Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(5,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 11, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.s (of order \(22\), degree \(10\), 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: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{22})\) |
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: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{22}]$ |
Embedding invariants
Embedding label | 209.2 | ||
Root | \(0.235759 + 0.971812i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 804.209 |
Dual form | 804.2.s.a.377.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{22}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 1.30900 | − | 1.13425i | 0.755750 | − | 0.654861i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.40541 | − | 0.633402i | −1.66509 | − | 0.239404i | −0.755570 | − | 0.655068i | \(-0.772640\pi\) |
−0.909518 | + | 0.415664i | \(0.863549\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.426945 | − | 2.96946i | 0.142315 | − | 0.989821i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.903862 | − | 0.412780i | 0.250686 | − | 0.114485i | −0.286109 | − | 0.958197i | \(-0.592362\pi\) |
0.536795 | + | 0.843712i | \(0.319635\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.11815 | − | 7.77691i | −0.256521 | − | 1.78414i | −0.557158 | − | 0.830406i | \(-0.688108\pi\) |
0.300637 | − | 0.953739i | \(-0.402801\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.48510 | + | 4.16772i | −1.41517 | + | 0.909472i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.07708 | − | 4.54816i | −0.415415 | − | 0.909632i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.80925 | − | 4.37128i | −0.540641 | − | 0.841254i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.98538 | − | 2.73343i | −1.07501 | − | 0.490939i | −0.202369 | − | 0.979309i | \(-0.564864\pi\) |
−0.872636 | + | 0.488371i | \(0.837591\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.14797 | −0.353123 | −0.176562 | − | 0.984290i | \(-0.556497\pi\) | ||||
−0.176562 | + | 0.984290i | \(0.556497\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.714956 | − | 1.56553i | 0.114485 | − | 0.250686i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.833910 | + | 2.84004i | 0.127170 | + | 0.433102i | 0.998322 | − | 0.0579125i | \(-0.0184445\pi\) |
−0.871152 | + | 0.491014i | \(0.836626\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.2900 | + | 3.60866i | 1.75571 | + | 0.515524i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.2846 | − | 8.91168i | −1.36223 | − | 1.18038i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.17314 | + | 12.7177i | 1.04646 | + | 1.62833i | 0.734996 | + | 0.678072i | \(0.237184\pi\) |
0.311467 | + | 0.950257i | \(0.399180\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.76173 | + | 12.8113i | −0.473934 | + | 1.61407i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.89885 | + | 6.55754i | 0.598490 | + | 0.801131i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.3792 | − | 8.59828i | 1.56592 | − | 1.00635i | 0.585206 | − | 0.810885i | \(-0.301014\pi\) |
0.980710 | − | 0.195468i | \(-0.0626226\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.87764 | − | 3.59760i | −0.909632 | − | 0.415415i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.23526 | + | 1.47749i | −0.363995 | + | 0.166231i | −0.589013 | − | 0.808124i | \(-0.700483\pi\) |
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.63544 | − | 2.53559i | −0.959493 | − | 0.281733i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.24334 | + | 1.24596i | −0.444823 | + | 0.130612i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.9352 | + | 3.21088i | −1.13393 | + | 0.332952i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.50648i | − | 0.152960i | −0.997071 | − | 0.0764798i | \(-0.975632\pi\) | ||
0.997071 | − | 0.0764798i | \(-0.0243681\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.241998 | + | 0.529902i | −0.0238448 | + | 0.0522128i | −0.921180 | − | 0.389138i | \(-0.872773\pi\) |
0.897335 | + | 0.441350i | \(0.145500\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.8886 | − | 7.71276i | 1.61763 | − | 0.738749i | 0.618733 | − | 0.785602i | \(-0.287646\pi\) |
0.998902 | + | 0.0468528i | \(0.0149192\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.81168 | + | 2.43633i | −0.266873 | + | 0.231247i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.839836 | − | 2.86022i | −0.0776429 | − | 0.264427i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.56957 | − | 10.0060i | −0.415415 | − | 0.909632i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.52772 | − | 17.5807i | 0.224299 | − | 1.56003i | −0.497211 | − | 0.867630i | \(-0.665643\pi\) |
0.721510 | − | 0.692404i | \(-0.243448\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.31291 | + | 2.77174i | 0.379730 | + | 0.244038i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 34.9687i | 3.03217i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.6697 | − | 19.7144i | 1.07463 | − | 1.67215i | 0.444118 | − | 0.895969i | \(-0.353517\pi\) |
0.630509 | − | 0.776182i | \(-0.282846\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 20.1807 | − | 9.21621i | 1.66447 | − | 0.760140i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.8075 | − | 4.64150i | 1.28640 | − | 0.377720i | 0.434141 | − | 0.900845i | \(-0.357052\pi\) |
0.852256 | + | 0.523125i | \(0.175234\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.7772 | + | 17.0538i | 1.17935 | + | 1.36104i | 0.918381 | + | 0.395698i | \(0.129497\pi\) |
0.260971 | + | 0.965347i | \(0.415957\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.5076 | −1.13632 | −0.568161 | − | 0.822917i | \(-0.692345\pi\) | ||||
−0.568161 | + | 0.822917i | \(0.692345\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.86661 | + | 9.07855i | −0.605124 | + | 0.698350i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −23.5706 | −1.80249 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.26955 | + | 21.3521i | 0.473934 | + | 1.61407i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.72107 | + | 8.91058i | 0.573902 | + | 0.662318i | 0.966282 | − | 0.257485i | \(-0.0828937\pi\) |
−0.392380 | + | 0.919803i | \(0.628348\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 25.1236 | + | 7.37696i | 1.85719 | + | 0.545321i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.60713 | + | 21.0367i | 0.698816 | + | 1.53019i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.5134 | + | 25.2108i | −0.828751 | + | 1.81471i | −0.350068 | + | 0.936724i | \(0.613841\pi\) |
−0.478684 | + | 0.877987i | \(0.658886\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.68451 | − | 25.6263i | 0.261188 | − | 1.81660i | −0.262770 | − | 0.964858i | \(-0.584636\pi\) |
0.523958 | − | 0.851744i | \(-0.324455\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.8505 | + | 3.02726i | 0.976937 | + | 0.213527i | ||||
\(202\) | 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 | ||||||||
\(211\) | −0.229341 | + | 0.264674i | −0.0157885 | + | 0.0182209i | −0.763589 | − | 0.645703i | \(-0.776565\pi\) |
0.747800 | + | 0.663924i | \(0.231110\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.6367 | + | 15.8330i | 1.67245 | + | 1.07482i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.76069 | − | 26.4305i | 0.524419 | − | 1.78601i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.1509 | + | 19.7931i | −1.14851 | + | 1.32545i | −0.210997 | + | 0.977487i | \(0.567671\pi\) |
−0.937509 | + | 0.347960i | \(0.886874\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.3924 | + | 4.22599i | −0.959493 | + | 0.281733i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.0574 | − | 11.9000i | −1.72192 | − | 0.786377i | −0.995024 | − | 0.0996338i | \(-0.968233\pi\) |
−0.726900 | − | 0.686743i | \(-0.759040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.55910 | + | 5.60364i | −0.166231 | + | 0.363995i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.0993 | − | 16.7730i | 1.68120 | − | 1.08044i | 0.819313 | − | 0.573346i | \(-0.194355\pi\) |
0.861889 | − | 0.507097i | \(-0.169281\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.1798 | + | 6.47568i | −0.909632 | + | 0.415415i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.22081 | − | 6.56770i | −0.268563 | − | 0.417893i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.46267 | + | 1.36053i | 0.587981 | + | 0.0845390i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(264\) | 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 | ||||||||
\(271\) | −19.0827 | + | 16.5353i | −1.15919 | + | 1.00445i | −0.159340 | + | 0.987224i | \(0.550937\pi\) |
−0.999852 | + | 0.0172215i | \(0.994518\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.14129 | + | 6.44397i | −0.250642 | + | 0.390007i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.38366 | + | 30.4890i | −0.263388 | + | 1.83191i | 0.243508 | + | 0.969899i | \(0.421702\pi\) |
−0.506896 | + | 0.862007i | \(0.669207\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.6722 | + | 16.6063i | −0.638931 | + | 0.994196i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.63073 | − | 32.2074i | −0.275268 | − | 1.91453i | −0.389404 | − | 0.921067i | \(-0.627319\pi\) |
0.114135 | − | 0.993465i | \(-0.463590\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.3013 | − | 9.19089i | 0.841254 | − | 0.540641i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.70873 | − | 1.97197i | −0.100167 | − | 0.115599i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.87483 | − | 13.0397i | −0.108063 | − | 0.751598i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0262 | − | 21.9544i | 0.572227 | − | 1.25300i | −0.373376 | − | 0.927680i | \(-0.621800\pi\) |
0.945603 | − | 0.325322i | \(-0.105473\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.284268 | + | 0.968127i | 0.0161714 | + | 0.0550748i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.4379 | + | 16.8430i | 1.09869 | + | 0.952024i | 0.999075 | − | 0.0430013i | \(-0.0136920\pi\) |
0.0996196 | + | 0.995026i | \(0.468237\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.75478 | − | 3.25353i | −0.208278 | − | 0.180474i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.3589 | − | 29.2519i | 0.738749 | − | 1.61763i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.61786 | + | 12.3213i | −0.198856 | + | 0.677240i | 0.798327 | + | 0.602224i | \(0.205719\pi\) |
−0.997182 | + | 0.0750153i | \(0.976099\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.917062 | + | 6.37831i | −0.0502547 | + | 0.349529i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 36.3103 | + | 5.22063i | 1.97795 | + | 0.284386i | 0.994864 | + | 0.101218i | \(0.0322738\pi\) |
0.983082 | + | 0.183168i | \(0.0586352\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −23.5171 | − | 10.7399i | −1.26980 | − | 0.579900i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.8112 | − | 10.2215i | −1.86340 | − | 0.547144i | −0.999018 | − | 0.0443098i | \(-0.985891\pi\) |
−0.864383 | − | 0.502834i | \(-0.832291\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.34355 | − | 2.79143i | −0.231842 | − | 0.148996i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −40.9997 | + | 12.0386i | −2.15788 | + | 0.633610i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.3308 | − | 7.91472i | −0.909632 | − | 0.415415i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.8607 | + | 22.4084i | 1.34992 | + | 1.16971i | 0.969555 | + | 0.244874i | \(0.0787465\pi\) |
0.380363 | + | 0.924837i | \(0.375799\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 36.6272i | − | 1.89649i | −0.317546 | − | 0.948243i | \(-0.602859\pi\) | ||
0.317546 | − | 0.948243i | \(-0.397141\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.88608 | + | 1.63430i | −0.0968817 | + | 0.0839484i | −0.701955 | − | 0.712221i | \(-0.747689\pi\) |
0.605073 | + | 0.796170i | \(0.293144\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.6322 | − | 25.8801i | −0.852091 | − | 1.32588i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.78943 | − | 1.26373i | 0.446792 | − | 0.0642389i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.5179 | − | 14.4714i | −1.13014 | − | 0.726297i | −0.164551 | − | 0.986369i | \(-0.552617\pi\) |
−0.965589 | + | 0.260072i | \(0.916254\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 39.6633 | + | 45.7739i | 1.98565 | + | 2.29156i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.53826 | −0.325694 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.8733 | − | 4.58269i | −1.57604 | − | 0.226600i | −0.701898 | − | 0.712278i | \(-0.747664\pi\) |
−0.874138 | + | 0.485678i | \(0.838573\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.77653 | − | 40.1766i | −0.282878 | − | 1.96746i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.78506 | − | 40.2360i | −0.281946 | − | 1.96098i | −0.276567 | − | 0.960995i | \(-0.589197\pi\) |
−0.00537983 | − | 0.999986i | \(-0.501712\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.9506 | − | 61.2034i | −1.35263 | − | 2.96184i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.0531 | + | 6.41784i | 0.675349 | + | 0.308421i | 0.723406 | − | 0.690423i | \(-0.242576\pi\) |
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.0823 | −0.863019 | −0.431509 | − | 0.902108i | \(-0.642019\pi\) | ||||
−0.431509 | + | 0.902108i | \(0.642019\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.9629 | − | 34.9540i | 0.760140 | − | 1.66447i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.4273 | − | 24.0054i | 0.724840 | − | 1.12787i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.5015 | − | 36.1333i | −0.771908 | − | 1.69024i | −0.722406 | − | 0.691469i | \(-0.756964\pi\) |
−0.0495022 | − | 0.998774i | \(-0.515763\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.77090 | + | 12.0918i | 0.361145 | + | 0.561952i | 0.973516 | − | 0.228618i | \(-0.0734207\pi\) |
−0.612372 | + | 0.790570i | \(0.709784\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.4279 | − | 31.9916i | −0.804745 | − | 1.47723i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 38.6867 | + | 5.56231i | 1.78259 | + | 0.256298i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −33.0481 | + | 21.2387i | −1.51635 | + | 0.974501i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.94146 | + | 0.886637i | −0.0885231 | + | 0.0404272i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.42884 | + | 15.0832i | −0.200690 | + | 0.683487i | 0.796225 | + | 0.605000i | \(0.206827\pi\) |
−0.996915 | + | 0.0784867i | \(0.974991\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.9904 | + | 16.4553i | −0.858775 | + | 0.744133i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 42.0596i | − | 1.88285i | −0.337229 | − | 0.941423i | \(-0.609490\pi\) | ||
0.337229 | − | 0.941423i | \(-0.390510\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.8065i | 0.924050i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −64.3870 | + | 29.4046i | −2.84831 | + | 1.30078i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −30.8539 | + | 26.7350i | −1.36223 | + | 1.18038i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.9901 | + | 41.5824i | 0.830377 | + | 1.81827i | 0.445212 | + | 0.895425i | \(0.353128\pi\) |
0.385165 | + | 0.922848i | \(0.374145\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 32.4255 | + | 20.8386i | 1.41517 | + | 0.909472i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.27324 | + | 22.7659i | −0.142315 | + | 0.989821i | ||||
\(530\) | 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 | ||||||||
\(541\) | 3.41260 | − | 5.31011i | 0.146719 | − | 0.228299i | −0.760114 | − | 0.649790i | \(-0.774857\pi\) |
0.906833 | + | 0.421491i | \(0.138493\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.2137 | + | 2.90629i | 0.867453 | + | 0.124721i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.6714 | + | 29.0533i | −0.798333 | + | 1.24223i | 0.168216 | + | 0.985750i | \(0.446199\pi\) |
−0.966549 | + | 0.256481i | \(0.917437\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 41.2541 | − | 18.8401i | 1.76068 | − | 0.804076i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.1885 | − | 4.45975i | 0.645881 | − | 0.189648i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.92605 | + | 2.22278i | 0.0814633 | + | 0.0940136i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 36.4366 | + | 16.6400i | 1.53019 | + | 0.698816i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.4260 | − | 17.8025i | 0.645558 | − | 0.745013i | −0.334790 | − | 0.942293i | \(-0.608665\pi\) |
0.980347 | + | 0.197280i | \(0.0632107\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.2906 | + | 35.0467i | 0.428404 | + | 1.45901i | 0.837458 | + | 0.546501i | \(0.184041\pi\) |
−0.409054 | + | 0.912510i | \(0.634141\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.5244 | + | 46.0599i | 0.562055 | + | 1.91418i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.5651 | + | 49.6041i | −0.600144 | + | 2.04390i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.2437 | − | 37.7239i | −0.992229 | − | 1.54394i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.31118 | − | 43.8952i | 0.257438 | − | 1.79052i | −0.293481 | − | 0.955965i | \(-0.594814\pi\) |
0.550919 | − | 0.834559i | \(-0.314277\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.5639 | − | 11.7473i | 0.878150 | − | 0.478385i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 45.5003 | + | 13.3601i | 1.84680 | + | 0.542270i | 0.999945 | + | 0.0104491i | \(0.00332612\pi\) |
0.846857 | + | 0.531821i | \(0.178492\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.2309 | + | 17.5774i | −0.615170 | + | 0.709944i | −0.974782 | − | 0.223157i | \(-0.928364\pi\) |
0.359612 | + | 0.933102i | \(0.382909\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.31582 | + | 3.41627i | 0.213661 | + | 0.137312i | 0.643094 | − | 0.765787i | \(-0.277650\pi\) |
−0.429433 | + | 0.903099i | \(0.641287\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.3715 | + | 18.8937i | −0.654861 | + | 0.755750i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.6925 | − | 20.4104i | −1.77918 | − | 0.812524i | −0.976312 | − | 0.216369i | \(-0.930579\pi\) |
−0.802869 | − | 0.596156i | \(-0.796694\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.606587i | 0.0241097i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.5980 | − | 1.81132i | 0.499152 | − | 0.0717673i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.8979 | + | 16.0009i | −0.981877 | + | 0.631014i | −0.929969 | − | 0.367638i | \(-0.880167\pi\) |
−0.0519076 | + | 0.998652i | \(0.516530\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 50.2080 | − | 7.21882i | 1.96781 | − | 0.282928i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −19.8201 | − | 43.4000i | −0.773257 | − | 1.69320i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.4964 | + | 6.25383i | 1.69181 | + | 0.243246i | 0.919807 | − | 0.392370i | \(-0.128345\pi\) |
0.772005 | + | 0.635616i | \(0.219254\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 45.3626i | 1.75382i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.6199 | + | 10.0687i | −0.447913 | + | 0.388119i | −0.849403 | − | 0.527744i | \(-0.823038\pi\) |
0.401490 | + | 0.915863i | \(0.368492\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.0463 | + | 21.8564i | −0.540641 | + | 0.841254i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.954206 | + | 6.63665i | −0.0366191 | + | 0.254691i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −47.6068 | + | 13.9786i | −1.81631 | + | 0.533317i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.9668 | − | 23.7571i | 1.40628 | − | 0.903764i | 0.406334 | − | 0.913725i | \(-0.366807\pi\) |
0.999950 | + | 0.00996078i | \(0.00317067\pi\) | |||||||
\(692\) | 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 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.40175 | + | 16.7045i | 0.0905837 | + | 0.630023i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.24089 | − | 20.2347i | 0.347049 | − | 0.759931i | −0.652948 | − | 0.757403i | \(-0.726468\pi\) |
0.999997 | − | 0.00252851i | \(-0.000804851\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.00609 | + | 10.2378i | 0.112737 | + | 0.383948i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.40174 | − | 2.18115i | 0.0522036 | − | 0.0812304i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.1391 | − | 51.5589i | 0.563028 | − | 1.91750i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.9760 | + | 27.7073i | 1.18592 | + | 1.02761i | 0.998976 | + | 0.0452379i | \(0.0144046\pi\) |
0.186947 | + | 0.982370i | \(0.440141\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.2162 | + | 24.5601i | −0.415415 | + | 0.909632i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.7766 | − | 50.3245i | 0.545786 | − | 1.85878i | 0.0344317 | − | 0.999407i | \(-0.489038\pi\) |
0.511354 | − | 0.859370i | \(-0.329144\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.8874 | + | 6.45384i | 1.65121 | + | 0.237408i | 0.904109 | − | 0.427302i | \(-0.140536\pi\) |
0.747101 | + | 0.664710i | \(0.231445\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.9744 | − | 3.80964i | −0.476628 | − | 0.139951i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.1905 | − | 12.6819i | −1.57604 | − | 0.462768i | −0.627290 | − | 0.778785i | \(-0.715836\pi\) |
−0.948753 | + | 0.316017i | \(0.897654\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.4569 | − | 35.9226i | 1.50678 | − | 1.30563i | 0.701654 | − | 0.712517i | \(-0.252445\pi\) |
0.805121 | − | 0.593111i | \(-0.202100\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −79.2865 | + | 23.2806i | −2.87036 | + | 0.842815i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.7758 | + | 16.2693i | 0.677071 | + | 0.586686i | 0.924021 | − | 0.382343i | \(-0.124883\pi\) |
−0.246949 | + | 0.969028i | \(0.579428\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.9000i | 1.18180i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.9298 | − | 8.95212i | 0.499728 | − | 0.321156i | ||||
\(778\) | 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 | ||||||||
\(787\) | −13.9459 | − | 47.4952i | −0.497116 | − | 1.69302i | −0.700272 | − | 0.713876i | \(-0.746938\pi\) |
0.203156 | − | 0.979146i | \(-0.434880\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.6370 | + | 8.12129i | 0.448752 | + | 0.288396i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(798\) | 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 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.1477 | + | 6.63504i | 1.62047 | + | 0.232988i | 0.891981 | − | 0.452074i | \(-0.149316\pi\) |
0.728485 | + | 0.685062i | \(0.240225\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.22405 | + | 43.2892i | −0.218287 | + | 1.51822i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.1543 | − | 9.66083i | 0.740094 | − | 0.337990i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.88815 | + | 13.1324i | 0.0659774 | + | 0.458883i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.46901 | + | 31.0826i | 0.155780 | + | 1.08347i | 0.906303 | + | 0.422628i | \(0.138892\pi\) |
−0.750523 | + | 0.660844i | \(0.770198\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.2808 | − | 31.2706i | −0.495992 | − | 1.08607i | −0.977751 | − | 0.209768i | \(-0.932729\pi\) |
0.481759 | − | 0.876304i | \(-0.339998\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.8440 | + | 44.8822i | 1.00059 | + | 1.55694i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.86584 | + | 33.8427i | 0.168188 | + | 1.16977i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.7930 | + | 46.9747i | 0.473934 | + | 1.61407i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −42.5929 | − | 36.9070i | −1.46179 | − | 1.26664i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.1649 | + | 8.56360i | 0.998588 | + | 0.293212i | 0.739877 | − | 0.672743i | \(-0.234884\pi\) |
0.258712 | + | 0.965955i | \(0.416702\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.11892 | + | 6.82947i | 0.106416 | + | 0.233019i | 0.955348 | − | 0.295484i | \(-0.0954809\pi\) |
−0.848932 | + | 0.528503i | \(0.822754\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.29558 | − | 28.2521i | 0.281733 | − | 0.959493i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.13470 | + | 3.90496i | 0.241750 | + | 0.132315i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.47343 | − | 0.643182i | −0.151403 | − | 0.0217684i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.3128 | − | 23.3368i | 1.22620 | − | 0.788028i | 0.242901 | − | 0.970051i | \(-0.421901\pi\) |
0.983294 | + | 0.182023i | \(0.0582646\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.5799 | + | 13.5087i | −0.995444 | + | 0.454604i | −0.845434 | − | 0.534080i | \(-0.820658\pi\) |
−0.150010 | + | 0.988684i | \(0.547931\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.2713 | + | 75.8491i | −0.746955 | + | 2.54390i | ||||
\(890\) | 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 | ||||||||
\(903\) | −17.2445 | − | 14.9424i | −0.573861 | − | 0.497253i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.86473 | + | 8.46257i | −0.128326 | + | 0.280995i | −0.962879 | − | 0.269932i | \(-0.912999\pi\) |
0.834553 | + | 0.550927i | \(0.185726\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.7879 | − | 7.73353i | 1.77430 | − | 0.255106i | 0.824032 | − | 0.566543i | \(-0.191719\pi\) |
0.950267 | + | 0.311437i | \(0.100810\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.7775 | − | 40.1105i | −0.388082 | − | 1.32168i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.46148 | + | 9.76929i | 0.146693 | + | 0.321212i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.47020 | + | 0.944843i | 0.0482879 | + | 0.0310327i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.3222 | − | 99.6131i | 0.469391 | − | 3.26469i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 45.8555i | − | 1.49803i | −0.662552 | − | 0.749016i | \(-0.730527\pi\) | ||
0.662552 | − | 0.749016i | \(-0.269473\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 44.5484 | 1.45378 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.54374 | − | 13.2943i | 0.277342 | − | 0.431552i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.05243 | + | 9.29300i | 0.259756 | + | 0.299774i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.4087 | −1.01003 | −0.505017 | − | 0.863109i | \(-0.668514\pi\) | ||||
−0.505017 | + | 0.863109i | \(0.668514\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −68.3021 | + | 78.8249i | −2.18967 | + | 2.52701i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.60532 | −0.275591 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.6923 | − | 53.4430i | −0.501016 | − | 1.70630i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.97137 | + | 13.5252i | −0.126155 | + | 0.429644i | −0.998213 | − | 0.0597587i | \(-0.980967\pi\) |
0.872058 | + | 0.489402i | \(0.162785\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.23969 | + | 20.2321i | 0.293213 | + | 0.642046i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.2964 | + | 48.8222i | −0.706133 | + | 1.54621i | 0.126241 | + | 0.992000i | \(0.459709\pi\) |
−0.832373 | + | 0.554215i | \(0.813018\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.03418 | + | 9.38936i | 0.190913 | + | 0.297066i |
(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.s.a.209.2 | ✓ | 20 | |
3.2 | odd | 2 | CM | 804.2.s.a.209.2 | ✓ | 20 | |
67.42 | odd | 22 | inner | 804.2.s.a.377.2 | yes | 20 | |
201.176 | even | 22 | inner | 804.2.s.a.377.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.s.a.209.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
804.2.s.a.209.2 | ✓ | 20 | 3.2 | odd | 2 | CM | |
804.2.s.a.377.2 | yes | 20 | 67.42 | odd | 22 | inner | |
804.2.s.a.377.2 | yes | 20 | 201.176 | even | 22 | inner |