396192 | −0.198096 | − | 0.980183i | \(-0.563476\pi\) | ||||
−0.198096 | + | 0.980183i | \(0.563476\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.88174 | 0.134068 | 0.0670341 | − | 0.997751i | \(-0.478646\pi\) | ||||
0.0670341 | + | 0.997751i | \(0.478646\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.5716 | 0.891177 | 0.445588 | − | 0.895238i | \(-0.352994\pi\) | ||||
0.445588 | + | 0.895238i | \(0.352994\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.8307 | −1.18128 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.6918 | 0.816589 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.61547 | −0.111745 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.36602 | 0.438255 | 0.219128 | − | 0.975696i | \(-0.429679\pi\) | ||||
0.219128 | + | 0.975696i | \(0.429679\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.8518 | −0.740086 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.9281 | −0.945504 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.358587 | 0.0241212 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.64410 | −0.444922 | −0.222461 | − | 0.974942i | \(-0.571409\pi\) | ||||
−0.222461 | + | 0.974942i | \(0.571409\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.5943 | −0.902283 | −0.451141 | − | 0.892452i | \(-0.648983\pi\) | ||||
−0.451141 | + | 0.892452i | \(0.648983\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.63788 | 0.174316 | 0.0871581 | − | 0.996194i | \(-0.472221\pi\) | ||||
0.0871581 | + | 0.996194i | \(0.472221\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.00390 | 0.458841 | 0.229421 | − | 0.973327i | \(-0.426317\pi\) | ||||
0.229421 | + | 0.973327i | \(0.426317\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.28877 | −0.605933 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.7992 | −1.66881 | −0.834405 | − | 0.551151i | \(-0.814189\pi\) | ||||
−0.834405 | + | 0.551151i | \(0.814189\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.3423 | 1.18153 | 0.590766 | − | 0.806843i | \(-0.298826\pi\) | ||||
0.590766 | + | 0.806843i | \(0.298826\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.7964 | 0.753643 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.61547 | 0.102790 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.6467 | 1.24009 | 0.620045 | − | 0.784567i | \(-0.287115\pi\) | ||||
0.620045 | + | 0.784567i | \(0.287115\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.63731 | 0.228676 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.560963 | −0.0349919 | −0.0174960 | − | 0.999847i | \(-0.505569\pi\) | ||||
−0.0174960 | + | 0.999847i | \(0.505569\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.3321 | −0.828415 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.7183 | −1.21588 | −0.607941 | − | 0.793982i | \(-0.708004\pi\) | ||||
−0.607941 | + | 0.793982i | \(0.708004\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.21717 | −0.566206 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.46021 | 0.393886 | 0.196943 | − | 0.980415i | \(-0.436899\pi\) | ||||
0.196943 | + | 0.980415i | \(0.436899\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.19802 | −0.376503 | −0.188251 | − | 0.982121i | \(-0.560282\pi\) | ||||
−0.188251 | + | 0.982121i | \(0.560282\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.83125 | −0.170731 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.5272 | 0.752684 | 0.376342 | − | 0.926481i | \(-0.377182\pi\) | ||||
0.376342 | + | 0.926481i | \(0.377182\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.2555 | 0.731100 | 0.365550 | − | 0.930792i | \(-0.380881\pi\) | ||||
0.365550 | + | 0.930792i | \(0.380881\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.4527 | −1.21579 | −0.607895 | − | 0.794018i | \(-0.707986\pi\) | ||||
−0.607895 | + | 0.794018i | \(0.707986\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.7588 | −1.81564 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8714 | −0.992436 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.1591 | −1.06087 | −0.530434 | − | 0.847726i | \(-0.677971\pi\) | ||||
−0.530434 | + | 0.847726i | \(0.677971\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.57660 | 0.382905 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.63731 | −0.210351 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 28.5490 | 1.64554 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.2084 | −0.813573 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.64263 | −0.207896 | −0.103948 | − | 0.994583i | \(-0.533148\pi\) | ||||
−0.103948 | + | 0.994583i | \(0.533148\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.7439 | 1.23298 | 0.616490 | − | 0.787362i | \(-0.288554\pi\) | ||||
0.616490 | + | 0.787362i | \(0.288554\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.0408 | 1.41539 | 0.707696 | − | 0.706517i | \(-0.249735\pi\) | ||||
0.707696 | + | 0.706517i | \(0.249735\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.86751 | 0.273387 | 0.136693 | − | 0.990613i | \(-0.456353\pi\) | ||||
0.136693 | + | 0.990613i | \(0.456353\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.34418 | 0.243228 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.579287 | 0.0322324 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.83125 | 0.157050 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.4370 | 1.34725 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.8638 | −0.597129 | −0.298564 | − | 0.954390i | \(-0.596508\pi\) | ||||
−0.298564 | + | 0.954390i | \(0.596508\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.11129 | 0.224624 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.46856 | 0.406839 | 0.203419 | − | 0.979092i | \(-0.434795\pi\) | ||||
0.203419 | + | 0.979092i | \(0.434795\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.59501 | 0.194681 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.91390 | −0.211331 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.8039 | 1.70732 | 0.853661 | − | 0.520829i | \(-0.174377\pi\) | ||||
0.853661 | + | 0.520829i | \(0.174377\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.0688 | −1.39543 | −0.697716 | − | 0.716375i | \(-0.745800\pi\) | ||||
−0.697716 | + | 0.716375i | \(0.745800\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.04111 | 0.0554124 | 0.0277062 | − | 0.999616i | \(-0.491180\pi\) | ||||
0.0277062 | + | 0.999616i | \(0.491180\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.2412 | −0.968141 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.9301 | −1.47409 | −0.737047 | − | 0.675841i | \(-0.763781\pi\) | ||||
−0.737047 | + | 0.675841i | \(0.763781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.3902 | −0.862645 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.4352 | −0.598546 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.127912 | 0.00667693 | 0.00333846 | − | 0.999994i | \(-0.498937\pi\) | ||||
0.00333846 | + | 0.999994i | \(0.498937\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.2486 | 1.25892 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.5491 | 0.908658 | 0.454329 | − | 0.890834i | \(-0.349879\pi\) | ||||
0.454329 | + | 0.890834i | \(0.349879\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.34418 | −0.223737 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.93633 | 0.407662 | 0.203831 | − | 0.979006i | \(-0.434661\pi\) | ||||
0.203831 | + | 0.979006i | \(0.434661\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.88396 | −0.249559 | −0.124779 | − | 0.992185i | \(-0.539822\pi\) | ||||
−0.124779 | + | 0.992185i | \(0.539822\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.70556 | −0.290782 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.5314 | 1.19309 | 0.596545 | − | 0.802579i | \(-0.296540\pi\) | ||||
0.596545 | + | 0.802579i | \(0.296540\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.30429 | −0.0659608 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.79842 | 0.140804 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.7374 | 1.34191 | 0.670955 | − | 0.741498i | \(-0.265884\pi\) | ||||
0.670955 | + | 0.741498i | \(0.265884\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.3306 | 0.565823 | 0.282912 | − | 0.959146i | \(-0.408700\pi\) | ||||
0.282912 | + | 0.959146i | \(0.408700\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.59501 | −0.179080 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.44115 | 0.170572 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.1722 | −0.750215 | −0.375108 | − | 0.926981i | \(-0.622394\pi\) | ||||
−0.375108 | + | 0.926981i | \(0.622394\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.3018 | −0.851365 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.6350 | −0.816580 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.3469 | 0.603185 | 0.301593 | − | 0.953437i | \(-0.402482\pi\) | ||||
0.301593 | + | 0.953437i | \(0.402482\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.3375 | −1.33235 | −0.666174 | − | 0.745797i | \(-0.732069\pi\) | ||||
−0.666174 | + | 0.745797i | \(0.732069\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.01525 | 0.0492468 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 37.3797 | 1.80893 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.8646 | 0.523332 | 0.261666 | − | 0.965159i | \(-0.415728\pi\) | ||||
0.261666 | + | 0.965159i | \(0.415728\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.5697 | 0.652118 | 0.326059 | − | 0.945349i | \(-0.394279\pi\) | ||||
0.326059 | + | 0.945349i | \(0.394279\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.87598 | −0.281086 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.0316692 | 0.00151149 | 0.000755743 | − | 1.00000i | \(-0.499759\pi\) | ||||
0.000755743 | 1.00000i | \(0.499759\pi\) | ||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.47120 | −0.354967 | −0.177484 | − | 0.984124i | \(-0.556796\pi\) | ||||
−0.177484 | + | 0.984124i | \(0.556796\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.35396 | 0.0641838 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.3196 | −1.66684 | −0.833418 | − | 0.552644i | \(-0.813619\pi\) | ||||
−0.833418 | + | 0.552644i | \(0.813619\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.93919 | 0.373842 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.70556 | 0.267481 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.7897 | −0.785389 | −0.392694 | − | 0.919669i | \(-0.628457\pi\) | ||||
−0.392694 | + | 0.919669i | \(0.628457\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.80827 | −0.270518 | −0.135259 | − | 0.990810i | \(-0.543187\pi\) | ||||
−0.135259 | + | 0.990810i | \(0.543187\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.15664 | 0.332597 | 0.166299 | − | 0.986075i | \(-0.446818\pi\) | ||||
0.166299 | + | 0.986075i | \(0.446818\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.424222 | −0.0196307 | −0.00981534 | − | 0.999952i | \(-0.503124\pi\) | ||||
−0.00981534 | + | 0.999952i | \(0.503124\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.8160 | −0.499438 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.36881 | −0.338818 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.57381 | 0.209861 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.2157 | −1.60905 | −0.804523 | − | 0.593922i | \(-0.797579\pi\) | ||||
−0.804523 | + | 0.593922i | \(0.797579\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.44115 | −0.156903 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.58533 | −0.0719863 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.24388 | −0.237623 | −0.118811 | − | 0.992917i | \(-0.537908\pi\) | ||||
−0.118811 | + | 0.992917i | \(0.537908\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.1111 | 1.04299 | 0.521495 | − | 0.853255i | \(-0.325375\pi\) | ||||
0.521495 | + | 0.853255i | \(0.325375\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.55777 | −0.0701583 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 47.9890 | 2.15260 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.2763 | 1.57918 | 0.789592 | − | 0.613632i | \(-0.210292\pi\) | ||||
0.789592 | + | 0.613632i | \(0.210292\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.12032 | −0.183716 | −0.0918579 | − | 0.995772i | \(-0.529281\pi\) | ||||
−0.0918579 | + | 0.995772i | \(0.529281\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.80941 | 0.169517 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.8017 | −0.877695 | −0.438848 | − | 0.898562i | \(-0.644613\pi\) | ||||
−0.438848 | + | 0.898562i | \(0.644613\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.0838 | 1.33083 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.14077 | −0.402790 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.30745 | −0.277401 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.0260 | −1.05260 | −0.526299 | − | 0.850299i | \(-0.676421\pi\) | ||||
−0.526299 | + | 0.850299i | \(0.676421\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.7130 | −1.08062 | −0.540312 | − | 0.841465i | \(-0.681694\pi\) | ||||
−0.540312 | + | 0.841465i | \(0.681694\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.28912 | −0.0561550 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.76997 | −0.424781 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.93919 | −0.343885 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.8194 | −0.597466 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.01022 | 0.345025 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.07660 | 0.0462866 | 0.0231433 | − | 0.999732i | \(-0.492633\pi\) | ||||
0.0231433 | + | 0.999732i | \(0.492633\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.19889 | 0.0941899 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.9622 | 1.11007 | 0.555033 | − | 0.831829i | \(-0.312706\pi\) | ||||
0.555033 | + | 0.831829i | \(0.312706\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.01791 | −0.298973 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.36212 | −0.313069 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.2787 | −0.859238 | −0.429619 | − | 0.903010i | \(-0.641352\pi\) | ||||
−0.429619 | + | 0.903010i | \(0.641352\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.36881 | 0.311667 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.3183 | 0.477009 | 0.238505 | − | 0.971141i | \(-0.423343\pi\) | ||||
0.238505 | + | 0.971141i | \(0.423343\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.155837 | 0.00655610 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.4664 | 1.65452 | 0.827259 | − | 0.561820i | \(-0.189899\pi\) | ||||
0.827259 | + | 0.561820i | \(0.189899\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.9002 | −0.958345 | −0.479173 | − | 0.877721i | \(-0.659063\pi\) | ||||
−0.479173 | + | 0.877721i | \(0.659063\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.2981 | −0.429462 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.49293 | −0.353565 | −0.176783 | − | 0.984250i | \(-0.556569\pi\) | ||||
−0.176783 | + | 0.984250i | \(0.556569\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 43.7635 | 1.81561 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.25883 | −0.259214 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.4232 | 1.09060 | 0.545301 | − | 0.838240i | \(-0.316415\pi\) | ||||
0.545301 | + | 0.838240i | \(0.316415\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.80764 | −0.239299 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.1371 | −0.580539 | −0.290270 | − | 0.956945i | \(-0.593745\pi\) | ||||
−0.290270 | + | 0.956945i | \(0.593745\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.04594 | 0.0838752 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.6374 | −1.74212 | −0.871058 | − | 0.491179i | \(-0.836566\pi\) | ||||
−0.871058 | + | 0.491179i | \(0.836566\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.6487 | −1.65810 | −0.829048 | − | 0.559177i | \(-0.811117\pi\) | ||||
−0.829048 | + | 0.559177i | \(0.811117\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.47267 | 0.0598724 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.6346 | −1.32460 | −0.662299 | − | 0.749240i | \(-0.730419\pi\) | ||||
−0.662299 | + | 0.749240i | \(0.730419\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.30745 | 0.255172 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.7363 | −0.999089 | −0.499545 | − | 0.866288i | \(-0.666499\pi\) | ||||
−0.499545 | + | 0.866288i | \(0.666499\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.131133 | −0.00527921 | −0.00263960 | − | 0.999997i | \(-0.500840\pi\) | ||||
−0.00263960 | + | 0.999997i | \(0.500840\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.9776 | −0.883355 | −0.441677 | − | 0.897174i | \(-0.645616\pi\) | ||||
−0.441677 | + | 0.897174i | \(0.645616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.56200 | −0.142709 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.82774 | −0.113110 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.23395 | −0.0492009 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.1059 | −0.481927 | −0.240963 | − | 0.970534i | \(-0.577463\pi\) | ||||
−0.240963 | + | 0.970534i | \(0.577463\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.24582 | −0.208174 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.01022 | −0.317377 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.6952 | 1.56787 | 0.783934 | − | 0.620845i | \(-0.213210\pi\) | ||||
0.783934 | + | 0.620845i | \(0.213210\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.7326 | 1.48803 | 0.744014 | − | 0.668164i | \(-0.232920\pi\) | ||||
0.744014 | + | 0.668164i | \(0.232920\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.5335 | 0.532055 | 0.266027 | − | 0.963965i | \(-0.414289\pi\) | ||||
0.266027 | + | 0.963965i | \(0.414289\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.46578 | 0.175297 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.12921 | 0.357253 | 0.178627 | − | 0.983917i | \(-0.442835\pi\) | ||||
0.178627 | + | 0.983917i | \(0.442835\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.7718 | −0.889769 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.5551 | −0.839669 | −0.419834 | − | 0.907601i | \(-0.637912\pi\) | ||||
−0.419834 | + | 0.907601i | \(0.637912\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.4701 | 0.446133 | 0.223067 | − | 0.974803i | \(-0.428393\pi\) | ||||
0.223067 | + | 0.974803i | \(0.428393\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.21717 | 0.357427 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.8011 | 0.611823 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.64810 | −0.372461 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.42666 | −0.286277 | −0.143138 | − | 0.989703i | \(-0.545719\pi\) | ||||
−0.143138 | + | 0.989703i | \(0.545719\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.4725 | −0.940553 | −0.470277 | − | 0.882519i | \(-0.655846\pi\) | ||||
−0.470277 | + | 0.882519i | \(0.655846\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.17071 | 0.160057 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.7755 | −0.718423 | −0.359212 | − | 0.933256i | \(-0.616954\pi\) | ||||
−0.359212 | + | 0.933256i | \(0.616954\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.25020 | −0.353432 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.25883 | 0.238442 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.1286 | 1.33635 | 0.668177 | − | 0.744002i | \(-0.267075\pi\) | ||||
0.668177 | + | 0.744002i | \(0.267075\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.92618 | −0.148929 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.84689 | −0.107834 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.54581 | 0.247232 | 0.123616 | − | 0.992330i | \(-0.460551\pi\) | ||||
0.123616 | + | 0.992330i | \(0.460551\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.55909 | −0.209665 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.0218 | −0.376910 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.59417 | −0.0598701 | −0.0299351 | − | 0.999552i | \(-0.509530\pi\) | ||||
−0.0299351 | + | 0.999552i | \(0.509530\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.0762 | 0.489706 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.47267 | −0.0550746 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.1874 | −0.640981 | −0.320491 | − | 0.947252i | \(-0.603848\pi\) | ||||
−0.320491 | + | 0.947252i | \(0.603848\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.0476 | 0.895579 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.2995 | −0.456791 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.1746 | 0.414444 | 0.207222 | − | 0.978294i | \(-0.433558\pi\) | ||||
0.207222 | + | 0.978294i | \(0.433558\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.64236 | 0.0977311 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.1965 | 1.52163 | 0.760814 | − | 0.648970i | \(-0.224800\pi\) | ||||
0.760814 | + | 0.648970i | \(0.224800\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.79173 | 0.102835 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.11177 | −0.114468 | −0.0572341 | − | 0.998361i | \(-0.518228\pi\) | ||||
−0.0572341 | + | 0.998361i | \(0.518228\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.27261 | −0.156747 | −0.0783734 | − | 0.996924i | \(-0.524973\pi\) | ||||
−0.0783734 | + | 0.996924i | \(0.524973\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.28349 | −0.0836608 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 36.3563 | 1.32843 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.9379 | −0.581581 | −0.290790 | − | 0.956787i | \(-0.593918\pi\) | ||||
−0.290790 | + | 0.956787i | \(0.593918\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.37627 | −0.341237 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.64398 | 0.314171 | 0.157085 | − | 0.987585i | \(-0.449790\pi\) | ||||
0.157085 | + | 0.987585i | \(0.449790\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.0798 | 1.23539 | 0.617695 | − | 0.786418i | \(-0.288067\pi\) | ||||
0.617695 | + | 0.786418i | \(0.288067\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.78485 | −0.209426 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.46578 | −0.161250 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 48.7430 | 1.75772 | 0.878859 | − | 0.477081i | \(-0.158305\pi\) | ||||
0.878859 | + | 0.477081i | \(0.158305\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −55.1652 | −1.98415 | −0.992077 | − | 0.125635i | \(-0.959903\pi\) | ||||
−0.992077 | + | 0.125635i | \(0.959903\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.1784 | −0.365618 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.8255 | −0.459523 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.3865 | −0.443223 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.3154 | −0.403864 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.1185 | −0.859731 | −0.429865 | − | 0.902893i | \(-0.641439\pi\) | ||||
−0.429865 | + | 0.902893i | \(0.641439\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.409977 | −0.0145771 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.64810 | 0.342614 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −43.1069 | −1.52692 | −0.763462 | − | 0.645852i | \(-0.776502\pi\) | ||||
−0.763462 | + | 0.645852i | \(0.776502\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.26177 | 0.0800156 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.76497 | −0.274020 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.7529 | −0.731443 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.5330 | 1.00317 | 0.501584 | − | 0.865109i | \(-0.332751\pi\) | ||||
0.501584 | + | 0.865109i | \(0.332751\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.0062 | 1.47504 | 0.737519 | − | 0.675326i | \(-0.235997\pi\) | ||||
0.737519 | + | 0.675326i | \(0.235997\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.99453 | 0.139922 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.9041 | 0.416472 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.00522 | 0.209584 | 0.104792 | − | 0.994494i | \(-0.466582\pi\) | ||||
0.104792 | + | 0.994494i | \(0.466582\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.2735 | 0.636975 | 0.318487 | − | 0.947927i | \(-0.396825\pi\) | ||||
0.318487 | + | 0.947927i | \(0.396825\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.4278 | −0.501705 | −0.250852 | − | 0.968025i | \(-0.580711\pi\) | ||||
−0.250852 | + | 0.968025i | \(0.580711\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.3470 | 0.428829 | 0.214414 | − | 0.976743i | \(-0.431216\pi\) | ||||
0.214414 | + | 0.976743i | \(0.431216\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.87236 | −0.0995213 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.1502 | −0.766540 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.6121 | 1.33304 | 0.666518 | − | 0.745489i | \(-0.267784\pi\) | ||||
0.666518 | + | 0.745489i | \(0.267784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.1281 | −0.349244 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.47267 | 0.0506613 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.87430 | −0.133123 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.5165 | 0.429062 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.4552 | 0.563415 | 0.281707 | − | 0.959500i | \(-0.409099\pi\) | ||||
0.281707 | + | 0.959500i | \(0.409099\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.3498 | 0.763453 | 0.381727 | − | 0.924275i | \(-0.375330\pi\) | ||||
0.381727 | + | 0.924275i | \(0.375330\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.20787 | 0.245929 | 0.122965 | − | 0.992411i | \(-0.460760\pi\) | ||||
0.122965 | + | 0.992411i | \(0.460760\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.223096 | 0.00759427 | 0.00379714 | − | 0.999993i | \(-0.498791\pi\) | ||||
0.00379714 | + | 0.999993i | \(0.498791\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.948690 | 0.0322564 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.90024 | 0.0644613 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.79173 | −0.0945943 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 44.6817 | 1.51052 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.6907 | −0.631141 | −0.315571 | − | 0.948902i | \(-0.602196\pi\) | ||||
−0.315571 | + | 0.948902i | \(0.602196\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.6184 | 1.26740 | 0.633699 | − | 0.773580i | \(-0.281536\pi\) | ||||
0.633699 | + | 0.773580i | \(0.281536\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.28355 | 0.0431948 | 0.0215974 | − | 0.999767i | \(-0.493125\pi\) | ||||
0.0215974 | + | 0.999767i | \(0.493125\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.54431 | 0.186160 | 0.0930798 | − | 0.995659i | \(-0.470329\pi\) | ||||
0.0930798 | + | 0.995659i | \(0.470329\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.8007 | 0.462862 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.1895 | 0.340979 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.6217 | −1.09042 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.6174 | 0.520868 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.24433 | 0.0747696 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.0505 | 0.799465 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.6975 | 1.01929 | 0.509647 | − | 0.860384i | \(-0.329776\pi\) | ||||
0.509647 | + | 0.860384i | \(0.329776\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.7108 | 0.421129 | 0.210564 | − | 0.977580i | \(-0.432470\pi\) | ||||
0.210564 | + | 0.977580i | \(0.432470\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.2958 | −0.373838 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 59.9083 | 1.97835 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.6384 | −1.37352 | −0.686761 | − | 0.726883i | \(-0.740968\pi\) | ||||
−0.686761 | + | 0.726883i | \(0.740968\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.3865 | 0.407706 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.74278 | −0.320341 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.294049 | 0.00964744 | 0.00482372 | − | 0.999988i | \(-0.498465\pi\) | ||||
0.00482372 | + | 0.999988i | \(0.498465\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.9403 | −0.424101 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.528079 | −0.0172700 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.9679 | −0.652323 | −0.326161 | − | 0.945314i | \(-0.605755\pi\) | ||||
−0.326161 | + | 0.945314i | \(0.605755\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.2835 | −0.889417 | −0.444708 | − | 0.895675i | \(-0.646693\pi\) | ||||
−0.444708 | + | 0.895675i | \(0.646693\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.8773 | 0.940374 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.9164 | 1.00465 | 0.502324 | − | 0.864680i | \(-0.332479\pi\) | ||||
0.502324 | + | 0.864680i | \(0.332479\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.76497 | 0.252062 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.1519 | 1.07389 | 0.536947 | − | 0.843616i | \(-0.319577\pi\) | ||||
0.536947 | + | 0.843616i | \(0.319577\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.26363 | −0.202686 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.3355 | 0.785834 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.0759 | −0.583094 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.10568 | −0.260931 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.22167 | 0.167918 | 0.0839588 | − | 0.996469i | \(-0.473244\pi\) | ||||
0.0839588 | + | 0.996469i | \(0.473244\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.8532 | 0.733394 | 0.366697 | − | 0.930340i | \(-0.380489\pi\) | ||||
0.366697 | + | 0.930340i | \(0.380489\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.3290 | 0.331134 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.9044 | −0.348861 | −0.174431 | − | 0.984669i | \(-0.555809\pi\) | ||||
−0.174431 | + | 0.984669i | \(0.555809\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.919392 | 0.0293839 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −40.3042 | −1.28550 | −0.642752 | − | 0.766074i | \(-0.722208\pi\) | ||||
−0.642752 | + | 0.766074i | \(0.722208\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.77117 | 0.0882969 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26.8026 | −0.852275 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.7525 | 1.73927 | 0.869635 | − | 0.493695i | \(-0.164354\pi\) | ||||
0.869635 | + | 0.493695i | \(0.164354\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.5138 | 0.586926 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.3700 | 0.328422 | 0.164211 | − | 0.986425i | \(-0.447492\pi\) | ||||
0.164211 | + | 0.986425i | \(0.447492\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5148.2.a.s.1.4 | ✓ | 5 | |
3.2 | odd | 2 | 5148.2.a.t.1.2 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5148.2.a.s.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial | |
5148.2.a.t.1.2 | yes | 5 | 3.2 | odd | 2 |