Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(575,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("4032.575");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.h (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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.653473922154496.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{10} + 13x^{8} - 28x^{6} + 52x^{4} - 64x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 575.10 | ||
Root | \(0.892524 + 1.09700i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.575 |
Dual form | 4032.2.h.h.575.3 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.56483i | 1.14703i | 0.819197 | + | 0.573513i | \(0.194420\pi\) | ||||
−0.819197 | + | 0.573513i | \(0.805580\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.15061 | −0.346923 | −0.173461 | − | 0.984841i | \(-0.555495\pi\) | ||||
−0.173461 | + | 0.984841i | \(0.555495\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.578337 | 0.160402 | 0.0802009 | − | 0.996779i | \(-0.474444\pi\) | ||||
0.0802009 | + | 0.996779i | \(0.474444\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 5.39325i | − 1.30806i | −0.756470 | − | 0.654028i | \(-0.773078\pi\) | ||||
0.756470 | − | 0.654028i | \(-0.226922\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 6.20555i | − 1.42365i | −0.702356 | − | 0.711825i | \(-0.747869\pi\) | ||||
0.702356 | − | 0.711825i | \(-0.252131\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.62536 | 1.59000 | 0.794999 | − | 0.606611i | \(-0.207471\pi\) | ||||
0.794999 | + | 0.606611i | \(0.207471\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.57834 | −0.315667 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 1.41421i | − 0.262613i | −0.991342 | − | 0.131306i | \(-0.958083\pi\) | ||||
0.991342 | − | 0.131306i | \(-0.0419172\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 5.04888i | − 0.906805i | −0.891306 | − | 0.453402i | \(-0.850210\pi\) | ||||
0.891306 | − | 0.453402i | \(-0.149790\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.56483 | −0.433535 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.83276 | −1.61650 | −0.808248 | − | 0.588842i | \(-0.799584\pi\) | ||||
−0.808248 | + | 0.588842i | \(0.799584\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.21115i | 0.970018i | 0.874509 | + | 0.485009i | \(0.161184\pi\) | ||||
−0.874509 | + | 0.485009i | \(0.838816\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 11.2544i | − 1.71628i | −0.513413 | − | 0.858142i | \(-0.671619\pi\) | ||||
0.513413 | − | 0.858142i | \(-0.328381\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.0772 | −1.61578 | −0.807888 | − | 0.589336i | \(-0.799389\pi\) | ||||
−0.807888 | + | 0.589336i | \(0.799389\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 4.53333i | − 0.622701i | −0.950295 | − | 0.311351i | \(-0.899219\pi\) | ||||
0.950295 | − | 0.311351i | \(-0.100781\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 2.95112i | − 0.397929i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.83896 | 0.629979 | 0.314990 | − | 0.949095i | \(-0.397999\pi\) | ||||
0.314990 | + | 0.949095i | \(0.397999\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.951124 | −0.121779 | −0.0608895 | − | 0.998145i | \(-0.519394\pi\) | ||||
−0.0608895 | + | 0.998145i | \(0.519394\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.48333i | 0.183985i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.78389i | 0.340106i | 0.985435 | + | 0.170053i | \(0.0543939\pi\) | ||||
−0.985435 | + | 0.170053i | \(0.945606\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.68835 | 0.437726 | 0.218863 | − | 0.975756i | \(-0.429765\pi\) | ||||
0.218863 | + | 0.975756i | \(0.429765\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.0383 | 1.64306 | 0.821530 | − | 0.570165i | \(-0.193121\pi\) | ||||
0.821530 | + | 0.570165i | \(0.193121\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.15061i | − 0.131125i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 12.8816i | − 1.44930i | −0.689118 | − | 0.724649i | \(-0.742002\pi\) | ||||
0.689118 | − | 0.724649i | \(-0.257998\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.77597 | 0.963288 | 0.481644 | − | 0.876367i | \(-0.340040\pi\) | ||||
0.481644 | + | 0.876367i | \(0.340040\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.8328 | 1.50037 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 5.68395i | − 0.602497i | −0.953546 | − | 0.301249i | \(-0.902597\pi\) | ||||
0.953546 | − | 0.301249i | \(-0.0974034\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.578337i | 0.0606262i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.9162 | 1.63296 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.8816 | −1.30793 | −0.653966 | − | 0.756524i | \(-0.726896\pi\) | ||||
−0.653966 | + | 0.756524i | \(0.726896\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 3.75747i | − 0.373882i | −0.982371 | − | 0.186941i | \(-0.940143\pi\) | ||||
0.982371 | − | 0.186941i | \(-0.0598574\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1.79445i | − 0.176812i | −0.996085 | − | 0.0884062i | \(-0.971823\pi\) | ||||
0.996085 | − | 0.0884062i | \(-0.0281774\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.1631 | 0.982503 | 0.491252 | − | 0.871018i | \(-0.336540\pi\) | ||||
0.491252 | + | 0.871018i | \(0.336540\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.2544 | 1.46111 | 0.730555 | − | 0.682854i | \(-0.239262\pi\) | ||||
0.730555 | + | 0.682854i | \(0.239262\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.06053i | 0.476055i | 0.971258 | + | 0.238027i | \(0.0765008\pi\) | ||||
−0.971258 | + | 0.238027i | \(0.923499\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.5577i | 1.82377i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.39325 | 0.494399 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.67609 | −0.879644 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.77597i | 0.784947i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.470539i | 0.0417536i | 0.999782 | + | 0.0208768i | \(0.00664577\pi\) | ||||
−0.999782 | + | 0.0208768i | \(0.993354\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.9162 | 1.39060 | 0.695301 | − | 0.718719i | \(-0.255271\pi\) | ||||
0.695301 | + | 0.718719i | \(0.255271\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.20555 | 0.538089 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.55440i | 0.730852i | 0.930840 | + | 0.365426i | \(0.119077\pi\) | ||||
−0.930840 | + | 0.365426i | \(0.880923\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 16.0000i | − 1.35710i | −0.734553 | − | 0.678551i | \(-0.762608\pi\) | ||||
0.734553 | − | 0.678551i | \(-0.237392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.665442 | −0.0556471 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.62721 | 0.301224 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.8032i | 1.37657i | 0.725441 | + | 0.688285i | \(0.241636\pi\) | ||||
−0.725441 | + | 0.688285i | \(0.758364\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.09775i | 0.170713i | 0.996350 | + | 0.0853563i | \(0.0272029\pi\) | ||||
−0.996350 | + | 0.0853563i | \(0.972797\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.9495 | 1.04013 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.3622 | −1.38566 | −0.692828 | − | 0.721103i | \(-0.743636\pi\) | ||||
−0.692828 | + | 0.721103i | \(0.743636\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.62536i | 0.600963i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.470539i | 0.0368554i | 0.999830 | + | 0.0184277i | \(0.00586606\pi\) | ||||
−0.999830 | + | 0.0184277i | \(0.994134\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.7551 | 1.60608 | 0.803040 | − | 0.595925i | \(-0.203215\pi\) | ||||
0.803040 | + | 0.595925i | \(0.203215\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6655 | −0.974271 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 14.1692i | − 1.07727i | −0.842540 | − | 0.538633i | \(-0.818941\pi\) | ||||
0.842540 | − | 0.538633i | \(-0.181059\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 1.57834i | − 0.119311i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.15061 | −0.0860009 | −0.0430004 | − | 0.999075i | \(-0.513692\pi\) | ||||
−0.0430004 | + | 0.999075i | \(0.513692\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.83276 | −0.284887 | −0.142444 | − | 0.989803i | \(-0.545496\pi\) | ||||
−0.142444 | + | 0.989803i | \(0.545496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 25.2193i | − 1.85416i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.20555i | 0.453795i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.92659 | −0.718263 | −0.359131 | − | 0.933287i | \(-0.616927\pi\) | ||||
−0.359131 | + | 0.933287i | \(0.616927\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.6761 | 0.912445 | 0.456222 | − | 0.889866i | \(-0.349202\pi\) | ||||
0.456222 | + | 0.889866i | \(0.349202\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.70491i | − 0.121469i | −0.998154 | − | 0.0607347i | \(-0.980656\pi\) | ||||
0.998154 | − | 0.0607347i | \(-0.0193444\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 14.8433i | − 1.05222i | −0.850418 | − | 0.526108i | \(-0.823651\pi\) | ||||
0.850418 | − | 0.526108i | \(-0.176349\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.41421 | 0.0992583 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.9305 | −1.11264 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.14019i | 0.493897i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.15667i | 0.0796287i | 0.999207 | + | 0.0398144i | \(0.0126767\pi\) | ||||
−0.999207 | + | 0.0398144i | \(0.987323\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 28.8657 | 1.96862 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.04888 | 0.342740 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 3.11912i | − 0.209815i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.6655i | 1.58476i | 0.610027 | + | 0.792380i | \(0.291158\pi\) | ||||
−0.610027 | + | 0.792380i | \(0.708842\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.44142 | 0.626649 | 0.313324 | − | 0.949646i | \(-0.398557\pi\) | ||||
0.313324 | + | 0.949646i | \(0.398557\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.578337 | 0.0382176 | 0.0191088 | − | 0.999817i | \(-0.493917\pi\) | ||||
0.0191088 | + | 0.999817i | \(0.493917\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 0.305630i | − 0.0200225i | −0.999950 | − | 0.0100112i | \(-0.996813\pi\) | ||||
0.999950 | − | 0.0100112i | \(-0.00318673\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 28.4111i | − 1.85334i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.92659 | 0.642098 | 0.321049 | − | 0.947063i | \(-0.395965\pi\) | ||||
0.321049 | + | 0.947063i | \(0.395965\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.29274 | 0.598598 | 0.299299 | − | 0.954159i | \(-0.403247\pi\) | ||||
0.299299 | + | 0.954159i | \(0.403247\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 2.56483i | − 0.163861i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 3.58890i | − 0.228356i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.93701 | −0.248502 | −0.124251 | − | 0.992251i | \(-0.539653\pi\) | ||||
−0.124251 | + | 0.992251i | \(0.539653\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.77384 | −0.551607 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 15.8891i | − 0.991133i | −0.868570 | − | 0.495566i | \(-0.834960\pi\) | ||||
0.868570 | − | 0.495566i | \(-0.165040\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 9.83276i | − 0.610978i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.38712 | 0.0855336 | 0.0427668 | − | 0.999085i | \(-0.486383\pi\) | ||||
0.0427668 | + | 0.999085i | \(0.486383\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.6272 | 0.714254 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 1.60869i | − 0.0980837i | −0.998797 | − | 0.0490419i | \(-0.984383\pi\) | ||||
0.998797 | − | 0.0490419i | \(-0.0156168\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 8.30330i | − 0.504390i | −0.967676 | − | 0.252195i | \(-0.918848\pi\) | ||||
0.967676 | − | 0.252195i | \(-0.0811524\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.81606 | 0.109512 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.83276 | 0.230288 | 0.115144 | − | 0.993349i | \(-0.463267\pi\) | ||||
0.115144 | + | 0.993349i | \(0.463267\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.9348i | 1.72610i | 0.505115 | + | 0.863052i | \(0.331450\pi\) | ||||
−0.505115 | + | 0.863052i | \(0.668550\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 31.0278i | − 1.84441i | −0.386703 | − | 0.922204i | \(-0.626386\pi\) | ||||
0.386703 | − | 0.922204i | \(-0.373614\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.21115 | −0.366632 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.0872 | −0.711011 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 5.01850i | − 0.293184i | −0.989197 | − | 0.146592i | \(-0.953170\pi\) | ||||
0.989197 | − | 0.146592i | \(-0.0468305\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.4111i | 0.722602i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.41003 | 0.255039 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.2544 | 0.648694 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 2.43947i | − 0.139684i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.3622i | 0.876768i | 0.898788 | + | 0.438384i | \(0.144449\pi\) | ||||
−0.898788 | + | 0.438384i | \(0.855551\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.83896 | 0.274392 | 0.137196 | − | 0.990544i | \(-0.456191\pi\) | ||||
0.137196 | + | 0.990544i | \(0.456191\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.7633 | 1.11709 | 0.558543 | − | 0.829475i | \(-0.311360\pi\) | ||||
0.558543 | + | 0.829475i | \(0.311360\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 5.96248i | − 0.334886i | −0.985882 | − | 0.167443i | \(-0.946449\pi\) | ||||
0.985882 | − | 0.167443i | \(-0.0535511\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.62721i | 0.0911064i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.4681 | −1.86222 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.912811 | −0.0506336 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 11.0772i | − 0.610706i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.15667i | 0.0635766i | 0.999495 | + | 0.0317883i | \(0.0101202\pi\) | ||||
−0.999495 | + | 0.0317883i | \(0.989880\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.14019 | −0.390110 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.25443 | 0.177280 | 0.0886399 | − | 0.996064i | \(-0.471748\pi\) | ||||
0.0886399 | + | 0.996064i | \(0.471748\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.80930i | 0.314591i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.4013 | 0.880470 | 0.440235 | − | 0.897883i | \(-0.354895\pi\) | ||||
0.440235 | + | 0.897883i | \(0.354895\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.20555 | 0.439233 | 0.219617 | − | 0.975586i | \(-0.429519\pi\) | ||||
0.219617 | + | 0.975586i | \(0.429519\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 24.9557i | − 1.32826i | −0.747617 | − | 0.664130i | \(-0.768802\pi\) | ||||
0.747617 | − | 0.664130i | \(-0.231198\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.45998i | 0.502083i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.38712 | 0.0732095 | 0.0366048 | − | 0.999330i | \(-0.488346\pi\) | ||||
0.0366048 | + | 0.999330i | \(0.488346\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.5089 | −1.02678 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.0058i | 1.88463i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 10.9200i | − 0.570017i | −0.958525 | − | 0.285008i | \(-0.908004\pi\) | ||||
0.958525 | − | 0.285008i | \(-0.0919964\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.53333 | 0.235359 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.6655 | −1.53602 | −0.768011 | − | 0.640436i | \(-0.778754\pi\) | ||||
−0.768011 | + | 0.640436i | \(0.778754\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 0.817892i | − 0.0421236i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.66553i | 0.393752i | 0.980428 | + | 0.196876i | \(0.0630796\pi\) | ||||
−0.980428 | + | 0.196876i | \(0.936920\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.8407 | 0.553933 | 0.276967 | − | 0.960880i | \(-0.410671\pi\) | ||||
0.276967 | + | 0.960880i | \(0.410671\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.95112 | 0.150403 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.6125i | 1.14650i | 0.819381 | + | 0.573249i | \(0.194317\pi\) | ||||
−0.819381 | + | 0.573249i | \(0.805683\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 41.1255i | − 2.07981i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 33.0392 | 1.66238 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.5577 | 1.08195 | 0.540976 | − | 0.841038i | \(-0.318055\pi\) | ||||
0.540976 | + | 0.841038i | \(0.318055\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.26176i | 0.0630095i | 0.999504 | + | 0.0315047i | \(0.0100299\pi\) | ||||
−0.999504 | + | 0.0315047i | \(0.989970\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 2.91995i | − 0.145453i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.3137 | 0.560800 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.4494 | −1.70341 | −0.851707 | − | 0.524018i | \(-0.824432\pi\) | ||||
−0.851707 | + | 0.524018i | \(0.824432\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.83896i | 0.238110i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.5089i | 1.10492i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.5816 | −0.810064 | −0.405032 | − | 0.914302i | \(-0.632740\pi\) | ||||
−0.405032 | + | 0.914302i | \(0.632740\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.36274 | 0.407575 | 0.203788 | − | 0.979015i | \(-0.434675\pi\) | ||||
0.203788 | + | 0.979015i | \(0.434675\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.51237i | 0.412911i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 0.951124i | − 0.0460281i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.1565 | −1.78976 | −0.894882 | − | 0.446303i | \(-0.852740\pi\) | ||||
−0.894882 | + | 0.446303i | \(0.852740\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.56777 | −0.363684 | −0.181842 | − | 0.983328i | \(-0.558206\pi\) | ||||
−0.181842 | + | 0.983328i | \(0.558206\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 47.3196i | − 2.26360i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 16.8222i | − 0.802880i | −0.915885 | − | 0.401440i | \(-0.868510\pi\) | ||||
0.915885 | − | 0.401440i | \(-0.131490\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.4643 | −0.592198 | −0.296099 | − | 0.955157i | \(-0.595686\pi\) | ||||
−0.296099 | + | 0.955157i | \(0.595686\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.5783 | 0.691079 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.44582i | 0.351390i | 0.984445 | + | 0.175695i | \(0.0562172\pi\) | ||||
−0.984445 | + | 0.175695i | \(0.943783\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 7.14663i | − 0.336522i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.48333 | −0.0695398 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.68665 | −0.266010 | −0.133005 | − | 0.991115i | \(-0.542463\pi\) | ||||
−0.133005 | + | 0.991115i | \(0.542463\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.790801i | 0.0368313i | 0.999830 | + | 0.0184156i | \(0.00586221\pi\) | ||||
−0.999830 | + | 0.0184156i | \(0.994138\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 25.2927i | − 1.17545i | −0.809060 | − | 0.587727i | \(-0.800023\pi\) | ||||
0.809060 | − | 0.587727i | \(-0.199977\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −40.8448 | −1.89007 | −0.945036 | − | 0.326966i | \(-0.893974\pi\) | ||||
−0.945036 | + | 0.326966i | \(0.893974\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.78389 | −0.128548 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.9495i | 0.595418i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.79445i | 0.449400i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.2507 | −0.696823 | −0.348412 | − | 0.937342i | \(-0.613279\pi\) | ||||
−0.348412 | + | 0.937342i | \(0.613279\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.68665 | −0.259289 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 33.0392i | − 1.50023i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 24.6066i | − 1.11503i | −0.830166 | − | 0.557516i | \(-0.811755\pi\) | ||||
0.830166 | − | 0.557516i | \(-0.188245\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.3472 | 1.41468 | 0.707339 | − | 0.706875i | \(-0.249896\pi\) | ||||
0.707339 | + | 0.706875i | \(0.249896\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.62721 | −0.343512 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.68835i | 0.165445i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 11.2544i | − 0.503817i | −0.967751 | − | 0.251909i | \(-0.918942\pi\) | ||||
0.967751 | − | 0.251909i | \(-0.0810583\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.6588 | −1.23325 | −0.616623 | − | 0.787259i | \(-0.711500\pi\) | ||||
−0.616623 | + | 0.787259i | \(0.711500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.63726 | 0.428852 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 29.7947i | − 1.32063i | −0.750990 | − | 0.660313i | \(-0.770423\pi\) | ||||
0.750990 | − | 0.660313i | \(-0.229577\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.0383i | 0.621018i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.60245 | 0.202808 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.7456 | 0.560550 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 1.84520i | − 0.0808397i | −0.999183 | − | 0.0404199i | \(-0.987130\pi\) | ||||
0.999183 | − | 0.0404199i | \(-0.0128696\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 16.0000i | − 0.699631i | −0.936819 | − | 0.349816i | \(-0.886244\pi\) | ||||
0.936819 | − | 0.349816i | \(-0.113756\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −27.2299 | −1.18615 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.1461 | 1.52809 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.59214i | 0.155593i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.0666i | 1.12696i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.15061 | 0.0495604 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.3416 | 1.13251 | 0.566257 | − | 0.824229i | \(-0.308391\pi\) | ||||
0.566257 | + | 0.824229i | \(0.308391\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 39.1250i | 1.67593i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.805013i | 0.0344199i | 0.999852 | + | 0.0172099i | \(0.00547836\pi\) | ||||
−0.999852 | + | 0.0172099i | \(0.994522\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.77597 | −0.373869 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.8816 | 0.547783 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.8909i | 0.630948i | 0.948934 | + | 0.315474i | \(0.102164\pi\) | ||||
−0.948934 | + | 0.315474i | \(0.897836\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 6.50885i | − 0.275295i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −43.3825 | −1.82836 | −0.914178 | − | 0.405313i | \(-0.867163\pi\) | ||||
−0.914178 | + | 0.405313i | \(0.867163\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.9794 | −0.546047 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 21.8786i | − 0.917201i | −0.888643 | − | 0.458600i | \(-0.848351\pi\) | ||||
0.888643 | − | 0.458600i | \(-0.151649\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.7038i | 1.57786i | 0.614485 | + | 0.788928i | \(0.289364\pi\) | ||||
−0.614485 | + | 0.788928i | \(0.710636\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.0354 | −0.501910 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.4111 | −1.09951 | −0.549754 | − | 0.835326i | \(-0.685279\pi\) | ||||
−0.549754 | + | 0.835326i | \(0.685279\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.77597i | 0.364089i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.21611i | 0.216029i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.1527 | 0.666692 | 0.333346 | − | 0.942805i | \(-0.391822\pi\) | ||||
0.333346 | + | 0.942805i | \(0.391822\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.3311 | −1.29097 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 6.44765i | − 0.264773i | −0.991198 | − | 0.132387i | \(-0.957736\pi\) | ||||
0.991198 | − | 0.132387i | \(-0.0422641\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.8328i | 0.567088i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.9391 | 0.773829 | 0.386915 | − | 0.922116i | \(-0.373541\pi\) | ||||
0.386915 | + | 0.922116i | \(0.373541\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.4111 | 0.751004 | 0.375502 | − | 0.926821i | \(-0.377470\pi\) | ||||
0.375502 | + | 0.926821i | \(0.377470\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 24.8175i | − 1.00897i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.6066i | 0.998751i | 0.866386 | + | 0.499376i | \(0.166437\pi\) | ||||
−0.866386 | + | 0.499376i | \(0.833563\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.40636 | −0.259173 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.09775 | −0.327065 | −0.163533 | − | 0.986538i | \(-0.552289\pi\) | ||||
−0.163533 | + | 0.986538i | \(0.552289\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.14459i | 0.207113i | 0.994624 | + | 0.103557i | \(0.0330223\pi\) | ||||
−0.994624 | + | 0.103557i | \(0.966978\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.2922i | 1.45871i | 0.684137 | + | 0.729354i | \(0.260179\pi\) | ||||
−0.684137 | + | 0.729354i | \(0.739821\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.68395 | 0.227722 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.4005 | −1.21602 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 53.0306i | 2.11447i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 19.7250i | − 0.785238i | −0.919701 | − | 0.392619i | \(-0.871569\pi\) | ||||
0.919701 | − | 0.392619i | \(-0.128431\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.20685 | −0.0478924 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.578337 | −0.0229145 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.6860i | 0.817048i | 0.912748 | + | 0.408524i | \(0.133956\pi\) | ||||
−0.912748 | + | 0.408524i | \(0.866044\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 15.0278i | − 0.592637i | −0.955089 | − | 0.296318i | \(-0.904241\pi\) | ||||
0.955089 | − | 0.296318i | \(-0.0957589\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.3909 | 0.880277 | 0.440139 | − | 0.897930i | \(-0.354929\pi\) | ||||
0.440139 | + | 0.897930i | \(0.354929\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.56777 | −0.218554 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.0978i | 1.21695i | 0.793573 | + | 0.608475i | \(0.208218\pi\) | ||||
−0.793573 | + | 0.608475i | \(0.791782\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 40.8222i | 1.59506i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.1631 | −0.395898 | −0.197949 | − | 0.980212i | \(-0.563428\pi\) | ||||
−0.197949 | + | 0.980212i | \(0.563428\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.1255 | 0.588314 | 0.294157 | − | 0.955757i | \(-0.404961\pi\) | ||||
0.294157 | + | 0.955757i | \(0.404961\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.9162i | 0.617202i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 10.7839i | − 0.417554i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.09438 | 0.0422479 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.8716 | 1.42130 | 0.710648 | − | 0.703548i | \(-0.248402\pi\) | ||||
0.710648 | + | 0.703548i | \(0.248402\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.3705i | 0.398569i | 0.979942 | + | 0.199285i | \(0.0638618\pi\) | ||||
−0.979942 | + | 0.199285i | \(0.936138\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 12.8816i | − 0.494352i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.19275 | 0.351751 | 0.175875 | − | 0.984412i | \(-0.443724\pi\) | ||||
0.175875 | + | 0.984412i | \(0.443724\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.9406 | −0.838306 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 2.62179i | − 0.0998824i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.8433i | 0.869001i | 0.900672 | + | 0.434501i | \(0.143075\pi\) | ||||
−0.900672 | + | 0.434501i | \(0.856925\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 41.0372 | 1.55663 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.4983 | 1.26884 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.1044i | 0.721563i | 0.932650 | + | 0.360782i | \(0.117490\pi\) | ||||
−0.932650 | + | 0.360782i | \(0.882510\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 61.0177i | 2.30133i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.75747 | 0.141314 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.56777 | 0.359325 | 0.179663 | − | 0.983728i | \(-0.442499\pi\) | ||||
0.179663 | + | 0.983728i | \(0.442499\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 38.4995i | − 1.44182i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.70674i | − 0.0638286i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.5014 | −1.13751 | −0.568756 | − | 0.822506i | \(-0.692575\pi\) | ||||
−0.568756 | + | 0.822506i | \(0.692575\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.79445 | 0.0668288 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.23211i | 0.0828983i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.5189i | 1.20606i | 0.797719 | + | 0.603030i | \(0.206040\pi\) | ||||
−0.797719 | + | 0.603030i | \(0.793960\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −60.6980 | −2.24500 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.0106 | −0.702171 | −0.351086 | − | 0.936343i | \(-0.614187\pi\) | ||||
−0.351086 | + | 0.936343i | \(0.614187\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 3.20318i | − 0.117991i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.7250i | 0.725595i | 0.931868 | + | 0.362797i | \(0.118178\pi\) | ||||
−0.931868 | + | 0.362797i | \(0.881822\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.8849 | −1.24312 | −0.621558 | − | 0.783368i | \(-0.713500\pi\) | ||||
−0.621558 | + | 0.783368i | \(0.713500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −43.0972 | −1.57896 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.1631i | 0.371351i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.5089i | 1.11328i | 0.830753 | + | 0.556642i | \(0.187910\pi\) | ||||
−0.830753 | + | 0.556642i | \(0.812090\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.38037 | −0.195812 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.0766 | 1.74737 | 0.873687 | − | 0.486488i | \(-0.161722\pi\) | ||||
0.873687 | + | 0.486488i | \(0.161722\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 13.4055i | − 0.485950i | −0.970033 | − | 0.242975i | \(-0.921877\pi\) | ||||
0.970033 | − | 0.242975i | \(-0.0781232\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.2544i | 0.552247i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.79855 | 0.101050 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.4700 | 0.485741 | 0.242871 | − | 0.970059i | \(-0.421911\pi\) | ||||
0.242871 | + | 0.970059i | \(0.421911\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 28.5479i | − 1.02680i | −0.858151 | − | 0.513398i | \(-0.828387\pi\) | ||||
0.858151 | − | 0.513398i | \(-0.171613\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.96883i | 0.286249i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 38.5436 | 1.38097 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.24386 | −0.151857 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 44.5311i | − 1.58938i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 25.7633i | − 0.918362i | −0.888343 | − | 0.459181i | \(-0.848143\pi\) | ||||
0.888343 | − | 0.459181i | \(-0.151857\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.06053 | −0.179932 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.550070 | −0.0195336 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 23.3741i | − 0.827954i | −0.910287 | − | 0.413977i | \(-0.864139\pi\) | ||||
0.910287 | − | 0.413977i | \(-0.135861\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 59.7422i | 2.11353i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.1527 | −0.570015 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.5577 | −0.689319 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 20.6019i | − 0.724326i | −0.932115 | − | 0.362163i | \(-0.882038\pi\) | ||||
0.932115 | − | 0.362163i | \(-0.117962\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 2.64782i | − 0.0929776i | −0.998919 | − | 0.0464888i | \(-0.985197\pi\) | ||||
0.998919 | − | 0.0464888i | \(-0.0148032\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.20685 | −0.0422741 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −69.8399 | −2.44339 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 43.5201i | − 1.51886i | −0.650589 | − | 0.759430i | \(-0.725478\pi\) | ||||
0.650589 | − | 0.759430i | \(-0.274522\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 10.5683i | − 0.368387i | −0.982890 | − | 0.184194i | \(-0.941033\pi\) | ||||
0.982890 | − | 0.184194i | \(-0.0589674\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.92486 | −0.136481 | −0.0682403 | − | 0.997669i | \(-0.521738\pi\) | ||||
−0.0682403 | + | 0.997669i | \(0.521738\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.2061 | −0.528129 | −0.264064 | − | 0.964505i | \(-0.585063\pi\) | ||||
−0.264064 | + | 0.964505i | \(0.585063\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.39325i | 0.186865i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 53.2333i | 1.84221i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.2841 | 0.424093 | 0.212046 | − | 0.977260i | \(-0.431987\pi\) | ||||
0.212046 | + | 0.977260i | \(0.431987\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0000 | 0.931034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 32.4849i | − 1.11751i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 9.67609i | − 0.332474i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −74.9784 | −2.57022 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.2056 | −0.554867 | −0.277434 | − | 0.960745i | \(-0.589484\pi\) | ||||
−0.277434 | + | 0.960745i | \(0.589484\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 15.9873i | − 0.546117i | −0.961997 | − | 0.273059i | \(-0.911965\pi\) | ||||
0.961997 | − | 0.273059i | \(-0.0880353\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 31.9688i | − 1.09076i | −0.838188 | − | 0.545381i | \(-0.816385\pi\) | ||||
0.838188 | − | 0.545381i | \(-0.183615\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.9847 | 1.32705 | 0.663527 | − | 0.748153i | \(-0.269059\pi\) | ||||
0.663527 | + | 0.748153i | \(0.269059\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.3416 | 1.23565 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.8218i | 0.502795i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.61003i | 0.0545536i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.77597 | −0.296682 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.07663 | 0.205193 | 0.102597 | − | 0.994723i | \(-0.467285\pi\) | ||||
0.102597 | + | 0.994723i | \(0.467285\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 15.9575i | − 0.537621i | −0.963193 | − | 0.268810i | \(-0.913370\pi\) | ||||
0.963193 | − | 0.268810i | \(-0.0866305\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.2544i | 1.45563i | 0.685775 | + | 0.727814i | \(0.259463\pi\) | ||||
−0.685775 | + | 0.727814i | \(0.740537\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −46.1811 | −1.55061 | −0.775305 | − | 0.631587i | \(-0.782404\pi\) | ||||
−0.775305 | + | 0.631587i | \(0.782404\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.470539 | −0.0157814 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 68.7401i | 2.30030i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 2.95112i | − 0.0986452i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.14019 | −0.238139 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.4494 | −0.814528 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 9.83037i | − 0.326773i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.94108i | 0.296884i | 0.988921 | + | 0.148442i | \(0.0474258\pi\) | ||||
−0.988921 | + | 0.148442i | \(0.952574\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.8219 | −1.25310 | −0.626548 | − | 0.779383i | \(-0.715533\pi\) | ||||
−0.626548 | + | 0.779383i | \(0.715533\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.0978 | −0.334187 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.9162i | 0.525598i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 38.7244i | − 1.27740i | −0.769455 | − | 0.638701i | \(-0.779472\pi\) | ||||
0.769455 | − | 0.638701i | \(-0.220528\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.13311 | 0.0702121 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.5194 | 0.510275 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.9222i | 0.391154i | 0.980688 | + | 0.195577i | \(0.0626580\pi\) | ||||
−0.980688 | + | 0.195577i | \(0.937342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.20555i | 0.203379i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.9162 | −0.520514 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.1744 | 0.920417 | 0.460208 | − | 0.887811i | \(-0.347775\pi\) | ||||
0.460208 | + | 0.887811i | \(0.347775\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 53.9054i | − 1.75727i | −0.477496 | − | 0.878634i | \(-0.658456\pi\) | ||||
0.477496 | − | 0.878634i | \(-0.341544\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 47.3622i | 1.54233i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.7275 | −1.19348 | −0.596742 | − | 0.802433i | \(-0.703538\pi\) | ||||
−0.596742 | + | 0.802433i | \(0.703538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.11888 | 0.263550 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 58.9090i | 1.90825i | 0.299408 | + | 0.954125i | \(0.403211\pi\) | ||||
−0.299408 | + | 0.954125i | \(0.596789\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 25.4600i | − 0.823865i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.55440 | −0.276236 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.50885 | 0.177705 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32.5120i | 1.04660i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 43.6061i | − 1.40228i | −0.713025 | − | 0.701139i | \(-0.752675\pi\) | ||||
0.713025 | − | 0.701139i | \(-0.247325\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 59.7960 | 1.91895 | 0.959473 | − | 0.281801i | \(-0.0909317\pi\) | ||||
0.959473 | + | 0.281801i | \(0.0909317\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.0000 | 0.512936 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.5794i | 1.33024i | 0.746736 | + | 0.665121i | \(0.231620\pi\) | ||||
−0.746736 | + | 0.665121i | \(0.768380\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.54002i | 0.209020i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.428934 | 0.0136809 | 0.00684043 | − | 0.999977i | \(-0.497823\pi\) | ||||
0.00684043 | + | 0.999977i | \(0.497823\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.37279 | 0.139329 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 85.8190i | − 2.72889i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 31.5466i | − 1.00211i | −0.865415 | − | 0.501056i | \(-0.832945\pi\) | ||||
0.865415 | − | 0.501056i | \(-0.167055\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 38.0706 | 1.20692 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.7144 | −1.09942 | −0.549708 | − | 0.835357i | \(-0.685261\pi\) | ||||
−0.549708 | + | 0.835357i | \(0.685261\pi\) | |||||||
\(998\) | 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 | 4032.2.h.h.575.10 | 12 | ||
3.2 | odd | 2 | inner | 4032.2.h.h.575.4 | 12 | ||
4.3 | odd | 2 | inner | 4032.2.h.h.575.9 | 12 | ||
8.3 | odd | 2 | 252.2.e.a.71.5 | ✓ | 12 | ||
8.5 | even | 2 | 252.2.e.a.71.7 | yes | 12 | ||
12.11 | even | 2 | inner | 4032.2.h.h.575.3 | 12 | ||
24.5 | odd | 2 | 252.2.e.a.71.6 | yes | 12 | ||
24.11 | even | 2 | 252.2.e.a.71.8 | yes | 12 | ||
56.13 | odd | 2 | 1764.2.e.g.1079.7 | 12 | |||
56.27 | even | 2 | 1764.2.e.g.1079.5 | 12 | |||
168.83 | odd | 2 | 1764.2.e.g.1079.8 | 12 | |||
168.125 | even | 2 | 1764.2.e.g.1079.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.e.a.71.5 | ✓ | 12 | 8.3 | odd | 2 | ||
252.2.e.a.71.6 | yes | 12 | 24.5 | odd | 2 | ||
252.2.e.a.71.7 | yes | 12 | 8.5 | even | 2 | ||
252.2.e.a.71.8 | yes | 12 | 24.11 | even | 2 | ||
1764.2.e.g.1079.5 | 12 | 56.27 | even | 2 | |||
1764.2.e.g.1079.6 | 12 | 168.125 | even | 2 | |||
1764.2.e.g.1079.7 | 12 | 56.13 | odd | 2 | |||
1764.2.e.g.1079.8 | 12 | 168.83 | odd | 2 | |||
4032.2.h.h.575.3 | 12 | 12.11 | even | 2 | inner | ||
4032.2.h.h.575.4 | 12 | 3.2 | odd | 2 | inner | ||
4032.2.h.h.575.9 | 12 | 4.3 | odd | 2 | inner | ||
4032.2.h.h.575.10 | 12 | 1.1 | even | 1 | trivial |