Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(41,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([0, 33, 53]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.ba (of order \(66\), degree \(20\), 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: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{66}]$ |
Embedding invariants
Embedding label | 413.1 | ||
Root | \(0.580057 - 0.814576i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 804.413 |
Dual form | 804.2.ba.a.329.1 |
$q$-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 \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{59}{66}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.57553 | + | 0.719520i | −0.909632 | + | 0.415415i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.842599 | + | 4.37182i | −0.318473 | + | 1.65239i | 0.371408 | + | 0.928470i | \(0.378875\pi\) |
−0.689881 | + | 0.723923i | \(0.742337\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.96458 | − | 2.26725i | 0.654861 | − | 0.755750i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.690079 | − | 0.723734i | \(-0.257576\pi\) | ||||
−0.690079 | + | 0.723734i | \(0.742424\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.17337 | − | 0.341710i | 1.98953 | − | 0.0947732i | 0.990461 | − | 0.137795i | \(-0.0440016\pi\) |
0.999074 | + | 0.0430222i | \(0.0136986\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.35738 | + | 1.22528i | −1.45848 | + | 0.281099i | −0.855976 | − | 0.517015i | \(-0.827043\pi\) |
−0.602506 | + | 0.798114i | \(0.705831\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.81807 | − | 7.49420i | −0.396736 | − | 1.63537i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.20627 | + | 2.70320i | −0.841254 | + | 0.540641i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.46393 | + | 4.98567i | −0.281733 | + | 0.959493i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.75556 | − | 0.226535i | −0.854123 | − | 0.0406869i | −0.384048 | − | 0.923313i | \(-0.625470\pi\) |
−0.470075 | + | 0.882626i | \(0.655773\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.07910 | + | 10.5293i | −0.999398 | + | 1.73101i | −0.469661 | + | 0.882847i | \(0.655624\pi\) |
−0.529738 | + | 0.848162i | \(0.677710\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.0560 | + | 5.69976i | −1.77037 | + | 0.912691i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.371662 | − | 0.928368i | \(-0.621212\pi\) | ||||
0.371662 | + | 0.928368i | \(0.378788\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.51453 | + | 0.792870i | 0.840958 | + | 0.120911i | 0.549315 | − | 0.835616i | \(-0.314889\pi\) |
0.291643 | + | 0.956527i | \(0.405798\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11.9043 | − | 4.76575i | −1.70061 | − | 0.680821i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.13462 | − | 6.50473i | 1.20991 | − | 0.861573i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.09645 | + | 5.34500i | 0.652533 | + | 0.684357i | 0.964001 | − | 0.265900i | \(-0.0856690\pi\) |
−0.311467 | + | 0.950257i | \(0.600820\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.25665 | + | 10.4992i | 1.04024 | + | 1.32277i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.90436 | − | 2.12630i | −0.965671 | − | 0.259769i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.03940 | + | 7.66555i | −0.940941 | + | 0.897185i | −0.994850 | − | 0.101361i | \(-0.967680\pi\) |
0.0539089 | + | 0.998546i | \(0.482832\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.68209 | − | 7.28547i | 0.540641 | − | 0.841254i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.45319 | + | 2.81879i | −0.163496 | + | 0.317138i | −0.956325 | − | 0.292306i | \(-0.905577\pi\) |
0.792829 | + | 0.609445i | \(0.208608\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.28083 | − | 8.90839i | −0.142315 | − | 0.989821i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.55038 | + | 31.6486i | −0.477010 | + | 3.31768i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.65551 | − | 3.06480i | 0.793840 | − | 0.317805i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.7932 | − | 6.23144i | −1.09588 | − | 0.632707i | −0.160744 | − | 0.986996i | \(-0.551390\pi\) |
−0.935136 | + | 0.354289i | \(0.884723\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.945001 | − | 0.327068i | \(-0.893939\pi\) | ||||
0.945001 | + | 0.327068i | \(0.106061\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.498621 | − | 10.4674i | 0.0491306 | − | 1.03138i | −0.830888 | − | 0.556440i | \(-0.812167\pi\) |
0.880019 | − | 0.474939i | \(-0.157530\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.59842 | − | 2.48719i | −0.153101 | − | 0.238230i | 0.756227 | − | 0.654309i | \(-0.227040\pi\) |
−0.909329 | + | 0.416079i | \(0.863404\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00175 | − | 20.9633i | 0.189998 | − | 1.98975i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 0.971812 | − | 0.235759i | \(-0.0757576\pi\) | ||||
−0.971812 | + | 0.235759i | \(0.924242\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.3179 | − | 16.9351i | 1.23124 | − | 1.56565i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.523401 | − | 10.9875i | −0.0475819 | − | 0.998867i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 22.1314 | + | 4.26548i | 1.96385 | + | 0.378501i | 0.982533 | + | 0.186091i | \(0.0595819\pi\) |
0.981315 | + | 0.192410i | \(0.0616302\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.25879 | + | 2.71862i | −0.815191 | + | 0.239362i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 28.8257i | − | 2.49951i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.28614 | + | 18.0029i | 0.448365 | + | 1.52699i | 0.805304 | + | 0.592862i | \(0.202002\pi\) |
−0.356939 | + | 0.934128i | \(0.616180\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 22.1846 | − | 1.05678i | 1.82975 | − | 0.0871618i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.4290 | + | 12.1335i | 1.25560 | + | 0.987411i | 0.999786 | + | 0.0206838i | \(0.00658434\pi\) |
0.255809 | + | 0.966727i | \(0.417658\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.7634 | + | 2.36462i | 1.97633 | + | 0.188717i | 0.999661 | − | 0.0260253i | \(-0.00828506\pi\) |
0.976671 | + | 0.214742i | \(0.0688911\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.35057 | − | 7.53540i | −0.340763 | − | 0.590218i | 0.643812 | − | 0.765184i | \(-0.277352\pi\) |
−0.984575 | + | 0.174966i | \(0.944019\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 38.3993 | − | 3.66669i | 2.95379 | − | 0.282053i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.71157 | + | 16.8209i | −0.742662 | + | 1.28633i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.27372 | − | 20.6668i | −0.625435 | − | 1.56226i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.6312 | + | 20.5466i | −1.08753 | + | 1.52722i | −0.260153 | + | 0.965567i | \(0.583773\pi\) |
−0.827374 | + | 0.561651i | \(0.810166\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.8754 | − | 4.75421i | −0.877857 | − | 0.351441i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −20.5630 | − | 10.6009i | −1.49574 | − | 0.771105i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.814576 | − | 0.580057i | \(-0.196970\pi\) | ||||
−0.814576 | + | 0.580057i | \(0.803030\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.4810 | + | 13.8050i | 1.54624 | + | 0.993705i | 0.986261 | + | 0.165195i | \(0.0528253\pi\) |
0.559974 | + | 0.828510i | \(0.310811\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | −0.618159 | − | 0.786053i | \(-0.712121\pi\) | ||||
0.618159 | + | 0.786053i | \(0.287879\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.08081 | − | 23.3480i | −0.572834 | − | 1.65509i | −0.742698 | − | 0.669626i | \(-0.766454\pi\) |
0.169865 | − | 0.985467i | \(-0.445667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.9835 | − | 2.33729i | 0.986317 | − | 0.164860i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.8572 | + | 22.2683i | 1.09165 | + | 1.53301i | 0.821509 | + | 0.570195i | \(0.193132\pi\) |
0.270146 | + | 0.962819i | \(0.412928\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.99740 | − | 20.5996i | 0.339246 | − | 1.39839i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.15079 | − | 17.8618i | 0.483206 | − | 1.20699i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.9893 | − | 26.2529i | 0.802864 | − | 1.75803i | 0.167412 | − | 0.985887i | \(-0.446459\pi\) |
0.635452 | − | 0.772140i | \(-0.280814\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.13472 | + | 14.8473i | −0.142315 | + | 0.989821i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.5227 | + | 20.4113i | 0.695362 | + | 1.34881i | 0.926649 | + | 0.375929i | \(0.122676\pi\) |
−0.231287 | + | 0.972886i | \(0.574293\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.0950560 | − | 0.995472i | \(-0.530303\pi\) | ||||
0.0950560 | + | 0.995472i | \(0.469697\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.261363 | − | 5.48668i | 0.0169773 | − | 0.356398i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.1993 | − | 7.98643i | −1.75206 | − | 0.514451i | −0.761103 | − | 0.648630i | \(-0.775342\pi\) |
−0.990957 | + | 0.134179i | \(0.957160\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.42776 | + | 13.1138i | 0.540641 | + | 0.841254i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −45.1851 | + | 10.9618i | −2.87506 | + | 0.697482i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.618159 | − | 0.786053i | \(-0.287879\pi\) | ||||
−0.618159 | + | 0.786053i | \(0.712121\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −40.9100 | − | 35.4487i | −2.54203 | − | 2.20268i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.2219 | + | 13.3452i | −1.77511 | + | 0.810664i | −0.796582 | + | 0.604530i | \(0.793361\pi\) |
−0.978524 | + | 0.206133i | \(0.933912\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −15.6025 | − | 53.1374i | −0.944309 | − | 3.21602i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.96986 | + | 5.73553i | −0.298610 | + | 0.344614i | −0.885150 | − | 0.465306i | \(-0.845944\pi\) |
0.586540 | + | 0.809920i | \(0.300490\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.85629 | + | 10.3370i | −0.590081 | + | 0.618859i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.998867 | − | 0.0475819i | \(-0.0151515\pi\) | ||||
−0.998867 | + | 0.0475819i | \(0.984848\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.1894 | + | 20.9916i | 1.08125 | + | 1.24782i | 0.967110 | + | 0.254358i | \(0.0818643\pi\) |
0.114135 | + | 0.993465i | \(0.463590\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00790 | + | 16.5208i | 0.235759 | + | 0.971812i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.4886 | + | 2.05191i | 1.25968 | + | 0.120285i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.11282 | + | 23.4405i | −0.467615 | + | 1.35109i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.5019 | − | 12.1160i | 1.34132 | − | 0.691499i | 0.369947 | − | 0.929053i | \(-0.379376\pi\) |
0.971374 | + | 0.237553i | \(0.0763455\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.74588 | + | 16.8504i | 0.383759 | + | 0.958585i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.6320 | − | 14.4459i | −1.78795 | − | 0.816528i | −0.970720 | − | 0.240212i | \(-0.922783\pi\) |
−0.817227 | − | 0.576316i | \(-0.804490\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −29.2494 | + | 20.8284i | −1.62246 | + | 1.15535i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.30795 | + | 2.76855i | 0.238230 | + | 0.153101i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.3238 | + | 28.3870i | 1.22703 | + | 1.56029i | 0.709708 | + | 0.704496i | \(0.248827\pi\) |
0.517317 | + | 0.855794i | \(0.326931\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.9297 | + | 34.4685i | 0.653742 | + | 1.88886i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.3615 | − | 9.12381i | 1.43600 | − | 0.497006i | 0.505352 | − | 0.862913i | \(-0.331363\pi\) |
0.930651 | + | 0.365907i | \(0.119241\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.0159 | − | 21.8092i | 0.756789 | − | 1.17759i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.458227 | − | 0.888835i | \(-0.348485\pi\) | ||||
−0.458227 | + | 0.888835i | \(0.651515\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.02341 | + | 7.11795i | 0.0547817 | + | 0.381015i | 0.998706 | + | 0.0508535i | \(0.0161942\pi\) |
−0.943924 | + | 0.330162i | \(0.892897\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.79763 | + | 36.2643i | −0.469582 | + | 1.93565i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.371662 | − | 0.928368i | \(-0.378788\pi\) | ||||
−0.371662 | + | 0.928368i | \(0.621212\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.2759 | − | 8.51760i | 1.11979 | − | 0.448295i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.73039 | + | 16.9346i | 0.458227 | + | 0.888835i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.36828 | − | 35.2742i | −0.175823 | − | 1.84130i | −0.466552 | − | 0.884494i | \(-0.654504\pi\) |
0.290730 | − | 0.956805i | \(-0.406102\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.0614 | − | 19.0880i | 1.71185 | − | 0.988340i | 0.779795 | − | 0.626035i | \(-0.215323\pi\) |
0.932060 | − | 0.362305i | \(-0.118010\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.90330 | − | 19.9323i | 0.0977662 | − | 1.02385i | −0.804871 | − | 0.593450i | \(-0.797765\pi\) |
0.902637 | − | 0.430403i | \(-0.141629\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −37.9378 | + | 9.20361i | −1.94361 | + | 0.471515i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.189251 | − | 0.981929i | \(-0.560606\pi\) | ||||
0.189251 | + | 0.981929i | \(0.439394\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.6314 | − | 10.9452i | 0.642089 | − | 0.556373i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.8740 | + | 6.71641i | −1.14801 | + | 0.337087i | −0.799763 | − | 0.600315i | \(-0.795042\pi\) |
−0.348249 | + | 0.937402i | \(0.613224\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 20.7407 | + | 45.4158i | 1.03833 | + | 2.27363i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −34.1908 | −1.70316 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.490026 | − | 2.54250i | 0.0242302 | − | 0.125718i | −0.967800 | − | 0.251722i | \(-0.919003\pi\) |
0.992030 | + | 0.126004i | \(0.0402152\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.2819 | − | 24.5607i | −1.04218 | − | 1.20274i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.7876 | + | 6.70476i | −1.69544 | + | 0.326770i | −0.943228 | − | 0.332147i | \(-0.892227\pi\) |
−0.752216 | + | 0.658917i | \(0.771015\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.6616 | + | 17.7771i | −1.33864 | + | 0.860292i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.0107 | + | 1.71540i | 1.73056 | + | 0.0824369i | 0.889053 | − | 0.457804i | \(-0.151364\pi\) |
0.841511 | + | 0.540241i | \(0.181667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.6409 | − | 35.7511i | 0.985136 | − | 1.70631i | 0.343805 | − | 0.939041i | \(-0.388284\pi\) |
0.641331 | − | 0.767264i | \(-0.278382\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −34.1920 | + | 17.6272i | −1.62819 | + | 0.839392i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.371662 | − | 0.928368i | \(-0.621212\pi\) | ||||
0.371662 | + | 0.928368i | \(0.378788\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −33.0392 | − | 8.01521i | −1.55232 | − | 0.376588i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.7202 | + | 8.10434i | 0.735361 | + | 0.379105i | 0.784863 | − | 0.619669i | \(-0.212733\pi\) |
−0.0495022 | + | 0.998774i | \(0.515763\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.78938 | − | 7.12050i | −0.315529 | − | 0.330918i | 0.546802 | − | 0.837262i | \(-0.315845\pi\) |
−0.862331 | + | 0.506344i | \(0.830996\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.9560 | − | 32.7648i | 0.736781 | − | 1.51294i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −40.7168 | + | 14.0922i | −1.87613 | + | 0.649335i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.4286 | − | 22.3392i | 1.07498 | − | 1.02499i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −40.0097 | + | 77.6080i | −1.82428 | + | 3.53862i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.09682 | + | 22.7228i | −0.412216 | + | 1.02967i | 0.566429 | + | 0.824110i | \(0.308325\pi\) |
−0.978645 | + | 0.205556i | \(0.934100\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.2763 | + | 8.74193i | 0.555154 | + | 0.395324i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.73117 | + | 4.46359i | 0.346095 | + | 0.199818i | 0.662964 | − | 0.748651i | \(-0.269298\pi\) |
−0.316869 | + | 0.948469i | \(0.602632\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.945001 | − | 0.327068i | \(-0.893939\pi\) | ||||
0.945001 | + | 0.327068i | \(0.106061\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −57.8610 | + | 33.4061i | −2.56970 | + | 1.48362i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26.7384 | − | 41.6058i | −1.18284 | − | 1.84053i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.19786 | − | 33.4895i | 0.141189 | − | 1.47860i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.86868 | + | 39.2283i | 0.0817115 | + | 1.71533i | 0.552855 | + | 0.833278i | \(0.313538\pi\) |
−0.471143 | + | 0.882057i | \(0.656158\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 27.9056 | + | 26.6080i | 1.21790 | + | 1.16127i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.5844 | + | 4.35278i | 0.981929 | + | 0.189251i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.54545 | − | 32.5088i | −0.410391 | − | 1.39766i | −0.862661 | − | 0.505782i | \(-0.831204\pi\) |
0.452270 | − | 0.891881i | \(-0.350614\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.26815 | − | 42.8992i | 0.354820 | − | 1.84098i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.90970 | − | 4.10038i | 0.167167 | − | 0.175319i | −0.634822 | − | 0.772658i | \(-0.718927\pi\) |
0.801989 | + | 0.597339i | \(0.203775\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 22.1308 | − | 1.05422i | 0.944521 | − | 0.0449931i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.0988 | − | 8.72818i | −0.471968 | − | 0.371160i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 39.8287 | + | 3.80318i | 1.68457 | + | 0.160857i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 40.0251 | + | 1.90663i | 1.68090 | + | 0.0800710i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.7558 | − | 4.36915i | 1.91482 | − | 0.182843i | 0.931378 | − | 0.364054i | \(-0.118607\pi\) |
0.983444 | + | 0.181210i | \(0.0580014\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.4004 | + | 38.4684i | 0.641128 | + | 1.60146i | 0.790350 | + | 0.612656i | \(0.209899\pi\) |
−0.149222 | + | 0.988804i | \(0.547677\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −43.7769 | − | 6.29416i | −1.81930 | − | 0.261577i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.971812 | − | 0.235759i | \(-0.924242\pi\) | ||||
0.971812 | + | 0.235759i | \(0.0757576\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.5104 | − | 4.38674i | 1.25716 | − | 0.180752i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.814576 | − | 0.580057i | \(-0.196970\pi\) | ||||
−0.814576 | + | 0.580057i | \(0.803030\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.5309 | + | 30.9711i | 1.20862 | + | 1.26756i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.618159 | − | 0.786053i | \(-0.712121\pi\) | ||||
0.618159 | + | 0.786053i | \(0.287879\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.5368 | + | 44.8905i | 0.633757 | + | 1.83112i | 0.550919 | + | 0.834559i | \(0.314277\pi\) |
0.0828381 | + | 0.996563i | \(0.473602\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −20.3496 | + | 13.7438i | −0.828700 | + | 0.559692i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.3098 | + | 22.2631i | −1.14906 | + | 0.903631i | −0.996411 | − | 0.0846490i | \(-0.973023\pi\) |
−0.152650 | + | 0.988280i | \(0.548781\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.8404 | − | 22.2447i | −0.639788 | − | 0.898456i | 0.359612 | − | 0.933102i | \(-0.382909\pi\) |
−0.999400 | + | 0.0346459i | \(0.988970\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.739352 | + | 3.04765i | −0.0297171 | + | 0.122495i | −0.984738 | − | 0.174042i | \(-0.944317\pi\) |
0.955021 | + | 0.296538i | \(0.0958321\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.3854 | − | 22.7408i | 0.415415 | − | 0.909632i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.9558 | − | 44.5281i | −0.913857 | − | 1.77263i | −0.523789 | − | 0.851848i | \(-0.675482\pi\) |
−0.390068 | − | 0.920786i | \(-0.627548\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −41.0060 | − | 23.6748i | −1.62984 | − | 0.940989i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −87.0222 | − | 30.1187i | −3.44794 | − | 1.19335i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.1475 | − | 7.09036i | −0.952286 | − | 0.279616i | −0.231548 | − | 0.972824i | \(-0.574379\pi\) |
−0.720738 | + | 0.693207i | \(0.756197\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.0950560 | − | 0.995472i | \(-0.469697\pi\) | ||||
−0.0950560 | + | 0.995472i | \(0.530303\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.94825 | + | 36.0509i | 0.272323 | + | 1.41295i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.618159 | − | 0.786053i | \(-0.287879\pi\) | ||||
−0.618159 | + | 0.786053i | \(0.712121\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.58565 | + | 33.2869i | 0.0618622 | + | 1.29865i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.82623 | + | 2.44894i | 0.109928 | + | 0.0952528i | 0.708090 | − | 0.706122i | \(-0.249557\pi\) |
−0.598163 | + | 0.801375i | \(0.704102\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 49.9888i | 1.93268i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.2638 | − | 10.1675i | 0.858206 | − | 0.391930i | 0.0628142 | − | 0.998025i | \(-0.479992\pi\) |
0.795392 | + | 0.606096i | \(0.207265\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.31963 | − | 24.9284i | −0.281733 | − | 0.959493i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 0.189251 | − | 0.981929i | \(-0.439394\pi\) | ||||
−0.189251 | + | 0.981929i | \(0.560606\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.3371 | − | 41.9352i | 1.39449 | − | 1.60932i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.998867 | − | 0.0475819i | \(-0.0151515\pi\) | ||||
−0.998867 | + | 0.0475819i | \(0.984848\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −31.2652 | − | 24.5872i | −1.19284 | − | 0.938061i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.20973 | − | 33.8410i | −0.312313 | − | 1.28737i | −0.884227 | − | 0.467057i | \(-0.845314\pi\) |
0.571914 | − | 0.820313i | \(-0.306201\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.998867 | − | 0.0475819i | \(-0.984848\pi\) | ||||
0.998867 | + | 0.0475819i | \(0.0151515\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.7457 | − | 74.3875i | 0.971019 | − | 2.80558i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.0876 | − | 16.0268i | 1.16752 | − | 0.601898i | 0.238215 | − | 0.971212i | \(-0.423438\pi\) |
0.929305 | + | 0.369314i | \(0.120407\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.53599 | + | 8.83247i | 0.132610 | + | 0.331244i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 45.3412 | + | 10.9997i | 1.68860 | + | 0.409649i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 48.5997 | − | 6.98758i | 1.80744 | − | 0.259871i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.8977 | + | 26.2747i | −1.36846 | + | 0.974475i | −0.369483 | + | 0.929237i | \(0.620465\pi\) |
−0.998976 | + | 0.0452379i | \(0.985595\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.7138 | − | 14.5973i | −0.841254 | − | 0.540641i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.7724 | − | 40.4020i | −1.17354 | − | 1.49228i | −0.834065 | − | 0.551666i | \(-0.813992\pi\) |
−0.339477 | − | 0.940614i | \(-0.610250\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.9667 | − | 13.8326i | 1.47020 | − | 0.508841i | 0.529568 | − | 0.848268i | \(-0.322354\pi\) |
0.940633 | + | 0.339426i | \(0.110233\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 63.3032 | − | 49.7822i | 2.32550 | − | 1.82880i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.38669 | + | 9.64466i | 0.0506011 | + | 0.351939i | 0.999355 | + | 0.0359215i | \(0.0114366\pi\) |
−0.948753 | + | 0.316017i | \(0.897654\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.2062 | + | 30.7670i | 1.57035 | + | 1.11824i | 0.939606 | + | 0.342257i | \(0.111191\pi\) |
0.630748 | + | 0.775988i | \(0.282748\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.2204 | − | 4.89231i | 0.442408 | − | 0.177114i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.76998 | − | 49.9535i | −0.172010 | − | 1.80137i | −0.509953 | − | 0.860202i | \(-0.670337\pi\) |
0.337943 | − | 0.941167i | \(-0.390269\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.6155 | − | 11.9024i | 0.740531 | − | 0.427546i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 89.9610 | + | 26.4149i | 3.22733 | + | 0.947630i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.5167 | + | 26.0892i | −0.731343 | + | 0.929978i | −0.999442 | − | 0.0334133i | \(-0.989362\pi\) |
0.268099 | + | 0.963391i | \(0.413605\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 38.3851 | + | 36.6002i | 1.36310 | + | 1.29971i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.4925 | − | 54.4402i | 0.368441 | − | 1.91165i | −0.0406786 | − | 0.999172i | \(-0.512952\pi\) |
0.409120 | − | 0.912481i | \(-0.365836\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 36.4379 | − | 42.0515i | 1.27793 | − | 1.47481i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.0294 | + | 1.71629i | −1.26051 | + | 0.0600455i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 62.8157 | + | 72.4931i | 2.19496 | + | 2.53312i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.80076 | − | 1.11801i | 0.202202 | − | 0.0389712i | −0.0871445 | − | 0.996196i | \(-0.527774\pi\) |
0.289346 | + | 0.957224i | \(0.406562\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −48.4327 | + | 31.1258i | −1.68214 | + | 1.08104i | −0.829750 | + | 0.558135i | \(0.811517\pi\) |
−0.852388 | + | 0.522909i | \(0.824847\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.70333 | − | 12.6124i | 0.128467 | − | 0.437519i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.09121 | − | 23.3780i | 0.279673 | − | 0.808062i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.5000 | + | 25.1147i | −0.500000 | + | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48.4766 | + | 6.96988i | 1.66567 | + | 0.239488i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −43.7618 | − | 19.9853i | −1.50190 | − | 0.685895i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.8069 | + | 20.3400i | 1.73960 | + | 0.696429i | 0.999719 | + | 0.0236865i | \(0.00754034\pi\) |
0.739877 | + | 0.672743i | \(0.234884\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.1872 | + | 19.1713i | 1.26881 | + | 0.654117i | 0.955348 | − | 0.295484i | \(-0.0954809\pi\) |
0.313462 | + | 0.949601i | \(0.398511\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.2016 | − | 23.1452i | −0.618159 | − | 0.786053i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −57.4274 | − | 12.5518i | −1.94585 | − | 0.425301i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −35.3323 | + | 12.2286i | −1.19582 | + | 0.413876i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.8049 | − | 29.3724i | 1.04021 | − | 0.991834i | 0.0402330 | − | 0.999190i | \(-0.487190\pi\) |
0.999973 | + | 0.00735598i | \(0.00234150\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.87537 | + | 15.2761i | −0.265027 | + | 0.514081i | −0.983371 | − | 0.181607i | \(-0.941870\pi\) |
0.718344 | + | 0.695688i | \(0.244900\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.2959 | + | 93.1606i | −1.25086 | + | 3.12450i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.08389 | − | 42.7685i | −0.135903 | − | 1.42325i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.42987 | − | 51.0092i | 0.0806825 | − | 1.69373i | −0.489331 | − | 0.872098i | \(-0.662759\pi\) |
0.570013 | − | 0.821635i | \(-0.306938\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.88872 | − | 14.9881i | −0.0952901 | − | 0.494412i | −0.997947 | − | 0.0640502i | \(-0.979598\pi\) |
0.902657 | − | 0.430362i | \(-0.141614\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.3101 | + | 35.9992i | −0.932850 | + | 1.18622i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.89255 | − | 60.7222i | −0.0951066 | − | 1.99653i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.7525 | − | 21.6945i | −0.747290 | − | 0.712540i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 81.5193 | + | 15.7116i | 2.67169 | + | 0.514925i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.7921i | 1.36529i | 0.730750 | + | 0.682645i | \(0.239170\pi\) | ||||
−0.730750 | + | 0.682645i | \(0.760830\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 60.2312 | 1.96557 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −55.0502 | + | 57.7350i | −1.78701 | + | 1.87416i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.29563 | − | 0.792137i | −0.267601 | − | 0.0255528i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.15581 | − | 12.3942i | −0.230115 | − | 0.398571i | 0.727727 | − | 0.685867i | \(-0.240577\pi\) |
−0.957842 | + | 0.287296i | \(0.907244\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −83.1597 | + | 7.94079i | −2.66598 | + | 0.254570i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 31.0968 | − | 53.8613i | 0.995895 | − | 1.72494i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.77932 | − | 1.26228i | −0.280302 | − | 0.0403014i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.0394 | − | 7.91347i | 1.74838 | − | 0.251380i | 0.807442 | − | 0.589947i | \(-0.200851\pi\) |
0.940942 | + | 0.338567i | \(0.109942\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −55.5967 | − | 28.6621i | −1.76431 | − | 0.909565i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.2098 | + | 32.9105i | 1.62183 | + | 1.04229i | 0.954797 | + | 0.297259i | \(0.0960725\pi\) |
0.667033 | + | 0.745028i | \(0.267564\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −43.5964 | − | 45.7225i | −1.37933 | − | 1.44660i |
(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 | 804.2.ba.a.413.1 | yes | 20 | |
3.2 | odd | 2 | CM | 804.2.ba.a.413.1 | yes | 20 | |
67.61 | odd | 66 | inner | 804.2.ba.a.329.1 | ✓ | 20 | |
201.128 | even | 66 | inner | 804.2.ba.a.329.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.ba.a.329.1 | ✓ | 20 | 67.61 | odd | 66 | inner | |
804.2.ba.a.329.1 | ✓ | 20 | 201.128 | even | 66 | inner | |
804.2.ba.a.413.1 | yes | 20 | 1.1 | even | 1 | trivial | |
804.2.ba.a.413.1 | yes | 20 | 3.2 | odd | 2 | CM |