Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2700,2,Mod(901,2700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2700, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2700.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2700.i (of order \(3\), 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: | \(21.5596085457\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.142635249.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 3x^{6} + 3x^{5} - 11x^{4} + 6x^{3} + 12x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{5} \) |
Twist minimal: | no (minimal twist has level 900) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1801.1 | ||
Root | \(0.620769 + 1.27069i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2700.1801 |
Dual form | 2700.2.i.e.901.1 |
$q$-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 \(\left(\mathbb{Z}/2700\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1351\) | \(2377\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.70089 | + | 2.94604i | −0.642878 | + | 1.11350i | 0.341910 | + | 0.939733i | \(0.388926\pi\) |
−0.984787 | + | 0.173764i | \(0.944407\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.20089 | + | 3.81206i | −0.663595 | + | 1.14938i | 0.316070 | + | 0.948736i | \(0.397637\pi\) |
−0.979664 | + | 0.200644i | \(0.935697\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.03160 | + | 1.78679i | 0.286115 | + | 0.495565i | 0.972879 | − | 0.231315i | \(-0.0743028\pi\) |
−0.686764 | + | 0.726880i | \(0.740969\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.40179 | −0.339984 | −0.169992 | − | 0.985445i | \(-0.554374\pi\) | ||||
−0.169992 | + | 0.985445i | \(0.554374\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.35717 | −1.45843 | −0.729217 | − | 0.684283i | \(-0.760115\pi\) | ||||
−0.729217 | + | 0.684283i | \(0.760115\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.0539129 | − | 0.0933799i | −0.0112416 | − | 0.0194711i | 0.860350 | − | 0.509704i | \(-0.170245\pi\) |
−0.871591 | + | 0.490233i | \(0.836912\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.54089 | − | 7.86505i | 0.843222 | − | 1.46050i | −0.0439339 | − | 0.999034i | \(-0.513989\pi\) |
0.887156 | − | 0.461469i | \(-0.152678\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.53160 | − | 2.65281i | −0.275084 | − | 0.476459i | 0.695073 | − | 0.718940i | \(-0.255372\pi\) |
−0.970156 | + | 0.242481i | \(0.922039\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.95538 | −0.321462 | −0.160731 | − | 0.986998i | \(-0.551385\pi\) | ||||
−0.160731 | + | 0.986998i | \(0.551385\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.34788 | − | 7.53074i | −0.679024 | − | 1.17610i | −0.975275 | − | 0.220994i | \(-0.929070\pi\) |
0.296251 | − | 0.955110i | \(-0.404264\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.56320 | + | 6.17165i | −0.543383 | + | 0.941167i | 0.455323 | + | 0.890326i | \(0.349524\pi\) |
−0.998707 | + | 0.0508414i | \(0.983810\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.74179 | − | 6.48096i | 0.545795 | − | 0.945345i | −0.452761 | − | 0.891632i | \(-0.649561\pi\) |
0.998556 | − | 0.0537135i | \(-0.0171058\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.28608 | − | 3.95961i | −0.326583 | − | 0.565659i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.0975 | 1.79909 | 0.899543 | − | 0.436833i | \(-0.143900\pi\) | ||||
0.899543 | + | 0.436833i | \(0.143900\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.58966 | − | 11.4136i | −0.857901 | − | 1.48593i | −0.873928 | − | 0.486056i | \(-0.838435\pi\) |
0.0160267 | − | 0.999872i | \(-0.494898\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.862308 | − | 1.49356i | 0.110407 | − | 0.191231i | −0.805527 | − | 0.592559i | \(-0.798118\pi\) |
0.915935 | + | 0.401328i | \(0.131451\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.18787 | − | 10.7177i | −0.755969 | − | 1.30938i | −0.944891 | − | 0.327385i | \(-0.893833\pi\) |
0.188922 | − | 0.981992i | \(-0.439501\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.50961 | 0.891227 | 0.445614 | − | 0.895225i | \(-0.352986\pi\) | ||||
0.445614 | + | 0.895225i | \(0.352986\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.42037 | 0.634406 | 0.317203 | − | 0.948358i | \(-0.397256\pi\) | ||||
0.317203 | + | 0.948358i | \(0.397256\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.48698 | − | 12.9678i | −0.853220 | − | 1.47782i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.71806 | + | 8.17193i | −0.530824 | + | 0.919413i | 0.468529 | + | 0.883448i | \(0.344784\pi\) |
−0.999353 | + | 0.0359656i | \(0.988549\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.48698 | + | 7.77167i | −0.492510 | + | 0.853052i | −0.999963 | − | 0.00862744i | \(-0.997254\pi\) |
0.507453 | + | 0.861679i | \(0.330587\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.01576 | −0.425670 | −0.212835 | − | 0.977088i | \(-0.568270\pi\) | ||||
−0.212835 | + | 0.977088i | \(0.568270\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.01858 | −0.735747 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.08551 | − | 1.88017i | 0.110217 | − | 0.190902i | −0.805641 | − | 0.592405i | \(-0.798179\pi\) |
0.915858 | + | 0.401503i | \(0.131512\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.48698 | − | 2.57552i | 0.147960 | − | 0.256274i | −0.782513 | − | 0.622634i | \(-0.786063\pi\) |
0.930473 | + | 0.366360i | \(0.119396\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.31768 | + | 5.74640i | 0.326901 | + | 0.566209i | 0.981895 | − | 0.189425i | \(-0.0606622\pi\) |
−0.654994 | + | 0.755634i | \(0.727329\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.7878 | 1.33292 | 0.666459 | − | 0.745541i | \(-0.267809\pi\) | ||||
0.666459 | + | 0.745541i | \(0.267809\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.1347 | −1.73699 | −0.868495 | − | 0.495699i | \(-0.834912\pi\) | ||||
−0.868495 | + | 0.495699i | \(0.834912\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.0408909 | + | 0.0708250i | 0.00384669 | + | 0.00666266i | 0.867942 | − | 0.496665i | \(-0.165442\pi\) |
−0.864096 | + | 0.503328i | \(0.832109\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.38429 | − | 4.12972i | 0.218568 | − | 0.378571i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.18787 | − | 7.25361i | −0.380716 | − | 0.659419i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.5811 | −1.91501 | −0.957507 | − | 0.288410i | \(-0.906873\pi\) | ||||
−0.957507 | + | 0.288410i | \(0.906873\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.39391 | − | 9.34253i | −0.471268 | − | 0.816260i | 0.528192 | − | 0.849125i | \(-0.322870\pi\) |
−0.999460 | + | 0.0328649i | \(0.989537\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.8129 | − | 18.7284i | 0.937594 | − | 1.62396i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.75481 | + | 11.6997i | −0.577102 | + | 0.999570i | 0.418708 | + | 0.908121i | \(0.362483\pi\) |
−0.995810 | + | 0.0914491i | \(0.970850\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.30499 | − | 12.6526i | −0.619601 | − | 1.07318i | −0.989559 | − | 0.144132i | \(-0.953961\pi\) |
0.369958 | − | 0.929049i | \(-0.379372\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.08178 | −0.759457 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.0669350 | + | 0.115935i | 0.00548353 | + | 0.00949775i | 0.868754 | − | 0.495244i | \(-0.164921\pi\) |
−0.863271 | + | 0.504741i | \(0.831588\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.07249 | + | 5.32171i | −0.250036 | + | 0.433075i | −0.963535 | − | 0.267581i | \(-0.913776\pi\) |
0.713500 | + | 0.700656i | \(0.247109\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.38736 | + | 12.7953i | 0.589575 | + | 1.02117i | 0.994288 | + | 0.106730i | \(0.0340382\pi\) |
−0.404713 | + | 0.914444i | \(0.632628\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.366801 | 0.0289079 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.9451 | 1.24892 | 0.624458 | − | 0.781058i | \(-0.285320\pi\) | ||||
0.624458 | + | 0.781058i | \(0.285320\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.2497 | − | 17.7529i | −0.793143 | − | 1.37376i | −0.924012 | − | 0.382364i | \(-0.875110\pi\) |
0.130869 | − | 0.991400i | \(-0.458223\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.37160 | − | 7.57183i | 0.336277 | − | 0.582448i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.2957 | + | 19.5647i | −0.858796 | + | 1.48748i | 0.0142821 | + | 0.999898i | \(0.495454\pi\) |
−0.873078 | + | 0.487580i | \(0.837880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.5879 | −1.53881 | −0.769407 | − | 0.638759i | \(-0.779448\pi\) | ||||
−0.769407 | + | 0.638759i | \(0.779448\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.32830 | −0.619038 | −0.309519 | − | 0.950893i | \(-0.600168\pi\) | ||||
−0.309519 | + | 0.950893i | \(0.600168\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.08519 | − | 5.34370i | 0.225611 | − | 0.390770i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.39217 | + | 7.60747i | −0.317807 | + | 0.550457i | −0.980030 | − | 0.198849i | \(-0.936280\pi\) |
0.662224 | + | 0.749306i | \(0.269613\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.61538 | + | 6.26202i | 0.260241 | + | 0.450750i | 0.966306 | − | 0.257397i | \(-0.0828647\pi\) |
−0.706065 | + | 0.708147i | \(0.749531\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.17932 | −0.297764 | −0.148882 | − | 0.988855i | \(-0.547568\pi\) | ||||
−0.148882 | + | 0.988855i | \(0.547568\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.6518 | 1.10953 | 0.554763 | − | 0.832009i | \(-0.312809\pi\) | ||||
0.554763 | + | 0.832009i | \(0.312809\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.4472 | + | 26.7553i | 1.08418 | + | 1.87785i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.9914 | − | 24.2339i | 0.967809 | − | 1.67629i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0770 | + | 20.9179i | 0.831412 | + | 1.44005i | 0.896918 | + | 0.442196i | \(0.145801\pi\) |
−0.0655057 | + | 0.997852i | \(0.520866\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.4204 | 0.707381 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.44609 | − | 2.50470i | −0.0972743 | − | 0.168484i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.723206 | − | 1.25263i | 0.0484295 | − | 0.0838823i | −0.840794 | − | 0.541354i | \(-0.817912\pi\) |
0.889224 | + | 0.457472i | \(0.151245\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.2627 | + | 17.7755i | −0.681158 | + | 1.17980i | 0.293469 | + | 0.955969i | \(0.405190\pi\) |
−0.974628 | + | 0.223832i | \(0.928143\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.4743 | − | 18.1420i | −0.692160 | − | 1.19886i | −0.971129 | − | 0.238556i | \(-0.923326\pi\) |
0.278969 | − | 0.960300i | \(-0.410007\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.90112 | −0.648644 | −0.324322 | − | 0.945947i | \(-0.605136\pi\) | ||||
−0.324322 | + | 0.945947i | \(0.605136\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.05391 | + | 5.28953i | 0.197541 | + | 0.342151i | 0.947731 | − | 0.319072i | \(-0.103371\pi\) |
−0.750189 | + | 0.661223i | \(0.770038\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.148392 | − | 0.257022i | 0.00955875 | − | 0.0165562i | −0.861206 | − | 0.508255i | \(-0.830291\pi\) |
0.870765 | + | 0.491699i | \(0.163624\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.55806 | − | 11.3589i | −0.417279 | − | 0.722749i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.51643 | 0.285075 | 0.142537 | − | 0.989789i | \(-0.454474\pi\) | ||||
0.142537 | + | 0.989789i | \(0.454474\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.474626 | 0.0298395 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.79911 | − | 11.7764i | −0.424117 | − | 0.734591i | 0.572221 | − | 0.820100i | \(-0.306082\pi\) |
−0.996337 | + | 0.0855081i | \(0.972749\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.32589 | − | 5.76061i | 0.206661 | − | 0.357947i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.56179 | − | 6.16921i | 0.219630 | − | 0.380409i | −0.735065 | − | 0.677996i | \(-0.762848\pi\) |
0.954695 | + | 0.297587i | \(0.0961818\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.80358 | −0.536764 | −0.268382 | − | 0.963313i | \(-0.586489\pi\) | ||||
−0.268382 | + | 0.963313i | \(0.586489\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.95885 | −0.604957 | −0.302478 | − | 0.953156i | \(-0.597814\pi\) | ||||
−0.302478 | + | 0.953156i | \(0.597814\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.46467 | + | 7.73303i | −0.268256 | + | 0.464633i | −0.968411 | − | 0.249358i | \(-0.919781\pi\) |
0.700156 | + | 0.713990i | \(0.253114\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.0402 | − | 27.7825i | 0.956879 | − | 1.65736i | 0.226872 | − | 0.973925i | \(-0.427150\pi\) |
0.730008 | − | 0.683439i | \(-0.239516\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.18373 | − | 5.51437i | −0.189253 | − | 0.327796i | 0.755749 | − | 0.654862i | \(-0.227273\pi\) |
−0.945001 | + | 0.327066i | \(0.893940\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 29.5811 | 1.74612 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0350 | −0.884411 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.9506 | − | 24.1631i | −0.815000 | − | 1.41162i | −0.909328 | − | 0.416081i | \(-0.863403\pi\) |
0.0943273 | − | 0.995541i | \(-0.469930\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.111233 | − | 0.192662i | 0.00643278 | − | 0.0111419i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.1213 | − | 20.9946i | −0.698658 | − | 1.21011i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.2054 | 0.696597 | 0.348299 | − | 0.937384i | \(-0.386760\pi\) | ||||
0.348299 | + | 0.937384i | \(0.386760\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.45123 | − | 4.24565i | −0.138996 | − | 0.240749i | 0.788121 | − | 0.615521i | \(-0.211054\pi\) |
−0.927117 | + | 0.374772i | \(0.877721\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.79429 | + | 15.2322i | −0.497083 | + | 0.860972i | −0.999994 | − | 0.00336551i | \(-0.998929\pi\) |
0.502912 | + | 0.864338i | \(0.332262\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.78608 | + | 16.9500i | −0.549641 | + | 0.952007i | 0.448658 | + | 0.893704i | \(0.351902\pi\) |
−0.998299 | + | 0.0583028i | \(0.981431\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.9880 | + | 34.6203i | 1.11912 | + | 1.93836i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.91140 | 0.495844 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.7288 | + | 22.0469i | 0.701759 | + | 1.21548i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.29537 | + | 12.6360i | −0.400990 | + | 0.694535i | −0.993846 | − | 0.110774i | \(-0.964667\pi\) |
0.592856 | + | 0.805309i | \(0.298000\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.95429 | − | 8.58108i | −0.269877 | − | 0.467441i | 0.698953 | − | 0.715168i | \(-0.253650\pi\) |
−0.968830 | + | 0.247727i | \(0.920317\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.4836 | 0.730176 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.25897 | −0.445943 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.16000 | − | 8.93739i | −0.277004 | − | 0.479784i | 0.693635 | − | 0.720327i | \(-0.256008\pi\) |
−0.970639 | + | 0.240542i | \(0.922675\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.56767 | + | 14.8396i | −0.458617 | + | 0.794348i | −0.998888 | − | 0.0471429i | \(-0.984988\pi\) |
0.540271 | + | 0.841491i | \(0.318322\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.63055 | − | 11.4845i | 0.352909 | − | 0.611256i | −0.633849 | − | 0.773457i | \(-0.718526\pi\) |
0.986758 | + | 0.162201i | \(0.0518593\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.2817 | −0.753758 | −0.376879 | − | 0.926263i | \(-0.623003\pi\) | ||||
−0.376879 | + | 0.926263i | \(0.623003\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.4136 | 1.12703 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.79056 | − | 8.29749i | 0.250065 | − | 0.433125i | −0.713478 | − | 0.700677i | \(-0.752881\pi\) |
0.963543 | + | 0.267552i | \(0.0862147\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.2775 | + | 38.5858i | −1.15659 | + | 2.00328i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.0529 | − | 20.8763i | −0.624076 | − | 1.08093i | −0.988719 | − | 0.149784i | \(-0.952142\pi\) |
0.364642 | − | 0.931148i | \(-0.381191\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.7376 | 0.965033 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.73973 | 0.140730 | 0.0703651 | − | 0.997521i | \(-0.477584\pi\) | ||||
0.0703651 | + | 0.997521i | \(0.477584\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.6766 | − | 18.4924i | −0.545548 | − | 0.944917i | −0.998572 | − | 0.0534187i | \(-0.982988\pi\) |
0.453024 | − | 0.891498i | \(-0.350345\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.33485 | + | 12.7043i | −0.371892 | + | 0.644136i | −0.989857 | − | 0.142070i | \(-0.954624\pi\) |
0.617965 | + | 0.786206i | \(0.287957\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0755745 | + | 0.130899i | 0.00382197 | + | 0.00661984i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.43065 | −0.322745 | −0.161373 | − | 0.986894i | \(-0.551592\pi\) | ||||
−0.161373 | + | 0.986894i | \(0.551592\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.03748 | + | 15.6534i | 0.451310 | + | 0.781693i | 0.998468 | − | 0.0553373i | \(-0.0176234\pi\) |
−0.547157 | + | 0.837030i | \(0.684290\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.16000 | − | 5.47329i | 0.157411 | − | 0.272644i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.30358 | − | 7.45402i | 0.213320 | − | 0.369482i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.39532 | + | 16.2732i | 0.464569 | + | 0.804657i | 0.999182 | − | 0.0404403i | \(-0.0128761\pi\) |
−0.534613 | + | 0.845097i | \(0.679543\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 44.8333 | 2.20610 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.8297 | + | 34.3461i | 0.968745 | + | 1.67792i | 0.699198 | + | 0.714928i | \(0.253540\pi\) |
0.269547 | + | 0.962987i | \(0.413126\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.7682 | − | 32.5076i | 0.914708 | − | 1.58432i | 0.107380 | − | 0.994218i | \(-0.465754\pi\) |
0.807328 | − | 0.590103i | \(-0.200913\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.93339 | + | 5.08078i | 0.141957 | + | 0.245876i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.7357 | −0.806132 | −0.403066 | − | 0.915171i | \(-0.632055\pi\) | ||||
−0.403066 | + | 0.915171i | \(0.632055\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.0008 | −1.00924 | −0.504618 | − | 0.863343i | \(-0.668367\pi\) | ||||
−0.504618 | + | 0.863343i | \(0.668367\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.342733 | + | 0.593631i | 0.0163952 | + | 0.0283972i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.01576 | − | 5.22345i | 0.143934 | − | 0.249302i | −0.785041 | − | 0.619444i | \(-0.787358\pi\) |
0.928975 | + | 0.370143i | \(0.120691\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.16274 | + | 5.47803i | −0.150266 | + | 0.260269i | −0.931325 | − | 0.364188i | \(-0.881346\pi\) |
0.781059 | + | 0.624457i | \(0.214680\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.6594 | 0.880593 | 0.440296 | − | 0.897853i | \(-0.354873\pi\) | ||||
0.440296 | + | 0.897853i | \(0.354873\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 38.2769 | 1.80239 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.7923 | + | 23.8889i | −0.645176 | + | 1.11748i | 0.339085 | + | 0.940756i | \(0.389883\pi\) |
−0.984261 | + | 0.176722i | \(0.943451\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.76442 | + | 11.7163i | −0.315051 | + | 0.545684i | −0.979448 | − | 0.201696i | \(-0.935355\pi\) |
0.664398 | + | 0.747379i | \(0.268688\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.7421 | + | 23.8020i | 0.638650 | + | 1.10617i | 0.985729 | + | 0.168338i | \(0.0538402\pi\) |
−0.347079 | + | 0.937836i | \(0.612827\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 32.7515 | 1.51556 | 0.757779 | − | 0.652511i | \(-0.226284\pi\) | ||||
0.757779 | + | 0.652511i | \(0.226284\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 42.0997 | 1.94398 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.6845 | − | 27.1663i | −0.721172 | − | 1.24911i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.92783 | − | 5.07116i | 0.133776 | − | 0.231707i | −0.791353 | − | 0.611359i | \(-0.790623\pi\) |
0.925129 | + | 0.379652i | \(0.123956\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.01717 | − | 3.49384i | −0.0919750 | − | 0.159305i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.4864 | 0.747070 | 0.373535 | − | 0.927616i | \(-0.378146\pi\) | ||||
0.373535 | + | 0.927616i | \(0.378146\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.85302 | − | 11.8698i | −0.309272 | − | 0.535676i | 0.668931 | − | 0.743324i | \(-0.266752\pi\) |
−0.978203 | + | 0.207649i | \(0.933419\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.36537 | + | 11.0251i | −0.286682 | + | 0.496548i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.7731 | + | 22.1236i | −0.572950 | + | 0.992379i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.23482 | − | 3.87082i | −0.100044 | − | 0.173282i | 0.811658 | − | 0.584132i | \(-0.198565\pi\) |
−0.911703 | + | 0.410851i | \(0.865232\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.1010 | −0.807084 | −0.403542 | − | 0.914961i | \(-0.632221\pi\) | ||||
−0.403542 | + | 0.914961i | \(0.632221\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.6044 | − | 18.3674i | −0.470033 | − | 0.814120i | 0.529380 | − | 0.848385i | \(-0.322425\pi\) |
−0.999413 | + | 0.0342644i | \(0.989091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.21947 | + | 15.9686i | −0.407846 | + | 0.706409i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.4705 | + | 28.5278i | 0.724374 | + | 1.25465i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.4507 | 1.24645 | 0.623224 | − | 0.782043i | \(-0.285822\pi\) | ||||
0.623224 | + | 0.782043i | \(0.285822\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.5111 | −1.15925 | −0.579625 | − | 0.814884i | \(-0.696801\pi\) | ||||
−0.579625 | + | 0.814884i | \(0.696801\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.14698 | + | 3.71868i | 0.0935240 | + | 0.161988i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4942 | − | 19.9085i | 0.499747 | − | 0.865588i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.97055 | − | 15.5374i | 0.388558 | − | 0.673001i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.1257 | 0.866876 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.3132 | −0.615372 | −0.307686 | − | 0.951488i | \(-0.599555\pi\) | ||||
−0.307686 | + | 0.951488i | \(0.599555\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.82556 | − | 11.8222i | 0.291840 | − | 0.505482i | −0.682405 | − | 0.730974i | \(-0.739066\pi\) |
0.974245 | + | 0.225493i | \(0.0723992\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.8672 | + | 49.9994i | −1.22978 | + | 2.13005i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.0499 | − | 27.7992i | −0.682509 | − | 1.18214i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.4665 | −0.994306 | −0.497153 | − | 0.867663i | \(-0.665621\pi\) | ||||
−0.497153 | + | 0.867663i | \(0.665621\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.7032 | −0.621880 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.291226 | + | 0.504418i | 0.0122737 | + | 0.0212587i | 0.872097 | − | 0.489333i | \(-0.162760\pi\) |
−0.859823 | + | 0.510592i | \(0.829426\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.77994 | + | 4.81500i | −0.116541 | + | 0.201855i | −0.918395 | − | 0.395665i | \(-0.870514\pi\) |
0.801854 | + | 0.597521i | \(0.203847\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.3706 | + | 19.6945i | 0.475845 | + | 0.824188i | 0.999617 | − | 0.0276708i | \(-0.00880903\pi\) |
−0.523772 | + | 0.851858i | \(0.675476\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.5522 | 1.27191 | 0.635953 | − | 0.771728i | \(-0.280607\pi\) | ||||
0.635953 | + | 0.771728i | \(0.280607\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.2638 | − | 26.4376i | −0.633247 | − | 1.09682i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28.8263 | + | 49.9286i | −1.19386 | + | 2.06783i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.1817 | + | 17.6353i | −0.420245 | + | 0.727886i | −0.995963 | − | 0.0897626i | \(-0.971389\pi\) |
0.575718 | + | 0.817648i | \(0.304722\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.73664 | + | 16.8644i | 0.401191 | + | 0.694884i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.5199 | 0.637326 | 0.318663 | − | 0.947868i | \(-0.396766\pi\) | ||||
0.318663 | + | 0.947868i | \(0.396766\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.6288 | + | 25.3379i | 0.597717 | + | 1.03528i | 0.993157 | + | 0.116785i | \(0.0372588\pi\) |
−0.395440 | + | 0.918492i | \(0.629408\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.15254 | − | 15.8527i | 0.373340 | − | 0.646644i | −0.616737 | − | 0.787169i | \(-0.711546\pi\) |
0.990077 | + | 0.140526i | \(0.0448792\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.42037 | + | 14.5845i | 0.341772 | + | 0.591967i | 0.984762 | − | 0.173908i | \(-0.0556395\pi\) |
−0.642990 | + | 0.765875i | \(0.722306\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.4401 | 0.624640 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.5954 | −0.549113 | −0.274556 | − | 0.961571i | \(-0.588531\pi\) | ||||
−0.274556 | + | 0.961571i | \(0.588531\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.6567 | + | 25.3861i | 0.590056 | + | 1.02201i | 0.994224 | + | 0.107322i | \(0.0342277\pi\) |
−0.404168 | + | 0.914685i | \(0.632439\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.08211 | + | 10.5345i | −0.244461 | + | 0.423418i | −0.961980 | − | 0.273121i | \(-0.911944\pi\) |
0.717519 | + | 0.696539i | \(0.245278\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.83038 | − | 11.8306i | 0.273653 | − | 0.473982i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.74103 | 0.109292 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.45471 | 0.217148 | 0.108574 | − | 0.994088i | \(-0.465371\pi\) | ||||
0.108574 | + | 0.994088i | \(0.465371\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.71665 | − | 8.16948i | 0.186881 | − | 0.323687i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.839996 | + | 1.45492i | −0.0331779 | + | 0.0574657i | −0.882138 | − | 0.470992i | \(-0.843896\pi\) |
0.848960 | + | 0.528458i | \(0.177229\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.84173 | − | 4.92202i | −0.112067 | − | 0.194106i | 0.804537 | − | 0.593903i | \(-0.202414\pi\) |
−0.916603 | + | 0.399797i | \(0.869080\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.3064 | −1.34872 | −0.674361 | − | 0.738401i | \(-0.735581\pi\) | ||||
−0.674361 | + | 0.738401i | \(0.735581\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 58.0126 | 2.27719 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.31486 | − | 10.9377i | −0.247120 | − | 0.428024i | 0.715606 | − | 0.698504i | \(-0.246151\pi\) |
−0.962725 | + | 0.270480i | \(0.912817\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.16697 | + | 5.48535i | −0.123368 | + | 0.213679i | −0.921094 | − | 0.389341i | \(-0.872703\pi\) |
0.797726 | + | 0.603020i | \(0.206036\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.8448 | + | 32.6401i | 0.732978 | + | 1.26955i | 0.955605 | + | 0.294651i | \(0.0952033\pi\) |
−0.222628 | + | 0.974904i | \(0.571463\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.979251 | −0.0379167 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.79570 | + | 6.57434i | 0.146531 | + | 0.253800i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.3273 | − | 26.5477i | 0.590824 | − | 1.02334i | −0.403298 | − | 0.915069i | \(-0.632136\pi\) |
0.994122 | − | 0.108268i | \(-0.0345306\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.4358 | + | 25.0035i | −0.554813 | + | 0.960964i | 0.443105 | + | 0.896470i | \(0.353877\pi\) |
−0.997918 | + | 0.0644945i | \(0.979456\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.69269 | + | 6.39593i | 0.141712 | + | 0.245453i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −47.0352 | −1.79975 | −0.899875 | − | 0.436147i | \(-0.856343\pi\) | ||||
−0.899875 | + | 0.436147i | \(0.856343\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.5114 | + | 23.4025i | 0.514745 | + | 0.891564i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.425186 | + | 0.736443i | −0.0161748 | + | 0.0280156i | −0.874000 | − | 0.485927i | \(-0.838482\pi\) |
0.857825 | + | 0.513942i | \(0.171815\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.09480 | + | 10.5565i | 0.230857 | + | 0.399856i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.6821 | 1.34770 | 0.673848 | − | 0.738870i | \(-0.264640\pi\) | ||||
0.673848 | + | 0.738870i | \(0.264640\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.4307 | 0.468831 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.05838 | + | 8.76138i | 0.190240 | + | 0.329506i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.69543 | + | 13.3289i | −0.289008 | + | 0.500576i | −0.973573 | − | 0.228375i | \(-0.926659\pi\) |
0.684565 | + | 0.728951i | \(0.259992\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.165146 | + | 0.286042i | −0.00618477 | + | 0.0107123i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.5846 | −0.954144 | −0.477072 | − | 0.878864i | \(-0.658302\pi\) | ||||
−0.477072 | + | 0.878864i | \(0.658302\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.5721 | −0.840630 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.06867 | − | 5.31509i | 0.113811 | − | 0.197126i | −0.803493 | − | 0.595314i | \(-0.797028\pi\) |
0.917304 | + | 0.398188i | \(0.130361\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.99486 | − | 8.65135i | 0.184741 | − | 0.319982i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.56520 | + | 4.44306i | 0.0947478 | + | 0.164108i | 0.909503 | − | 0.415697i | \(-0.136462\pi\) |
−0.814756 | + | 0.579805i | \(0.803129\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 54.4754 | 2.00663 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.8784 | 0.694454 | 0.347227 | − | 0.937781i | \(-0.387123\pi\) | ||||
0.347227 | + | 0.937781i | \(0.387123\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.9784 | − | 19.0152i | −0.402759 | − | 0.697600i | 0.591298 | − | 0.806453i | \(-0.298616\pi\) |
−0.994058 | + | 0.108853i | \(0.965282\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.4516 | + | 40.6194i | −0.856904 | + | 1.48420i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.58037 | + | 2.73728i | 0.0576686 | + | 0.0998849i | 0.893418 | − | 0.449225i | \(-0.148300\pi\) |
−0.835750 | + | 0.549110i | \(0.814967\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.1753 | −1.42385 | −0.711926 | − | 0.702255i | \(-0.752177\pi\) | ||||
−0.711926 | + | 0.702255i | \(0.752177\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.03916 | + | 8.72807i | 0.182669 | + | 0.316392i | 0.942789 | − | 0.333391i | \(-0.108193\pi\) |
−0.760119 | + | 0.649783i | \(0.774860\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.8452 | − | 53.4255i | 1.11667 | − | 1.93413i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.5958 | − | 23.5486i | 0.490916 | − | 0.850292i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.5790 | − | 18.3233i | −0.381487 | − | 0.660755i | 0.609788 | − | 0.792565i | \(-0.291255\pi\) |
−0.991275 | + | 0.131810i | \(0.957921\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 43.2543 | 1.55575 | 0.777874 | − | 0.628420i | \(-0.216298\pi\) | ||||
0.777874 | + | 0.628420i | \(0.216298\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.6402 | + | 47.8742i | 0.990312 | + | 1.71527i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.5279 | + | 28.6271i | −0.591414 | + | 1.02436i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.589986 | − | 1.02189i | −0.0210307 | − | 0.0364263i | 0.855318 | − | 0.518103i | \(-0.173361\pi\) |
−0.876349 | + | 0.481676i | \(0.840028\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.278204 | −0.00989180 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.55823 | 0.126357 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.571407 | + | 0.989706i | 0.0202403 | + | 0.0350572i | 0.875968 | − | 0.482369i | \(-0.160224\pi\) |
−0.855728 | + | 0.517426i | \(0.826890\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.24519 | + | 9.08494i | −0.185562 | + | 0.321402i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.9297 | + | 20.6628i | −0.420988 | + | 0.729173i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.3723 | 0.399828 | 0.199914 | − | 0.979813i | \(-0.435934\pi\) | ||||
0.199914 | + | 0.979813i | \(0.435934\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.08590 | 0.0732459 | 0.0366230 | − | 0.999329i | \(-0.488340\pi\) | ||||
0.0366230 | + | 0.999329i | \(0.488340\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.6519 | − | 39.2342i | 0.792489 | − | 1.37263i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.89564 | − | 13.6757i | 0.275560 | − | 0.477284i | −0.694716 | − | 0.719284i | \(-0.744470\pi\) |
0.970276 | + | 0.242000i | \(0.0778034\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.66042 | + | 6.34003i | 0.127594 | + | 0.221000i | 0.922744 | − | 0.385413i | \(-0.125941\pi\) |
−0.795150 | + | 0.606413i | \(0.792608\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.8401 | −0.516040 | −0.258020 | − | 0.966140i | \(-0.583070\pi\) | ||||
−0.258020 | + | 0.966140i | \(0.583070\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.3346 | −0.810444 | −0.405222 | − | 0.914218i | \(-0.632806\pi\) | ||||
−0.405222 | + | 0.914218i | \(0.632806\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.20461 | + | 5.55054i | 0.111033 | + | 0.192315i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.33826 | + | 12.7102i | −0.253345 | + | 0.438806i | −0.964445 | − | 0.264285i | \(-0.914864\pi\) |
0.711100 | + | 0.703091i | \(0.248197\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.7394 | − | 46.3140i | −0.922048 | − | 1.59703i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.4925 | 0.979014 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.105420 | + | 0.182593i | 0.00361375 | + | 0.00625920i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.2611 | − | 21.2369i | 0.419812 | − | 0.727136i | −0.576108 | − | 0.817374i | \(-0.695429\pi\) |
0.995920 | + | 0.0902375i | \(0.0287626\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.79396 | + | 4.83929i | −0.0954400 | + | 0.165307i | −0.909792 | − | 0.415064i | \(-0.863759\pi\) |
0.814352 | + | 0.580371i | \(0.197092\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0309 | + | 34.6946i | 0.683447 | + | 1.18376i | 0.973922 | + | 0.226882i | \(0.0728531\pi\) |
−0.290476 | + | 0.956882i | \(0.593814\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.2157 | −0.926432 | −0.463216 | − | 0.886246i | \(-0.653305\pi\) | ||||
−0.463216 | + | 0.886246i | \(0.653305\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.7679 | − | 35.9711i | −0.704503 | − | 1.22024i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.7668 | − | 22.1128i | 0.432588 | − | 0.749264i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.9399 | − | 20.6806i | −0.403183 | − | 0.698334i | 0.590925 | − | 0.806727i | \(-0.298763\pi\) |
−0.994108 | + | 0.108393i | \(0.965430\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.3585 | −0.955421 | −0.477710 | − | 0.878517i | \(-0.658533\pi\) | ||||
−0.477710 | + | 0.878517i | \(0.658533\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.3449 | −0.953881 | −0.476941 | − | 0.878936i | \(-0.658254\pi\) | ||||
−0.476941 | + | 0.878936i | \(0.658254\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.257544 | − | 0.446080i | −0.00864749 | − | 0.0149779i | 0.861669 | − | 0.507470i | \(-0.169419\pi\) |
−0.870317 | + | 0.492492i | \(0.836086\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.7072 | − | 63.5787i | 1.23112 | − | 2.13236i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −23.7871 | + | 41.2005i | −0.796007 | + | 1.37872i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.8193 | −0.927827 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.3600 | −0.611660 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.08211 | − | 1.87426i | 0.0359308 | − | 0.0622339i | −0.847501 | − | 0.530794i | \(-0.821894\pi\) |
0.883432 | + | 0.468560i | \(0.155227\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.2332 | − | 33.3129i | 0.637226 | − | 1.10371i | −0.348813 | − | 0.937192i | \(-0.613415\pi\) |
0.986039 | − | 0.166515i | \(-0.0532513\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.7507 | − | 34.2093i | −0.653654 | − | 1.13216i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.6979 | 1.21187 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.6992 | 0.616830 | 0.308415 | − | 0.951252i | \(-0.400201\pi\) | ||||
0.308415 | + | 0.951252i | \(0.400201\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.74693 | + | 13.4181i | 0.254993 | + | 0.441661i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.10335 | + | 1.91106i | −0.0361999 | + | 0.0627000i | −0.883558 | − | 0.468322i | \(-0.844859\pi\) |
0.847358 | + | 0.531022i | \(0.178192\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.5330 | + | 25.1719i | 0.476300 | + | 0.824976i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.3429 | 0.697242 | 0.348621 | − | 0.937264i | \(-0.386650\pi\) | ||||
0.348621 | + | 0.937264i | \(0.386650\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.589661 | − | 1.02132i | −0.0192224 | − | 0.0332942i | 0.856254 | − | 0.516555i | \(-0.172786\pi\) |
−0.875477 | + | 0.483261i | \(0.839452\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.468813 | + | 0.812008i | −0.0152667 | + | 0.0264426i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.8445 | − | 20.5152i | 0.384894 | − | 0.666655i | −0.606861 | − | 0.794808i | \(-0.707572\pi\) |
0.991754 | + | 0.128153i | \(0.0409048\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.59166 | + | 9.68504i | 0.181513 | + | 0.314390i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.8125 | −0.415038 | −0.207519 | − | 0.978231i | \(-0.566539\pi\) | ||||
−0.207519 | + | 0.978231i | \(0.566539\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.9784 | − | 39.7998i | −0.742012 | − | 1.28520i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.8084 | − | 18.7207i | 0.348658 | − | 0.603893i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.46326 | − | 9.46264i | −0.175686 | − | 0.304298i | 0.764712 | − | 0.644372i | \(-0.222881\pi\) |
−0.940399 | + | 0.340074i | \(0.889548\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.7933 | −0.506831 | −0.253415 | − | 0.967358i | \(-0.581554\pi\) | ||||
−0.253415 | + | 0.967358i | \(0.581554\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 49.7001 | 1.59331 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.7490 | − | 32.4742i | −0.599833 | − | 1.03894i | −0.992845 | − | 0.119409i | \(-0.961900\pi\) |
0.393012 | − | 0.919533i | \(-0.371433\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.83826 | − | 15.3083i | 0.282472 | − | 0.489256i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.7661 | − | 20.3795i | 0.375280 | − | 0.650004i | −0.615089 | − | 0.788458i | \(-0.710880\pi\) |
0.990369 | + | 0.138454i | \(0.0442132\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.768410 | 0.0244340 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.7019 | 1.48353 | 0.741767 | − | 0.670658i | \(-0.233988\pi\) | ||||
0.741767 | + | 0.670658i | \(0.233988\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.4290 | + | 37.1161i | −0.678663 | + | 1.17548i | 0.296721 | + | 0.954964i | \(0.404107\pi\) |
−0.975384 | + | 0.220514i | \(0.929226\pi\) | |||||||
\(998\) | 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 | 2700.2.i.e.1801.1 | 8 | ||
3.2 | odd | 2 | 900.2.i.d.601.1 | yes | 8 | ||
5.2 | odd | 4 | 2700.2.s.d.2449.2 | 16 | |||
5.3 | odd | 4 | 2700.2.s.d.2449.7 | 16 | |||
5.4 | even | 2 | 2700.2.i.d.1801.4 | 8 | |||
9.2 | odd | 6 | 8100.2.a.x.1.4 | 4 | |||
9.4 | even | 3 | inner | 2700.2.i.e.901.1 | 8 | ||
9.5 | odd | 6 | 900.2.i.d.301.1 | ✓ | 8 | ||
9.7 | even | 3 | 8100.2.a.y.1.4 | 4 | |||
15.2 | even | 4 | 900.2.s.d.349.4 | 16 | |||
15.8 | even | 4 | 900.2.s.d.349.5 | 16 | |||
15.14 | odd | 2 | 900.2.i.e.601.4 | yes | 8 | ||
45.2 | even | 12 | 8100.2.d.q.649.7 | 8 | |||
45.4 | even | 6 | 2700.2.i.d.901.4 | 8 | |||
45.7 | odd | 12 | 8100.2.d.s.649.7 | 8 | |||
45.13 | odd | 12 | 2700.2.s.d.1549.2 | 16 | |||
45.14 | odd | 6 | 900.2.i.e.301.4 | yes | 8 | ||
45.22 | odd | 12 | 2700.2.s.d.1549.7 | 16 | |||
45.23 | even | 12 | 900.2.s.d.49.4 | 16 | |||
45.29 | odd | 6 | 8100.2.a.z.1.1 | 4 | |||
45.32 | even | 12 | 900.2.s.d.49.5 | 16 | |||
45.34 | even | 6 | 8100.2.a.ba.1.1 | 4 | |||
45.38 | even | 12 | 8100.2.d.q.649.2 | 8 | |||
45.43 | odd | 12 | 8100.2.d.s.649.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.2.i.d.301.1 | ✓ | 8 | 9.5 | odd | 6 | ||
900.2.i.d.601.1 | yes | 8 | 3.2 | odd | 2 | ||
900.2.i.e.301.4 | yes | 8 | 45.14 | odd | 6 | ||
900.2.i.e.601.4 | yes | 8 | 15.14 | odd | 2 | ||
900.2.s.d.49.4 | 16 | 45.23 | even | 12 | |||
900.2.s.d.49.5 | 16 | 45.32 | even | 12 | |||
900.2.s.d.349.4 | 16 | 15.2 | even | 4 | |||
900.2.s.d.349.5 | 16 | 15.8 | even | 4 | |||
2700.2.i.d.901.4 | 8 | 45.4 | even | 6 | |||
2700.2.i.d.1801.4 | 8 | 5.4 | even | 2 | |||
2700.2.i.e.901.1 | 8 | 9.4 | even | 3 | inner | ||
2700.2.i.e.1801.1 | 8 | 1.1 | even | 1 | trivial | ||
2700.2.s.d.1549.2 | 16 | 45.13 | odd | 12 | |||
2700.2.s.d.1549.7 | 16 | 45.22 | odd | 12 | |||
2700.2.s.d.2449.2 | 16 | 5.2 | odd | 4 | |||
2700.2.s.d.2449.7 | 16 | 5.3 | odd | 4 | |||
8100.2.a.x.1.4 | 4 | 9.2 | odd | 6 | |||
8100.2.a.y.1.4 | 4 | 9.7 | even | 3 | |||
8100.2.a.z.1.1 | 4 | 45.29 | odd | 6 | |||
8100.2.a.ba.1.1 | 4 | 45.34 | even | 6 | |||
8100.2.d.q.649.2 | 8 | 45.38 | even | 12 | |||
8100.2.d.q.649.7 | 8 | 45.2 | even | 12 | |||
8100.2.d.s.649.2 | 8 | 45.43 | odd | 12 | |||
8100.2.d.s.649.7 | 8 | 45.7 | odd | 12 |