Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3328,2,Mod(1665,3328)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3328, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3328.1665");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3328 = 2^{8} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3328.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(26.5742137927\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 416) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1665.3 | ||
Root | \(1.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3328.1665 |
Dual form | 3328.2.b.u.1665.2 |
$q$-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 \(\left(\mathbb{Z}/3328\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(769\) | \(1535\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.56155i | 0.901563i | 0.892634 | + | 0.450781i | \(0.148855\pi\) | ||||
−0.892634 | + | 0.450781i | \(0.851145\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.56155i | − 1.59277i | −0.604787 | − | 0.796387i | \(-0.706742\pi\) | ||||
0.604787 | − | 0.796387i | \(-0.293258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.56155 | −1.34614 | −0.673070 | − | 0.739579i | \(-0.735025\pi\) | ||||
−0.673070 | + | 0.739579i | \(0.735025\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.561553 | 0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000i | 0.603023i | 0.953463 | + | 0.301511i | \(0.0974911\pi\) | ||||
−0.953463 | + | 0.301511i | \(0.902509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.56155 | 1.43599 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.56155 | 0.863803 | 0.431902 | − | 0.901921i | \(-0.357843\pi\) | ||||
0.431902 | + | 0.901921i | \(0.357843\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 6.00000i | − 1.37649i | −0.725476 | − | 0.688247i | \(-0.758380\pi\) | ||||
0.725476 | − | 0.688247i | \(-0.241620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 5.56155i | − 1.21363i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.68466 | −1.53693 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.56155i | 1.07032i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 8.24621i | − 1.53128i | −0.643268 | − | 0.765641i | \(-0.722422\pi\) | ||||
0.643268 | − | 0.765641i | \(-0.277578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.12311 | −0.201716 | −0.100858 | − | 0.994901i | \(-0.532159\pi\) | ||||
−0.100858 | + | 0.994901i | \(0.532159\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.12311 | −0.543663 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.6847i | 2.14410i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.68466i | 0.441355i | 0.975347 | + | 0.220678i | \(0.0708268\pi\) | ||||
−0.975347 | + | 0.220678i | \(0.929173\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.56155 | −0.250049 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.12311 | 0.175400 | 0.0876998 | − | 0.996147i | \(-0.472048\pi\) | ||||
0.0876998 | + | 0.996147i | \(0.472048\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.8078i | 1.80067i | 0.435200 | + | 0.900334i | \(0.356677\pi\) | ||||
−0.435200 | + | 0.900334i | \(0.643323\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 2.00000i | − 0.298142i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.6847 | −1.55852 | −0.779259 | − | 0.626702i | \(-0.784404\pi\) | ||||
−0.779259 | + | 0.626702i | \(0.784404\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.68466 | 0.812094 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.56155i | 0.778773i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 13.1231i | − 1.80260i | −0.433198 | − | 0.901299i | \(-0.642615\pi\) | ||||
0.433198 | − | 0.901299i | \(-0.357385\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.12311 | 0.960479 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.36932 | 1.24100 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 6.00000i | − 0.781133i | −0.920575 | − | 0.390567i | \(-0.872279\pi\) | ||||
0.920575 | − | 0.390567i | \(-0.127721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.3693i | 1.45569i | 0.685741 | + | 0.727846i | \(0.259478\pi\) | ||||
−0.685741 | + | 0.727846i | \(0.740522\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.00000 | −0.251976 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.56155 | 0.441756 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.00000i | − 0.733017i | −0.930415 | − | 0.366508i | \(-0.880553\pi\) | ||||
0.930415 | − | 0.366508i | \(-0.119447\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.6847 | −1.26804 | −0.634018 | − | 0.773318i | \(-0.718595\pi\) | ||||
−0.634018 | + | 0.773318i | \(0.718595\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.0000 | −1.17041 | −0.585206 | − | 0.810885i | \(-0.698986\pi\) | ||||
−0.585206 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 12.0000i | − 1.38564i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 7.12311i | − 0.811753i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0000 | 1.35011 | 0.675053 | − | 0.737769i | \(-0.264121\pi\) | ||||
0.675053 | + | 0.737769i | \(0.264121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 7.36932i | − 0.808888i | −0.914563 | − | 0.404444i | \(-0.867465\pi\) | ||||
0.914563 | − | 0.404444i | \(-0.132535\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 12.6847i | − 1.37584i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.8769 | 1.38055 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.24621 | −0.874097 | −0.437048 | − | 0.899438i | \(-0.643976\pi\) | ||||
−0.437048 | + | 0.899438i | \(0.643976\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 3.56155i | − 0.373352i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 1.75379i | − 0.181859i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −21.3693 | −2.19245 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.12311i | 0.112876i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.12311i | 0.111753i | 0.998438 | + | 0.0558766i | \(0.0177953\pi\) | ||||
−0.998438 | + | 0.0558766i | \(0.982205\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −19.8078 | −1.93304 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 12.0000i | − 1.16008i | −0.814587 | − | 0.580042i | \(-0.803036\pi\) | ||||
0.814587 | − | 0.580042i | \(-0.196964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 10.6847i | − 1.02340i | −0.859163 | − | 0.511702i | \(-0.829015\pi\) | ||||
0.859163 | − | 0.511702i | \(-0.170985\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.19224 | −0.397909 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.24621 | −0.775738 | −0.387869 | − | 0.921714i | \(-0.626789\pi\) | ||||
−0.387869 | + | 0.921714i | \(0.626789\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.561553i | 0.0519156i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.6847 | −1.16280 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.75379i | 0.158134i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.56155i | 0.855211i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.2462 | −1.26415 | −0.632073 | − | 0.774909i | \(-0.717796\pi\) | ||||
−0.632073 | + | 0.774909i | \(0.717796\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.4384 | −1.62341 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 3.31534i | − 0.289663i | −0.989456 | − | 0.144831i | \(-0.953736\pi\) | ||||
0.989456 | − | 0.144831i | \(-0.0462640\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.3693i | 1.85295i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 19.8078 | 1.70478 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.1231 | −1.12118 | −0.560591 | − | 0.828093i | \(-0.689426\pi\) | ||||
−0.560591 | + | 0.828093i | \(0.689426\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 4.68466i | − 0.397348i | −0.980066 | − | 0.198674i | \(-0.936337\pi\) | ||||
0.980066 | − | 0.198674i | \(-0.0636634\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 16.6847i | − 1.40510i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.00000 | −0.167248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −29.3693 | −2.43899 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.87689i | 0.732154i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.24621i | 0.675556i | 0.941226 | + | 0.337778i | \(0.109675\pi\) | ||||
−0.941226 | + | 0.337778i | \(0.890325\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.6847 | −1.84605 | −0.923026 | − | 0.384738i | \(-0.874292\pi\) | ||||
−0.923026 | + | 0.384738i | \(0.874292\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000i | 0.321288i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2.00000i | − 0.159617i | −0.996810 | − | 0.0798087i | \(-0.974569\pi\) | ||||
0.996810 | − | 0.0798087i | \(-0.0254309\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 20.4924 | 1.62515 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.3693i | 1.20382i | 0.798565 | + | 0.601909i | \(0.205593\pi\) | ||||
−0.798565 | + | 0.601909i | \(0.794407\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.1231i | 0.865933i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.3693 | −1.18931 | −0.594657 | − | 0.803980i | \(-0.702712\pi\) | ||||
−0.594657 | + | 0.803980i | \(0.702712\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 3.36932i | − 0.257658i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.36932i | 0.256164i | 0.991764 | + | 0.128082i | \(0.0408821\pi\) | ||||
−0.991764 | + | 0.128082i | \(0.959118\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 27.3693 | 2.06893 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.36932 | 0.704241 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 18.0540i | − 1.34942i | −0.738084 | − | 0.674709i | \(-0.764269\pi\) | ||||
0.738084 | − | 0.674709i | \(-0.235731\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 7.36932i | − 0.547757i | −0.961764 | − | 0.273879i | \(-0.911693\pi\) | ||||
0.961764 | − | 0.273879i | \(-0.0883066\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.7538 | −1.31240 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.56155 | 0.702979 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.12311i | 0.520893i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 19.8078i | − 1.44080i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.36932 | 0.388510 | 0.194255 | − | 0.980951i | \(-0.437771\pi\) | ||||
0.194255 | + | 0.980951i | \(0.437771\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.3693 | −1.68216 | −0.841080 | − | 0.540911i | \(-0.818080\pi\) | ||||
−0.841080 | + | 0.540911i | \(0.818080\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.56155i | 0.398271i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.31534i | 0.0937142i | 0.998902 | + | 0.0468571i | \(0.0149205\pi\) | ||||
−0.998902 | + | 0.0468571i | \(0.985079\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.36932 | 0.664173 | 0.332087 | − | 0.943249i | \(-0.392247\pi\) | ||||
0.332087 | + | 0.943249i | \(0.392247\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.36932 | 0.660861 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 29.3693i | 2.06132i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 4.00000i | − 0.279372i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 23.8078i | − 1.63899i | −0.573083 | − | 0.819497i | \(-0.694253\pi\) | ||||
0.573083 | − | 0.819497i | \(-0.305747\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 16.6847i | − 1.14321i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 42.0540 | 2.86806 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000 | 0.271538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 15.6155i | − 1.05520i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.56155i | 0.239576i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.19224 | 0.414663 | 0.207331 | − | 0.978271i | \(-0.433522\pi\) | ||||
0.207331 | + | 0.978271i | \(0.433522\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.31534 | −0.287689 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.36932i | 0.223629i | 0.993729 | + | 0.111815i | \(0.0356663\pi\) | ||||
−0.993729 | + | 0.111815i | \(0.964334\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.31534i | 0.0869202i | 0.999055 | + | 0.0434601i | \(0.0138381\pi\) | ||||
−0.999055 | + | 0.0434601i | \(0.986162\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.1231 | 0.731847 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.31534 | −0.0861709 | −0.0430854 | − | 0.999071i | \(-0.513719\pi\) | ||||
−0.0430854 | + | 0.999071i | \(0.513719\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 38.0540i | 2.48237i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.7386i | 1.21721i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.31534 | 0.602559 | 0.301280 | − | 0.953536i | \(-0.402586\pi\) | ||||
0.301280 | + | 0.953536i | \(0.402586\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.75379i | 0.369106i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 20.2462i | − 1.29348i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.00000 | 0.381771 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.5076 | 0.729263 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 16.0000i | − 1.00991i | −0.863145 | − | 0.504956i | \(-0.831509\pi\) | ||||
0.863145 | − | 0.504956i | \(-0.168491\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 19.8078 | 1.24041 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.9309 | −0.806605 | −0.403303 | − | 0.915067i | \(-0.632138\pi\) | ||||
−0.403303 | + | 0.915067i | \(0.632138\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 9.56155i | − 0.594126i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 4.63068i | − 0.286632i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.7386 | 1.40212 | 0.701062 | − | 0.713100i | \(-0.252710\pi\) | ||||
0.701062 | + | 0.713100i | \(0.252710\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −46.7386 | −2.87113 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 12.8769i | − 0.788053i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 3.36932i | − 0.205431i | −0.994711 | − | 0.102715i | \(-0.967247\pi\) | ||||
0.994711 | − | 0.102715i | \(-0.0327531\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.6847 | −0.649047 | −0.324523 | − | 0.945878i | \(-0.605204\pi\) | ||||
−0.324523 | + | 0.945878i | \(0.605204\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.56155 | 0.336600 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 15.3693i | − 0.926805i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.3693i | 1.40413i | 0.712115 | + | 0.702063i | \(0.247738\pi\) | ||||
−0.712115 | + | 0.702063i | \(0.752262\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.630683 | −0.0377580 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.75379 | −0.223932 | −0.111966 | − | 0.993712i | \(-0.535715\pi\) | ||||
−0.111966 | + | 0.993712i | \(0.535715\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 14.2462i | − 0.846849i | −0.905931 | − | 0.423425i | \(-0.860828\pi\) | ||||
0.905931 | − | 0.423425i | \(-0.139172\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 33.3693i | − 1.97663i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.00000 | −0.236113 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.31534 | −0.253844 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 9.36932i | − 0.549239i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 27.5616i | − 1.61016i | −0.593164 | − | 0.805082i | \(-0.702121\pi\) | ||||
0.593164 | − | 0.805082i | \(-0.297879\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.3693 | −1.24417 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.1231 | −0.645428 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 42.0540i | − 2.42395i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.75379 | −0.100753 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 40.4924 | 2.31859 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.00000i | 0.342438i | 0.985233 | + | 0.171219i | \(0.0547706\pi\) | ||||
−0.985233 | + | 0.171219i | \(0.945229\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.36932 | −0.531285 | −0.265643 | − | 0.964072i | \(-0.585584\pi\) | ||||
−0.265643 | + | 0.964072i | \(0.585584\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.0540 | 1.13352 | 0.566759 | − | 0.823884i | \(-0.308197\pi\) | ||||
0.566759 | + | 0.823884i | \(0.308197\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.12311i | 0.401342i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.7538i | 0.884821i | 0.896813 | + | 0.442410i | \(0.145877\pi\) | ||||
−0.896813 | + | 0.442410i | \(0.854123\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.4924 | 0.923398 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.7386 | 1.04589 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 21.3693i | − 1.18902i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 7.68466i | − 0.426268i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.6847 | 0.922664 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 38.0540 | 2.09798 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 3.36932i | − 0.185194i | −0.995704 | − | 0.0925972i | \(-0.970483\pi\) | ||||
0.995704 | − | 0.0925972i | \(-0.0295169\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.50758i | 0.0826147i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.3693 | −1.16753 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −36.0540 | −1.96399 | −0.981993 | − | 0.188919i | \(-0.939501\pi\) | ||||
−0.981993 | + | 0.188919i | \(0.939501\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 12.8769i | − 0.699377i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 2.24621i | − 0.121639i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.68466 | 0.252948 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 28.6847i | − 1.53987i | −0.638120 | − | 0.769937i | \(-0.720288\pi\) | ||||
0.638120 | − | 0.769937i | \(-0.279712\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.05398i | 0.431119i | 0.976491 | + | 0.215560i | \(0.0691576\pi\) | ||||
−0.976491 | + | 0.215560i | \(0.930842\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.56155 | −0.296854 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.8617 | 1.69583 | 0.847915 | − | 0.530133i | \(-0.177858\pi\) | ||||
0.847915 | + | 0.530133i | \(0.177858\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 38.0540i | 2.01970i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 19.8078i | − 1.04834i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.36932 | −0.388938 | −0.194469 | − | 0.980909i | \(-0.562298\pi\) | ||||
−0.194469 | + | 0.980909i | \(0.562298\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.9309i | 0.573722i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 35.6155i | 1.86420i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.63068 | −0.137321 | −0.0686603 | − | 0.997640i | \(-0.521872\pi\) | ||||
−0.0686603 | + | 0.997640i | \(0.521872\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.630683 | 0.0328321 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 46.7386i | 2.42655i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.3693i | 0.588681i | 0.955701 | + | 0.294340i | \(0.0951000\pi\) | ||||
−0.955701 | + | 0.294340i | \(0.904900\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.9309 | −0.771027 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.24621 | 0.424701 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.1231i | 1.29049i | 0.763977 | + | 0.645244i | \(0.223244\pi\) | ||||
−0.763977 | + | 0.645244i | \(0.776756\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 22.2462i | − 1.13971i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.6847 | 0.545961 | 0.272980 | − | 0.962020i | \(-0.411991\pi\) | ||||
0.272980 | + | 0.962020i | \(0.411991\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −25.3693 | −1.29294 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.63068i | 0.337057i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.75379i | 0.190325i | 0.995462 | + | 0.0951623i | \(0.0303370\pi\) | ||||
−0.995462 | + | 0.0951623i | \(0.969663\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.17708 | 0.261149 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 42.7386i | − 2.15041i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.00000i | 0.301131i | 0.988600 | + | 0.150566i | \(0.0481095\pi\) | ||||
−0.988600 | + | 0.150566i | \(0.951890\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −33.3693 | −1.67056 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.8769 | 1.14242 | 0.571209 | − | 0.820805i | \(-0.306475\pi\) | ||||
0.571209 | + | 0.820805i | \(0.306475\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.12311i | − 0.0559459i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 24.9309i | 1.23882i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.36932 | −0.266147 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.3693 | 1.55111 | 0.775556 | − | 0.631278i | \(-0.217469\pi\) | ||||
0.775556 | + | 0.631278i | \(0.217469\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 20.4924i | − 1.01082i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 21.3693i | 1.05152i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −26.2462 | −1.28838 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.31534 | 0.358234 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.0540i | 1.07741i | 0.842495 | + | 0.538704i | \(0.181086\pi\) | ||||
−0.842495 | + | 0.538704i | \(0.818914\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 21.3153i | − 1.03885i | −0.854517 | − | 0.519423i | \(-0.826147\pi\) | ||||
0.854517 | − | 0.519423i | \(-0.173853\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.00000 | −0.291730 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −27.3693 | −1.32761 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 40.4924i | − 1.95957i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 3.12311i | − 0.150785i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.68466 | −0.321989 | −0.160994 | − | 0.986955i | \(-0.551470\pi\) | ||||
−0.160994 | + | 0.986955i | \(0.551470\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.6847 | 1.28238 | 0.641191 | − | 0.767381i | \(-0.278440\pi\) | ||||
0.641191 | + | 0.767381i | \(0.278440\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 45.8617i | − 2.19890i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.384472 | 0.0183498 | 0.00917492 | − | 0.999958i | \(-0.497079\pi\) | ||||
0.00917492 | + | 0.999958i | \(0.497079\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.19224 | 0.152011 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.68466i | 0.222575i | 0.993788 | + | 0.111287i | \(0.0354974\pi\) | ||||
−0.993788 | + | 0.111287i | \(0.964503\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29.3693i | 1.39224i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.8769 | −0.609056 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.24621i | 0.105770i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 35.4233i | − 1.66433i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.6847 | −0.594666 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.0000 | 0.654892 | 0.327446 | − | 0.944870i | \(-0.393812\pi\) | ||||
0.327446 | + | 0.944870i | \(0.393812\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.8078i | 0.924547i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.8078i | 1.94718i | 0.228300 | + | 0.973591i | \(0.426683\pi\) | ||||
−0.228300 | + | 0.973591i | \(0.573317\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.6155 | −0.818663 | −0.409332 | − | 0.912386i | \(-0.634238\pi\) | ||||
−0.409332 | + | 0.912386i | \(0.634238\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.24621 | −0.289661 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.7386i | 1.60751i | 0.594959 | + | 0.803756i | \(0.297168\pi\) | ||||
−0.594959 | + | 0.803756i | \(0.702832\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.3693i | 0.986743i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.12311 | 0.143905 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.6155 | −1.08584 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 46.1080i | 2.11558i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 7.36932i | − 0.337418i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.3153 | 0.973923 | 0.486961 | − | 0.873423i | \(-0.338105\pi\) | ||||
0.486961 | + | 0.873423i | \(0.338105\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.68466 | −0.122410 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.3693i | 0.970331i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.8769 | 0.492879 | 0.246440 | − | 0.969158i | \(-0.420739\pi\) | ||||
0.246440 | + | 0.969158i | \(0.420739\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.0000 | −1.08532 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.3153i | 1.05221i | 0.850421 | + | 0.526103i | \(0.176347\pi\) | ||||
−0.850421 | + | 0.526103i | \(0.823653\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 29.3693i | − 1.32273i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.00000 | 0.179787 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 38.0540 | 1.70695 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 25.1231i | − 1.12466i | −0.826911 | − | 0.562332i | \(-0.809904\pi\) | ||||
0.826911 | − | 0.562332i | \(-0.190096\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 24.0000i | − 1.07224i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.3693 | 1.30951 | 0.654757 | − | 0.755840i | \(-0.272771\pi\) | ||||
0.654757 | + | 0.755840i | \(0.272771\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.00000 | 0.177998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 1.56155i | − 0.0693510i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 22.4924i | − 0.996959i | −0.866901 | − | 0.498480i | \(-0.833892\pi\) | ||||
0.866901 | − | 0.498480i | \(-0.166108\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35.6155 | 1.57554 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 33.3693 | 1.47329 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 21.3693i | − 0.939821i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.26137 | −0.230948 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.43845 | −0.369695 | −0.184848 | − | 0.982767i | \(-0.559179\pi\) | ||||
−0.184848 | + | 0.982767i | \(0.559179\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 7.50758i | − 0.328283i | −0.986437 | − | 0.164142i | \(-0.947515\pi\) | ||||
0.986437 | − | 0.164142i | \(-0.0524854\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 42.7386i | 1.86527i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.00000 | −0.174243 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 3.36932i | − 0.146216i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.12311i | 0.0486471i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −42.7386 | −1.84775 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 28.1922 | 1.21658 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.3693i | 0.489711i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.6847i | 1.31924i | 0.751601 | + | 0.659618i | \(0.229282\pi\) | ||||
−0.751601 | + | 0.659618i | \(0.770718\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.5076 | 0.493837 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −38.0540 | −1.63005 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0540i | 0.600905i | 0.953797 | + | 0.300452i | \(0.0971376\pi\) | ||||
−0.953797 | + | 0.300452i | \(0.902862\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.38447i | 0.272483i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −49.4773 | −2.10780 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −42.7386 | −1.81743 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14.9309i | 0.633780i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 10.3002i | − 0.436433i | −0.975900 | − | 0.218216i | \(-0.929976\pi\) | ||||
0.975900 | − | 0.218216i | \(-0.0700239\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.8078 | −0.499415 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.1231 | −0.469618 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 31.3153i | − 1.31978i | −0.751360 | − | 0.659892i | \(-0.770602\pi\) | ||||
0.751360 | − | 0.659892i | \(-0.229398\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29.3693i | 1.23558i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 24.9309 | 1.04700 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.3153 | 0.558208 | 0.279104 | − | 0.960261i | \(-0.409963\pi\) | ||||
0.279104 | + | 0.960261i | \(0.409963\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 21.5616i | − 0.902323i | −0.892442 | − | 0.451161i | \(-0.851010\pi\) | ||||
0.892442 | − | 0.451161i | \(-0.148990\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.38447i | 0.350266i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.7386 | 1.86249 | 0.931247 | − | 0.364389i | \(-0.118722\pi\) | ||||
0.931247 | + | 0.364389i | \(0.118722\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 36.4924i | − 1.51657i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.2462i | 1.08888i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.2462 | 1.08701 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.00000 | 0.0826898 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.3693i | 0.634360i | 0.948365 | + | 0.317180i | \(0.102736\pi\) | ||||
−0.948365 | + | 0.317180i | \(0.897264\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.73863i | 0.277661i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.05398 | −0.0844893 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.75379 | 0.154150 | 0.0770748 | − | 0.997025i | \(-0.475442\pi\) | ||||
0.0770748 | + | 0.997025i | \(0.475442\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 45.1771i | 1.85208i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.6307i | 0.598794i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.6307 | −0.434358 | −0.217179 | − | 0.976132i | \(-0.569686\pi\) | ||||
−0.217179 | + | 0.976132i | \(0.569686\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.0540 | −0.654855 | −0.327428 | − | 0.944876i | \(-0.606182\pi\) | ||||
−0.327428 | + | 0.944876i | \(0.606182\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 3.36932i | − 0.137209i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 24.9309i | − 1.01358i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.8617 | −1.04970 | −0.524848 | − | 0.851196i | \(-0.675878\pi\) | ||||
−0.524848 | + | 0.851196i | \(0.675878\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −45.8617 | −1.85841 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 10.6847i | − 0.432255i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.0000i | 0.403896i | 0.979396 | + | 0.201948i | \(0.0647272\pi\) | ||||
−0.979396 | + | 0.201948i | \(0.935273\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.24621 | 0.251872 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.6155 | −0.709174 | −0.354587 | − | 0.935023i | \(-0.615379\pi\) | ||||
−0.354587 | + | 0.935023i | \(0.615379\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 15.3693i | − 0.617745i | −0.951103 | − | 0.308873i | \(-0.900048\pi\) | ||||
0.951103 | − | 0.308873i | \(-0.0999516\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 29.3693 | 1.17666 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.36932 | −0.174773 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.7386i | 0.748349i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.56155i | 0.381244i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.94602 | −0.157089 | −0.0785444 | − | 0.996911i | \(-0.525027\pi\) | ||||
−0.0785444 | + | 0.996911i | \(0.525027\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 37.1771 | 1.47766 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 50.7386i | 2.01350i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.68466i | 0.225234i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.00000 | −0.237356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.4924 | −0.888397 | −0.444199 | − | 0.895928i | \(-0.646512\pi\) | ||||
−0.444199 | + | 0.895928i | \(0.646512\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.0000i | 0.709851i | 0.934895 | + | 0.354925i | \(0.115494\pi\) | ||||
−0.934895 | + | 0.354925i | \(0.884506\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 65.6695i | 2.58573i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −44.1080 | −1.73406 | −0.867031 | − | 0.498254i | \(-0.833975\pi\) | ||||
−0.867031 | + | 0.498254i | \(0.833975\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.0000 | 0.471041 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.24621i | 0.244808i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.38447i | 0.249844i | 0.992167 | + | 0.124922i | \(0.0398680\pi\) | ||||
−0.992167 | + | 0.124922i | \(0.960132\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.8078 | −0.461368 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.61553 | −0.219083 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 12.0000i | − 0.467454i | −0.972302 | − | 0.233727i | \(-0.924908\pi\) | ||||
0.972302 | − | 0.233727i | \(-0.0750921\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.7386i | 1.11780i | 0.829234 | + | 0.558902i | \(0.188777\pi\) | ||||
−0.829234 | + | 0.558902i | \(0.811223\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.56155 | −0.215993 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 76.1080 | 2.95134 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.66950i | 0.373845i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.7386 | −0.877815 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.0540 | 0.618835 | 0.309418 | − | 0.950926i | \(-0.399866\pi\) | ||||
0.309418 | + | 0.950926i | \(0.399866\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 42.7386i | − 1.64501i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 3.36932i | − 0.129493i | −0.997902 | − | 0.0647467i | \(-0.979376\pi\) | ||||
0.997902 | − | 0.0647467i | \(-0.0206239\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.3693 | 0.820079 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.26137 | −0.201616 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.3693i | 0.741146i | 0.928803 | + | 0.370573i | \(0.120839\pi\) | ||||
−0.928803 | + | 0.370573i | \(0.879161\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 46.7386i | 1.78579i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.05398 | −0.0783640 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.1231 | 0.499951 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.1231i | 0.499226i | 0.968346 | + | 0.249613i | \(0.0803035\pi\) | ||||
−0.968346 | + | 0.249613i | \(0.919697\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 4.00000i | − 0.151947i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.6847 | −0.632885 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | 0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 2.05398i | − 0.0776885i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.3693i | 0.580491i | 0.956952 | + | 0.290246i | \(0.0937370\pi\) | ||||
−0.956952 | + | 0.290246i | \(0.906263\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.1080 | 0.607523 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −59.4233 | −2.23801 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4.00000i | − 0.150435i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 32.7386i | − 1.22953i | −0.788712 | − | 0.614763i | \(-0.789252\pi\) | ||||
0.788712 | − | 0.614763i | \(-0.210748\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.73863 | 0.252719 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.12311i | 0.266389i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.5464i | 0.543245i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.36932 | 0.349417 | 0.174708 | − | 0.984620i | \(-0.444102\pi\) | ||||
0.174708 | + | 0.984620i | \(0.444102\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.12311i | 0.116150i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 63.3693i | 2.35348i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.384472 | 0.0142593 | 0.00712964 | − | 0.999975i | \(-0.497731\pi\) | ||||
0.00712964 | + | 0.999975i | \(0.497731\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.9848 | −1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 42.0540i | 1.55542i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 12.0540i | − 0.445224i | −0.974907 | − | 0.222612i | \(-0.928542\pi\) | ||||
0.974907 | − | 0.222612i | \(-0.0714583\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 31.6155 | 1.16616 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.0000 | 0.442026 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 22.1080i | − 0.813254i | −0.913594 | − | 0.406627i | \(-0.866705\pi\) | ||||
0.913594 | − | 0.406627i | \(-0.133295\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.36932i | 0.344190i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.31534 | −0.0482552 | −0.0241276 | − | 0.999709i | \(-0.507681\pi\) | ||||
−0.0241276 | + | 0.999709i | \(0.507681\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.3693 | 1.07601 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 4.13826i | − 0.151411i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 42.7386i | 1.56164i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.75379 | −0.355921 | −0.177960 | − | 0.984038i | \(-0.556950\pi\) | ||||
−0.177960 | + | 0.984038i | \(0.556950\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.9848 | 0.910498 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 80.7926i | 2.94034i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.3693i | 0.558607i | 0.960203 | + | 0.279304i | \(0.0901036\pi\) | ||||
−0.960203 | + | 0.279304i | \(0.909896\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.0000 | 1.08750 | 0.543750 | − | 0.839248i | \(-0.317004\pi\) | ||||
0.543750 | + | 0.839248i | \(0.317004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38.0540i | 1.37765i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 7.12311i | − 0.257536i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.00000 | 0.216647 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.3693 | −0.554232 | −0.277116 | − | 0.960837i | \(-0.589379\pi\) | ||||
−0.277116 | + | 0.960837i | \(0.589379\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 20.1922i | − 0.727206i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 13.3153i | − 0.478920i | −0.970906 | − | 0.239460i | \(-0.923030\pi\) | ||||
0.970906 | − | 0.239460i | \(-0.0769703\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.63068 | 0.310023 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.9309 | 0.535642 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 6.73863i | − 0.241437i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 21.3693i | − 0.764654i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 45.8617 | 1.63896 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.12311 | −0.254235 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.61553i | 0.200172i | 0.994979 | + | 0.100086i | \(0.0319118\pi\) | ||||
−0.994979 | + | 0.100086i | \(0.968088\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 35.5076i | 1.26410i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.3693 | 1.04425 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.3693 | −0.403736 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 72.9848i | − 2.58851i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 36.7386i | − 1.30135i | −0.759357 | − | 0.650675i | \(-0.774486\pi\) | ||||
0.759357 | − | 0.650675i | \(-0.225514\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.0540 | −1.34625 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.63068 | −0.163617 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 20.0000i | − 0.705785i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.26137 | 0.185209 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.0691 | 0.389170 | 0.194585 | − | 0.980886i | \(-0.437664\pi\) | ||||
0.194585 | + | 0.980886i | \(0.437664\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 31.8617i | − 1.11882i | −0.828892 | − | 0.559408i | \(-0.811028\pi\) | ||||
0.828892 | − | 0.559408i | \(-0.188972\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 16.6847i | − 0.585157i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 54.7386 | 1.91741 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 70.8466 | 2.47861 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 2.00000i | − 0.0698857i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 32.0540i | − 1.11869i | −0.828934 | − | 0.559346i | \(-0.811052\pi\) | ||||
0.828934 | − | 0.559346i | \(-0.188948\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.6307 | 0.509994 | 0.254997 | − | 0.966942i | \(-0.417926\pi\) | ||||
0.254997 | + | 0.966942i | \(0.417926\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 24.0000 | 0.835573 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.7386i | 0.442966i | 0.975164 | + | 0.221483i | \(0.0710897\pi\) | ||||
−0.975164 | + | 0.221483i | \(0.928910\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 16.7386i | − 0.581357i | −0.956821 | − | 0.290678i | \(-0.906119\pi\) | ||||
0.956821 | − | 0.290678i | \(-0.0938810\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.4924 | −1.26591 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.2462 | 0.701490 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 54.7386i | 1.89431i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 6.24621i | − 0.215901i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.1080 | 1.31563 | 0.657816 | − | 0.753178i | \(-0.271480\pi\) | ||||
0.657816 | + | 0.753178i | \(0.271480\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −39.0000 | −1.34483 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 5.86174i | − 0.201889i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.56155i | 0.122521i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.9309 | −0.856635 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.2462 | 0.763488 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.31534i | 0.318951i | 0.987202 | + | 0.159476i | \(0.0509803\pi\) | ||||
−0.987202 | + | 0.159476i | \(0.949020\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.0000 | −0.410391 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.7538 | 0.538139 | 0.269070 | − | 0.963121i | \(-0.413284\pi\) | ||||
0.269070 | + | 0.963121i | \(0.413284\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 36.0000i | − 1.22830i | −0.789188 | − | 0.614152i | \(-0.789498\pi\) | ||||
0.789188 | − | 0.614152i | \(-0.210502\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 6.24621i | − 0.212870i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.0540 | 0.410322 | 0.205161 | − | 0.978728i | \(-0.434228\pi\) | ||||
0.205161 | + | 0.978728i | \(0.434228\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0000 | 0.408012 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 6.73863i | − 0.228856i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.0000i | 0.814144i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.00000 | 0.203302 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.36932 | −0.114034 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 34.0540i | − 1.15123i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 54.7926i | − 1.85021i | −0.379705 | − | 0.925107i | \(-0.623975\pi\) | ||||
0.379705 | − | 0.925107i | \(-0.376025\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 43.0388 | 1.45166 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.3002 | 1.15560 | 0.577801 | − | 0.816177i | \(-0.303911\pi\) | ||||
0.577801 | + | 0.816177i | \(0.303911\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.5616i | 0.725604i | 0.931866 | + | 0.362802i | \(0.118180\pi\) | ||||
−0.931866 | + | 0.362802i | \(0.881820\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 33.3693i | − 1.12170i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.0000 | −0.402921 | −0.201460 | − | 0.979497i | \(-0.564569\pi\) | ||||
−0.201460 | + | 0.979497i | \(0.564569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 50.7386 | 1.70172 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 14.0000i | − 0.469018i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 64.1080i | 2.14529i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −64.3002 | −2.14932 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.26137i | 0.308884i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 46.7386i | − 1.55709i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 65.6695 | 2.18534 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26.2462 | −0.872454 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 35.4233i | − 1.17621i | −0.808784 | − | 0.588106i | \(-0.799874\pi\) | ||||
0.808784 | − | 0.588106i | \(-0.200126\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.630683i | 0.0209184i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.63068 | −0.0871584 | −0.0435792 | − | 0.999050i | \(-0.513876\pi\) | ||||
−0.0435792 | + | 0.999050i | \(0.513876\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.7386 | 0.487778 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 63.2311i | 2.09035i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.8078i | 0.389927i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.2462 | −1.65747 | −0.828735 | − | 0.559642i | \(-0.810939\pi\) | ||||
−0.828735 | + | 0.559642i | \(0.810939\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.36932 | −0.308729 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 10.6847i | − 0.351690i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 20.6307i | − 0.678333i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.61553 | −0.184240 | −0.0921198 | − | 0.995748i | \(-0.529364\pi\) | ||||
−0.0921198 | + | 0.995748i | \(0.529364\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 34.1080i | − 1.11784i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 14.6307i | − 0.478987i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 25.3693 | 0.829665 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.73863 | 0.285479 | 0.142739 | − | 0.989760i | \(-0.454409\pi\) | ||||
0.142739 | + | 0.989760i | \(0.454409\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.3153i | 1.02194i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 25.3153i | − 0.825257i | −0.910900 | − | 0.412628i | \(-0.864611\pi\) | ||||
0.910900 | − | 0.412628i | \(-0.135389\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −70.5464 | −2.29487 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 2.00000i | − 0.0649913i | −0.999472 | − | 0.0324956i | \(-0.989654\pi\) | ||||
0.999472 | − | 0.0324956i | \(-0.0103455\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 10.0000i | − 0.324614i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.6004 | −0.797722 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.8078 | 1.35429 | 0.677143 | − | 0.735851i | \(-0.263218\pi\) | ||||
0.677143 | + | 0.735851i | \(0.263218\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 19.1231i | − 0.618809i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25.7538i | 0.832502i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 46.7386 | 1.50927 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.7386 | −0.959311 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 6.73863i | − 0.217149i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 83.2311i | 2.67930i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53.4233 | −1.71798 | −0.858989 | − | 0.511995i | \(-0.828907\pi\) | ||||
−0.858989 | + | 0.511995i | \(0.828907\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33.3693 | 1.07198 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 3.31534i | − 0.106394i | −0.998584 | − | 0.0531972i | \(-0.983059\pi\) | ||||
0.998584 | − | 0.0531972i | \(-0.0169412\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.6847i | 0.534886i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.0000 | 0.384308 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.9848 | −0.479408 | −0.239704 | − | 0.970846i | \(-0.577050\pi\) | ||||
−0.239704 | + | 0.970846i | \(0.577050\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 16.4924i | − 0.527100i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 6.00000i | − 0.191565i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.4233 | 0.683297 | 0.341648 | − | 0.939828i | \(-0.389015\pi\) | ||||
0.341648 | + | 0.939828i | \(0.389015\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.68466 | 0.149266 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 59.4233i | 1.89146i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.3693 | −0.678819 | −0.339409 | − | 0.940639i | \(-0.610227\pi\) | ||||
−0.339409 | + | 0.940639i | \(0.610227\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.26137 | 0.166964 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 33.3693i | − 1.05788i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 4.73863i | − 0.150074i | −0.997181 | − | 0.0750370i | \(-0.976093\pi\) | ||||
0.997181 | − | 0.0750370i | \(-0.0239075\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.9309 | −0.472392 |
(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 | 3328.2.b.u.1665.3 | 4 | ||
4.3 | odd | 2 | 3328.2.b.ba.1665.2 | 4 | |||
8.3 | odd | 2 | 3328.2.b.ba.1665.3 | 4 | |||
8.5 | even | 2 | inner | 3328.2.b.u.1665.2 | 4 | ||
16.3 | odd | 4 | 416.2.a.c.1.2 | ✓ | 2 | ||
16.5 | even | 4 | 832.2.a.l.1.2 | 2 | |||
16.11 | odd | 4 | 832.2.a.o.1.1 | 2 | |||
16.13 | even | 4 | 416.2.a.e.1.1 | yes | 2 | ||
48.5 | odd | 4 | 7488.2.a.cf.1.1 | 2 | |||
48.11 | even | 4 | 7488.2.a.ce.1.1 | 2 | |||
48.29 | odd | 4 | 3744.2.a.y.1.2 | 2 | |||
48.35 | even | 4 | 3744.2.a.x.1.2 | 2 | |||
208.51 | odd | 4 | 5408.2.a.p.1.2 | 2 | |||
208.77 | even | 4 | 5408.2.a.bd.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
416.2.a.c.1.2 | ✓ | 2 | 16.3 | odd | 4 | ||
416.2.a.e.1.1 | yes | 2 | 16.13 | even | 4 | ||
832.2.a.l.1.2 | 2 | 16.5 | even | 4 | |||
832.2.a.o.1.1 | 2 | 16.11 | odd | 4 | |||
3328.2.b.u.1665.2 | 4 | 8.5 | even | 2 | inner | ||
3328.2.b.u.1665.3 | 4 | 1.1 | even | 1 | trivial | ||
3328.2.b.ba.1665.2 | 4 | 4.3 | odd | 2 | |||
3328.2.b.ba.1665.3 | 4 | 8.3 | odd | 2 | |||
3744.2.a.x.1.2 | 2 | 48.35 | even | 4 | |||
3744.2.a.y.1.2 | 2 | 48.29 | odd | 4 | |||
5408.2.a.p.1.2 | 2 | 208.51 | odd | 4 | |||
5408.2.a.bd.1.1 | 2 | 208.77 | even | 4 | |||
7488.2.a.ce.1.1 | 2 | 48.11 | even | 4 | |||
7488.2.a.cf.1.1 | 2 | 48.5 | odd | 4 |