Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.21 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.c.1609.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.22744 | − | 0.196195i | −0.996143 | − | 0.0877411i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.128273i | − | 0.0484827i | −0.999706 | − | 0.0242413i | \(-0.992283\pi\) | ||
0.999706 | − | 0.0242413i | \(-0.00771701\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0389925 | 0.0117567 | 0.00587834 | − | 0.999983i | \(-0.498129\pi\) | ||||
0.00587834 | + | 0.999983i | \(0.498129\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.81852i | 1.05907i | 0.848289 | + | 0.529533i | \(0.177633\pi\) | ||||
−0.848289 | + | 0.529533i | \(0.822367\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.196195 | − | 2.22744i | 0.0506573 | − | 0.575124i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.63903i | − | 1.61020i | −0.593137 | − | 0.805101i | \(-0.702111\pi\) | ||
0.593137 | − | 0.805101i | \(-0.297889\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.30512 | 1.67591 | 0.837955 | − | 0.545739i | \(-0.183751\pi\) | ||||
0.837955 | + | 0.545739i | \(0.183751\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.128273 | 0.0279915 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.64921i | 0.760914i | 0.924799 | + | 0.380457i | \(0.124233\pi\) | ||||
−0.924799 | + | 0.380457i | \(0.875767\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.92301 | + | 0.874027i | 0.984603 | + | 0.174805i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.25219 | −1.53239 | −0.766197 | − | 0.642606i | \(-0.777853\pi\) | ||||
−0.766197 | + | 0.642606i | \(0.777853\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.07939 | −1.27150 | −0.635748 | − | 0.771896i | \(-0.719308\pi\) | ||||
−0.635748 | + | 0.771896i | \(0.719308\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.0389925i | 0.00678772i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0251666 | + | 0.285721i | −0.00425392 | + | 0.0482957i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.37252i | 1.21204i | 0.795451 | + | 0.606018i | \(0.207234\pi\) | ||||
−0.795451 | + | 0.606018i | \(0.792766\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.81852 | −0.611452 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.87351 | 0.292593 | 0.146296 | − | 0.989241i | \(-0.453265\pi\) | ||||
0.146296 | + | 0.989241i | \(0.453265\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.72398i | 1.17790i | 0.808171 | + | 0.588948i | \(0.200458\pi\) | ||||
−0.808171 | + | 0.588948i | \(0.799542\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.22744 | + | 0.196195i | 0.332048 | + | 0.0292470i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 9.62406i | − | 1.40381i | −0.712269 | − | 0.701907i | \(-0.752332\pi\) | ||
0.712269 | − | 0.701907i | \(-0.247668\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.98355 | 0.997649 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.63903 | 0.929651 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.82384i | 0.525244i | 0.964899 | + | 0.262622i | \(0.0845872\pi\) | ||||
−0.964899 | + | 0.262622i | \(0.915413\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0868535 | − | 0.00765013i | −0.0117113 | − | 0.00103154i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.30512i | 0.967587i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.48802 | 1.23524 | 0.617618 | − | 0.786478i | \(-0.288098\pi\) | ||||
0.617618 | + | 0.786478i | \(0.288098\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.69509 | −0.857218 | −0.428609 | − | 0.903490i | \(-0.640996\pi\) | ||||
−0.428609 | + | 0.903490i | \(0.640996\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.128273i | 0.0161609i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.749174 | − | 8.50553i | 0.0929236 | − | 1.05498i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000i | 0.122169i | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.64921 | −0.439314 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.88025 | 0.579179 | 0.289590 | − | 0.957151i | \(-0.406481\pi\) | ||||
0.289590 | + | 0.957151i | \(0.406481\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.309819i | 0.0362615i | 0.999836 | + | 0.0181308i | \(0.00577152\pi\) | ||||
−0.999836 | + | 0.0181308i | \(0.994228\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.874027 | + | 4.92301i | −0.100924 | + | 0.568461i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.00500168i | − | 0.000569995i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.72909 | −0.644573 | −0.322286 | − | 0.946642i | \(-0.604451\pi\) | ||||
−0.322286 | + | 0.946642i | \(0.604451\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.6840i | 1.61178i | 0.592066 | + | 0.805889i | \(0.298312\pi\) | ||||
−0.592066 | + | 0.805889i | \(0.701688\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.30255 | + | 14.7881i | −0.141281 | + | 1.60399i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 8.25219i | − | 0.884728i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.6793 | −1.23800 | −0.619000 | − | 0.785391i | \(-0.712462\pi\) | ||||
−0.619000 | + | 0.785391i | \(0.712462\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.489813 | 0.0513464 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 7.07939i | − | 0.734099i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.2718 | − | 1.43323i | −1.66945 | − | 0.147046i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 7.10494i | − | 0.721397i | −0.932682 | − | 0.360699i | \(-0.882538\pi\) | ||
0.932682 | − | 0.360699i | \(-0.117462\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.0389925 | −0.00391889 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.7135 | −1.06604 | −0.533018 | − | 0.846104i | \(-0.678942\pi\) | ||||
−0.533018 | + | 0.846104i | \(0.678942\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 14.2892i | − | 1.40796i | −0.710220 | − | 0.703980i | \(-0.751405\pi\) | ||
0.710220 | − | 0.703980i | \(-0.248595\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.285721 | − | 0.0251666i | −0.0278835 | − | 0.00245600i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 8.57849i | − | 0.829314i | −0.909978 | − | 0.414657i | \(-0.863902\pi\) | ||
0.909978 | − | 0.414657i | \(-0.136098\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.4768 | −1.86554 | −0.932771 | − | 0.360470i | \(-0.882616\pi\) | ||||
−0.932771 | + | 0.360470i | \(0.882616\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.37252 | −0.699769 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.6083i | 1.28016i | 0.768307 | + | 0.640082i | \(0.221100\pi\) | ||||
−0.768307 | + | 0.640082i | \(0.778900\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.715958 | − | 8.12842i | 0.0667634 | − | 0.757979i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 3.81852i | − | 0.353022i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.851610 | −0.0780669 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9985 | −0.999862 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.87351i | 0.168929i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.7943 | − | 2.91272i | −0.965468 | − | 0.260521i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.3524i | 1.18483i | 0.805631 | + | 0.592417i | \(0.201826\pi\) | ||||
−0.805631 | + | 0.592417i | \(0.798174\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.72398 | −0.680058 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.7666 | −0.940684 | −0.470342 | − | 0.882484i | \(-0.655869\pi\) | ||||
−0.470342 | + | 0.882484i | \(0.655869\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 0.937051i | − | 0.0812526i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.196195 | + | 2.22744i | −0.0168858 | + | 0.191708i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.39755i | − | 0.717451i | −0.933443 | − | 0.358726i | \(-0.883211\pi\) | ||
0.933443 | − | 0.358726i | \(-0.116789\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.3819 | −1.72877 | −0.864387 | − | 0.502827i | \(-0.832293\pi\) | ||||
−0.864387 | + | 0.502827i | \(0.832293\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.62406 | 0.810492 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.148893i | 0.0124511i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.3813 | + | 1.61904i | 1.52648 | + | 0.134454i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.98355i | 0.575993i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.64717 | −0.708404 | −0.354202 | − | 0.935169i | \(-0.615247\pi\) | ||||
−0.354202 | + | 0.935169i | \(0.615247\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.9792 | −0.974854 | −0.487427 | − | 0.873164i | \(-0.662065\pi\) | ||||
−0.487427 | + | 0.873164i | \(0.662065\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.63903i | 0.536734i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.7690 | + | 1.38894i | 1.26659 | + | 0.111563i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.35135i | 0.666510i | 0.942837 | + | 0.333255i | \(0.108147\pi\) | ||||
−0.942837 | + | 0.333255i | \(0.891853\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.82384 | −0.303250 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.468096 | 0.0368911 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.06915i | 0.397046i | 0.980096 | + | 0.198523i | \(0.0636145\pi\) | ||||
−0.980096 | + | 0.198523i | \(0.936385\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.00765013 | − | 0.0868535i | 0.000595562 | − | 0.00676154i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 0.558745i | − | 0.0432370i | −0.999766 | − | 0.0216185i | \(-0.993118\pi\) | ||
0.999766 | − | 0.0216185i | \(-0.00688191\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.58107 | −0.121621 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.30512 | −0.558637 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 13.7845i | − | 1.04802i | −0.851714 | − | 0.524008i | \(-0.824436\pi\) | ||
0.851714 | − | 0.524008i | \(-0.175564\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.112114 | − | 0.631490i | 0.00847504 | − | 0.0477362i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.48802i | 0.713163i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.05610 | 0.602141 | 0.301071 | − | 0.953602i | \(-0.402656\pi\) | ||||
0.301071 | + | 0.953602i | \(0.402656\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.8933 | 1.10701 | 0.553506 | − | 0.832845i | \(-0.313289\pi\) | ||||
0.553506 | + | 0.832845i | \(0.313289\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 6.69509i | − | 0.494915i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.44645 | − | 16.4219i | 0.106345 | − | 1.20736i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.258872i | − | 0.0189306i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.128273 | −0.00933050 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.66876 | 0.265462 | 0.132731 | − | 0.991152i | \(-0.457625\pi\) | ||||
0.132731 | + | 0.991152i | \(0.457625\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.1084i | 0.871585i | 0.900047 | + | 0.435793i | \(0.143532\pi\) | ||||
−0.900047 | + | 0.435793i | \(0.856468\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.50553 | + | 0.749174i | 0.609094 | + | 0.0536495i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.59577i | 0.256188i | 0.991762 | + | 0.128094i | \(0.0408859\pi\) | ||||
−0.991762 | + | 0.128094i | \(0.959114\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.80795 | −0.553491 | −0.276745 | − | 0.960943i | \(-0.589256\pi\) | ||||
−0.276745 | + | 0.960943i | \(0.589256\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.05853i | 0.0742946i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.17314 | − | 0.367573i | −0.291464 | − | 0.0256724i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 3.64921i | − | 0.253638i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.284845 | 0.0197031 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.8266 | −1.64029 | −0.820146 | − | 0.572154i | \(-0.806108\pi\) | ||||
−0.820146 | + | 0.572154i | \(0.806108\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.88025i | 0.334389i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.51541 | − | 17.2047i | 0.103350 | − | 1.17335i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.908096i | 0.0616456i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.309819 | −0.0209356 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.3513 | 1.70531 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.63279i | 0.578094i | 0.957315 | + | 0.289047i | \(0.0933384\pi\) | ||||
−0.957315 | + | 0.289047i | \(0.906662\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.92301 | − | 0.874027i | −0.328201 | − | 0.0582685i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.58160i | 0.569581i | 0.958590 | + | 0.284790i | \(0.0919240\pi\) | ||||
−0.958590 | + | 0.284790i | \(0.908076\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.20564 | −0.211835 | −0.105917 | − | 0.994375i | \(-0.533778\pi\) | ||||
−0.105917 | + | 0.994375i | \(0.533778\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.00500168 | 0.000329087 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 11.2934i | − | 0.739854i | −0.929061 | − | 0.369927i | \(-0.879383\pi\) | ||
0.929061 | − | 0.369927i | \(-0.120617\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.88819 | + | 21.4371i | −0.123172 | + | 1.39840i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 5.72909i | − | 0.372144i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.5672 | −1.39507 | −0.697534 | − | 0.716552i | \(-0.745719\pi\) | ||||
−0.697534 | + | 0.716552i | \(0.745719\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.36087 | 0.602987 | 0.301493 | − | 0.953468i | \(-0.402515\pi\) | ||||
0.301493 | + | 0.953468i | \(0.402515\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.5555 | − | 1.37014i | −0.993802 | − | 0.0875349i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.8947i | 1.77490i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.6840 | −0.930561 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.7667 | −0.679589 | −0.339794 | − | 0.940500i | \(-0.610358\pi\) | ||||
−0.339794 | + | 0.940500i | \(0.610358\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.142292i | 0.00894581i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14.7881 | − | 1.30255i | −0.926065 | − | 0.0815686i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.0839i | 1.37756i | 0.724972 | + | 0.688779i | \(0.241853\pi\) | ||||
−0.724972 | + | 0.688779i | \(0.758147\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.945697 | 0.0587627 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.25219 | 0.510798 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 21.5995i | − | 1.33188i | −0.746006 | − | 0.665940i | \(-0.768031\pi\) | ||
0.746006 | − | 0.665940i | \(-0.231969\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.750218 | − | 8.51738i | 0.0460855 | − | 0.523218i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 11.6793i | − | 0.714759i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.86649 | −0.418657 | −0.209329 | − | 0.977845i | \(-0.567128\pi\) | ||||
−0.209329 | + | 0.977845i | \(0.567128\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.7804 | −0.837101 | −0.418550 | − | 0.908194i | \(-0.637462\pi\) | ||||
−0.418550 | + | 0.908194i | \(0.637462\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.489813i | 0.0296448i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.191960 | + | 0.0340805i | 0.0115757 | + | 0.00205513i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 13.0593i | − | 0.784660i | −0.919825 | − | 0.392330i | \(-0.871669\pi\) | ||
0.919825 | − | 0.392330i | \(-0.128331\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.07939 | 0.423832 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.32410 | −0.0789894 | −0.0394947 | − | 0.999220i | \(-0.512575\pi\) | ||||
−0.0394947 | + | 0.999220i | \(0.512575\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 5.70161i | − | 0.338926i | −0.985537 | − | 0.169463i | \(-0.945797\pi\) | ||
0.985537 | − | 0.169463i | \(-0.0542033\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.43323 | − | 16.2718i | 0.0848972 | − | 0.963855i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 0.240321i | − | 0.0141857i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −27.0768 | −1.59275 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.10494 | 0.416499 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.4885i | 1.19695i | 0.801142 | + | 0.598475i | \(0.204226\pi\) | ||||
−0.801142 | + | 0.598475i | \(0.795774\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.1340 | − | 1.86150i | −1.23047 | − | 0.108381i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 0.0389925i | − | 0.00226257i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.9346 | −0.805858 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.990778 | 0.0571075 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 10.7135i | − | 0.615476i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.9129 | + | 1.31354i | 0.853912 | + | 0.0752132i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 30.2141i | − | 1.72441i | −0.506559 | − | 0.862205i | \(-0.669083\pi\) | ||
0.506559 | − | 0.862205i | \(-0.330917\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.2892 | 0.812886 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.73813 | −0.268675 | −0.134337 | − | 0.990936i | \(-0.542891\pi\) | ||||
−0.134337 | + | 0.990936i | \(0.542891\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.2789i | 1.59842i | 0.601053 | + | 0.799209i | \(0.294748\pi\) | ||||
−0.601053 | + | 0.799209i | \(0.705252\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0251666 | − | 0.285721i | 0.00141797 | − | 0.0160986i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 17.4748i | − | 0.981484i | −0.871305 | − | 0.490742i | \(-0.836726\pi\) | ||
0.871305 | − | 0.490742i | \(-0.163274\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.321773 | −0.0180159 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.57849 | 0.478805 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 48.4990i | − | 2.69855i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.33749 | + | 18.7986i | −0.185131 | + | 1.04276i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 19.4768i | − | 1.07707i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.23451 | −0.0680607 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.5657 | 0.800602 | 0.400301 | − | 0.916384i | \(-0.368906\pi\) | ||||
0.400301 | + | 0.916384i | \(0.368906\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 7.37252i | − | 0.404012i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.196195 | − | 2.22744i | 0.0107193 | − | 0.121698i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.5522i | 0.629286i | 0.949210 | + | 0.314643i | \(0.101885\pi\) | ||||
−0.949210 | + | 0.314643i | \(0.898115\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.6083 | −0.739103 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.276043 | −0.0149486 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.79371i | − | 0.0968514i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.12842 | + | 0.715958i | 0.437619 | + | 0.0385459i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 35.1190i | 1.88529i | 0.333802 | + | 0.942643i | \(0.391668\pi\) | ||||
−0.333802 | + | 0.942643i | \(0.608332\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.5558 | 0.725625 | 0.362813 | − | 0.931862i | \(-0.381817\pi\) | ||||
0.362813 | + | 0.931862i | \(0.381817\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.81852 | 0.203817 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.02952i | 0.108021i | 0.998540 | + | 0.0540103i | \(0.0172004\pi\) | ||||
−0.998540 | + | 0.0540103i | \(0.982800\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.8705 | − | 0.957482i | −0.576946 | − | 0.0508178i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 0.851610i | − | 0.0450720i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.15157 | −0.377445 | −0.188723 | − | 0.982030i | \(-0.560435\pi\) | ||||
−0.188723 | + | 0.982030i | \(0.560435\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 34.3648 | 1.80867 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 10.9985i | − | 0.577270i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.0607849 | − | 0.690104i | 0.00318163 | − | 0.0361217i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.1192i | 1.46781i | 0.679251 | + | 0.733906i | \(0.262305\pi\) | ||||
−0.679251 | + | 0.733906i | \(0.737695\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.87351 | −0.0975309 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.490495 | 0.0254652 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.3825i | 1.72848i | 0.503079 | + | 0.864240i | \(0.332200\pi\) | ||||
−0.503079 | + | 0.864240i | \(0.667800\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.91272 | − | 10.7943i | 0.150412 | − | 0.557413i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 31.5111i | − | 1.62291i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.25718 | 0.321410 | 0.160705 | − | 0.987002i | \(-0.448623\pi\) | ||||
0.160705 | + | 0.987002i | \(0.448623\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.3524 | −0.684064 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 21.9335i | − | 1.12075i | −0.828239 | − | 0.560375i | \(-0.810657\pi\) | ||
0.828239 | − | 0.560375i | \(-0.189343\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.000981306 | 0.0111410i | −5.00120e−5 | 0.000567797i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 7.72398i | − | 0.392632i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.3986 | −0.780739 | −0.390369 | − | 0.920658i | \(-0.627653\pi\) | ||||
−0.390369 | + | 0.920658i | \(0.627653\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.2273 | 1.22523 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 10.7666i | − | 0.543104i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.7612 | + | 1.12402i | 0.642087 | + | 0.0565555i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.69910i | − | 0.185652i | −0.995682 | − | 0.0928262i | \(-0.970410\pi\) | ||
0.995682 | − | 0.0928262i | \(-0.0295901\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.937051 | 0.0469112 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.1620 | −1.25653 | −0.628265 | − | 0.777999i | \(-0.716235\pi\) | ||||
−0.628265 | + | 0.777999i | \(0.716235\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 27.0328i | − | 1.34660i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.22744 | − | 0.196195i | −0.110683 | − | 0.00974901i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.287473i | 0.0142495i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.9226 | −0.688430 | −0.344215 | − | 0.938891i | \(-0.611855\pi\) | ||||
−0.344215 | + | 0.938891i | \(0.611855\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.39755 | 0.414221 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.21706i | − | 0.0598875i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.88093 | − | 32.7078i | 0.141419 | − | 1.60556i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 20.3819i | − | 0.998108i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.28480 | 0.307033 | 0.153516 | − | 0.988146i | \(-0.450940\pi\) | ||||
0.153516 | + | 0.988146i | \(0.450940\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.2864 | 1.47607 | 0.738035 | − | 0.674763i | \(-0.235754\pi\) | ||||
0.738035 | + | 0.674763i | \(0.235754\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.62406i | 0.467938i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.80270 | − | 32.6841i | 0.281472 | − | 1.58541i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.858799i | 0.0415602i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.148893 | −0.00718864 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.21790 | 0.347674 | 0.173837 | − | 0.984774i | \(-0.444383\pi\) | ||||
0.173837 | + | 0.984774i | \(0.444383\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 21.0149i | − | 1.00991i | −0.863145 | − | 0.504957i | \(-0.831508\pi\) | ||
0.863145 | − | 0.504957i | \(-0.168492\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.61904 | + | 18.3813i | −0.0776270 | + | 0.881316i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.6580i | 1.27522i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 37.4029 | 1.78514 | 0.892572 | − | 0.450905i | \(-0.148899\pi\) | ||||
0.892572 | + | 0.450905i | \(0.148899\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.98355 | −0.332550 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.5717i | 1.30997i | 0.755641 | + | 0.654986i | \(0.227325\pi\) | ||||
−0.755641 | + | 0.654986i | \(0.772675\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.0149 | + | 2.29141i | 1.23322 | + | 0.108623i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 8.64717i | − | 0.408997i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.43854 | 0.351046 | 0.175523 | − | 0.984475i | \(-0.443838\pi\) | ||||
0.175523 | + | 0.984475i | \(0.443838\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0730527 | 0.00343992 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 11.9792i | − | 0.562832i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.09103 | − | 0.0960989i | −0.0511483 | − | 0.00450519i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.6425i | 0.778505i | 0.921131 | + | 0.389253i | \(0.127267\pi\) | ||||
−0.921131 | + | 0.389253i | \(0.872733\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.63903 | −0.309884 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.7119 | 1.10438 | 0.552188 | − | 0.833720i | \(-0.313793\pi\) | ||||
0.552188 | + | 0.833720i | \(0.313793\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.3481i | 1.27097i | 0.772112 | + | 0.635486i | \(0.219200\pi\) | ||||
−0.772112 | + | 0.635486i | \(0.780800\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.38894 | + | 15.7690i | −0.0644106 | + | 0.731268i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.6793i | 0.818102i | 0.912512 | + | 0.409051i | \(0.134140\pi\) | ||||
−0.912512 | + | 0.409051i | \(0.865860\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.128273 | 0.00592310 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.35135 | −0.384810 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.301177i | 0.0138481i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 35.9632 | + | 6.38488i | 1.65011 | + | 0.292958i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 3.82384i | − | 0.175081i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.5193 | −0.983242 | −0.491621 | − | 0.870809i | \(-0.663595\pi\) | ||||
−0.491621 | + | 0.870809i | \(0.663595\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.1521 | −1.28363 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.468096i | 0.0212991i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.39395 | + | 15.8259i | −0.0632962 | + | 0.718615i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 35.6523i | − | 1.61556i | −0.589485 | − | 0.807780i | \(-0.700669\pi\) | ||
0.589485 | − | 0.807780i | \(-0.299331\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.06915 | −0.229235 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.7609 | −1.70413 | −0.852064 | − | 0.523438i | \(-0.824649\pi\) | ||||
−0.852064 | + | 0.523438i | \(0.824649\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 54.7866i | 2.46746i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.0868535 | + | 0.00765013i | 0.00390378 | + | 0.000343848i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 0.626005i | − | 0.0280802i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.8673 | −0.755084 | −0.377542 | − | 0.925992i | \(-0.623231\pi\) | ||||
−0.377542 | + | 0.925992i | \(0.623231\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.558745 | 0.0249629 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.4352i | 0.911162i | 0.890194 | + | 0.455581i | \(0.150568\pi\) | ||||
−0.890194 | + | 0.455581i | \(0.849432\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.8638 | + | 2.10194i | 1.06192 | + | 0.0935351i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.58107i | − | 0.0702180i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 37.1112 | 1.64492 | 0.822462 | − | 0.568820i | \(-0.192600\pi\) | ||||
0.822462 | + | 0.568820i | \(0.192600\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.0397414 | 0.00175806 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 7.30512i | − | 0.322529i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.80348 | + | 31.8285i | −0.123536 | + | 1.40253i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.375266i | − | 0.0165042i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.7845 | 0.605072 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.14633 | 0.269276 | 0.134638 | − | 0.990895i | \(-0.457013\pi\) | ||||
0.134638 | + | 0.990895i | \(0.457013\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.5742i | 0.987103i | 0.869717 | + | 0.493551i | \(0.164301\pi\) | ||||
−0.869717 | + | 0.493551i | \(0.835699\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.631490 | + | 0.112114i | 0.0275605 | + | 0.00489306i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 47.0003i | 2.04737i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.68324 | 0.421010 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.48802 | −0.411745 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.15402i | 0.309875i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.68306 | + | 19.1081i | −0.0727649 | + | 0.826116i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.05610i | 0.347646i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.272306 | 0.0117290 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.5657 | 0.454254 | 0.227127 | − | 0.973865i | \(-0.427067\pi\) | ||||
0.227127 | + | 0.973865i | \(0.427067\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.8933i | 0.639134i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 43.3835 | + | 3.82126i | 1.85835 | + | 0.163685i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 38.7727i | − | 1.65780i | −0.559397 | − | 0.828900i | \(-0.688967\pi\) | ||
0.559397 | − | 0.828900i | \(-0.311033\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.69509 | 0.285739 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −60.2833 | −2.56815 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.734888i | 0.0312506i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16.4219 | + | 1.44645i | 0.697070 | + | 0.0613985i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.3818i | 0.694119i | 0.937843 | + | 0.347059i | \(0.112820\pi\) | ||||
−0.937843 | + | 0.347059i | \(0.887180\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.4941 | −1.24747 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.258872 | 0.0109296 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 14.7878i | − | 0.623231i | −0.950208 | − | 0.311616i | \(-0.899130\pi\) | ||
0.950208 | − | 0.311616i | \(-0.100870\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.66989 | − | 30.3118i | 0.112323 | − | 1.27523i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 0.128273i | − | 0.00538696i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.0863 | 1.47089 | 0.735447 | − | 0.677582i | \(-0.236972\pi\) | ||||
0.735447 | + | 0.677582i | \(0.236972\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.3369 | 0.432585 | 0.216292 | − | 0.976329i | \(-0.430604\pi\) | ||||
0.216292 | + | 0.976329i | \(0.430604\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.66876i | 0.153265i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.18951 | + | 17.9651i | −0.133012 | + | 0.749198i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.76255i | 0.0733760i | 0.999327 | + | 0.0366880i | \(0.0116808\pi\) | ||||
−0.999327 | + | 0.0366880i | \(0.988319\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.1084 | −0.503210 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.88356 | 0.0781434 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.149101i | 0.00617512i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.749174 | + | 8.50553i | −0.0309745 | + | 0.351661i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 4.55117i | − | 0.187847i | −0.995579 | − | 0.0939235i | \(-0.970059\pi\) | ||
0.995579 | − | 0.0939235i | \(-0.0299409\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −51.7158 | −2.13091 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.59577 | −0.147910 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 2.67480i | − | 0.109841i | −0.998491 | − | 0.0549203i | \(-0.982510\pi\) | ||
0.998491 | − | 0.0549203i | \(-0.0174905\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.89691 | + | 0.167082i | 0.0777658 | + | 0.00684968i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 7.80795i | − | 0.319558i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.0897 | −1.06600 | −0.532998 | − | 0.846116i | \(-0.678935\pi\) | ||||
−0.532998 | + | 0.846116i | \(0.678935\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.9540 | −1.54818 | −0.774088 | − | 0.633078i | \(-0.781791\pi\) | ||||
−0.774088 | + | 0.633078i | \(0.781791\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.00000i | − | 0.0407231i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.4985 | + | 2.15785i | 0.996006 | + | 0.0877290i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 14.7399i | − | 0.598273i | −0.954210 | − | 0.299137i | \(-0.903301\pi\) | ||
0.954210 | − | 0.299137i | \(-0.0966986\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.05853 | −0.0428940 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 36.7497 | 1.48673 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 13.6655i | − | 0.551944i | −0.961166 | − | 0.275972i | \(-0.911000\pi\) | ||
0.961166 | − | 0.275972i | \(-0.0889996\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.367573 | − | 4.17314i | 0.0148220 | − | 0.168277i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 40.4183i | − | 1.62718i | −0.581438 | − | 0.813590i | \(-0.697510\pi\) | ||
0.581438 | − | 0.813590i | \(-0.302490\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.32869 | −0.173985 | −0.0869923 | − | 0.996209i | \(-0.527726\pi\) | ||||
−0.0869923 | + | 0.996209i | \(0.527726\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.64921 | 0.146438 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.49814i | 0.0600215i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.4722 | + | 8.60570i | 0.938886 | + | 0.344228i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.284845i | 0.0113756i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 48.9464 | 1.95162 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.0385 | −0.519054 | −0.259527 | − | 0.965736i | \(-0.583567\pi\) | ||||
−0.259527 | + | 0.965736i | \(0.583567\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 23.8266i | − | 0.947023i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.61968 | − | 29.7417i | 0.103959 | − | 1.18026i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.6668i | 1.05658i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.88025 | −0.193060 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.0995 | 0.675391 | 0.337695 | − | 0.941255i | \(-0.390353\pi\) | ||||
0.337695 | + | 0.941255i | \(0.390353\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 0.255024i | − | 0.0100571i | −0.999987 | − | 0.00502857i | \(-0.998399\pi\) | ||
0.999987 | − | 0.00502857i | \(-0.00160065\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.2047 | + | 1.51541i | 0.677435 | + | 0.0596691i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 31.4978i | − | 1.23831i | −0.785270 | − | 0.619153i | \(-0.787476\pi\) | ||
0.785270 | − | 0.619153i | \(-0.212524\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.369961 | 0.0145223 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.908096 | −0.0355911 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 24.0739i | − | 0.942083i | −0.882111 | − | 0.471042i | \(-0.843878\pi\) | ||
0.882111 | − | 0.471042i | \(-0.156122\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.9820 | + | 2.11236i | 0.937056 | + | 0.0825367i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 0.309819i | − | 0.0120872i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −48.0291 | −1.87095 | −0.935474 | − | 0.353397i | \(-0.885027\pi\) | ||||
−0.935474 | + | 0.353397i | \(0.885027\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.6120 | 0.957295 | 0.478647 | − | 0.878007i | \(-0.341127\pi\) | ||||
0.478647 | + | 0.878007i | \(0.341127\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 25.3513i | 0.984562i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.183845 | + | 2.08723i | −0.00712919 | + | 0.0809392i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 30.1140i | − | 1.16602i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.63279 | −0.333763 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.261058 | −0.0100780 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.8417i | 1.07322i | 0.843831 | + | 0.536609i | \(0.180295\pi\) | ||||
−0.843831 | + | 0.536609i | \(0.819705\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.874027 | − | 4.92301i | 0.0336413 | − | 0.189487i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 43.7995i | − | 1.68335i | −0.539983 | − | 0.841676i | \(-0.681569\pi\) | ||
0.539983 | − | 0.841676i | \(-0.318431\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.911372 | −0.0349753 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.58160 | −0.328848 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 2.92819i | − | 0.112044i | −0.998430 | − | 0.0560221i | \(-0.982158\pi\) | ||
0.998430 | − | 0.0560221i | \(-0.0178417\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.64756 | + | 18.7051i | −0.0629500 | + | 0.714684i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 3.20564i | − | 0.122303i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.6014 | −0.556268 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.44751 | 0.207233 | 0.103617 | − | 0.994617i | \(-0.466959\pi\) | ||||
0.103617 | + | 0.994617i | \(0.466959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.00500168i | 0.000189998i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 45.3997 | + | 3.99884i | 1.72211 | + | 0.151685i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 12.4383i | − | 0.471134i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.2934 | 0.427155 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.7153 | 1.53780 | 0.768898 | − | 0.639372i | \(-0.220806\pi\) | ||||
0.768898 | + | 0.639372i | \(0.220806\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 53.8572i | 2.03126i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −21.4371 | − | 1.88819i | −0.807367 | − | 0.0711135i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.37426i | 0.0516843i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.6966 | 1.22795 | 0.613974 | − | 0.789326i | \(-0.289570\pi\) | ||||
0.613974 | + | 0.789326i | \(0.289570\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.72909 | 0.214858 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 25.8342i | − | 0.967499i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0292122 | − | 0.331652i | 0.00109247 | − | 0.0124031i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 21.5672i | − | 0.805442i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.1366 | −0.937436 | −0.468718 | − | 0.883348i | \(-0.655284\pi\) | ||||
−0.468718 | + | 0.883348i | \(0.655284\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.83292 | −0.0682616 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.36087i | 0.348135i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −40.6257 | − | 7.21264i | −1.50880 | − | 0.267871i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.0875i | 0.559564i | 0.960064 | + | 0.279782i | \(0.0902622\pi\) | ||||
−0.960064 | + | 0.279782i | \(0.909738\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 51.2797 | 1.89665 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.1707i | 0.781959i | 0.920399 | + | 0.390980i | \(0.127864\pi\) | ||||
−0.920399 | + | 0.390980i | \(0.872136\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.37014 | − | 15.5555i | 0.0505383 | − | 0.573772i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.0389925i | 0.00143631i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.3401 | −1.22643 | −0.613217 | − | 0.789914i | \(-0.710125\pi\) | ||||
−0.613217 | + | 0.789914i | \(0.710125\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −27.8947 | −1.02474 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.8561i | 0.618391i | 0.950998 | + | 0.309196i | \(0.100060\pi\) | ||||
−0.950998 | + | 0.309196i | \(0.899940\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.2611 | + | 1.69653i | 0.705672 | + | 0.0621561i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 14.6840i | − | 0.537260i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.10039 | −0.0402074 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.45818 | 0.345134 | 0.172567 | − | 0.984998i | \(-0.444794\pi\) | ||||
0.172567 | + | 0.984998i | \(0.444794\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 10.7667i | − | 0.392361i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26.6830 | + | 2.35026i | 0.971095 | + | 0.0855348i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 37.9574i | − | 1.37959i | −0.724007 | − | 0.689793i | \(-0.757702\pi\) | ||
0.724007 | − | 0.689793i | \(-0.242298\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.142292 | −0.00516487 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.9280 | 1.08489 | 0.542444 | − | 0.840092i | \(-0.317499\pi\) | ||||
0.542444 | + | 0.840092i | \(0.317499\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.49835i | 0.0904465i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.30255 | − | 14.7881i | 0.0470936 | − | 0.534664i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 36.2302i | 1.30820i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.03061 | 0.181408 | 0.0907042 | − | 0.995878i | \(-0.471088\pi\) | ||||
0.0907042 | + | 0.995878i | \(0.471088\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.0839 | −0.795333 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.4372i | 0.663141i | 0.943430 | + | 0.331571i | \(0.107579\pi\) | ||||
−0.943430 | + | 0.331571i | \(0.892421\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34.8520 | − | 6.18758i | −1.25192 | − | 0.222264i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.945697i | 0.0339267i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.6862 | 0.490359 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.190293 | 0.00680922 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.25219i | 0.294909i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.63849 | − | 18.6022i | 0.0584804 | − | 0.663940i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.9859i | 1.28276i | 0.767224 | + | 0.641379i | \(0.221637\pi\) | ||||
−0.767224 | + | 0.641379i | \(0.778363\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.5995 | 0.768961 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.74558 | 0.0620658 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 25.5653i | − | 0.907850i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.51738 | + | 0.750218i | 0.302080 | + | 0.0266075i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.9803i | 1.34533i | 0.739947 | + | 0.672665i | \(0.234851\pi\) | ||||
−0.739947 | + | 0.672665i | \(0.765149\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −63.8945 | −2.26043 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.6793 | 0.412666 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.0120806i | 0.000426315i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.04266 | − | 0.0918381i | −0.0367489 | − | 0.00323687i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 6.86649i | − | 0.241712i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.6319 | −0.408954 | −0.204477 | − | 0.978871i | \(-0.565549\pi\) | ||||
−0.204477 | + | 0.978871i | \(0.565549\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.24573 | −0.0437436 | −0.0218718 | − | 0.999761i | \(-0.506963\pi\) | ||||
−0.0218718 | + | 0.999761i | \(0.506963\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 13.7804i | − | 0.483300i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.994542 | − | 11.2912i | 0.0348373 | − | 0.395515i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56.4246i | 1.97405i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.489813 | −0.0171155 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.3315 | 0.849176 | 0.424588 | − | 0.905387i | \(-0.360419\pi\) | ||||
0.424588 | + | 0.905387i | \(0.360419\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.47183i | 0.0513049i | 0.999671 | + | 0.0256524i | \(0.00816632\pi\) | ||||
−0.999671 | + | 0.0256524i | \(0.991834\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.0340805 | + | 0.191960i | −0.00118653 | + | 0.00668321i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.9758i | 1.25100i | 0.780223 | + | 0.625501i | \(0.215105\pi\) | ||||
−0.780223 | + | 0.625501i | \(0.784895\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.293129 | 0.0101808 | 0.00509040 | − | 0.999987i | \(-0.498380\pi\) | ||||
0.00509040 | + | 0.999987i | \(0.498380\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.0593 | 0.453024 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 46.3640i | − | 1.60642i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.109623 | + | 1.24457i | −0.00379366 | + | 0.0430702i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.07939i | 0.244700i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −51.0206 | −1.76143 | −0.880713 | − | 0.473651i | \(-0.842936\pi\) | ||||
−0.880713 | + | 0.473651i | \(0.842936\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.0987 | 1.34823 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 1.32410i | − | 0.0456046i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.52175 | + | 0.310199i | 0.121152 | + | 0.0106712i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.41081i | 0.0484760i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.70161 | 0.195679 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.9039 | −0.922254 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.28002i | 0.0438272i | 0.999760 | + | 0.0219136i | \(0.00697587\pi\) | ||||
−0.999760 | + | 0.0219136i | \(0.993024\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.2718 | + | 1.43323i | 0.556482 | + | 0.0490154i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 20.9886i | − | 0.716957i | −0.933538 | − | 0.358479i | \(-0.883296\pi\) | ||
0.933538 | − | 0.358479i | \(-0.116704\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.4651 | 1.82421 | 0.912103 | − | 0.409960i | \(-0.134457\pi\) | ||||
0.912103 | + | 0.409960i | \(0.134457\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.240321 | 0.00819011 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.2543i | 1.02987i | 0.857230 | + | 0.514934i | \(0.172183\pi\) | ||||
−0.857230 | + | 0.514934i | \(0.827817\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.70445 | + | 30.7042i | −0.0919540 | + | 1.04397i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 27.0768i | − | 0.919576i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.223391 | −0.00757803 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.81852 | −0.129386 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.10494i | 0.240466i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.373623 | + | 1.38461i | −0.0126308 | + | 0.0468085i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 56.9298i | 1.92238i | 0.275882 | + | 0.961192i | \(0.411030\pi\) | ||||
−0.275882 | + | 0.961192i | \(0.588970\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.4885 | −0.691059 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.1820 | −0.679949 | −0.339975 | − | 0.940435i | \(-0.610418\pi\) | ||||
−0.339975 | + | 0.940435i | \(0.610418\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.3122i | 0.414339i | 0.978305 | + | 0.207170i | \(0.0664252\pi\) | ||||
−0.978305 | + | 0.207170i | \(0.933575\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.86150 | − | 21.1340i | 0.0625738 | − | 0.710413i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.8050i | 1.57156i | 0.618507 | + | 0.785779i | \(0.287738\pi\) | ||||
−0.618507 | + | 0.785779i | \(0.712262\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.71275 | 0.0574439 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.0389925 | 0.00130630 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 70.3050i | − | 2.35267i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.9445 | − | 1.58057i | −0.599819 | − | 0.0528325i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 13.9346i | − | 0.465262i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 58.4205 | 1.94843 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.3866 | 0.845749 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.990778i | 0.0329710i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33.1741 | − | 2.92200i | −1.10274 | − | 0.0971305i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 38.5478i | − | 1.27996i | −0.768393 | − | 0.639979i | \(-0.778943\pi\) | ||
0.768393 | − | 0.639979i | \(-0.221057\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.7135 | 0.355345 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.15058 | −0.170646 | −0.0853231 | − | 0.996353i | \(-0.527192\pi\) | ||||
−0.0853231 | + | 0.996353i | \(0.527192\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.572566i | 0.0189492i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.31354 | + | 14.9129i | −0.0434244 | + | 0.493006i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.38107i | 0.0456069i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.1528 | −0.763741 | −0.381870 | − | 0.924216i | \(-0.624720\pi\) | ||||
−0.381870 | + | 0.924216i | \(0.624720\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.2141 | 0.995589 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.6353i | 0.613389i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.44379 | + | 36.2950i | −0.211870 | + | 1.19337i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.2892i | 0.469320i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.27644 | 0.107496 | 0.0537482 | − | 0.998555i | \(-0.482883\pi\) | ||||
0.0537482 | + | 0.998555i | \(0.482883\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51.0157 | 1.67197 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 4.73813i | − | 0.155120i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.0507895 | + | 0.576624i | −0.00166099 | + | 0.0188576i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.8785i | 0.518727i | 0.965780 | + | 0.259364i | \(0.0835128\pi\) | ||||
−0.965780 | + | 0.259364i | \(0.916487\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.2789 | −0.922847 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.1579 | 1.04832 | 0.524159 | − | 0.851620i | \(-0.324380\pi\) | ||||
0.524159 | + | 0.851620i | \(0.324380\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.83683i | 0.222638i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.285721 | + | 0.0251666i | 0.00929451 | + | 0.000818668i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 27.2041i | − | 0.884016i | −0.897011 | − | 0.442008i | \(-0.854266\pi\) | ||
0.897011 | − | 0.442008i | \(-0.145734\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.18305 | −0.0384034 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.4748 | 0.566660 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.0736i | 1.03896i | 0.854481 | + | 0.519482i | \(0.173875\pi\) | ||||
−0.854481 | + | 0.519482i | \(0.826125\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.17195 | − | 0.719792i | −0.264438 | − | 0.0232919i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 0.321773i | − | 0.0104015i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.07718 | −0.0347840 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.1178 | 0.616703 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.57849i | 0.276438i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.37562 | − | 26.9709i | 0.0764738 | − | 0.868224i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.0799i | 0.774358i | 0.922005 | + | 0.387179i | \(0.126550\pi\) | ||||
−0.922005 | + | 0.387179i | \(0.873450\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 48.4990 | 1.55801 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.76129 | −0.152797 | −0.0763985 | − | 0.997077i | \(-0.524342\pi\) | ||||
−0.0763985 | + | 0.997077i | \(0.524342\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.61446i | 0.0838156i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −18.7986 | − | 3.33749i | −0.602038 | − | 0.106885i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.80650i | 0.217759i | 0.994055 | + | 0.108880i | \(0.0347263\pi\) | ||||
−0.994055 | + | 0.108880i | \(0.965274\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.455403 | −0.0145548 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.4768 | 0.621847 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 30.9051i | − | 0.985719i | −0.870109 | − | 0.492859i | \(-0.835952\pi\) | ||
0.870109 | − | 0.492859i | \(-0.164048\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.705472 | − | 8.00937i | 0.0224782 | − | 0.255200i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 1.23451i | − | 0.0392948i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.1864 | −0.896277 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.30741 | −0.0415313 | −0.0207657 | − | 0.999784i | \(-0.506610\pi\) | ||||
−0.0207657 | + | 0.999784i | \(0.506610\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.5657i | 0.462228i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.3918 | + | 1.53188i | 0.551356 | + | 0.0485639i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 58.9319i | 1.86639i | 0.359370 | + | 0.933195i | \(0.382992\pi\) | ||||
−0.359370 | + | 0.933195i | \(0.617008\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.37252 | 0.233256 |
(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 | 4020.2.g.c.1609.21 | yes | 38 | |
5.4 | even | 2 | inner | 4020.2.g.c.1609.2 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.c.1609.2 | ✓ | 38 | 5.4 | even | 2 | inner | |
4020.2.g.c.1609.21 | yes | 38 | 1.1 | even | 1 | trivial |