Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(721,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 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("2880.721");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.t (of order \(4\), degree \(2\), not 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: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 720) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2161.4 | ||
Character | \(\chi\) | \(=\) | 2880.2161 |
Dual form | 2880.2.t.e.721.4 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.707107 | − | 0.707107i | −0.316228 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.511707i | 0.193407i | 0.995313 | + | 0.0967035i | \(0.0308299\pi\) | ||||
−0.995313 | + | 0.0967035i | \(0.969170\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.751529 | + | 0.751529i | 0.226594 | + | 0.226594i | 0.811268 | − | 0.584674i | \(-0.198778\pi\) |
−0.584674 | + | 0.811268i | \(0.698778\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.22826 | + | 4.22826i | −1.17271 | + | 1.17271i | −0.191146 | + | 0.981562i | \(0.561220\pi\) |
−0.981562 | + | 0.191146i | \(0.938780\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.73728 | −1.14896 | −0.574479 | − | 0.818519i | \(-0.694795\pi\) | ||||
−0.574479 | + | 0.818519i | \(0.694795\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.78289 | − | 4.78289i | 1.09727 | − | 1.09727i | 0.102542 | − | 0.994729i | \(-0.467302\pi\) |
0.994729 | − | 0.102542i | \(-0.0326976\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.0927028i | − | 0.0193299i | −0.999953 | − | 0.00966493i | \(-0.996924\pi\) | ||
0.999953 | − | 0.00966493i | \(-0.00307649\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.979239 | − | 0.979239i | 0.181840 | − | 0.181840i | −0.610317 | − | 0.792157i | \(-0.708958\pi\) |
0.792157 | + | 0.610317i | \(0.208958\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.03913 | 0.545845 | 0.272922 | − | 0.962036i | \(-0.412010\pi\) | ||||
0.272922 | + | 0.962036i | \(0.412010\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.361831 | − | 0.361831i | 0.0611606 | − | 0.0611606i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.17130 | + | 1.17130i | 0.192561 | + | 0.192561i | 0.796802 | − | 0.604241i | \(-0.206524\pi\) |
−0.604241 | + | 0.796802i | \(0.706524\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 11.9119i | − | 1.86032i | −0.367150 | − | 0.930162i | \(-0.619667\pi\) | ||
0.367150 | − | 0.930162i | \(-0.380333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.52641 | − | 6.52641i | −0.995268 | − | 0.995268i | 0.00472051 | − | 0.999989i | \(-0.498497\pi\) |
−0.999989 | + | 0.00472051i | \(0.998497\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.91895 | 0.863367 | 0.431684 | − | 0.902025i | \(-0.357920\pi\) | ||||
0.431684 | + | 0.902025i | \(0.357920\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.73816 | 0.962594 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.44018 | − | 6.44018i | −0.884626 | − | 0.884626i | 0.109374 | − | 0.994001i | \(-0.465115\pi\) |
−0.994001 | + | 0.109374i | \(0.965115\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.06282i | − | 0.143311i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.60826 | − | 7.60826i | −0.990511 | − | 0.990511i | 0.00944406 | − | 0.999955i | \(-0.496994\pi\) |
−0.999955 | + | 0.00944406i | \(0.996994\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.76756 | + | 2.76756i | −0.354349 | + | 0.354349i | −0.861725 | − | 0.507376i | \(-0.830616\pi\) |
0.507376 | + | 0.861725i | \(0.330616\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.97966 | 0.741685 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.94156 | + | 4.94156i | −0.603708 | + | 0.603708i | −0.941294 | − | 0.337587i | \(-0.890389\pi\) |
0.337587 | + | 0.941294i | \(0.390389\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.80855i | − | 1.16406i | −0.813167 | − | 0.582031i | \(-0.802258\pi\) | ||
0.813167 | − | 0.582031i | \(-0.197742\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.10381i | 0.597356i | 0.954354 | + | 0.298678i | \(0.0965457\pi\) | ||||
−0.954354 | + | 0.298678i | \(0.903454\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.384562 | + | 0.384562i | −0.0438249 | + | 0.0438249i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.92723 | 0.779374 | 0.389687 | − | 0.920947i | \(-0.372583\pi\) | ||||
0.389687 | + | 0.920947i | \(0.372583\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.04926 | − | 8.04926i | 0.883521 | − | 0.883521i | −0.110370 | − | 0.993891i | \(-0.535203\pi\) |
0.993891 | + | 0.110370i | \(0.0352035\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.34976 | + | 3.34976i | 0.363332 | + | 0.363332i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.41356i | − | 0.255837i | −0.991785 | − | 0.127919i | \(-0.959170\pi\) | ||
0.991785 | − | 0.127919i | \(-0.0408296\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.16363 | − | 2.16363i | −0.226810 | − | 0.226810i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.76403 | −0.693975 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.51711 | −0.458643 | −0.229321 | − | 0.973351i | \(-0.573651\pi\) | ||||
−0.229321 | + | 0.973351i | \(0.573651\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.90898 | + | 2.90898i | 0.289454 | + | 0.289454i | 0.836864 | − | 0.547410i | \(-0.184386\pi\) |
−0.547410 | + | 0.836864i | \(0.684386\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 6.98357i | − | 0.688111i | −0.938949 | − | 0.344056i | \(-0.888199\pi\) | ||
0.938949 | − | 0.344056i | \(-0.111801\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.31968 | − | 5.31968i | −0.514273 | − | 0.514273i | 0.401560 | − | 0.915833i | \(-0.368468\pi\) |
−0.915833 | + | 0.401560i | \(0.868468\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.50835 | + | 3.50835i | −0.336039 | + | 0.336039i | −0.854874 | − | 0.518835i | \(-0.826366\pi\) |
0.518835 | + | 0.854874i | \(0.326366\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.57039 | −0.524018 | −0.262009 | − | 0.965065i | \(-0.584385\pi\) | ||||
−0.262009 | + | 0.965065i | \(0.584385\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0655508 | + | 0.0655508i | −0.00611264 | + | 0.00611264i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.42410i | − | 0.222216i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 9.87041i | − | 0.897310i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.707107 | − | 0.707107i | 0.0632456 | − | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.39206 | 0.123525 | 0.0617626 | − | 0.998091i | \(-0.480328\pi\) | ||||
0.0617626 | + | 0.998091i | \(0.480328\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.4259 | + | 14.4259i | −1.26039 | + | 1.26039i | −0.309493 | + | 0.950902i | \(0.600159\pi\) |
−0.950902 | + | 0.309493i | \(0.899841\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.44744 | + | 2.44744i | 0.212220 | + | 0.212220i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.30854i | − | 0.197232i | −0.995126 | − | 0.0986158i | \(-0.968559\pi\) | ||
0.995126 | − | 0.0986158i | \(-0.0314415\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.4111 | − | 12.4111i | −1.05270 | − | 1.05270i | −0.998532 | − | 0.0541659i | \(-0.982750\pi\) |
−0.0541659 | − | 0.998532i | \(-0.517250\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.35531 | −0.531458 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.38485 | −0.115006 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.09810 | − | 5.09810i | −0.417653 | − | 0.417653i | 0.466741 | − | 0.884394i | \(-0.345428\pi\) |
−0.884394 | + | 0.466741i | \(0.845428\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.1276i | 1.31245i | 0.754567 | + | 0.656223i | \(0.227847\pi\) | ||||
−0.754567 | + | 0.656223i | \(0.772153\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.14899 | − | 2.14899i | −0.172611 | − | 0.172611i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.2703 | + | 15.2703i | −1.21871 | + | 1.21871i | −0.250621 | + | 0.968085i | \(0.580635\pi\) |
−0.968085 | + | 0.250621i | \(0.919365\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0474366 | 0.00373853 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.5036 | − | 11.5036i | 0.901033 | − | 0.901033i | −0.0944929 | − | 0.995526i | \(-0.530123\pi\) |
0.995526 | + | 0.0944929i | \(0.0301230\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 21.7707i | − | 1.68467i | −0.538958 | − | 0.842333i | \(-0.681182\pi\) | ||
0.538958 | − | 0.842333i | \(-0.318818\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 22.7563i | − | 1.75049i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.88873 | − | 6.88873i | 0.523740 | − | 0.523740i | −0.394959 | − | 0.918699i | \(-0.629241\pi\) |
0.918699 | + | 0.394959i | \(0.129241\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.511707 | −0.0386814 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.7914 | − | 13.7914i | 1.03082 | − | 1.03082i | 0.0313081 | − | 0.999510i | \(-0.490033\pi\) |
0.999510 | − | 0.0313081i | \(-0.00996730\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.89478 | − | 8.89478i | −0.661144 | − | 0.661144i | 0.294506 | − | 0.955650i | \(-0.404845\pi\) |
−0.955650 | + | 0.294506i | \(0.904845\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1.65647i | − | 0.121786i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.56020 | − | 3.56020i | −0.260348 | − | 0.260348i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.8682 | −0.786392 | −0.393196 | − | 0.919455i | \(-0.628631\pi\) | ||||
−0.393196 | + | 0.919455i | \(0.628631\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.7380 | 1.78068 | 0.890339 | − | 0.455298i | \(-0.150467\pi\) | ||||
0.890339 | + | 0.455298i | \(0.150467\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.70710 | − | 5.70710i | −0.406614 | − | 0.406614i | 0.473942 | − | 0.880556i | \(-0.342831\pi\) |
−0.880556 | + | 0.473942i | \(0.842831\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.60444i | 0.609952i | 0.952360 | + | 0.304976i | \(0.0986485\pi\) | ||||
−0.952360 | + | 0.304976i | \(0.901352\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.501083 | + | 0.501083i | 0.0351692 | + | 0.0351692i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.42297 | + | 8.42297i | −0.588286 | + | 0.588286i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.18896 | 0.497271 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.85260 | + | 3.85260i | −0.265224 | + | 0.265224i | −0.827172 | − | 0.561949i | \(-0.810052\pi\) |
0.561949 | + | 0.827172i | \(0.310052\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.22974i | 0.629463i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.55515i | 0.105570i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.0304 | − | 20.0304i | 1.34739 | − | 1.34739i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.8126 | 1.32675 | 0.663374 | − | 0.748288i | \(-0.269124\pi\) | ||||
0.663374 | + | 0.748288i | \(0.269124\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.4672 | − | 12.4672i | 0.827479 | − | 0.827479i | −0.159689 | − | 0.987167i | \(-0.551049\pi\) |
0.987167 | + | 0.159689i | \(0.0510490\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.02737 | − | 5.02737i | −0.332218 | − | 0.332218i | 0.521210 | − | 0.853428i | \(-0.325481\pi\) |
−0.853428 | + | 0.521210i | \(0.825481\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.461523i | 0.0302354i | 0.999886 | + | 0.0151177i | \(0.00481230\pi\) | ||||
−0.999886 | + | 0.0151177i | \(0.995188\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.18533 | − | 4.18533i | −0.273021 | − | 0.273021i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.95248 | −0.190980 | −0.0954900 | − | 0.995430i | \(-0.530442\pi\) | ||||
−0.0954900 | + | 0.995430i | \(0.530442\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.8276 | 1.01955 | 0.509773 | − | 0.860309i | \(-0.329729\pi\) | ||||
0.509773 | + | 0.860309i | \(0.329729\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.76460 | − | 4.76460i | −0.304399 | − | 0.304399i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 40.4466i | 2.57356i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.34784 | − | 9.34784i | −0.590030 | − | 0.590030i | 0.347609 | − | 0.937639i | \(-0.386994\pi\) |
−0.937639 | + | 0.347609i | \(0.886994\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0696688 | − | 0.0696688i | 0.00438004 | − | 0.00438004i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.3509 | −0.645671 | −0.322836 | − | 0.946455i | \(-0.604636\pi\) | ||||
−0.322836 | + | 0.946455i | \(0.604636\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.599363 | + | 0.599363i | −0.0372426 | + | 0.0372426i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 21.3723i | − | 1.31787i | −0.752198 | − | 0.658937i | \(-0.771007\pi\) | ||
0.752198 | − | 0.658937i | \(-0.228993\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.10779i | 0.559487i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.7481 | + | 14.7481i | −0.899208 | + | 0.899208i | −0.995366 | − | 0.0961584i | \(-0.969344\pi\) |
0.0961584 | + | 0.995366i | \(0.469344\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.8661 | 0.842308 | 0.421154 | − | 0.906989i | \(-0.361625\pi\) | ||||
0.421154 | + | 0.906989i | \(0.361625\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.751529 | + | 0.751529i | −0.0453189 | + | 0.0453189i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.33259 | − | 3.33259i | −0.200236 | − | 0.200236i | 0.599865 | − | 0.800101i | \(-0.295221\pi\) |
−0.800101 | + | 0.599865i | \(0.795221\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 0.301204i | − | 0.0179683i | −0.999960 | − | 0.00898416i | \(-0.997140\pi\) | ||
0.999960 | − | 0.00898416i | \(-0.00285978\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.9592 | − | 12.9592i | −0.770347 | − | 0.770347i | 0.207820 | − | 0.978167i | \(-0.433363\pi\) |
−0.978167 | + | 0.207820i | \(0.933363\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.09539 | 0.359799 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.44178 | 0.320105 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.6268 | + | 11.6268i | 0.679244 | + | 0.679244i | 0.959829 | − | 0.280585i | \(-0.0905286\pi\) |
−0.280585 | + | 0.959829i | \(0.590529\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.7597i | 0.626454i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.391971 | + | 0.391971i | 0.0226683 | + | 0.0226683i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.33961 | − | 3.33961i | 0.192492 | − | 0.192492i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.91392 | 0.224110 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.0025 | + | 14.0025i | −0.799164 | + | 0.799164i | −0.982964 | − | 0.183799i | \(-0.941160\pi\) |
0.183799 | + | 0.982964i | \(0.441160\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.3773i | 1.55243i | 0.630471 | + | 0.776213i | \(0.282862\pi\) | ||||
−0.630471 | + | 0.776213i | \(0.717138\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 29.4232i | − | 1.66310i | −0.555453 | − | 0.831548i | \(-0.687455\pi\) | ||
0.555453 | − | 0.831548i | \(-0.312545\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.2115 | + | 18.2115i | −1.02286 | + | 1.02286i | −0.0231291 | + | 0.999732i | \(0.507363\pi\) |
−0.999732 | + | 0.0231291i | \(0.992637\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.47185 | 0.0824080 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.6579 | + | 22.6579i | −1.26072 | + | 1.26072i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.22826 | − | 4.22826i | −0.234542 | − | 0.234542i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.02877i | 0.166981i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.61201 | − | 1.61201i | −0.0886040 | − | 0.0886040i | 0.661416 | − | 0.750020i | \(-0.269956\pi\) |
−0.750020 | + | 0.661416i | \(0.769956\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.98842 | 0.381818 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.9784 | 0.924874 | 0.462437 | − | 0.886652i | \(-0.346975\pi\) | ||||
0.462437 | + | 0.886652i | \(0.346975\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.28400 | + | 2.28400i | 0.123685 | + | 0.123685i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.02991i | 0.379579i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.4829 | + | 23.4829i | 1.26063 | + | 1.26063i | 0.950789 | + | 0.309839i | \(0.100275\pi\) |
0.309839 | + | 0.950789i | \(0.399725\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0616 | − | 14.0616i | 0.752699 | − | 0.752699i | −0.222283 | − | 0.974982i | \(-0.571351\pi\) |
0.974982 | + | 0.222283i | \(0.0713509\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.5402 | −1.04002 | −0.520009 | − | 0.854161i | \(-0.674071\pi\) | ||||
−0.520009 | + | 0.854161i | \(0.674071\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.93569 | + | 6.93569i | −0.368108 | + | 0.368108i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.6910i | 1.56703i | 0.621372 | + | 0.783516i | \(0.286576\pi\) | ||||
−0.621372 | + | 0.783516i | \(0.713424\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 26.7521i | − | 1.40801i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.60894 | − | 3.60894i | 0.188901 | − | 0.188901i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.925465 | 0.0483089 | 0.0241544 | − | 0.999708i | \(-0.492311\pi\) | ||||
0.0241544 | + | 0.999708i | \(0.492311\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.29548 | − | 3.29548i | 0.171093 | − | 0.171093i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.29793 | + | 4.29793i | 0.222538 | + | 0.222538i | 0.809566 | − | 0.587028i | \(-0.199702\pi\) |
−0.587028 | + | 0.809566i | \(0.699702\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.28095i | 0.426491i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.20296 | + | 9.20296i | 0.472724 | + | 0.472724i | 0.902795 | − | 0.430071i | \(-0.141511\pi\) |
−0.430071 | + | 0.902795i | \(0.641511\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.2021 | 0.878984 | 0.439492 | − | 0.898247i | \(-0.355159\pi\) | ||||
0.439492 | + | 0.898247i | \(0.355159\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.543853 | 0.0277173 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.9608 | − | 20.9608i | −1.06276 | − | 1.06276i | −0.997894 | − | 0.0648607i | \(-0.979340\pi\) |
−0.0648607 | − | 0.997894i | \(-0.520660\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.439159i | 0.0222092i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.89829 | − | 4.89829i | −0.246460 | − | 0.246460i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.6135 | + | 17.6135i | −0.883995 | + | 0.883995i | −0.993938 | − | 0.109943i | \(-0.964933\pi\) |
0.109943 | + | 0.993938i | \(0.464933\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.4827 | 0.573419 | 0.286709 | − | 0.958018i | \(-0.407439\pi\) | ||||
0.286709 | + | 0.958018i | \(0.407439\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.8502 | + | 12.8502i | −0.640116 | + | 0.640116i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.76053i | 0.0872664i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 14.0740i | − | 0.695916i | −0.937510 | − | 0.347958i | \(-0.886875\pi\) | ||
0.937510 | − | 0.347958i | \(-0.113125\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.89320 | − | 3.89320i | 0.191572 | − | 0.191572i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.3834 | −0.558788 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.6490 | − | 14.6490i | 0.715650 | − | 0.715650i | −0.252062 | − | 0.967711i | \(-0.581109\pi\) |
0.967711 | + | 0.252062i | \(0.0811085\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0244 | + | 11.0244i | 0.537296 | + | 0.537296i | 0.922734 | − | 0.385437i | \(-0.125949\pi\) |
−0.385437 | + | 0.922734i | \(0.625949\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 4.73728i | − | 0.229792i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.41618 | − | 1.41618i | −0.0685336 | − | 0.0685336i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.9583 | −0.816851 | −0.408426 | − | 0.912792i | \(-0.633922\pi\) | ||||
−0.408426 | + | 0.912792i | \(0.633922\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.0507 | −1.01163 | −0.505816 | − | 0.862642i | \(-0.668808\pi\) | ||||
−0.505816 | + | 0.862642i | \(0.668808\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.443387 | − | 0.443387i | −0.0212101 | − | 0.0212101i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 40.2881i | − | 1.92285i | −0.275071 | − | 0.961424i | \(-0.588701\pi\) | ||
0.275071 | − | 0.961424i | \(-0.411299\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.4658 | + | 17.4658i | 0.829827 | + | 0.829827i | 0.987493 | − | 0.157665i | \(-0.0503968\pi\) |
−0.157665 | + | 0.987493i | \(0.550397\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.70665 | + | 1.70665i | −0.0809028 | + | 0.0809028i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.56773 | 0.451529 | 0.225765 | − | 0.974182i | \(-0.427512\pi\) | ||||
0.225765 | + | 0.974182i | \(0.427512\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.95212 | − | 8.95212i | 0.421539 | − | 0.421539i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.05983i | 0.143447i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.5509i | 0.540330i | 0.962814 | + | 0.270165i | \(0.0870783\pi\) | ||||
−0.962814 | + | 0.270165i | \(0.912922\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.2403 | − | 21.2403i | 0.989260 | − | 0.989260i | −0.0106834 | − | 0.999943i | \(-0.503401\pi\) |
0.999943 | + | 0.0106834i | \(0.00340069\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.9880 | −0.603605 | −0.301802 | − | 0.953370i | \(-0.597588\pi\) | ||||
−0.301802 | + | 0.953370i | \(0.597588\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.552173 | + | 0.552173i | −0.0255515 | + | 0.0255515i | −0.719767 | − | 0.694216i | \(-0.755751\pi\) |
0.694216 | + | 0.719767i | \(0.255751\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.52863 | − | 2.52863i | −0.116761 | − | 0.116761i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 9.80957i | − | 0.451045i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.78289 | + | 4.78289i | 0.219454 | + | 0.219454i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.8968 | 1.59447 | 0.797237 | − | 0.603666i | \(-0.206294\pi\) | ||||
0.797237 | + | 0.603666i | \(0.206294\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.90512 | −0.451635 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.19408 | + | 3.19408i | 0.145036 | + | 0.145036i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.2023i | 1.27797i | 0.769220 | + | 0.638984i | \(0.220645\pi\) | ||||
−0.769220 | + | 0.638984i | \(0.779355\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.1166 | + | 10.1166i | 0.456556 | + | 0.456556i | 0.897523 | − | 0.440967i | \(-0.145365\pi\) |
−0.440967 | + | 0.897523i | \(0.645365\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.63893 | + | 4.63893i | −0.208927 | + | 0.208927i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.01910 | 0.225138 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.8551 | − | 23.8551i | 1.06790 | − | 1.06790i | 0.0703790 | − | 0.997520i | \(-0.477579\pi\) |
0.997520 | − | 0.0703790i | \(-0.0224209\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 26.2491i | − | 1.17039i | −0.810892 | − | 0.585195i | \(-0.801018\pi\) | ||
0.810892 | − | 0.585195i | \(-0.198982\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 4.11391i | − | 0.183067i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.0368 | + | 29.0368i | −1.28704 | + | 1.28704i | −0.350456 | + | 0.936579i | \(0.613974\pi\) |
−0.936579 | + | 0.350456i | \(0.886026\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.61165 | −0.115533 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.93813 | + | 4.93813i | −0.217600 | + | 0.217600i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.44826 | + | 4.44826i | 0.195634 | + | 0.195634i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.2624i | 0.712468i | 0.934397 | + | 0.356234i | \(0.115939\pi\) | ||||
−0.934397 | + | 0.356234i | \(0.884061\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.5530 | + | 10.5530i | 0.461451 | + | 0.461451i | 0.899131 | − | 0.437680i | \(-0.144200\pi\) |
−0.437680 | + | 0.899131i | \(0.644200\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.3972 | −0.627153 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.9914 | 0.999626 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 50.3665 | + | 50.3665i | 2.18161 | + | 2.18161i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.52316i | 0.325255i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.06392 | + | 5.06392i | 0.218118 | + | 0.218118i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.0580 | + | 17.0580i | −0.733380 | + | 0.733380i | −0.971288 | − | 0.237908i | \(-0.923538\pi\) |
0.237908 | + | 0.971288i | \(0.423538\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.96155 | 0.212530 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.4561 | + | 12.4561i | −0.532584 | + | 0.532584i | −0.921341 | − | 0.388757i | \(-0.872905\pi\) |
0.388757 | + | 0.921341i | \(0.372905\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 9.36719i | − | 0.399056i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.54471i | 0.150736i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.43060 | + | 4.43060i | −0.187731 | + | 0.187731i | −0.794714 | − | 0.606984i | \(-0.792379\pi\) |
0.606984 | + | 0.794714i | \(0.292379\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 55.1907 | 2.33432 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.8113 | + | 25.8113i | −1.08782 | + | 1.08782i | −0.0920639 | + | 0.995753i | \(0.529346\pi\) |
−0.995753 | + | 0.0920639i | \(0.970654\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.93886 | + | 3.93886i | 0.165709 | + | 0.165709i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.0679i | 1.00898i | 0.863418 | + | 0.504489i | \(0.168319\pi\) | ||||
−0.863418 | + | 0.504489i | \(0.831681\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.4966 | − | 19.4966i | −0.815909 | − | 0.815909i | 0.169603 | − | 0.985512i | \(-0.445751\pi\) |
−0.985512 | + | 0.169603i | \(0.945751\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.0927028 | 0.00386597 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.5789 | −0.606929 | −0.303464 | − | 0.952843i | \(-0.598143\pi\) | ||||
−0.303464 | + | 0.952843i | \(0.598143\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.11886 | + | 4.11886i | 0.170879 | + | 0.170879i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 9.67996i | − | 0.400903i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.3865 | − | 17.3865i | −0.717618 | − | 0.717618i | 0.250499 | − | 0.968117i | \(-0.419405\pi\) |
−0.968117 | + | 0.250499i | \(0.919405\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.5359 | − | 14.5359i | 0.598939 | − | 0.598939i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.4761 | −1.21044 | −0.605220 | − | 0.796058i | \(-0.706915\pi\) | ||||
−0.605220 | + | 0.796058i | \(0.706915\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.71409 | + | 1.71409i | −0.0702710 | + | 0.0702710i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.8704i | 1.71078i | 0.517985 | + | 0.855390i | \(0.326682\pi\) | ||||
−0.517985 | + | 0.855390i | \(0.673318\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.2862i | 1.43936i | 0.694308 | + | 0.719678i | \(0.255710\pi\) | ||||
−0.694308 | + | 0.719678i | \(0.744290\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.97943 | + | 6.97943i | −0.283754 | + | 0.283754i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.7338 | −1.45039 | −0.725194 | − | 0.688544i | \(-0.758250\pi\) | ||||
−0.725194 | + | 0.688544i | \(0.758250\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.0268 | + | 25.0268i | −1.01248 | + | 1.01248i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.7737 | − | 27.7737i | −1.12177 | − | 1.12177i | −0.991475 | − | 0.130295i | \(-0.958408\pi\) |
−0.130295 | − | 0.991475i | \(-0.541592\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.2603i | 1.66108i | 0.556962 | + | 0.830538i | \(0.311967\pi\) | ||||
−0.556962 | + | 0.830538i | \(0.688033\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.8755 | − | 28.8755i | −1.16060 | − | 1.16060i | −0.984344 | − | 0.176261i | \(-0.943600\pi\) |
−0.176261 | − | 0.984344i | \(-0.556400\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.23504 | 0.0494807 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.54878 | − | 5.54878i | −0.221244 | − | 0.221244i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 19.1784i | − | 0.763481i | −0.924270 | − | 0.381740i | \(-0.875325\pi\) | ||
0.924270 | − | 0.381740i | \(-0.124675\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.984333 | − | 0.984333i | −0.0390621 | − | 0.0390621i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28.4907 | + | 28.4907i | −1.12884 | + | 1.12884i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5636 | 0.654223 | 0.327111 | − | 0.944986i | \(-0.393925\pi\) | ||||
0.327111 | + | 0.944986i | \(0.393925\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.0589 | − | 27.0589i | 1.06710 | − | 1.06710i | 0.0695192 | − | 0.997581i | \(-0.477854\pi\) |
0.997581 | − | 0.0695192i | \(-0.0221465\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.7374i | 1.16910i | 0.811358 | + | 0.584550i | \(0.198729\pi\) | ||||
−0.811358 | + | 0.584550i | \(0.801271\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 11.4357i | − | 0.448889i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.504139 | − | 0.504139i | 0.0197285 | − | 0.0197285i | −0.697174 | − | 0.716902i | \(-0.745559\pi\) |
0.716902 | + | 0.697174i | \(0.245559\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.4013 | 0.797144 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.1441 | − | 12.1441i | 0.473066 | − | 0.473066i | −0.429839 | − | 0.902905i | \(-0.641430\pi\) |
0.902905 | + | 0.429839i | \(0.141430\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.2032 | − | 10.2032i | −0.396859 | − | 0.396859i | 0.480265 | − | 0.877124i | \(-0.340541\pi\) |
−0.877124 | + | 0.480265i | \(0.840541\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 3.46120i | − | 0.134220i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.0907782 | − | 0.0907782i | −0.00351495 | − | 0.00351495i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.15980 | −0.160587 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.8274 | 0.417367 | 0.208683 | − | 0.977983i | \(-0.433082\pi\) | ||||
0.208683 | + | 0.977983i | \(0.433082\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.8507 | + | 22.8507i | 0.878224 | + | 0.878224i | 0.993351 | − | 0.115127i | \(-0.0367275\pi\) |
−0.115127 | + | 0.993351i | \(0.536728\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 2.31143i | − | 0.0887047i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.24450 | + | 3.24450i | 0.124147 | + | 0.124147i | 0.766451 | − | 0.642303i | \(-0.222021\pi\) |
−0.642303 | + | 0.766451i | \(0.722021\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.63238 | + | 1.63238i | −0.0623701 | + | 0.0623701i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 54.4615 | 2.07482 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.77564 | + | 3.77564i | −0.143632 | + | 0.143632i | −0.775266 | − | 0.631634i | \(-0.782384\pi\) |
0.631634 | + | 0.775266i | \(0.282384\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.5520i | 0.665785i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 56.4299i | 2.13743i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.6912 | + | 28.6912i | −1.08365 | + | 1.08365i | −0.0874865 | + | 0.996166i | \(0.527883\pi\) |
−0.996166 | + | 0.0874865i | \(0.972117\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.2044 | 0.422582 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.48854 | + | 1.48854i | −0.0559824 | + | 0.0559824i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.56582 | + | 6.56582i | 0.246585 | + | 0.246585i | 0.819567 | − | 0.572983i | \(-0.194214\pi\) |
−0.572983 | + | 0.819567i | \(0.694214\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 0.281736i | − | 0.0105511i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.49389 | + | 4.49389i | 0.168062 | + | 0.168062i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.8676 | −1.48681 | −0.743405 | − | 0.668842i | \(-0.766790\pi\) | ||||
−0.743405 | + | 0.668842i | \(0.766790\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.57354 | 0.133086 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.979239 | + | 0.979239i | 0.0363680 | + | 0.0363680i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 18.7495i | − | 0.695380i | −0.937610 | − | 0.347690i | \(-0.886966\pi\) | ||
0.937610 | − | 0.347690i | \(-0.113034\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.9174 | + | 30.9174i | 1.14352 | + | 1.14352i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.3263 | − | 33.3263i | 1.23093 | − | 1.23093i | 0.267329 | − | 0.963605i | \(-0.413859\pi\) |
0.963605 | − | 0.267329i | \(-0.0861410\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.42745 | −0.273594 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.5069 | − | 15.5069i | 0.570429 | − | 0.570429i | −0.361819 | − | 0.932248i | \(-0.617844\pi\) |
0.932248 | + | 0.361819i | \(0.117844\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 11.4896i | − | 0.421514i | −0.977538 | − | 0.210757i | \(-0.932407\pi\) | ||
0.977538 | − | 0.210757i | \(-0.0675929\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.20980i | 0.264147i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.72212 | − | 2.72212i | 0.0994640 | − | 0.0994640i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.4720 | −1.22141 | −0.610706 | − | 0.791857i | \(-0.709114\pi\) | ||||
−0.610706 | + | 0.791857i | \(0.709114\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.4039 | − | 11.4039i | 0.415032 | − | 0.415032i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.7408 | + | 26.7408i | 0.971910 | + | 0.971910i | 0.999616 | − | 0.0277060i | \(-0.00882023\pi\) |
−0.0277060 | + | 0.999616i | \(0.508820\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 6.83099i | − | 0.247623i | −0.992306 | − | 0.123812i | \(-0.960488\pi\) | ||
0.992306 | − | 0.123812i | \(-0.0395118\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.79525 | − | 1.79525i | −0.0649922 | − | 0.0649922i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 64.3394 | 2.32316 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.5044 | 0.847590 | 0.423795 | − | 0.905758i | \(-0.360698\pi\) | ||||
0.423795 | + | 0.905758i | \(0.360698\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.848545 | − | 0.848545i | −0.0305200 | − | 0.0305200i | 0.691682 | − | 0.722202i | \(-0.256870\pi\) |
−0.722202 | + | 0.691682i | \(0.756870\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.03913i | 0.109169i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −56.9732 | − | 56.9732i | −2.04128 | − | 2.04128i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.37141 | − | 7.37141i | 0.263770 | − | 0.263770i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.5955 | 0.770778 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.03949 | + | 6.03949i | −0.215285 | + | 0.215285i | −0.806508 | − | 0.591223i | \(-0.798645\pi\) |
0.591223 | + | 0.806508i | \(0.298645\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 2.85040i | − | 0.101349i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 23.4039i | − | 0.831096i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.1586 | − | 24.1586i | 0.855742 | − | 0.855742i | −0.135091 | − | 0.990833i | \(-0.543133\pi\) |
0.990833 | + | 0.135091i | \(0.0431327\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.0397 | −0.991973 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.83566 | + | 3.83566i | −0.135358 | + | 0.135358i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.0335428 | − | 0.0335428i | −0.00118223 | − | 0.00118223i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1.35392i | − | 0.0476012i | −0.999717 | − | 0.0238006i | \(-0.992423\pi\) | ||
0.999717 | − | 0.0238006i | \(-0.00757668\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.36687 | + | 6.36687i | 0.223571 | + | 0.223571i | 0.810000 | − | 0.586429i | \(-0.199467\pi\) |
−0.586429 | + | 0.810000i | \(0.699467\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.2686 | −0.569863 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −62.4302 | −2.18416 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.6457 | + | 17.6457i | 0.615840 | + | 0.615840i | 0.944462 | − | 0.328622i | \(-0.106584\pi\) |
−0.328622 | + | 0.944462i | \(0.606584\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.2150i | 0.948654i | 0.880349 | + | 0.474327i | \(0.157309\pi\) | ||||
−0.880349 | + | 0.474327i | \(0.842691\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.4348 | + | 11.4348i | 0.397627 | + | 0.397627i | 0.877395 | − | 0.479768i | \(-0.159279\pi\) |
−0.479768 | + | 0.877395i | \(0.659279\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.300129 | + | 0.300129i | −0.0104239 | + | 0.0104239i | −0.712300 | − | 0.701876i | \(-0.752346\pi\) |
0.701876 | + | 0.712300i | \(0.252346\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −31.9205 | −1.10598 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.3942 | + | 15.3942i | −0.532738 | + | 0.532738i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.0790i | 0.382488i | 0.981543 | + | 0.191244i | \(0.0612522\pi\) | ||||
−0.981543 | + | 0.191244i | \(0.938748\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0822i | 0.933868i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.0911 | + | 16.0911i | −0.553552 | + | 0.553552i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.05075 | 0.173546 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.108583 | − | 0.108583i | 0.00372217 | − | 0.00372217i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.3141 | + | 20.3141i | 0.695541 | + | 0.695541i | 0.963446 | − | 0.267904i | \(-0.0863311\pi\) |
−0.267904 | + | 0.963446i | \(0.586331\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 23.8031i | − | 0.813099i | −0.913629 | − | 0.406549i | \(-0.866732\pi\) | ||
0.913629 | − | 0.406549i | \(-0.133268\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.8263 | + | 22.8263i | 0.778822 | + | 0.778822i | 0.979631 | − | 0.200808i | \(-0.0643568\pi\) |
−0.200808 | + | 0.979631i | \(0.564357\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.0336 | 0.647911 | 0.323956 | − | 0.946072i | \(-0.394987\pi\) | ||||
0.323956 | + | 0.946072i | \(0.394987\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.74213 | −0.331242 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.20601 | + | 5.20601i | 0.176602 | + | 0.176602i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 41.7884i | − | 1.41595i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.361831 | + | 0.361831i | 0.0122321 | + | 0.0122321i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.77519 | − | 6.77519i | 0.228782 | − | 0.228782i | −0.583402 | − | 0.812184i | \(-0.698279\pi\) |
0.812184 | + | 0.583402i | \(0.198279\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.1867 | −1.15178 | −0.575890 | − | 0.817527i | \(-0.695344\pi\) | ||||
−0.575890 | + | 0.817527i | \(0.695344\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.99012 | + | 6.99012i | −0.235236 | + | 0.235236i | −0.814874 | − | 0.579638i | \(-0.803194\pi\) |
0.579638 | + | 0.814874i | \(0.303194\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 9.23335i | − | 0.310026i | −0.987912 | − | 0.155013i | \(-0.950458\pi\) | ||
0.987912 | − | 0.155013i | \(-0.0495419\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.712325i | 0.0238906i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.3097 | − | 28.3097i | 0.947348 | − | 0.947348i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.5040 | −0.651946 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.97604 | − | 2.97604i | 0.0992565 | − | 0.0992565i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.5089 | + | 30.5089i | 1.01640 | + | 1.01640i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.5791i | 0.418144i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.5823 | + | 27.5823i | 0.915854 | + | 0.915854i | 0.996725 | − | 0.0808703i | \(-0.0257700\pi\) |
−0.0808703 | + | 0.996725i | \(0.525770\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.80204 | 0.225362 | 0.112681 | − | 0.993631i | \(-0.464056\pi\) | ||||
0.112681 | + | 0.993631i | \(0.464056\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0985 | 0.400402 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.38182 | − | 7.38182i | −0.243769 | − | 0.243769i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 40.4075i | − | 1.33292i | −0.745541 | − | 0.666460i | \(-0.767809\pi\) | ||
0.745541 | − | 0.666460i | \(-0.232191\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 41.4731 | + | 41.4731i | 1.36510 | + | 1.36510i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.17130 | + | 1.17130i | −0.0385121 | + | 0.0385121i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49.3976 | 1.62068 | 0.810342 | − | 0.585957i | \(-0.199281\pi\) | ||||
0.810342 | + | 0.585957i | \(0.199281\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.2279 | − | 32.2279i | 1.05623 | − | 1.05623i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.03488i | 0.164658i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.0115i | 1.01310i | 0.862210 | + | 0.506551i | \(0.169080\pi\) | ||||
−0.862210 | + | 0.506551i | \(0.830920\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.2147 | + | 13.2147i | −0.430786 | + | 0.430786i | −0.888896 | − | 0.458110i | \(-0.848527\pi\) |
0.458110 | + | 0.888896i | \(0.348527\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.10426 | −0.0359598 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.219269 | − | 0.219269i | 0.00712528 | − | 0.00712528i | −0.703535 | − | 0.710660i | \(-0.748396\pi\) |
0.710660 | + | 0.703535i | \(0.248396\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.5802 | − | 21.5802i | −0.700524 | − | 0.700524i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.8339i | 1.41992i | 0.704242 | + | 0.709960i | \(0.251287\pi\) | ||||
−0.704242 | + | 0.709960i | \(0.748713\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.68494 | + | 7.68494i | 0.248679 | + | 0.248679i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.18129 | 0.0381460 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.7637 | −0.702054 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.4924 | − | 17.4924i | −0.563100 | − | 0.563100i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 45.5600i | − | 1.46511i | −0.680707 | − | 0.732556i | \(-0.738327\pi\) | ||
0.680707 | − | 0.732556i | \(-0.261673\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.79605 | + | 3.79605i | 0.121821 | + | 0.121821i | 0.765389 | − | 0.643568i | \(-0.222547\pi\) |
−0.643568 | + | 0.765389i | \(0.722547\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.35086 | − | 6.35086i | 0.203599 | − | 0.203599i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46.9906 | −1.50336 | −0.751682 | − | 0.659526i | \(-0.770757\pi\) | ||||
−0.751682 | + | 0.659526i | \(0.770757\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.81386 | − | 1.81386i | 0.0579713 | − | 0.0579713i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 5.05860i | − | 0.161344i | −0.996741 | − | 0.0806722i | \(-0.974293\pi\) | ||
0.996741 | − | 0.0806722i | \(-0.0257067\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.07106i | 0.257165i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.605017 | + | 0.605017i | −0.0192384 | + | 0.0192384i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.9925 | 1.20687 | 0.603436 | − | 0.797411i | \(-0.293798\pi\) | ||||
0.603436 | + | 0.797411i | \(0.293798\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.08425 | − | 6.08425i | 0.192884 | − | 0.192884i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.28839 | + | 8.28839i | 0.262496 | + | 0.262496i | 0.826067 | − | 0.563571i | \(-0.190573\pi\) |
−0.563571 | + | 0.826067i | \(0.690573\pi\) | |||||||
\(998\) | 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 | 2880.2.t.e.2161.4 | 32 | ||
3.2 | odd | 2 | inner | 2880.2.t.e.2161.11 | 32 | ||
4.3 | odd | 2 | 720.2.t.e.181.12 | yes | 32 | ||
12.11 | even | 2 | 720.2.t.e.181.5 | ✓ | 32 | ||
16.3 | odd | 4 | 720.2.t.e.541.12 | yes | 32 | ||
16.13 | even | 4 | inner | 2880.2.t.e.721.4 | 32 | ||
48.29 | odd | 4 | inner | 2880.2.t.e.721.11 | 32 | ||
48.35 | even | 4 | 720.2.t.e.541.5 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
720.2.t.e.181.5 | ✓ | 32 | 12.11 | even | 2 | ||
720.2.t.e.181.12 | yes | 32 | 4.3 | odd | 2 | ||
720.2.t.e.541.5 | yes | 32 | 48.35 | even | 4 | ||
720.2.t.e.541.12 | yes | 32 | 16.3 | odd | 4 | ||
2880.2.t.e.721.4 | 32 | 16.13 | even | 4 | inner | ||
2880.2.t.e.721.11 | 32 | 48.29 | odd | 4 | inner | ||
2880.2.t.e.2161.4 | 32 | 1.1 | even | 1 | trivial | ||
2880.2.t.e.2161.11 | 32 | 3.2 | odd | 2 | inner |