Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(17,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1440.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.bj (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: | \(11.4984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.5 | ||
Character | \(\chi\) | \(=\) | 1440.17 |
Dual form | 1440.2.bj.a.593.5 |
$q$-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 \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.45381 | + | 1.69895i | −0.650165 | + | 0.759793i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.53029 | − | 1.53029i | −0.578394 | − | 0.578394i | 0.356066 | − | 0.934461i | \(-0.384118\pi\) |
−0.934461 | + | 0.356066i | \(0.884118\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.72480 | 0.821559 | 0.410779 | − | 0.911735i | \(-0.365257\pi\) | ||||
0.410779 | + | 0.911735i | \(0.365257\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.857617 | − | 0.857617i | −0.237860 | − | 0.237860i | 0.578103 | − | 0.815964i | \(-0.303793\pi\) |
−0.815964 | + | 0.578103i | \(0.803793\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.55531 | − | 2.55531i | 0.619753 | − | 0.619753i | −0.325715 | − | 0.945468i | \(-0.605605\pi\) |
0.945468 | + | 0.325715i | \(0.105605\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.54160 | −0.812500 | −0.406250 | − | 0.913762i | \(-0.633164\pi\) | ||||
−0.406250 | + | 0.913762i | \(0.633164\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.626051 | + | 0.626051i | 0.130541 | + | 0.130541i | 0.769358 | − | 0.638818i | \(-0.220576\pi\) |
−0.638818 | + | 0.769358i | \(0.720576\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.772849 | − | 4.93991i | −0.154570 | − | 0.987982i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.12260i | 0.951243i | 0.879650 | + | 0.475622i | \(0.157777\pi\) | ||||
−0.879650 | + | 0.475622i | \(0.842223\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.89544 | −1.41806 | −0.709031 | − | 0.705177i | \(-0.750868\pi\) | ||||
−0.709031 | + | 0.705177i | \(0.750868\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.82463 | − | 0.375125i | 0.815512 | − | 0.0634078i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.21539 | − | 4.21539i | 0.693005 | − | 0.693005i | −0.269887 | − | 0.962892i | \(-0.586986\pi\) |
0.962892 | + | 0.269887i | \(0.0869863\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 12.4074i | − | 1.93771i | −0.247638 | − | 0.968853i | \(-0.579654\pi\) | ||
0.247638 | − | 0.968853i | \(-0.420346\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.67823 | + | 5.67823i | 0.865922 | + | 0.865922i | 0.992018 | − | 0.126096i | \(-0.0402447\pi\) |
−0.126096 | + | 0.992018i | \(0.540245\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.45505 | − | 9.45505i | 1.37916 | − | 1.37916i | 0.533124 | − | 0.846037i | \(-0.321018\pi\) |
0.846037 | − | 0.533124i | \(-0.178982\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 2.31644i | − | 0.330920i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.46657 | − | 6.46657i | 0.888252 | − | 0.888252i | −0.106103 | − | 0.994355i | \(-0.533837\pi\) |
0.994355 | + | 0.106103i | \(0.0338373\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.96136 | + | 4.62930i | −0.534149 | + | 0.624214i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.51407i | 0.327304i | 0.986518 | + | 0.163652i | \(0.0523274\pi\) | ||||
−0.986518 | + | 0.163652i | \(0.947673\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.49179i | − | 1.21530i | −0.794205 | − | 0.607649i | \(-0.792113\pi\) | ||
0.794205 | − | 0.607649i | \(-0.207887\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.70386 | − | 0.210231i | 0.335373 | − | 0.0260760i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.91318 | − | 9.91318i | 1.21109 | − | 1.21109i | 0.240418 | − | 0.970669i | \(-0.422715\pi\) |
0.970669 | − | 0.240418i | \(-0.0772846\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.19671i | 0.260702i | 0.991468 | + | 0.130351i | \(0.0416104\pi\) | ||||
−0.991468 | + | 0.130351i | \(0.958390\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.71276 | + | 5.71276i | −0.668628 | + | 0.668628i | −0.957398 | − | 0.288771i | \(-0.906754\pi\) |
0.288771 | + | 0.957398i | \(0.406754\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.16973 | − | 4.16973i | −0.475185 | − | 0.475185i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.7576i | − | 1.43534i | −0.696384 | − | 0.717670i | \(-0.745209\pi\) | ||
0.696384 | − | 0.717670i | \(-0.254791\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.58072 | + | 3.58072i | −0.393035 | + | 0.393035i | −0.875768 | − | 0.482733i | \(-0.839644\pi\) |
0.482733 | + | 0.875768i | \(0.339644\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.626392 | + | 8.05627i | 0.0679418 | + | 0.873826i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.2214 | 1.08347 | 0.541734 | − | 0.840550i | \(-0.317768\pi\) | ||||
0.541734 | + | 0.840550i | \(0.317768\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.62480i | 0.275154i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.14884 | − | 6.01700i | 0.528259 | − | 0.617331i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.29731 | − | 1.29731i | −0.131722 | − | 0.131722i | 0.638172 | − | 0.769894i | \(-0.279691\pi\) |
−0.769894 | + | 0.638172i | \(0.779691\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.82360 | 0.579470 | 0.289735 | − | 0.957107i | \(-0.406433\pi\) | ||||
0.289735 | + | 0.957107i | \(0.406433\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.08360 | − | 3.08360i | 0.303836 | − | 0.303836i | −0.538677 | − | 0.842513i | \(-0.681076\pi\) |
0.842513 | + | 0.538677i | \(0.181076\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.49670 | + | 6.49670i | 0.628060 | + | 0.628060i | 0.947580 | − | 0.319520i | \(-0.103522\pi\) |
−0.319520 | + | 0.947580i | \(0.603522\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.41031 | −0.518213 | −0.259107 | − | 0.965849i | \(-0.583428\pi\) | ||||
−0.259107 | + | 0.965849i | \(0.583428\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.358788 | − | 0.358788i | −0.0337519 | − | 0.0337519i | 0.690029 | − | 0.723781i | \(-0.257598\pi\) |
−0.723781 | + | 0.690029i | \(0.757598\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.97379 | + | 0.153466i | −0.184057 | + | 0.0143108i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.82071 | −0.716923 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.57545 | −0.325041 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.51623 | + | 5.86868i | 0.851157 | + | 0.524911i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.916401 | + | 0.916401i | 0.0813174 | + | 0.0813174i | 0.746596 | − | 0.665278i | \(-0.231687\pi\) |
−0.665278 | + | 0.746596i | \(0.731687\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.5355 | −1.70683 | −0.853413 | − | 0.521235i | \(-0.825471\pi\) | ||||
−0.853413 | + | 0.521235i | \(0.825471\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.41968 | + | 5.41968i | 0.469945 | + | 0.469945i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.66611 | + | 7.66611i | −0.654960 | + | 0.654960i | −0.954183 | − | 0.299223i | \(-0.903273\pi\) |
0.299223 | + | 0.954183i | \(0.403273\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.7210 | −1.24862 | −0.624308 | − | 0.781178i | \(-0.714619\pi\) | ||||
−0.624308 | + | 0.781178i | \(0.714619\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.33684 | − | 2.33684i | −0.195416 | − | 0.195416i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.70304 | − | 7.44731i | −0.722748 | − | 0.618466i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.6300i | 1.28046i | 0.768182 | + | 0.640231i | \(0.221162\pi\) | ||||
−0.768182 | + | 0.640231i | \(0.778838\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.5889 | 1.43136 | 0.715682 | − | 0.698426i | \(-0.246116\pi\) | ||||
0.715682 | + | 0.698426i | \(0.246116\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.4785 | − | 13.4139i | 0.921975 | − | 1.07743i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.60352 | + | 7.60352i | −0.606827 | + | 0.606827i | −0.942116 | − | 0.335288i | \(-0.891166\pi\) |
0.335288 | + | 0.942116i | \(0.391166\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.91608i | − | 0.151008i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.53586 | − | 8.53586i | −0.668580 | − | 0.668580i | 0.288807 | − | 0.957387i | \(-0.406741\pi\) |
−0.957387 | + | 0.288807i | \(0.906741\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.11022 | − | 6.11022i | 0.472823 | − | 0.472823i | −0.430004 | − | 0.902827i | \(-0.641488\pi\) |
0.902827 | + | 0.430004i | \(0.141488\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.5290i | − | 0.886845i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.593720 | + | 0.593720i | −0.0451397 | + | 0.0451397i | −0.729316 | − | 0.684177i | \(-0.760162\pi\) |
0.684177 | + | 0.729316i | \(0.260162\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.37680 | + | 8.74217i | −0.482041 | + | 0.660846i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.3935i | 0.851593i | 0.904819 | + | 0.425796i | \(0.140006\pi\) | ||||
−0.904819 | + | 0.425796i | \(0.859994\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.31410i | − | 0.543653i | −0.962346 | − | 0.271827i | \(-0.912372\pi\) | ||
0.962346 | − | 0.271827i | \(-0.0876277\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.03333 | + | 13.2901i | 0.0759722 | + | 0.977108i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.96270 | − | 6.96270i | 0.509163 | − | 0.509163i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.32855i | − | 0.0961302i | −0.998844 | − | 0.0480651i | \(-0.984695\pi\) | ||
0.998844 | − | 0.0480651i | \(-0.0153055\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.5366 | + | 11.5366i | −0.830423 | + | 0.830423i | −0.987574 | − | 0.157152i | \(-0.949769\pi\) |
0.157152 | + | 0.987574i | \(0.449769\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.1999 | − | 16.1999i | −1.15420 | − | 1.15420i | −0.985703 | − | 0.168494i | \(-0.946110\pi\) |
−0.168494 | − | 0.985703i | \(-0.553890\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.09388i | 0.431984i | 0.976395 | + | 0.215992i | \(0.0692985\pi\) | ||||
−0.976395 | + | 0.215992i | \(0.930702\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.83906 | − | 7.83906i | 0.550194 | − | 0.550194i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.0795 | + | 18.0380i | 1.47225 | + | 1.25983i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.65017 | −0.667516 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 24.9318i | − | 1.71637i | −0.513338 | − | 0.858186i | \(-0.671591\pi\) | ||
0.513338 | − | 0.858186i | \(-0.328409\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.9021 | + | 1.39193i | −1.22091 | + | 0.0949286i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0823 | + | 12.0823i | 0.820200 | + | 0.820200i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.38295 | −0.294829 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.42573 | − | 5.42573i | 0.363334 | − | 0.363334i | −0.501705 | − | 0.865039i | \(-0.667294\pi\) |
0.865039 | + | 0.501705i | \(0.167294\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.15485 | − | 8.15485i | −0.541256 | − | 0.541256i | 0.382641 | − | 0.923897i | \(-0.375015\pi\) |
−0.923897 | + | 0.382641i | \(0.875015\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.5344 | −0.960462 | −0.480231 | − | 0.877142i | \(-0.659447\pi\) | ||||
−0.480231 | + | 0.877142i | \(0.659447\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.40471 | + | 2.40471i | 0.157538 | + | 0.157538i | 0.781475 | − | 0.623937i | \(-0.214468\pi\) |
−0.623937 | + | 0.781475i | \(0.714468\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.31775 | + | 29.8095i | 0.151194 | + | 1.94456i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.79965 | −0.439833 | −0.219917 | − | 0.975519i | \(-0.570578\pi\) | ||||
−0.219917 | + | 0.975519i | \(0.570578\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.2108 | 1.04423 | 0.522114 | − | 0.852876i | \(-0.325143\pi\) | ||||
0.522114 | + | 0.852876i | \(0.325143\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.93551 | + | 3.36767i | 0.251430 | + | 0.215153i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.03734 | + | 3.03734i | 0.193261 | + | 0.193261i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.56946 | −0.604019 | −0.302009 | − | 0.953305i | \(-0.597657\pi\) | ||||
−0.302009 | + | 0.953305i | \(0.597657\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.70587 | + | 1.70587i | 0.107247 | + | 0.107247i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.61999 | + | 5.61999i | −0.350566 | + | 0.350566i | −0.860320 | − | 0.509754i | \(-0.829736\pi\) |
0.509754 | + | 0.860320i | \(0.329736\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.9015 | −0.801661 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.0240 | + | 16.0240i | 0.988080 | + | 0.988080i | 0.999930 | − | 0.0118502i | \(-0.00377213\pi\) |
−0.0118502 | + | 0.999930i | \(0.503772\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.58518 | + | 20.3876i | 0.0973766 | + | 1.25240i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 8.90392i | − | 0.542882i | −0.962455 | − | 0.271441i | \(-0.912500\pi\) | ||
0.962455 | − | 0.271441i | \(-0.0875001\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0162 | 0.851422 | 0.425711 | − | 0.904859i | \(-0.360024\pi\) | ||||
0.425711 | + | 0.904859i | \(0.360024\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.10586 | − | 13.4603i | −0.126988 | − | 0.811685i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00404 | − | 2.00404i | 0.120411 | − | 0.120411i | −0.644333 | − | 0.764745i | \(-0.722865\pi\) |
0.764745 | + | 0.644333i | \(0.222865\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.33618i | 0.556950i | 0.960444 | + | 0.278475i | \(0.0898289\pi\) | ||||
−0.960444 | + | 0.278475i | \(0.910171\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.3583 | + | 22.3583i | 1.32906 | + | 1.32906i | 0.906187 | + | 0.422877i | \(0.138980\pi\) |
0.422877 | + | 0.906187i | \(0.361020\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.9868 | + | 18.9868i | −1.12076 | + | 1.12076i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.94082i | 0.231813i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.84966 | − | 5.84966i | 0.341741 | − | 0.341741i | −0.515281 | − | 0.857021i | \(-0.672312\pi\) |
0.857021 | + | 0.515281i | \(0.172312\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.27127 | − | 3.65499i | −0.248683 | − | 0.212802i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 1.07382i | − | 0.0621009i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 17.3787i | − | 1.00169i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.1261 | + | 13.7993i | 0.923375 | + | 0.790145i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.13875 | − | 6.13875i | 0.350357 | − | 0.350357i | −0.509886 | − | 0.860242i | \(-0.670312\pi\) |
0.860242 | + | 0.509886i | \(0.170312\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.0614i | 0.740642i | 0.928904 | + | 0.370321i | \(0.120752\pi\) | ||||
−0.928904 | + | 0.370321i | \(0.879248\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.0110 | − | 22.0110i | 1.24414 | − | 1.24414i | 0.285869 | − | 0.958269i | \(-0.407718\pi\) |
0.958269 | − | 0.285869i | \(-0.0922822\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.28577 | − | 6.28577i | −0.353044 | − | 0.353044i | 0.508197 | − | 0.861241i | \(-0.330312\pi\) |
−0.861241 | + | 0.508197i | \(0.830312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.9581i | 0.781502i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.04989 | + | 9.04989i | −0.503549 | + | 0.503549i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.57374 | + | 4.89936i | −0.198236 | + | 0.271768i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −28.9379 | −1.59540 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.2733i | 1.44411i | 0.691836 | + | 0.722055i | \(0.256802\pi\) | ||||
−0.691836 | + | 0.722055i | \(0.743198\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.43006 | + | 31.2539i | 0.132768 | + | 1.70758i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.4860 | + | 16.4860i | 0.898047 | + | 0.898047i | 0.995263 | − | 0.0972161i | \(-0.0309938\pi\) |
−0.0972161 | + | 0.995263i | \(0.530994\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.5135 | −1.16502 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.2568 | + | 14.2568i | −0.769797 | + | 0.769797i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.85611 | + | 2.85611i | 0.153324 | + | 0.153324i | 0.779601 | − | 0.626277i | \(-0.215422\pi\) |
−0.626277 | + | 0.779601i | \(0.715422\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.3216 | −1.03426 | −0.517130 | − | 0.855907i | \(-0.673000\pi\) | ||||
−0.517130 | + | 0.855907i | \(0.673000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.0194 | − | 17.0194i | −0.905850 | − | 0.905850i | 0.0900845 | − | 0.995934i | \(-0.471286\pi\) |
−0.995934 | + | 0.0900845i | \(0.971286\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.73210 | − | 3.19361i | −0.198079 | − | 0.169499i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.6210 | −0.771665 | −0.385832 | − | 0.922569i | \(-0.626086\pi\) | ||||
−0.385832 | + | 0.922569i | \(0.626086\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.45703 | −0.339844 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.40039 | − | 18.0110i | −0.0732998 | − | 0.942737i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.21722 | + | 8.21722i | 0.428935 | + | 0.428935i | 0.888266 | − | 0.459330i | \(-0.151911\pi\) |
−0.459330 | + | 0.888266i | \(0.651911\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.7914 | −1.02752 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.54965 | − | 9.54965i | −0.494462 | − | 0.494462i | 0.415247 | − | 0.909709i | \(-0.363695\pi\) |
−0.909709 | + | 0.415247i | \(0.863695\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.39323 | − | 4.39323i | 0.226263 | − | 0.226263i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.71237 | −0.498891 | −0.249445 | − | 0.968389i | \(-0.580248\pi\) | ||||
−0.249445 | + | 0.968389i | \(0.580248\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.97088 | + | 3.97088i | 0.202903 | + | 0.202903i | 0.801242 | − | 0.598340i | \(-0.204173\pi\) |
−0.598340 | + | 0.801242i | \(0.704173\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.1462 | − | 1.02214i | 0.669991 | − | 0.0520932i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.9006i | 0.806194i | 0.915157 | + | 0.403097i | \(0.132066\pi\) | ||||
−0.915157 | + | 0.403097i | \(0.867934\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.19950 | 0.161806 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.6745 | + | 18.5471i | 1.09056 | + | 0.933208i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.2354 | − | 17.2354i | 0.865019 | − | 0.865019i | −0.126897 | − | 0.991916i | \(-0.540502\pi\) |
0.991916 | + | 0.126897i | \(0.0405017\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.1249i | 0.655428i | 0.944777 | + | 0.327714i | \(0.106278\pi\) | ||||
−0.944777 | + | 0.327714i | \(0.893722\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.77127 | + | 6.77127i | 0.337301 | + | 0.337301i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.4861 | − | 11.4861i | 0.569345 | − | 0.569345i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 11.2852i | − | 0.558017i | −0.960289 | − | 0.279008i | \(-0.909994\pi\) | ||
0.960289 | − | 0.279008i | \(-0.0900058\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.84725 | − | 3.84725i | 0.189311 | − | 0.189311i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.877757 | − | 11.2892i | −0.0430874 | − | 0.554163i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.75266i | 0.232183i | 0.993239 | + | 0.116091i | \(0.0370365\pi\) | ||||
−0.993239 | + | 0.116091i | \(0.962963\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.283341i | 0.0138092i | 0.999976 | + | 0.00690460i | \(0.00219782\pi\) | ||||
−0.999976 | + | 0.00690460i | \(0.997802\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.5978 | − | 10.6481i | −0.708100 | − | 0.516510i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.5252 | + | 14.5252i | −0.702922 | + | 0.702922i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 10.1002i | − | 0.486508i | −0.969963 | − | 0.243254i | \(-0.921785\pi\) | ||
0.969963 | − | 0.243254i | \(-0.0782149\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.65232 | − | 5.65232i | 0.271633 | − | 0.271633i | −0.558124 | − | 0.829757i | \(-0.688479\pi\) |
0.829757 | + | 0.558124i | \(0.188479\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.21723 | − | 2.21723i | −0.106064 | − | 0.106064i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 17.0307i | − | 0.812831i | −0.913688 | − | 0.406415i | \(-0.866779\pi\) | ||
0.913688 | − | 0.406415i | \(-0.133221\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.8863 | − | 10.8863i | 0.517226 | − | 0.517226i | −0.399505 | − | 0.916731i | \(-0.630818\pi\) |
0.916731 | + | 0.399505i | \(0.130818\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.8600 | + | 17.3657i | −0.704434 | + | 0.823211i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.3509 | −0.488488 | −0.244244 | − | 0.969714i | \(-0.578540\pi\) | ||||
−0.244244 | + | 0.969714i | \(0.578540\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 33.8076i | − | 1.59194i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.45940 | − | 3.81598i | −0.209060 | − | 0.178896i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.38449 | + | 6.38449i | 0.298654 | + | 0.298654i | 0.840486 | − | 0.541833i | \(-0.182269\pi\) |
−0.541833 | + | 0.840486i | \(0.682269\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.07751 | −0.283058 | −0.141529 | − | 0.989934i | \(-0.545202\pi\) | ||||
−0.141529 | + | 0.989934i | \(0.545202\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.2374 | + | 22.2374i | −1.03346 | + | 1.03346i | −0.0340371 | + | 0.999421i | \(0.510836\pi\) |
−0.999421 | + | 0.0340371i | \(0.989164\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.6001 | − | 17.6001i | −0.814434 | − | 0.814434i | 0.170861 | − | 0.985295i | \(-0.445345\pi\) |
−0.985295 | + | 0.170861i | \(0.945345\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.3400 | −1.40097 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.4721 | + | 15.4721i | 0.711406 | + | 0.711406i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.73713 | + | 17.4952i | 0.125588 | + | 0.802735i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.47636 | −0.113148 | −0.0565740 | − | 0.998398i | \(-0.518018\pi\) | ||||
−0.0565740 | + | 0.998398i | \(0.518018\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.23038 | −0.329677 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.09012 | − | 0.318015i | 0.185723 | − | 0.0144403i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.3734 | − | 12.3734i | −0.560694 | − | 0.560694i | 0.368811 | − | 0.929505i | \(-0.379765\pi\) |
−0.929505 | + | 0.368811i | \(0.879765\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.1551 | 1.67679 | 0.838394 | − | 0.545064i | \(-0.183495\pi\) | ||||
0.838394 | + | 0.545064i | \(0.183495\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.0898 | + | 13.0898i | 0.589536 | + | 0.589536i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.36160 | − | 3.36160i | 0.150789 | − | 0.150789i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.8644 | −1.56075 | −0.780373 | − | 0.625315i | \(-0.784971\pi\) | ||||
−0.780373 | + | 0.625315i | \(0.784971\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.25041 | − | 1.25041i | −0.0557529 | − | 0.0557529i | 0.678681 | − | 0.734434i | \(-0.262552\pi\) |
−0.734434 | + | 0.678681i | \(0.762552\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.46644 | + | 9.89400i | −0.376752 | + | 0.440277i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.4393i | 1.70379i | 0.523711 | + | 0.851896i | \(0.324547\pi\) | ||||
−0.523711 | + | 0.851896i | \(0.675453\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.4843 | 0.773461 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.755895 | + | 9.72185i | 0.0333087 | + | 0.428396i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.7631 | − | 25.7631i | 1.13306 | − | 1.13306i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 19.1329i | − | 0.838226i | −0.907934 | − | 0.419113i | \(-0.862341\pi\) | ||
0.907934 | − | 0.419113i | \(-0.137659\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.870444 | + | 0.870444i | 0.0380619 | + | 0.0380619i | 0.725882 | − | 0.687820i | \(-0.241432\pi\) |
−0.687820 | + | 0.725882i | \(0.741432\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.1753 | + | 20.1753i | −0.878849 | + | 0.878849i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 22.2161i | − | 0.965918i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.6408 | + | 10.6408i | −0.460903 | + | 0.460903i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.4825 | + | 1.59256i | −0.885538 | + | 0.0688524i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 6.31183i | − | 0.271870i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.7259i | 0.805089i | 0.915400 | + | 0.402544i | \(0.131874\pi\) | ||||
−0.915400 | + | 0.402544i | \(0.868126\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.86558 | − | 9.19183i | 0.336924 | − | 0.393735i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.7085 | − | 25.7085i | 1.09922 | − | 1.09922i | 0.104713 | − | 0.994502i | \(-0.466608\pi\) |
0.994502 | − | 0.104713i | \(-0.0333924\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 18.1422i | − | 0.772885i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.5228 | + | 19.5228i | −0.830192 | + | 0.830192i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.85098 | + | 4.85098i | 0.205543 | + | 0.205543i | 0.802370 | − | 0.596827i | \(-0.203572\pi\) |
−0.596827 | + | 0.802370i | \(0.703572\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.73950i | − | 0.411937i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.13320 | − | 5.13320i | 0.216339 | − | 0.216339i | −0.590615 | − | 0.806954i | \(-0.701115\pi\) |
0.806954 | + | 0.590615i | \(0.201115\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.13117 | − | 0.0879511i | 0.0475888 | − | 0.00370013i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.4425 | 1.15045 | 0.575224 | − | 0.817996i | \(-0.304915\pi\) | ||||
0.575224 | + | 0.817996i | \(0.304915\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.73020i | 0.323499i | 0.986832 | + | 0.161749i | \(0.0517136\pi\) | ||||
−0.986832 | + | 0.161749i | \(0.948286\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.60879 | − | 3.57648i | 0.108794 | − | 0.149149i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.33858 | − | 9.33858i | −0.388770 | − | 0.388770i | 0.485478 | − | 0.874249i | \(-0.338645\pi\) |
−0.874249 | + | 0.485478i | \(0.838645\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.9591 | 0.454659 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.6201 | − | 17.6201i | 0.729751 | − | 0.729751i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.5419 | − | 20.5419i | −0.847856 | − | 0.847856i | 0.142010 | − | 0.989865i | \(-0.454644\pi\) |
−0.989865 | + | 0.142010i | \(0.954644\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.9625 | 1.15218 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.8708 | + | 15.8708i | 0.651734 | + | 0.651734i | 0.953410 | − | 0.301676i | \(-0.0975462\pi\) |
−0.301676 | + | 0.953410i | \(0.597546\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.3699 | − | 13.2870i | 0.466119 | − | 0.544713i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.5111 | 1.28751 | 0.643754 | − | 0.765232i | \(-0.277376\pi\) | ||||
0.643754 | + | 0.765232i | \(0.277376\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.28520 | 0.297169 | 0.148585 | − | 0.988900i | \(-0.452528\pi\) | ||||
0.148585 | + | 0.988900i | \(0.452528\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.19805 | − | 6.07451i | 0.211331 | − | 0.246964i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.1836 | + | 28.1836i | 1.14394 | + | 1.14394i | 0.987723 | + | 0.156213i | \(0.0499285\pi\) |
0.156213 | + | 0.987723i | \(0.450071\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.2176 | −0.656095 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.9782 | + | 24.9782i | 1.00886 | + | 1.00886i | 0.999960 | + | 0.00890069i | \(0.00283322\pi\) |
0.00890069 | + | 0.999960i | \(0.497167\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.7928 | − | 19.7928i | 0.796830 | − | 0.796830i | −0.185764 | − | 0.982594i | \(-0.559476\pi\) |
0.982594 | + | 0.185764i | \(0.0594761\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.0717 | 1.00772 | 0.503859 | − | 0.863786i | \(-0.331913\pi\) | ||||
0.503859 | + | 0.863786i | \(0.331913\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.6417 | − | 15.6417i | −0.626672 | − | 0.626672i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.8054 | + | 7.63561i | −0.952216 | + | 0.305424i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 21.5432i | − | 0.858984i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.42730 | −0.255867 | −0.127933 | − | 0.991783i | \(-0.540834\pi\) | ||||
−0.127933 | + | 0.991783i | \(0.540834\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.88919 | + | 0.224641i | −0.114654 | + | 0.00891460i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.98662 | + | 1.98662i | −0.0787126 | + | 0.0787126i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.9552i | 1.14366i | 0.820372 | + | 0.571830i | \(0.193766\pi\) | ||||
−0.820372 | + | 0.571830i | \(0.806234\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.0962 | − | 20.0962i | −0.792517 | − | 0.792517i | 0.189385 | − | 0.981903i | \(-0.439350\pi\) |
−0.981903 | + | 0.189385i | \(0.939350\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.5740 | − | 27.5740i | 1.08405 | − | 1.08405i | 0.0879193 | − | 0.996128i | \(-0.471978\pi\) |
0.996128 | − | 0.0879193i | \(-0.0280218\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.85034i | 0.268899i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.8261 | − | 17.8261i | 0.697590 | − | 0.697590i | −0.266300 | − | 0.963890i | \(-0.585801\pi\) |
0.963890 | + | 0.266300i | \(0.0858013\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.4010 | − | 33.1898i | 1.10972 | − | 1.29683i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.7533i | 1.47066i | 0.677709 | + | 0.735331i | \(0.262973\pi\) | ||||
−0.677709 | + | 0.735331i | \(0.737027\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.03049i | 0.234559i | 0.993099 | + | 0.117279i | \(0.0374173\pi\) | ||||
−0.993099 | + | 0.117279i | \(0.962583\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17.0869 | + | 1.32855i | −0.662603 | + | 0.0515188i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.20701 | + | 3.20701i | −0.124176 | + | 0.124176i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 25.8632i | − | 0.998439i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.75403 | − | 3.75403i | 0.144707 | − | 0.144707i | −0.631042 | − | 0.775749i | \(-0.717372\pi\) |
0.775749 | + | 0.631042i | \(0.217372\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.0579 | + | 12.0579i | 0.463421 | + | 0.463421i | 0.899775 | − | 0.436354i | \(-0.143730\pi\) |
−0.436354 | + | 0.899775i | \(0.643730\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.97052i | 0.152375i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.0083 | − | 18.0083i | 0.689068 | − | 0.689068i | −0.272958 | − | 0.962026i | \(-0.588002\pi\) |
0.962026 | + | 0.272958i | \(0.0880020\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.87922 | − | 24.1694i | −0.0718015 | − | 0.923467i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.0917 | −0.422560 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 37.0052i | − | 1.40774i | −0.710327 | − | 0.703872i | \(-0.751453\pi\) | ||
0.710327 | − | 0.703872i | \(-0.248547\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.4015 | − | 25.0102i | 0.811807 | − | 0.948689i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.7046 | − | 31.7046i | −1.20090 | − | 1.20090i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.8810 | −0.410968 | −0.205484 | − | 0.978660i | \(-0.565877\pi\) | ||||
−0.205484 | + | 0.978660i | \(0.565877\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.9292 | + | 14.9292i | −0.563067 | + | 0.563067i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.91179 | − | 8.91179i | −0.335162 | − | 0.335162i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.9836 | 0.675389 | 0.337695 | − | 0.941256i | \(-0.390353\pi\) | ||||
0.337695 | + | 0.941256i | \(0.390353\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.94295 | − | 4.94295i | −0.185115 | − | 0.185115i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.36749 | − | 0.572838i | 0.275529 | − | 0.0214229i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.0959 | 1.19698 | 0.598488 | − | 0.801132i | \(-0.295769\pi\) | ||||
0.598488 | + | 0.801132i | \(0.295769\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.43759 | −0.351474 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.3052 | − | 3.95900i | 0.939811 | − | 0.147033i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.2813 | − | 15.2813i | −0.566754 | − | 0.566754i | 0.364464 | − | 0.931218i | \(-0.381252\pi\) |
−0.931218 | + | 0.364464i | \(0.881252\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.0192 | 1.07332 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.4494 | − | 25.4494i | −0.939996 | − | 0.939996i | 0.0583028 | − | 0.998299i | \(-0.481431\pi\) |
−0.998299 | + | 0.0583028i | \(0.981431\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27.0115 | − | 27.0115i | 0.994980 | − | 0.994980i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.6936 | 0.871584 | 0.435792 | − | 0.900047i | \(-0.356468\pi\) | ||||
0.435792 | + | 0.900047i | \(0.356468\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.4630 | − | 10.4630i | −0.383852 | − | 0.383852i | 0.488636 | − | 0.872488i | \(-0.337495\pi\) |
−0.872488 | + | 0.488636i | \(0.837495\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.5546 | − | 22.7232i | −0.972886 | − | 0.832513i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 19.8836i | − | 0.726532i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −51.4858 | −1.87874 | −0.939372 | − | 0.342899i | \(-0.888591\pi\) | ||||
−0.939372 | + | 0.342899i | \(0.888591\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.5710 | + | 29.8826i | −0.930623 | + | 1.08754i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.4014 | + | 20.4014i | −0.741501 | + | 0.741501i | −0.972867 | − | 0.231366i | \(-0.925681\pi\) |
0.231366 | + | 0.972867i | \(0.425681\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 13.3989i | − | 0.485709i | −0.970063 | − | 0.242855i | \(-0.921916\pi\) | ||
0.970063 | − | 0.242855i | \(-0.0780838\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.27933 | + | 8.27933i | 0.299732 | + | 0.299732i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.15611 | − | 2.15611i | 0.0778526 | − | 0.0778526i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.5493i | 0.560721i | 0.959895 | + | 0.280361i | \(0.0904540\pi\) | ||||
−0.959895 | + | 0.280361i | \(0.909546\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.70360 | + | 4.70360i | −0.169177 | + | 0.169177i | −0.786617 | − | 0.617441i | \(-0.788170\pi\) |
0.617441 | + | 0.786617i | \(0.288170\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.10198 | + | 39.0028i | 0.219190 | + | 1.40102i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 43.9420i | 1.57439i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.98561i | 0.214182i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.86388 | − | 23.9721i | −0.0665248 | − | 0.855601i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.45088 | + | 7.45088i | −0.265595 | + | 0.265595i | −0.827322 | − | 0.561727i | \(-0.810137\pi\) |
0.561727 | + | 0.827322i | \(0.310137\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.09810i | 0.0390439i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.14032 | + | 8.14032i | −0.289071 | + | 0.289071i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.5898 | + | 27.5898i | 0.977280 | + | 0.977280i | 0.999748 | − | 0.0224677i | \(-0.00715228\pi\) |
−0.0224677 | + | 0.999748i | \(0.507152\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 48.3211i | − | 1.70948i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.5661 | + | 15.5661i | −0.549317 | + | 0.549317i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.25531 | + | 2.78562i | 0.114735 | + | 0.0981802i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.93002 | 0.349121 | 0.174560 | − | 0.984646i | \(-0.444150\pi\) | ||||
0.174560 | + | 0.984646i | \(0.444150\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.144213i | 0.00506400i | 0.999997 | + | 0.00253200i | \(0.000805962\pi\) | ||||
−0.999997 | + | 0.00253200i | \(0.999194\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 26.9115 | − | 2.09243i | 0.942670 | − | 0.0732946i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.1100 | − | 20.1100i | −0.703562 | − | 0.703562i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.3654 | 0.710757 | 0.355379 | − | 0.934722i | \(-0.384352\pi\) | ||||
0.355379 | + | 0.934722i | \(0.384352\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.7594 | − | 31.7594i | 1.10706 | − | 1.10706i | 0.113529 | − | 0.993535i | \(-0.463784\pi\) |
0.993535 | − | 0.113529i | \(-0.0362156\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.5251 | + | 28.5251i | 0.991916 | + | 0.991916i | 0.999968 | − | 0.00805118i | \(-0.00256280\pi\) |
−0.00805118 | + | 0.999968i | \(0.502563\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −54.4189 | −1.89005 | −0.945024 | − | 0.327002i | \(-0.893962\pi\) | ||||
−0.945024 | + | 0.327002i | \(0.893962\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.91921 | − | 5.91921i | −0.205088 | − | 0.205088i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.49782 | + | 19.2641i | 0.0518343 | + | 0.666661i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47.3060 | −1.63318 | −0.816592 | − | 0.577215i | \(-0.804139\pi\) | ||||
−0.816592 | + | 0.577215i | \(0.804139\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.75894 | 0.0951360 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.5871 | + | 16.7610i | 0.673818 | + | 0.576596i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.47147 | + | 5.47147i | 0.188002 | + | 0.188002i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.27809 | 0.180931 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.9083 | + | 14.9083i | 0.510449 | + | 0.510449i | 0.914664 | − | 0.404215i | \(-0.132455\pi\) |
−0.404215 | + | 0.914664i | \(0.632455\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.64085 | + | 6.64085i | −0.226847 | + | 0.226847i | −0.811374 | − | 0.584527i | \(-0.801280\pi\) |
0.584527 | + | 0.811374i | \(0.301280\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.27984 | −0.111907 | −0.0559534 | − | 0.998433i | \(-0.517820\pi\) | ||||
−0.0559534 | + | 0.998433i | \(0.517820\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.7285 | − | 11.7285i | −0.399243 | − | 0.399243i | 0.478723 | − | 0.877966i | \(-0.341100\pi\) |
−0.877966 | + | 0.478723i | \(0.841100\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.145541 | − | 1.87186i | −0.00494854 | − | 0.0636451i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 34.7619i | − | 1.17922i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.0034 | −0.576139 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.58180 | − | 23.5433i | −0.188699 | − | 0.795910i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.6401 | − | 27.6401i | 0.933339 | − | 0.933339i | −0.0645744 | − | 0.997913i | \(-0.520569\pi\) |
0.997913 | + | 0.0645744i | \(0.0205690\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 37.9900i | − | 1.27991i | −0.768410 | − | 0.639957i | \(-0.778952\pi\) | ||
0.768410 | − | 0.639957i | \(-0.221048\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.6777 | − | 33.6777i | −1.13335 | − | 1.13335i | −0.989617 | − | 0.143729i | \(-0.954091\pi\) |
−0.143729 | − | 0.989617i | \(-0.545909\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.17366 | + | 1.17366i | −0.0394078 | + | 0.0394078i | −0.726536 | − | 0.687128i | \(-0.758871\pi\) |
0.687128 | + | 0.726536i | \(0.258871\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 2.80471i | − | 0.0940671i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.4861 | + | 33.4861i | −1.12057 | + | 1.12057i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.3570 | − | 16.5641i | −0.647034 | − | 0.553676i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 40.4452i | − | 1.34892i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 33.0482i | − | 1.10099i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.4263 | + | 10.6333i | 0.413064 | + | 0.353464i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.4248 | + | 16.4248i | −0.545377 | + | 0.545377i | −0.925100 | − | 0.379723i | \(-0.876019\pi\) |
0.379723 | + | 0.925100i | \(0.376019\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 32.3497i | − | 1.07179i | −0.844284 | − | 0.535897i | \(-0.819974\pi\) | ||
0.844284 | − | 0.535897i | \(-0.180026\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.75676 | + | 9.75676i | −0.322902 | + | 0.322902i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 29.8950 | + | 29.8950i | 0.987219 | + | 0.987219i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 5.60588i | − | 0.184921i | −0.995716 | − | 0.0924605i | \(-0.970527\pi\) | ||
0.995716 | − | 0.0924605i | \(-0.0294732\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.88394 | − | 1.88394i | 0.0620106 | − | 0.0620106i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.0815 | − | 17.5658i | −0.791794 | − | 0.577559i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.7413 | 1.13983 | 0.569913 | − | 0.821705i | \(-0.306977\pi\) | ||||
0.569913 | + | 0.821705i | \(0.306977\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.20391i | 0.268872i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.70680 | + | 21.9518i | 0.0558182 | + | 0.717899i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.80471 | + | 5.80471i | 0.189632 | + | 0.189632i | 0.795537 | − | 0.605905i | \(-0.207189\pi\) |
−0.605905 | + | 0.795537i | \(0.707189\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.7893 | −0.775510 | −0.387755 | − | 0.921762i | \(-0.626749\pi\) | ||||
−0.387755 | + | 0.921762i | \(0.626749\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.76765 | − | 7.76765i | 0.252949 | − | 0.252949i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.4008 | + | 12.4008i | 0.402972 | + | 0.402972i | 0.879279 | − | 0.476307i | \(-0.158025\pi\) |
−0.476307 | + | 0.879279i | \(0.658025\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.79872 | 0.318080 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.46081 | + | 4.46081i | 0.144500 | + | 0.144500i | 0.775656 | − | 0.631156i | \(-0.217419\pi\) |
−0.631156 | + | 0.775656i | \(0.717419\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.25713 | + | 1.93146i | 0.0730390 | + | 0.0625006i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 23.4627 | 0.757651 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.3380 | 1.01090 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.82801 | − | 36.3722i | −0.0910369 | − | 1.17086i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.74162 | − | 2.74162i | −0.0881645 | − | 0.0881645i | 0.661649 | − | 0.749814i | \(-0.269857\pi\) |
−0.749814 | + | 0.661649i | \(0.769857\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.5455 | −0.338421 | −0.169210 | − | 0.985580i | \(-0.554122\pi\) | ||||
−0.169210 | + | 0.985580i | \(0.554122\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.5273 | + | 22.5273i | 0.722193 | + | 0.722193i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.3372 | − | 13.3372i | 0.426695 | − | 0.426695i | −0.460806 | − | 0.887501i | \(-0.652440\pi\) |
0.887501 | + | 0.460806i | \(0.152440\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.8513 | 0.890133 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.84412 | + | 3.84412i | 0.122608 | + | 0.122608i | 0.765749 | − | 0.643140i | \(-0.222369\pi\) |
−0.643140 | + | 0.765749i | \(0.722369\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 51.0745 | − | 3.97115i | 1.62737 | − | 0.126531i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.10972i | 0.226076i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.9248 | −1.10942 | −0.554711 | − | 0.832043i | \(-0.687171\pi\) | ||||
−0.554711 | + | 0.832043i | \(0.687171\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.3532 | − | 8.85937i | −0.328218 | − | 0.280861i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.0217 | + | 11.0217i | −0.349062 | + | 0.349062i | −0.859760 | − | 0.510698i | \(-0.829387\pi\) |
0.510698 | + | 0.859760i | \(0.329387\pi\) | |||||||
\(998\) | 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 | 1440.2.bj.a.17.5 | 48 | ||
3.2 | odd | 2 | inner | 1440.2.bj.a.17.20 | 48 | ||
4.3 | odd | 2 | 360.2.x.a.197.22 | yes | 48 | ||
5.3 | odd | 4 | inner | 1440.2.bj.a.593.6 | 48 | ||
8.3 | odd | 2 | 360.2.x.a.197.10 | yes | 48 | ||
8.5 | even | 2 | inner | 1440.2.bj.a.17.19 | 48 | ||
12.11 | even | 2 | 360.2.x.a.197.3 | yes | 48 | ||
15.8 | even | 4 | inner | 1440.2.bj.a.593.19 | 48 | ||
20.3 | even | 4 | 360.2.x.a.53.15 | yes | 48 | ||
24.5 | odd | 2 | inner | 1440.2.bj.a.17.6 | 48 | ||
24.11 | even | 2 | 360.2.x.a.197.15 | yes | 48 | ||
40.3 | even | 4 | 360.2.x.a.53.3 | ✓ | 48 | ||
40.13 | odd | 4 | inner | 1440.2.bj.a.593.20 | 48 | ||
60.23 | odd | 4 | 360.2.x.a.53.10 | yes | 48 | ||
120.53 | even | 4 | inner | 1440.2.bj.a.593.5 | 48 | ||
120.83 | odd | 4 | 360.2.x.a.53.22 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.x.a.53.3 | ✓ | 48 | 40.3 | even | 4 | ||
360.2.x.a.53.10 | yes | 48 | 60.23 | odd | 4 | ||
360.2.x.a.53.15 | yes | 48 | 20.3 | even | 4 | ||
360.2.x.a.53.22 | yes | 48 | 120.83 | odd | 4 | ||
360.2.x.a.197.3 | yes | 48 | 12.11 | even | 2 | ||
360.2.x.a.197.10 | yes | 48 | 8.3 | odd | 2 | ||
360.2.x.a.197.15 | yes | 48 | 24.11 | even | 2 | ||
360.2.x.a.197.22 | yes | 48 | 4.3 | odd | 2 | ||
1440.2.bj.a.17.5 | 48 | 1.1 | even | 1 | trivial | ||
1440.2.bj.a.17.6 | 48 | 24.5 | odd | 2 | inner | ||
1440.2.bj.a.17.19 | 48 | 8.5 | even | 2 | inner | ||
1440.2.bj.a.17.20 | 48 | 3.2 | odd | 2 | inner | ||
1440.2.bj.a.593.5 | 48 | 120.53 | even | 4 | inner | ||
1440.2.bj.a.593.6 | 48 | 5.3 | odd | 4 | inner | ||
1440.2.bj.a.593.19 | 48 | 15.8 | even | 4 | inner | ||
1440.2.bj.a.593.20 | 48 | 40.13 | odd | 4 | inner |