Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,2,Mod(737,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 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("4140.737");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.s (of order \(4\), degree \(2\), 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: | \(33.0580664368\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 737.13 | ||
Character | \(\chi\) | \(=\) | 4140.737 |
Dual form | 4140.2.s.a.2393.13 |
$q$-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 \(\left(\mathbb{Z}/4140\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(2071\) | \(3961\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.210429 | − | 2.22614i | 0.0941068 | − | 0.995562i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.752416 | − | 0.752416i | −0.284386 | − | 0.284386i | 0.550469 | − | 0.834856i | \(-0.314449\pi\) |
−0.834856 | + | 0.550469i | \(0.814449\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.75883i | 1.43484i | 0.696640 | + | 0.717420i | \(0.254677\pi\) | ||||
−0.696640 | + | 0.717420i | \(0.745323\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.05967 | − | 2.05967i | 0.571249 | − | 0.571249i | −0.361228 | − | 0.932477i | \(-0.617643\pi\) |
0.932477 | + | 0.361228i | \(0.117643\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.677484 | + | 0.677484i | −0.164314 | + | 0.164314i | −0.784475 | − | 0.620161i | \(-0.787067\pi\) |
0.620161 | + | 0.784475i | \(0.287067\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.92461i | 1.35920i | 0.733583 | + | 0.679600i | \(0.237847\pi\) | ||||
−0.733583 | + | 0.679600i | \(0.762153\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.707107 | + | 0.707107i | 0.147442 | + | 0.147442i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.91144 | − | 0.936892i | −0.982288 | − | 0.187378i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.804303 | 0.149355 | 0.0746777 | − | 0.997208i | \(-0.476207\pi\) | ||||
0.0746777 | + | 0.997208i | \(0.476207\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.39171 | −0.788774 | −0.394387 | − | 0.918944i | \(-0.629043\pi\) | ||||
−0.394387 | + | 0.918944i | \(0.629043\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.83332 | + | 1.51666i | −0.309887 | + | 0.256362i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.33722 | − | 4.33722i | −0.713034 | − | 0.713034i | 0.254135 | − | 0.967169i | \(-0.418209\pi\) |
−0.967169 | + | 0.254135i | \(0.918209\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.94156i | 0.459395i | 0.973262 | + | 0.229698i | \(0.0737737\pi\) | ||||
−0.973262 | + | 0.229698i | \(0.926226\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.65092 | + | 7.65092i | −1.16675 | + | 1.16675i | −0.183789 | + | 0.982966i | \(0.558836\pi\) |
−0.982966 | + | 0.183789i | \(0.941164\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.31631 | + | 1.31631i | −0.192004 | + | 0.192004i | −0.796562 | − | 0.604557i | \(-0.793350\pi\) |
0.604557 | + | 0.796562i | \(0.293350\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.86774i | − | 0.838249i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.70484 | − | 2.70484i | −0.371539 | − | 0.371539i | 0.496499 | − | 0.868037i | \(-0.334619\pi\) |
−0.868037 | + | 0.496499i | \(0.834619\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.5938 | + | 1.00140i | 1.42847 | + | 0.135028i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.18339 | 0.154065 | 0.0770324 | − | 0.997029i | \(-0.475456\pi\) | ||||
0.0770324 | + | 0.997029i | \(0.475456\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.39500 | −0.178612 | −0.0893060 | − | 0.996004i | \(-0.528465\pi\) | ||||
−0.0893060 | + | 0.996004i | \(0.528465\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.15170 | − | 5.01853i | −0.514955 | − | 0.622472i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.77662 | − | 5.77662i | −0.705727 | − | 0.705727i | 0.259907 | − | 0.965634i | \(-0.416308\pi\) |
−0.965634 | + | 0.259907i | \(0.916308\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.358118i | − | 0.0425008i | −0.999774 | − | 0.0212504i | \(-0.993235\pi\) | ||
0.999774 | − | 0.0212504i | \(-0.00676472\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.71045 | + | 7.71045i | −0.902440 | + | 0.902440i | −0.995647 | − | 0.0932072i | \(-0.970288\pi\) |
0.0932072 | + | 0.995647i | \(0.470288\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.58062 | − | 3.58062i | 0.408049 | − | 0.408049i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.1347i | 1.81529i | 0.419738 | + | 0.907645i | \(0.362122\pi\) | ||||
−0.419738 | + | 0.907645i | \(0.637878\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.51844 | − | 4.51844i | −0.495964 | − | 0.495964i | 0.414215 | − | 0.910179i | \(-0.364056\pi\) |
−0.910179 | + | 0.414215i | \(0.864056\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.36561 | + | 1.65074i | 0.148122 | + | 0.179048i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.32590 | 0.670544 | 0.335272 | − | 0.942121i | \(-0.391172\pi\) | ||||
0.335272 | + | 0.942121i | \(0.391172\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.09945 | −0.324911 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 13.1890 | + | 1.24671i | 1.35317 | + | 0.127910i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.86844 | − | 9.86844i | −1.00199 | − | 1.00199i | −0.999998 | − | 0.00198979i | \(-0.999367\pi\) |
−0.00198979 | − | 0.999998i | \(-0.500633\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.5152i | 1.74282i | 0.490553 | + | 0.871411i | \(0.336795\pi\) | ||||
−0.490553 | + | 0.871411i | \(0.663205\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.27073 | + | 6.27073i | −0.617874 | + | 0.617874i | −0.944986 | − | 0.327112i | \(-0.893925\pi\) |
0.327112 | + | 0.944986i | \(0.393925\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.948397 | + | 0.948397i | −0.0916850 | + | 0.0916850i | −0.751462 | − | 0.659777i | \(-0.770651\pi\) |
0.659777 | + | 0.751462i | \(0.270651\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 0.175410i | − | 0.0168013i | −0.999965 | − | 0.00840064i | \(-0.997326\pi\) | ||
0.999965 | − | 0.00840064i | \(-0.00267404\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.21524 | + | 9.21524i | 0.866897 | + | 0.866897i | 0.992128 | − | 0.125230i | \(-0.0399670\pi\) |
−0.125230 | + | 0.992128i | \(0.539967\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.72292 | − | 1.42533i | 0.160663 | − | 0.132912i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.01950 | 0.0934573 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.6465 | −1.05877 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.11917 | + | 10.7364i | −0.278987 | + | 0.960295i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.06887 | + | 8.06887i | 0.715996 | + | 0.715996i | 0.967783 | − | 0.251787i | \(-0.0810181\pi\) |
−0.251787 | + | 0.967783i | \(0.581018\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.80108i | 0.681583i | 0.940139 | + | 0.340792i | \(0.110695\pi\) | ||||
−0.940139 | + | 0.340792i | \(0.889305\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.45777 | − | 4.45777i | 0.386538 | − | 0.386538i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.63846 | + | 6.63846i | −0.567162 | + | 0.567162i | −0.931332 | − | 0.364170i | \(-0.881353\pi\) |
0.364170 | + | 0.931332i | \(0.381353\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.7140i | 1.24802i | 0.781416 | + | 0.624011i | \(0.214498\pi\) | ||||
−0.781416 | + | 0.624011i | \(0.785502\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.80160 | + | 9.80160i | 0.819651 | + | 0.819651i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.169249 | − | 1.79050i | 0.0140554 | − | 0.148693i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.5155 | 1.92646 | 0.963231 | − | 0.268676i | \(-0.0865862\pi\) | ||||
0.963231 | + | 0.268676i | \(0.0865862\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.84283 | 0.394104 | 0.197052 | − | 0.980393i | \(-0.436863\pi\) | ||||
0.197052 | + | 0.980393i | \(0.436863\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.924144 | + | 9.77657i | −0.0742290 | + | 0.785273i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.6371 | − | 13.6371i | −1.08836 | − | 1.08836i | −0.995697 | − | 0.0926642i | \(-0.970462\pi\) |
−0.0926642 | − | 0.995697i | \(-0.529538\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.06408i | − | 0.0838610i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.4726 | − | 12.4726i | 0.976930 | − | 0.976930i | −0.0228100 | − | 0.999740i | \(-0.507261\pi\) |
0.999740 | + | 0.0228100i | \(0.00726127\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.57572 | − | 4.57572i | 0.354080 | − | 0.354080i | −0.507545 | − | 0.861625i | \(-0.669447\pi\) |
0.861625 | + | 0.507545i | \(0.169447\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.51554i | 0.347349i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.6051 | + | 12.6051i | 0.958348 | + | 0.958348i | 0.999167 | − | 0.0408186i | \(-0.0129966\pi\) |
−0.0408186 | + | 0.999167i | \(0.512997\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.99051 | + | 4.40038i | 0.226061 | + | 0.332637i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.5123 | −1.08470 | −0.542351 | − | 0.840152i | \(-0.682466\pi\) | ||||
−0.542351 | + | 0.840152i | \(0.682466\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.93029 | 0.143478 | 0.0717388 | − | 0.997423i | \(-0.477145\pi\) | ||||
0.0717388 | + | 0.997423i | \(0.477145\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.5680 | + | 8.74260i | −0.776971 | + | 0.642769i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.22403 | − | 3.22403i | −0.235764 | − | 0.235764i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.7028i | 1.28093i | 0.767987 | + | 0.640465i | \(0.221258\pi\) | ||||
−0.767987 | + | 0.640465i | \(0.778742\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.7011 | − | 10.7011i | 0.770282 | − | 0.770282i | −0.207874 | − | 0.978156i | \(-0.566654\pi\) |
0.978156 | + | 0.207874i | \(0.0666544\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.13907 | + | 9.13907i | −0.651132 | + | 0.651132i | −0.953265 | − | 0.302134i | \(-0.902301\pi\) |
0.302134 | + | 0.953265i | \(0.402301\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 9.68060i | − | 0.686240i | −0.939292 | − | 0.343120i | \(-0.888516\pi\) | ||
0.939292 | − | 0.343120i | \(-0.111484\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.605170 | − | 0.605170i | −0.0424746 | − | 0.0424746i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.54835 | + | 0.618991i | 0.457356 | + | 0.0432322i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −28.1942 | −1.95024 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.3515 | −1.46990 | −0.734951 | − | 0.678121i | \(-0.762795\pi\) | ||||
−0.734951 | + | 0.678121i | \(0.762795\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.4221 | + | 18.6420i | 1.05178 | + | 1.27138i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.30439 | + | 3.30439i | 0.224317 | + | 0.224317i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.79078i | 0.187728i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.62746 | − | 2.62746i | 0.175948 | − | 0.175948i | −0.613639 | − | 0.789587i | \(-0.710295\pi\) |
0.789587 | + | 0.613639i | \(0.210295\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.99682 | + | 1.99682i | −0.132533 | + | 0.132533i | −0.770262 | − | 0.637728i | \(-0.779874\pi\) |
0.637728 | + | 0.770262i | \(0.279874\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.10903i | − | 0.403696i | −0.979417 | − | 0.201848i | \(-0.935305\pi\) | ||
0.979417 | − | 0.201848i | \(-0.0646947\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.2569 | + | 18.2569i | 1.19605 | + | 1.19605i | 0.975339 | + | 0.220710i | \(0.0708375\pi\) |
0.220710 | + | 0.975339i | \(0.429163\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.65331 | + | 3.20730i | 0.173083 | + | 0.209221i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.1979 | 1.24181 | 0.620906 | − | 0.783885i | \(-0.286765\pi\) | ||||
0.620906 | + | 0.783885i | \(0.286765\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.5227 | −1.19315 | −0.596577 | − | 0.802556i | \(-0.703473\pi\) | ||||
−0.596577 | + | 0.802556i | \(0.703473\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.0624 | − | 1.23474i | −0.834529 | − | 0.0788849i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.2027 | + | 12.2027i | 0.776441 | + | 0.776441i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 14.6176i | − | 0.922656i | −0.887230 | − | 0.461328i | \(-0.847373\pi\) | ||
0.887230 | − | 0.461328i | \(-0.152627\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.36500 | + | 3.36500i | −0.211556 | + | 0.211556i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.98931 | + | 2.98931i | −0.186468 | + | 0.186468i | −0.794167 | − | 0.607699i | \(-0.792093\pi\) |
0.607699 | + | 0.794167i | \(0.292093\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.52678i | 0.405555i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.30665 | + | 9.30665i | 0.573873 | + | 0.573873i | 0.933208 | − | 0.359336i | \(-0.116997\pi\) |
−0.359336 | + | 0.933208i | \(0.616997\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.59055 | + | 5.45219i | −0.404854 | + | 0.334926i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.69962 | −0.347512 | −0.173756 | − | 0.984789i | \(-0.555590\pi\) | ||||
−0.173756 | + | 0.984789i | \(0.555590\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.01919 | −0.183403 | −0.0917015 | − | 0.995787i | \(-0.529231\pi\) | ||||
−0.0917015 | + | 0.995787i | \(0.529231\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.45851 | − | 23.3727i | 0.268858 | − | 1.40943i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.44175 | + | 1.44175i | 0.0866265 | + | 0.0866265i | 0.749092 | − | 0.662466i | \(-0.230490\pi\) |
−0.662466 | + | 0.749092i | \(0.730490\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 21.0603i | − | 1.25635i | −0.778070 | − | 0.628177i | \(-0.783801\pi\) | ||
0.778070 | − | 0.628177i | \(-0.216199\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.5144 | − | 16.5144i | 0.981679 | − | 0.981679i | −0.0181560 | − | 0.999835i | \(-0.505780\pi\) |
0.999835 | + | 0.0181560i | \(0.00577955\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.21328 | − | 2.21328i | 0.130646 | − | 0.130646i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.0820i | 0.946002i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.89113 | + | 1.89113i | 0.110481 | + | 0.110481i | 0.760186 | − | 0.649705i | \(-0.225108\pi\) |
−0.649705 | + | 0.760186i | \(0.725108\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.249021 | − | 2.63441i | 0.0144985 | − | 0.153381i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.91281 | 0.168452 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.5133 | 0.663618 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.293550 | + | 3.10548i | −0.0168086 | + | 0.177819i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.36725 | + | 2.36725i | 0.135106 | + | 0.135106i | 0.771425 | − | 0.636320i | \(-0.219544\pi\) |
−0.636320 | + | 0.771425i | \(0.719544\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.14616i | 0.178402i | 0.996014 | + | 0.0892012i | \(0.0284314\pi\) | ||||
−0.996014 | + | 0.0892012i | \(0.971569\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.415125 | − | 0.415125i | 0.0234643 | − | 0.0234643i | −0.695277 | − | 0.718742i | \(-0.744718\pi\) |
0.718742 | + | 0.695277i | \(0.244718\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.71868 | − | 3.71868i | 0.208862 | − | 0.208862i | −0.594922 | − | 0.803784i | \(-0.702817\pi\) |
0.803784 | + | 0.594922i | \(0.202817\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.82754i | 0.214301i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.01383 | − | 4.01383i | −0.223335 | − | 0.223335i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.0456 | + | 8.18624i | −0.668171 | + | 0.454091i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.98083 | 0.109207 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.8665 | −1.09196 | −0.545981 | − | 0.837798i | \(-0.683843\pi\) | ||||
−0.545981 | + | 0.837798i | \(0.683843\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.0752 | + | 11.6440i | −0.769008 | + | 0.636181i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.5003 | − | 11.5003i | −0.626459 | − | 0.626459i | 0.320716 | − | 0.947175i | \(-0.396076\pi\) |
−0.947175 | + | 0.320716i | \(0.896076\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 20.8994i | − | 1.13176i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.68189 | + | 9.68189i | −0.522773 | + | 0.522773i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.4124 | − | 16.4124i | 0.881062 | − | 0.881062i | −0.112580 | − | 0.993643i | \(-0.535912\pi\) |
0.993643 | + | 0.112580i | \(0.0359115\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.94255i | 0.425155i | 0.977144 | + | 0.212578i | \(0.0681858\pi\) | ||||
−0.977144 | + | 0.212578i | \(0.931814\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.82194 | + | 5.82194i | 0.309870 | + | 0.309870i | 0.844859 | − | 0.534989i | \(-0.179684\pi\) |
−0.534989 | + | 0.844859i | \(0.679684\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.797223 | − | 0.0753585i | −0.0423122 | − | 0.00399962i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.5292 | −1.03071 | −0.515357 | − | 0.856976i | \(-0.672341\pi\) | ||||
−0.515357 | + | 0.856976i | \(0.672341\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.1011 | −0.847424 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.5421 | + | 18.7871i | 0.813509 | + | 0.983360i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.5735 | − | 24.5735i | −1.28273 | − | 1.28273i | −0.939111 | − | 0.343615i | \(-0.888349\pi\) |
−0.343615 | − | 0.939111i | \(-0.611651\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.07033i | 0.211321i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.3610 | + | 14.3610i | −0.743584 | + | 0.743584i | −0.973266 | − | 0.229681i | \(-0.926232\pi\) |
0.229681 | + | 0.973266i | \(0.426232\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.65660 | − | 1.65660i | 0.0853191 | − | 0.0853191i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.8036i | 1.89047i | 0.326387 | + | 0.945236i | \(0.394169\pi\) | ||||
−0.326387 | + | 0.945236i | \(0.605831\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.05818 | − | 7.05818i | −0.360656 | − | 0.360656i | 0.503398 | − | 0.864054i | \(-0.332083\pi\) |
−0.864054 | + | 0.503398i | \(0.832083\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.21751 | − | 8.72444i | −0.367838 | − | 0.444639i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −36.1347 | −1.83210 | −0.916051 | − | 0.401061i | \(-0.868641\pi\) | ||||
−0.916051 | + | 0.401061i | \(0.868641\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.958107 | −0.0484535 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 35.9181 | + | 3.39520i | 1.80723 | + | 0.170831i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.77660 | − | 3.77660i | −0.189542 | − | 0.189542i | 0.605956 | − | 0.795498i | \(-0.292791\pi\) |
−0.795498 | + | 0.605956i | \(0.792791\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.8787i | 0.593194i | 0.955003 | + | 0.296597i | \(0.0958517\pi\) | ||||
−0.955003 | + | 0.296597i | \(0.904148\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.04545 | + | 9.04545i | −0.450586 | + | 0.450586i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.6401 | − | 20.6401i | 1.02309 | − | 1.02309i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.02322i | − | 0.198935i | −0.995041 | − | 0.0994677i | \(-0.968286\pi\) | ||
0.995041 | − | 0.0994677i | \(-0.0317140\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.890404 | − | 0.890404i | −0.0438139 | − | 0.0438139i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.0095 | + | 9.10790i | −0.540436 | + | 0.447089i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.8221 | −1.35920 | −0.679600 | − | 0.733582i | \(-0.737847\pi\) | ||||
−0.679600 | + | 0.733582i | \(0.737847\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.3150 | 1.42873 | 0.714363 | − | 0.699775i | \(-0.246716\pi\) | ||||
0.714363 | + | 0.699775i | \(0.246716\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.96215 | − | 2.69269i | 0.192192 | − | 0.130615i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.04962 | + | 1.04962i | 0.0507948 | + | 0.0507948i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 21.0862i | − | 1.01569i | −0.861449 | − | 0.507844i | \(-0.830443\pi\) | ||
0.861449 | − | 0.507844i | \(-0.169557\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.21096 | + | 3.21096i | −0.154309 | + | 0.154309i | −0.780039 | − | 0.625730i | \(-0.784801\pi\) |
0.625730 | + | 0.780039i | \(0.284801\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.18934 | + | 4.18934i | −0.200403 | + | 0.200403i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 38.8334i | − | 1.85342i | −0.375782 | − | 0.926708i | \(-0.622626\pi\) | ||
0.375782 | − | 0.926708i | \(-0.377374\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.09689 | − | 2.09689i | −0.0996264 | − | 0.0996264i | 0.655537 | − | 0.755163i | \(-0.272442\pi\) |
−0.755163 | + | 0.655537i | \(0.772442\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.33115 | − | 14.0824i | 0.0631028 | − | 0.667568i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.2465 | −0.719529 | −0.359764 | − | 0.933043i | \(-0.617143\pi\) | ||||
−0.359764 | + | 0.933043i | \(0.617143\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.9984 | −0.659159 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.652216 | + | 6.89983i | −0.0305763 | + | 0.323469i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.2684 | + | 16.2684i | 0.761003 | + | 0.761003i | 0.976504 | − | 0.215501i | \(-0.0691385\pi\) |
−0.215501 | + | 0.976504i | \(0.569138\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3.97766i | − | 0.185258i | −0.995701 | − | 0.0926289i | \(-0.970473\pi\) | ||
0.995701 | − | 0.0926289i | \(-0.0295270\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.15033 | + | 2.15033i | −0.0999342 | + | 0.0999342i | −0.755306 | − | 0.655372i | \(-0.772512\pi\) |
0.655372 | + | 0.755306i | \(0.272512\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.21894 | + | 5.21894i | −0.241504 | + | 0.241504i | −0.817472 | − | 0.575968i | \(-0.804625\pi\) |
0.575968 | + | 0.817472i | \(0.304625\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.69284i | 0.401398i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −36.4094 | − | 36.4094i | −1.67411 | − | 1.67411i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.55072 | − | 29.0984i | 0.254685 | − | 1.33513i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.1775 | −0.876242 | −0.438121 | − | 0.898916i | \(-0.644356\pi\) | ||||
−0.438121 | + | 0.898916i | \(0.644356\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.8665 | −0.814640 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −24.0452 | + | 19.8920i | −1.09183 | + | 0.903247i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.74315 | + | 3.74315i | 0.169618 | + | 0.169618i | 0.786812 | − | 0.617193i | \(-0.211730\pi\) |
−0.617193 | + | 0.786812i | \(0.711730\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7.00716i | − | 0.316229i | −0.987421 | − | 0.158114i | \(-0.949459\pi\) | ||
0.987421 | − | 0.158114i | \(-0.0505415\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.544902 | + | 0.544902i | −0.0245412 | + | 0.0245412i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.269454 | + | 0.269454i | −0.0120866 | + | 0.0120866i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.16670i | 0.365592i | 0.983151 | + | 0.182796i | \(0.0585148\pi\) | ||||
−0.983151 | + | 0.182796i | \(0.941485\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.7553 | + | 26.7553i | 1.19296 | + | 1.19296i | 0.976233 | + | 0.216725i | \(0.0695375\pi\) |
0.216725 | + | 0.976233i | \(0.430462\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 38.9913 | + | 3.68570i | 1.73509 | + | 0.164012i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.1687 | 0.539367 | 0.269684 | − | 0.962949i | \(-0.413081\pi\) | ||||
0.269684 | + | 0.962949i | \(0.413081\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.6029 | 0.513283 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.6400 | + | 15.2791i | 0.556985 | + | 0.673278i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.26411 | − | 6.26411i | −0.275495 | − | 0.275495i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 30.4671i | − | 1.33479i | −0.744704 | − | 0.667395i | \(-0.767409\pi\) | ||
0.744704 | − | 0.667395i | \(-0.232591\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.0667 | + | 19.0667i | −0.833728 | + | 0.833728i | −0.988025 | − | 0.154297i | \(-0.950689\pi\) |
0.154297 | + | 0.988025i | \(0.450689\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.97531 | − | 2.97531i | 0.129607 | − | 0.129607i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.05864 | + | 6.05864i | 0.262429 | + | 0.262429i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.91170 | + | 2.31084i | 0.0826499 | + | 0.0999063i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.9236 | 1.20275 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.16672 | −0.0931544 | −0.0465772 | − | 0.998915i | \(-0.514831\pi\) | ||||
−0.0465772 | + | 0.998915i | \(0.514831\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.390489 | − | 0.0369115i | −0.0167267 | − | 0.00158112i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.99662 | − | 5.99662i | −0.256397 | − | 0.256397i | 0.567190 | − | 0.823587i | \(-0.308031\pi\) |
−0.823587 | + | 0.567190i | \(0.808031\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.76519i | 0.203004i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.1400 | − | 12.1400i | 0.516244 | − | 0.516244i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.21628 | + | 2.21628i | −0.0939068 | + | 0.0939068i | −0.752500 | − | 0.658593i | \(-0.771152\pi\) |
0.658593 | + | 0.752500i | \(0.271152\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.5167i | 1.33301i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.9971 | + | 31.9971i | 1.34852 | + | 1.34852i | 0.887273 | + | 0.461244i | \(0.152597\pi\) |
0.461244 | + | 0.887273i | \(0.347403\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.4536 | − | 18.5753i | 0.944631 | − | 0.781469i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.1810 | −1.18141 | −0.590704 | − | 0.806888i | \(-0.701150\pi\) | ||||
−0.590704 | + | 0.806888i | \(0.701150\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.49413 | −0.0625273 | −0.0312637 | − | 0.999511i | \(-0.509953\pi\) | ||||
−0.0312637 | + | 0.999511i | \(0.509953\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.81043 | − | 4.13539i | −0.117203 | − | 0.172458i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.2353 | − | 13.2353i | −0.550991 | − | 0.550991i | 0.375736 | − | 0.926727i | \(-0.377390\pi\) |
−0.926727 | + | 0.375736i | \(0.877390\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.79950i | 0.282091i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.8719 | − | 12.8719i | 0.533099 | − | 0.533099i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.5054 | − | 20.5054i | 0.846347 | − | 0.846347i | −0.143328 | − | 0.989675i | \(-0.545780\pi\) |
0.989675 | + | 0.143328i | \(0.0457804\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 26.0192i | − | 1.07210i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.4663 | − | 25.4663i | −1.04578 | − | 1.04578i | −0.998901 | − | 0.0468762i | \(-0.985073\pi\) |
−0.0468762 | − | 0.998901i | \(-0.514927\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.214532 | − | 2.26955i | 0.00879497 | − | 0.0930425i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.2740 | −0.705798 | −0.352899 | − | 0.935661i | \(-0.614804\pi\) | ||||
−0.352899 | + | 0.935661i | \(0.614804\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.3007 | 0.868875 | 0.434437 | − | 0.900702i | \(-0.356947\pi\) | ||||
0.434437 | + | 0.900702i | \(0.356947\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.45076 | + | 25.9267i | −0.0996374 | + | 1.05407i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.7145 | + | 24.7145i | 1.00313 | + | 1.00313i | 0.999995 | + | 0.00313487i | \(0.000997863\pi\) |
0.00313487 | + | 0.999995i | \(0.499002\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.42234i | 0.219364i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.2537 | − | 12.2537i | 0.494924 | − | 0.494924i | −0.414930 | − | 0.909853i | \(-0.636194\pi\) |
0.909853 | + | 0.414930i | \(0.136194\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.3191 | + | 16.3191i | −0.656981 | + | 0.656981i | −0.954665 | − | 0.297684i | \(-0.903786\pi\) |
0.297684 | + | 0.954665i | \(0.403786\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.6602i | 1.07157i | 0.844356 | + | 0.535783i | \(0.179983\pi\) | ||||
−0.844356 | + | 0.535783i | \(0.820017\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.75970 | − | 4.75970i | −0.190693 | − | 0.190693i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.2445 | + | 9.20298i | 0.929779 | + | 0.368119i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.87679 | 0.234323 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.09952 | −0.362246 | −0.181123 | − | 0.983460i | \(-0.557973\pi\) | ||||
−0.181123 | + | 0.983460i | \(0.557973\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.6604 | − | 16.2645i | 0.780199 | − | 0.645438i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.0856 | − | 12.0856i | −0.478849 | − | 0.478849i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 36.2440i | − | 1.43155i | −0.698331 | − | 0.715775i | \(-0.746073\pi\) | ||
0.698331 | − | 0.715775i | \(-0.253927\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.0010 | − | 20.0010i | 0.788762 | − | 0.788762i | −0.192529 | − | 0.981291i | \(-0.561669\pi\) |
0.981291 | + | 0.192529i | \(0.0616690\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.1564 | − | 29.1564i | 1.14626 | − | 1.14626i | 0.158976 | − | 0.987283i | \(-0.449181\pi\) |
0.987283 | − | 0.158976i | \(-0.0508191\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.63157i | 0.221058i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.95252 | + | 3.95252i | 0.154674 | + | 0.154674i | 0.780202 | − | 0.625528i | \(-0.215116\pi\) |
−0.625528 | + | 0.780202i | \(0.715116\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.3663 | + | 1.64158i | 0.678558 | + | 0.0641416i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.58589 | −0.100732 | −0.0503660 | − | 0.998731i | \(-0.516039\pi\) | ||||
−0.0503660 | + | 0.998731i | \(0.516039\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.1654 | −1.21219 | −0.606097 | − | 0.795391i | \(-0.707266\pi\) | ||||
−0.606097 | + | 0.795391i | \(0.707266\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.98560 | − | 10.8617i | −0.348447 | − | 0.421198i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.568728 | + | 0.568728i | 0.0220212 | + | 0.0220212i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 6.63859i | − | 0.256280i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.82376 | − | 1.82376i | 0.0703007 | − | 0.0703007i | −0.671082 | − | 0.741383i | \(-0.734170\pi\) |
0.741383 | + | 0.671082i | \(0.234170\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.5514 | − | 13.5514i | 0.520821 | − | 0.520821i | −0.396998 | − | 0.917819i | \(-0.629948\pi\) |
0.917819 | + | 0.396998i | \(0.129948\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.8503i | 0.569903i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.770907 | − | 0.770907i | −0.0294979 | − | 0.0294979i | 0.692204 | − | 0.721702i | \(-0.256640\pi\) |
−0.721702 | + | 0.692204i | \(0.756640\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.3812 | + | 16.1751i | 0.511271 | + | 0.618019i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.1422 | −0.424482 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.3301 | 0.697310 | 0.348655 | − | 0.937251i | \(-0.386639\pi\) | ||||
0.348655 | + | 0.937251i | \(0.386639\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32.7554 | + | 3.09625i | 1.24248 | + | 0.117447i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.99286 | − | 1.99286i | −0.0754850 | − | 0.0754850i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.4119i | 0.846486i | 0.906016 | + | 0.423243i | \(0.139108\pi\) | ||||
−0.906016 | + | 0.423243i | \(0.860892\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.6964 | − | 25.6964i | 0.969156 | − | 0.969156i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.1787 | − | 13.1787i | 0.495635 | − | 0.495635i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.7770i | 0.517406i | 0.965957 | + | 0.258703i | \(0.0832951\pi\) | ||||
−0.965957 | + | 0.258703i | \(0.916705\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.10541 | − | 3.10541i | −0.116298 | − | 0.116298i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.8823 | − | 19.7572i | 0.893149 | − | 0.738879i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.6104 | 0.880520 | 0.440260 | − | 0.897870i | \(-0.354886\pi\) | ||||
0.440260 | + | 0.897870i | \(0.354886\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.43640 | 0.351430 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.95029 | − | 0.753545i | −0.146710 | − | 0.0279860i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.23745 | − | 3.23745i | −0.120071 | − | 0.120071i | 0.644518 | − | 0.764589i | \(-0.277058\pi\) |
−0.764589 | + | 0.644518i | \(0.777058\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 10.3667i | − | 0.383428i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.09039 | + | 3.09039i | −0.114146 | + | 0.114146i | −0.761873 | − | 0.647727i | \(-0.775720\pi\) |
0.647727 | + | 0.761873i | \(0.275720\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27.4900 | − | 27.4900i | 1.01261 | − | 1.01261i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.8709i | 1.35632i | 0.734915 | + | 0.678160i | \(0.237222\pi\) | ||||
−0.734915 | + | 0.678160i | \(0.762778\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.3320 | − | 34.3320i | −1.25952 | − | 1.25952i | −0.951323 | − | 0.308195i | \(-0.900275\pi\) |
−0.308195 | − | 0.951323i | \(-0.599725\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.94834 | − | 52.3488i | 0.181293 | − | 1.91791i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.42718 | 0.0521479 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.2553 | 0.629654 | 0.314827 | − | 0.949149i | \(-0.398053\pi\) | ||||
0.314827 | + | 0.949149i | \(0.398053\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.01907 | − | 10.7808i | 0.0370879 | − | 0.392355i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.6446 | + | 22.6446i | 0.823034 | + | 0.823034i | 0.986542 | − | 0.163508i | \(-0.0522811\pi\) |
−0.163508 | + | 0.986542i | \(0.552281\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 30.7887i | − | 1.11609i | −0.829810 | − | 0.558045i | \(-0.811551\pi\) | ||
0.829810 | − | 0.558045i | \(-0.188449\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.131982 | + | 0.131982i | −0.00477805 | + | 0.00477805i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.43740 | − | 2.43740i | 0.0880093 | − | 0.0880093i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.4017i | 1.02419i | 0.858928 | + | 0.512096i | \(0.171131\pi\) | ||||
−0.858928 | + | 0.512096i | \(0.828869\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.72455 | + | 9.72455i | 0.349768 | + | 0.349768i | 0.860023 | − | 0.510255i | \(-0.170449\pi\) |
−0.510255 | + | 0.860023i | \(0.670449\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.5696 | + | 4.11456i | 0.774803 | + | 0.147799i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.4276 | −0.624410 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.70422 | 0.0609819 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −33.2279 | + | 27.4886i | −1.18595 | + | 0.981109i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.51220 | − | 2.51220i | −0.0895503 | − | 0.0895503i | 0.660913 | − | 0.750463i | \(-0.270169\pi\) |
−0.750463 | + | 0.660913i | \(0.770169\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 13.8674i | − | 0.493068i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.87325 | + | 2.87325i | −0.102032 | + | 0.102032i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.7070 | + | 31.7070i | −1.12312 | + | 1.12312i | −0.131851 | + | 0.991270i | \(0.542092\pi\) |
−0.991270 | + | 0.131851i | \(0.957908\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.78356i | − | 0.0630979i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −36.6927 | − | 36.6927i | −1.29486 | − | 1.29486i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.36879 | − | 0.223913i | −0.0834888 | − | 0.00789189i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.42494 | −0.225889 | −0.112944 | − | 0.993601i | \(-0.536028\pi\) | ||||
−0.112944 | + | 0.993601i | \(0.536028\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.9016 | 0.453036 | 0.226518 | − | 0.974007i | \(-0.427266\pi\) | ||||
0.226518 | + | 0.974007i | \(0.427266\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.1412 | − | 30.3904i | −0.880659 | − | 1.06453i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −45.3288 | − | 45.3288i | −1.58585 | − | 1.58585i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.5952i | 0.544275i | 0.962258 | + | 0.272137i | \(0.0877305\pi\) | ||||
−0.962258 | + | 0.272137i | \(0.912270\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.920837 | − | 0.920837i | 0.0320984 | − | 0.0320984i | −0.690875 | − | 0.722974i | \(-0.742775\pi\) |
0.722974 | + | 0.690875i | \(0.242775\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.0656 | + | 20.0656i | −0.697750 | + | 0.697750i | −0.963925 | − | 0.266175i | \(-0.914240\pi\) |
0.266175 | + | 0.963925i | \(0.414240\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 36.2679i | − | 1.25964i | −0.776742 | − | 0.629819i | \(-0.783129\pi\) | ||
0.776742 | − | 0.629819i | \(-0.216871\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.97530 | + | 3.97530i | 0.137736 | + | 0.137736i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.22335 | − | 11.1491i | −0.319187 | − | 0.385830i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.31011 | 0.217849 | 0.108925 | − | 0.994050i | \(-0.465259\pi\) | ||||
0.108925 | + | 0.994050i | \(0.465259\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3531 | −0.977693 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.0522 | + | 0.950202i | 0.345808 | + | 0.0326879i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.76297 | + | 8.76297i | 0.301099 | + | 0.301099i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 6.13375i | − | 0.210262i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.7452 | − | 28.7452i | 0.984218 | − | 0.984218i | −0.0156592 | − | 0.999877i | \(-0.504985\pi\) |
0.999877 | + | 0.0156592i | \(0.00498468\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.49362 | − | 2.49362i | 0.0851803 | − | 0.0851803i | −0.663233 | − | 0.748413i | \(-0.730816\pi\) |
0.748413 | + | 0.663233i | \(0.230816\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 23.7554i | − | 0.810523i | −0.914201 | − | 0.405261i | \(-0.867180\pi\) | ||
0.914201 | − | 0.405261i | \(-0.132820\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.18944 | + | 9.18944i | 0.312812 | + | 0.312812i | 0.845998 | − | 0.533186i | \(-0.179005\pi\) |
−0.533186 | + | 0.845998i | \(0.679005\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.7133 | − | 25.4083i | 1.04428 | − | 0.863908i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −76.7821 | −2.60465 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.7958 | −0.806291 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.4252 | − | 5.73134i | 0.352435 | − | 0.193755i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.5836 | − | 26.5836i | −0.897664 | − | 0.897664i | 0.0975647 | − | 0.995229i | \(-0.468895\pi\) |
−0.995229 | + | 0.0975647i | \(0.968895\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 42.1669i | − | 1.42064i | −0.703879 | − | 0.710320i | \(-0.748550\pi\) | ||
0.703879 | − | 0.710320i | \(-0.251450\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.15303 | − | 6.15303i | 0.207066 | − | 0.207066i | −0.595953 | − | 0.803019i | \(-0.703226\pi\) |
0.803019 | + | 0.595953i | \(0.203226\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.1052 | + | 13.1052i | −0.440030 | + | 0.440030i | −0.892022 | − | 0.451992i | \(-0.850714\pi\) |
0.451992 | + | 0.892022i | \(0.350714\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 12.1423i | − | 0.407239i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.79865 | − | 7.79865i | −0.260972 | − | 0.260972i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.05382 | + | 32.3065i | −0.102078 | + | 1.07989i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.53226 | −0.117808 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.66497 | 0.122098 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.406190 | − | 4.29711i | 0.0135022 | − | 0.142841i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.0082 | − | 33.0082i | −1.09602 | − | 1.09602i | −0.994871 | − | 0.101150i | \(-0.967748\pi\) |
−0.101150 | − | 0.994871i | \(-0.532252\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 54.8034i | − | 1.81572i | −0.419277 | − | 0.907858i | \(-0.637716\pi\) | ||
0.419277 | − | 0.907858i | \(-0.362284\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.5025 | − | 21.5025i | 0.711629 | − | 0.711629i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.86965 | − | 5.86965i | 0.193833 | − | 0.193833i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.5726i | 0.381744i | 0.981615 | + | 0.190872i | \(0.0611316\pi\) | ||||
−0.981615 | + | 0.190872i | \(0.938868\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.737604 | − | 0.737604i | −0.0242785 | − | 0.0242785i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.2385 | + | 25.3655i | 0.566798 | + | 0.834012i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 45.6821 | 1.49878 | 0.749391 | − | 0.662128i | \(-0.230346\pi\) | ||||
0.749391 | + | 0.662128i | \(0.230346\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.7641 | 1.13935 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.85558 | + | 6.49872i | −0.256905 | + | 0.212531i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.1344 | + | 39.1344i | 1.27847 | + | 1.27847i | 0.941526 | + | 0.336940i | \(0.109392\pi\) |
0.336940 | + | 0.941526i | \(0.390608\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.0632i | 1.63201i | 0.578042 | + | 0.816007i | \(0.303817\pi\) | ||||
−0.578042 | + | 0.816007i | \(0.696183\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.08000 | + | 2.08000i | −0.0677341 | + | 0.0677341i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.4334 | + | 12.4334i | −0.404033 | + | 0.404033i | −0.879652 | − | 0.475619i | \(-0.842224\pi\) |
0.475619 | + | 0.879652i | \(0.342224\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.7619i | 1.03104i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.4639 | − | 27.4639i | −0.889643 | − | 0.889643i | 0.104846 | − | 0.994489i | \(-0.466565\pi\) |
−0.994489 | + | 0.104846i | \(0.966565\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 39.4090 | + | 3.72519i | 1.27525 | + | 0.120544i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.98976 | 0.322586 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.7129 | −0.377836 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.5704 | − | 26.0740i | −0.694374 | − | 0.839352i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.6934 | − | 25.6934i | −0.826244 | − | 0.826244i | 0.160751 | − | 0.986995i | \(-0.448608\pi\) |
−0.986995 | + | 0.160751i | \(0.948608\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.0382i | 0.514689i | 0.966320 | + | 0.257344i | \(0.0828475\pi\) | ||||
−0.966320 | + | 0.257344i | \(0.917153\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.0710 | − | 11.0710i | 0.354920 | − | 0.354920i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.1255 | − | 22.1255i | 0.707856 | − | 0.707856i | −0.258228 | − | 0.966084i | \(-0.583139\pi\) |
0.966084 | + | 0.258228i | \(0.0831385\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.1039i | 0.962124i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.77526 | − | 1.77526i | −0.0566221 | − | 0.0566221i | 0.678229 | − | 0.734851i | \(-0.262748\pi\) |
−0.734851 | + | 0.678229i | \(0.762748\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.4218 | + | 22.2680i | 0.586966 | + | 0.709518i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.8200 | −0.344057 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.7684 | 0.786795 | 0.393397 | − | 0.919369i | \(-0.371300\pi\) | ||||
0.393397 | + | 0.919369i | \(0.371300\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.5504 | − | 2.03708i | −0.683194 | − | 0.0645798i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.8197 | − | 28.8197i | −0.912728 | − | 0.912728i | 0.0837577 | − | 0.996486i | \(-0.473308\pi\) |
−0.996486 | + | 0.0837577i | \(0.973308\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4140.2.s.a.737.13 | yes | 44 | |
3.2 | odd | 2 | inner | 4140.2.s.a.737.10 | ✓ | 44 | |
5.3 | odd | 4 | inner | 4140.2.s.a.2393.10 | yes | 44 | |
15.8 | even | 4 | inner | 4140.2.s.a.2393.13 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.2.s.a.737.10 | ✓ | 44 | 3.2 | odd | 2 | inner | |
4140.2.s.a.737.13 | yes | 44 | 1.1 | even | 1 | trivial | |
4140.2.s.a.2393.10 | yes | 44 | 5.3 | odd | 4 | inner | |
4140.2.s.a.2393.13 | yes | 44 | 15.8 | even | 4 | inner |