Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1241,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8280.1241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.p (of order \(2\), degree \(1\), 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: | \(66.1161328736\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1241.30 | ||
Character | \(\chi\) | \(=\) | 8280.1241 |
Dual form | 8280.2.p.a.1241.19 |
$q$-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 \(\left(\mathbb{Z}/8280\mathbb{Z}\right)^\times\).
\(n\) | \(1657\) | \(2071\) | \(3961\) | \(4141\) | \(4601\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.36101i | 0.514412i | 0.966357 | + | 0.257206i | \(0.0828019\pi\) | ||||
−0.966357 | + | 0.257206i | \(0.917198\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.32855 | 0.702083 | 0.351042 | − | 0.936360i | \(-0.385828\pi\) | ||||
0.351042 | + | 0.936360i | \(0.385828\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.17596 | 1.71290 | 0.856451 | − | 0.516228i | \(-0.172664\pi\) | ||||
0.856451 | + | 0.516228i | \(0.172664\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.91838 | 1.67795 | 0.838977 | − | 0.544166i | \(-0.183154\pi\) | ||||
0.838977 | + | 0.544166i | \(0.183154\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.609544i | − | 0.139839i | −0.997553 | − | 0.0699195i | \(-0.977726\pi\) | ||
0.997553 | − | 0.0699195i | \(-0.0222742\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.08664 | + | 2.50985i | 0.852124 | + | 0.523340i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 0.841999i | − | 0.156355i | −0.996939 | − | 0.0781776i | \(-0.975090\pi\) | ||
0.996939 | − | 0.0781776i | \(-0.0249101\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0981227 | 0.0176234 | 0.00881168 | − | 0.999961i | \(-0.497195\pi\) | ||||
0.00881168 | + | 0.999961i | \(0.497195\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 1.36101i | − | 0.230052i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.85378i | − | 1.12675i | −0.826200 | − | 0.563377i | \(-0.809502\pi\) | ||
0.826200 | − | 0.563377i | \(-0.190498\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.58549i | − | 1.02848i | −0.857646 | − | 0.514240i | \(-0.828074\pi\) | ||
0.857646 | − | 0.514240i | \(-0.171926\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.293064i | − | 0.0446919i | −0.999750 | − | 0.0223459i | \(-0.992886\pi\) | ||
0.999750 | − | 0.0223459i | \(-0.00711353\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.82138i | 0.557405i | 0.960377 | + | 0.278702i | \(0.0899043\pi\) | ||||
−0.960377 | + | 0.278702i | \(0.910096\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.14766 | 0.735380 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.36282 | 0.187198 | 0.0935989 | − | 0.995610i | \(-0.470163\pi\) | ||||
0.0935989 | + | 0.995610i | \(0.470163\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.32855 | −0.313981 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.1519i | 1.84242i | 0.389062 | + | 0.921212i | \(0.372799\pi\) | ||||
−0.389062 | + | 0.921212i | \(0.627201\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.54154i | − | 0.325411i | −0.986675 | − | 0.162705i | \(-0.947978\pi\) | ||
0.986675 | − | 0.162705i | \(-0.0520220\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.17596 | −0.766033 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 13.3006i | − | 1.62493i | −0.583011 | − | 0.812464i | \(-0.698125\pi\) | ||
0.583011 | − | 0.812464i | \(-0.301875\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.87925i | − | 0.579060i | −0.957169 | − | 0.289530i | \(-0.906501\pi\) | ||
0.957169 | − | 0.289530i | \(-0.0934991\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.41879 | 0.400140 | 0.200070 | − | 0.979782i | \(-0.435883\pi\) | ||||
0.200070 | + | 0.979782i | \(0.435883\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.16917i | 0.361160i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.39837i | − | 0.269838i | −0.990857 | − | 0.134919i | \(-0.956923\pi\) | ||
0.990857 | − | 0.134919i | \(-0.0430774\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.10006 | 0.230511 | 0.115256 | − | 0.993336i | \(-0.463231\pi\) | ||||
0.115256 | + | 0.993336i | \(0.463231\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.91838 | −0.750404 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.1331 | −1.39211 | −0.696053 | − | 0.717991i | \(-0.745062\pi\) | ||||
−0.696053 | + | 0.717991i | \(0.745062\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.40552i | 0.881138i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.609544i | 0.0625379i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.80719i | 0.792700i | 0.918100 | + | 0.396350i | \(0.129723\pi\) | ||||
−0.918100 | + | 0.396350i | \(0.870277\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.97034i | 0.494567i | 0.968943 | + | 0.247283i | \(0.0795379\pi\) | ||||
−0.968943 | + | 0.247283i | \(0.920462\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 7.93913i | − | 0.782266i | −0.920334 | − | 0.391133i | \(-0.872083\pi\) | ||
0.920334 | − | 0.391133i | \(-0.127917\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.38117 | −0.616891 | −0.308446 | − | 0.951242i | \(-0.599809\pi\) | ||||
−0.308446 | + | 0.951242i | \(0.599809\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.8958i | − | 1.23519i | −0.786496 | − | 0.617596i | \(-0.788107\pi\) | ||
0.786496 | − | 0.617596i | \(-0.211893\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.62398 | 0.340915 | 0.170458 | − | 0.985365i | \(-0.445475\pi\) | ||||
0.170458 | + | 0.985365i | \(0.445475\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.08664 | − | 2.50985i | −0.381081 | − | 0.234045i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.41596i | 0.863160i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.57787 | −0.507079 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6115 | 1.03035 | 0.515176 | − | 0.857084i | \(-0.327727\pi\) | ||||
0.515176 | + | 0.857084i | \(0.327727\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.1854i | 1.15201i | 0.817446 | + | 0.576005i | \(0.195389\pi\) | ||||
−0.817446 | + | 0.576005i | \(0.804611\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.829593 | 0.0719348 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.5459 | −1.07187 | −0.535934 | − | 0.844260i | \(-0.680041\pi\) | ||||
−0.535934 | + | 0.844260i | \(0.680041\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.0180 | −1.10417 | −0.552085 | − | 0.833788i | \(-0.686167\pi\) | ||||
−0.552085 | + | 0.833788i | \(0.686167\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.3810 | 1.20260 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.841999i | 0.0699242i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.638019 | 0.0522686 | 0.0261343 | − | 0.999658i | \(-0.491680\pi\) | ||||
0.0261343 | + | 0.999658i | \(0.491680\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.8378 | −0.881965 | −0.440983 | − | 0.897516i | \(-0.645370\pi\) | ||||
−0.440983 | + | 0.897516i | \(0.645370\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.0981227 | −0.00788141 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.59811i | 0.127543i | 0.997965 | + | 0.0637715i | \(0.0203129\pi\) | ||||
−0.997965 | + | 0.0637715i | \(0.979687\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.41593 | + | 5.56195i | −0.269213 | + | 0.438343i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.2578 | −1.11675 | −0.558377 | − | 0.829587i | \(-0.688576\pi\) | ||||
−0.558377 | + | 0.829587i | \(0.688576\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.30317i | 0.178225i | 0.996022 | + | 0.0891123i | \(0.0284030\pi\) | ||||
−0.996022 | + | 0.0891123i | \(0.971597\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.1425 | 1.93404 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 13.9985i | − | 1.06429i | −0.846654 | − | 0.532143i | \(-0.821387\pi\) | ||
0.846654 | − | 0.532143i | \(-0.178613\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.36101i | 0.102882i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 16.9442i | − | 1.26647i | −0.773960 | − | 0.633235i | \(-0.781727\pi\) | ||
0.773960 | − | 0.633235i | \(-0.218273\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.00241i | 0.223167i | 0.993755 | + | 0.111584i | \(0.0355923\pi\) | ||||
−0.993755 | + | 0.111584i | \(0.964408\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.85378i | 0.503900i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.1098 | 1.17806 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.1388 | −0.805974 | −0.402987 | − | 0.915206i | \(-0.632028\pi\) | ||||
−0.402987 | + | 0.915206i | \(0.632028\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.7159 | 1.77909 | 0.889546 | − | 0.456846i | \(-0.151021\pi\) | ||||
0.889546 | + | 0.456846i | \(0.151021\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.21643i | 0.157914i | 0.996878 | + | 0.0789571i | \(0.0251590\pi\) | ||||
−0.996878 | + | 0.0789571i | \(0.974841\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 6.02768i | − | 0.427291i | −0.976911 | − | 0.213646i | \(-0.931466\pi\) | ||
0.976911 | − | 0.213646i | \(-0.0685338\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.14597 | 0.0804310 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.58549i | 0.459951i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.41935i | − | 0.0981785i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.15202 | 0.492365 | 0.246183 | − | 0.969223i | \(-0.420824\pi\) | ||||
0.246183 | + | 0.969223i | \(0.420824\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.293064i | 0.0199868i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.133546i | 0.00906567i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 42.7277 | 2.87417 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.2153 | 1.68854 | 0.844272 | − | 0.535915i | \(-0.180033\pi\) | ||||
0.844272 | + | 0.535915i | \(0.180033\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.6367 | −0.905100 | −0.452550 | − | 0.891739i | \(-0.649486\pi\) | ||||
−0.452550 | + | 0.891739i | \(0.649486\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 14.1505i | − | 0.935090i | −0.883969 | − | 0.467545i | \(-0.845139\pi\) | ||
0.883969 | − | 0.467545i | \(-0.154861\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.22194i | 0.342100i | 0.985262 | + | 0.171050i | \(0.0547160\pi\) | ||||
−0.985262 | + | 0.171050i | \(0.945284\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 3.82138i | − | 0.249279i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.86141i | 0.637881i | 0.947775 | + | 0.318941i | \(0.103327\pi\) | ||||
−0.947775 | + | 0.318941i | \(0.896673\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.79014i | 0.308560i | 0.988027 | + | 0.154280i | \(0.0493058\pi\) | ||||
−0.988027 | + | 0.154280i | \(0.950694\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.14766 | −0.328872 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.76452i | − | 0.239530i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.80969 | 0.240466 | 0.120233 | − | 0.992746i | \(-0.461636\pi\) | ||||
0.120233 | + | 0.992746i | \(0.461636\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.51594 | + | 5.84431i | 0.598262 | + | 0.367429i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 13.3778i | − | 0.834484i | −0.908795 | − | 0.417242i | \(-0.862997\pi\) | ||
0.908795 | − | 0.417242i | \(-0.137003\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.32804 | 0.579616 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 29.3304 | 1.80859 | 0.904295 | − | 0.426907i | \(-0.140397\pi\) | ||||
0.904295 | + | 0.426907i | \(0.140397\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.36282 | −0.0837174 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.21872i | 0.379162i | 0.981865 | + | 0.189581i | \(0.0607130\pi\) | ||||
−0.981865 | + | 0.189581i | \(0.939287\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.778174 | −0.0472707 | −0.0236354 | − | 0.999721i | \(-0.507524\pi\) | ||||
−0.0236354 | + | 0.999721i | \(0.507524\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.32855 | 0.140417 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.9522 | −0.898393 | −0.449197 | − | 0.893433i | \(-0.648290\pi\) | ||||
−0.449197 | + | 0.893433i | \(0.648290\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.93159 | 0.115229 | 0.0576146 | − | 0.998339i | \(-0.481651\pi\) | ||||
0.0576146 | + | 0.998339i | \(0.481651\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 6.47867i | − | 0.385117i | −0.981285 | − | 0.192559i | \(-0.938321\pi\) | ||
0.981285 | − | 0.192559i | \(-0.0616785\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.96289 | 0.529063 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.8640 | 1.81553 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.59861 | 0.0933920 | 0.0466960 | − | 0.998909i | \(-0.485131\pi\) | ||||
0.0466960 | + | 0.998909i | \(0.485131\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 14.1519i | − | 0.823957i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 25.2389 | + | 15.5007i | 1.45961 | + | 0.896431i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.398862 | 0.0229900 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.54154i | 0.145528i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.8163 | 0.674393 | 0.337196 | − | 0.941434i | \(-0.390521\pi\) | ||||
0.337196 | + | 0.941434i | \(0.390521\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.1530i | 0.745836i | 0.927864 | + | 0.372918i | \(0.121643\pi\) | ||||
−0.927864 | + | 0.372918i | \(0.878357\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.4891i | 1.32768i | 0.747874 | + | 0.663841i | \(0.231075\pi\) | ||||
−0.747874 | + | 0.663841i | \(0.768925\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.2714i | 1.41938i | 0.704513 | + | 0.709691i | \(0.251165\pi\) | ||||
−0.704513 | + | 0.709691i | \(0.748835\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.96063i | − | 0.109774i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.21706i | − | 0.234643i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.17596 | 0.342581 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.20092 | −0.286736 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.8971 | 0.928750 | 0.464375 | − | 0.885639i | \(-0.346279\pi\) | ||||
0.464375 | + | 0.885639i | \(0.346279\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.3006i | 0.726690i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 19.2187i | − | 1.04691i | −0.852054 | − | 0.523454i | \(-0.824643\pi\) | ||
0.852054 | − | 0.523454i | \(-0.175357\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.228483 | 0.0123731 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.5330i | 0.892700i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.4391i | 0.721450i | 0.932672 | + | 0.360725i | \(0.117471\pi\) | ||||
−0.932672 | + | 0.360725i | \(0.882529\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.6613 | 0.624213 | 0.312106 | − | 0.950047i | \(-0.398965\pi\) | ||||
0.312106 | + | 0.950047i | \(0.398965\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.8041i | 1.53309i | 0.642193 | + | 0.766543i | \(0.278025\pi\) | ||||
−0.642193 | + | 0.766543i | \(0.721975\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.87925i | 0.258964i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.1562 | 0.905470 | 0.452735 | − | 0.891645i | \(-0.350448\pi\) | ||||
0.452735 | + | 0.891645i | \(0.350448\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.6285 | 0.980445 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.41879 | −0.178948 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 7.88954i | − | 0.411830i | −0.978570 | − | 0.205915i | \(-0.933983\pi\) | ||
0.978570 | − | 0.205915i | \(-0.0660171\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.85481i | 0.0962968i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 13.8450i | − | 0.716867i | −0.933555 | − | 0.358434i | \(-0.883311\pi\) | ||
0.933555 | − | 0.358434i | \(-0.116689\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 5.20015i | − | 0.267821i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.7397i | 0.808494i | 0.914650 | + | 0.404247i | \(0.132466\pi\) | ||||
−0.914650 | + | 0.404247i | \(0.867534\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.7447 | −1.57098 | −0.785491 | − | 0.618873i | \(-0.787589\pi\) | ||||
−0.785491 | + | 0.618873i | \(0.787589\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 3.16917i | − | 0.161516i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.3630 | 0.981741 | 0.490870 | − | 0.871233i | \(-0.336679\pi\) | ||||
0.490870 | + | 0.871233i | \(0.336679\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.2730 | + | 17.3641i | 1.42982 | + | 0.878141i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.39837i | 0.120675i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.5158 | 0.527774 | 0.263887 | − | 0.964554i | \(-0.414995\pi\) | ||||
0.263887 | + | 0.964554i | \(0.414995\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.7489 | −0.586713 | −0.293356 | − | 0.956003i | \(-0.594772\pi\) | ||||
−0.293356 | + | 0.956003i | \(0.594772\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.606002 | 0.0301871 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 15.9593i | − | 0.791076i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.5464 | −1.01595 | −0.507977 | − | 0.861371i | \(-0.669606\pi\) | ||||
−0.507977 | + | 0.861371i | \(0.669606\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −19.2609 | −0.947765 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.10006 | −0.103088 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.3644 | 0.750600 | 0.375300 | − | 0.926903i | \(-0.377540\pi\) | ||||
0.375300 | + | 0.926903i | \(0.377540\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 36.3261i | − | 1.77043i | −0.465186 | − | 0.885213i | \(-0.654012\pi\) | ||
0.465186 | − | 0.885213i | \(-0.345988\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.91838 | 0.335591 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.45905 | 0.167395 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.1957 | 1.06913 | 0.534564 | − | 0.845128i | \(-0.320476\pi\) | ||||
0.534564 | + | 0.845128i | \(0.320476\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 15.6554i | − | 0.752351i | −0.926548 | − | 0.376176i | \(-0.877239\pi\) | ||
0.926548 | − | 0.376176i | \(-0.122761\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.52986 | − | 2.49099i | 0.0731834 | − | 0.119160i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.6179 | −0.649946 | −0.324973 | − | 0.945723i | \(-0.605355\pi\) | ||||
−0.324973 | + | 0.945723i | \(0.605355\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.1520i | 0.909940i | 0.890507 | + | 0.454970i | \(0.150350\pi\) | ||||
−0.890507 | + | 0.454970i | \(0.849650\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.1331 | 0.622569 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 27.0825i | − | 1.27810i | −0.769164 | − | 0.639051i | \(-0.779327\pi\) | ||
0.769164 | − | 0.639051i | \(-0.220673\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 15.3346i | − | 0.722079i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 8.40552i | − | 0.394057i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 29.6948i | − | 1.38906i | −0.719463 | − | 0.694531i | \(-0.755612\pi\) | ||
0.719463 | − | 0.694531i | \(-0.244388\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 9.77211i | − | 0.455133i | −0.973763 | − | 0.227566i | \(-0.926923\pi\) | ||
0.973763 | − | 0.227566i | \(-0.0730768\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.2661 | −0.477106 | −0.238553 | − | 0.971129i | \(-0.576673\pi\) | ||||
−0.238553 | + | 0.971129i | \(0.576673\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.4893 | −0.994406 | −0.497203 | − | 0.867634i | \(-0.665640\pi\) | ||||
−0.497203 | + | 0.867634i | \(0.665640\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.1022 | 0.835883 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 0.682414i | − | 0.0313774i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 0.609544i | − | 0.0279678i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.13018 | 0.0973302 | 0.0486651 | − | 0.998815i | \(-0.484503\pi\) | ||||
0.0486651 | + | 0.998815i | \(0.484503\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 42.3287i | − | 1.93002i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 7.80719i | − | 0.354506i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.8695 | −1.08163 | −0.540816 | − | 0.841141i | \(-0.681885\pi\) | ||||
−0.540816 | + | 0.841141i | \(0.681885\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 40.6477i | 1.83441i | 0.398420 | + | 0.917203i | \(0.369559\pi\) | ||||
−0.398420 | + | 0.917203i | \(0.630441\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.82527i | − | 0.262357i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.64069 | 0.297876 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.3107 | 0.953997 | 0.476999 | − | 0.878904i | \(-0.341725\pi\) | ||||
0.476999 | + | 0.878904i | \(0.341725\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.2994 | 1.35098 | 0.675491 | − | 0.737368i | \(-0.263932\pi\) | ||||
0.675491 | + | 0.737368i | \(0.263932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 4.97034i | − | 0.221177i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 16.4954i | − | 0.731146i | −0.930783 | − | 0.365573i | \(-0.880873\pi\) | ||
0.930783 | − | 0.365573i | \(-0.119127\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.65300i | 0.205837i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.93913i | 0.349840i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.89825i | 0.391345i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.9661 | 0.699489 | 0.349745 | − | 0.936845i | \(-0.386268\pi\) | ||||
0.349745 | + | 0.936845i | \(0.386268\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.6409i | 1.33983i | 0.742437 | + | 0.669916i | \(0.233670\pi\) | ||||
−0.742437 | + | 0.669916i | \(0.766330\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.678851 | 0.0295712 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.4013 | + | 20.5137i | 0.452230 | + | 0.891902i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 40.6717i | − | 1.76169i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.38117 | 0.275882 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.9866 | 0.516298 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.65641 | 0.200195 | 0.100097 | − | 0.994978i | \(-0.468085\pi\) | ||||
0.100097 | + | 0.994978i | \(0.468085\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.8958i | 0.552394i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.7546 | −0.930158 | −0.465079 | − | 0.885269i | \(-0.653974\pi\) | ||||
−0.465079 | + | 0.885269i | \(0.653974\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.513235 | −0.0218645 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.26420 | 0.138808 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −40.5716 | −1.71907 | −0.859536 | − | 0.511075i | \(-0.829247\pi\) | ||||
−0.859536 | + | 0.511075i | \(0.829247\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.80995i | − | 0.0765529i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.4731 | −0.567822 | −0.283911 | − | 0.958851i | \(-0.591632\pi\) | ||||
−0.283911 | + | 0.958851i | \(0.591632\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.62398 | −0.152462 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.4298 | 0.604928 | 0.302464 | − | 0.953161i | \(-0.402191\pi\) | ||||
0.302464 | + | 0.953161i | \(0.402191\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.9229i | 0.708201i | 0.935207 | + | 0.354100i | \(0.115213\pi\) | ||||
−0.935207 | + | 0.354100i | \(0.884787\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.08664 | + | 2.50985i | 0.170425 | + | 0.104668i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.0757 | −1.16881 | −0.584403 | − | 0.811463i | \(-0.698671\pi\) | ||||
−0.584403 | + | 0.811463i | \(0.698671\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.85819i | 0.118578i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.17339 | 0.131428 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.6563i | 0.481105i | 0.970636 | + | 0.240553i | \(0.0773287\pi\) | ||||
−0.970636 | + | 0.240553i | \(0.922671\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 0.0598101i | − | 0.00246443i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.5861i | 0.968565i | 0.874912 | + | 0.484283i | \(0.160919\pi\) | ||||
−0.874912 | + | 0.484283i | \(0.839081\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 9.41596i | − | 0.386017i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.5437i | 0.512522i | 0.966608 | + | 0.256261i | \(0.0824907\pi\) | ||||
−0.966608 | + | 0.256261i | \(0.917509\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.82023 | 0.359785 | 0.179892 | − | 0.983686i | \(-0.442425\pi\) | ||||
0.179892 | + | 0.983686i | \(0.442425\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.57787 | 0.226773 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.9016 | −0.564248 | −0.282124 | − | 0.959378i | \(-0.591039\pi\) | ||||
−0.282124 | + | 0.959378i | \(0.591039\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.6007i | 0.954781i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 21.8968i | − | 0.884405i | −0.896915 | − | 0.442203i | \(-0.854197\pi\) | ||
0.896915 | − | 0.442203i | \(-0.145803\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.33977 | 0.174712 | 0.0873562 | − | 0.996177i | \(-0.472158\pi\) | ||||
0.0873562 | + | 0.996177i | \(0.472158\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.0721i | 0.887152i | 0.896237 | + | 0.443576i | \(0.146290\pi\) | ||||
−0.896237 | + | 0.443576i | \(0.853710\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 17.8742i | − | 0.716116i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 47.4171i | − | 1.89064i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.4052i | 1.29003i | 0.764170 | + | 0.645015i | \(0.223149\pi\) | ||||
−0.764170 | + | 0.645015i | \(0.776851\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.6115 | −0.460787 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 31.7918 | 1.25964 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.4591 | −1.55854 | −0.779270 | − | 0.626688i | \(-0.784410\pi\) | ||||
−0.779270 | + | 0.626688i | \(0.784410\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 39.2510i | − | 1.54791i | −0.633241 | − | 0.773954i | \(-0.718276\pi\) | ||
0.633241 | − | 0.773954i | \(-0.281724\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.6651i | 1.08763i | 0.839206 | + | 0.543814i | \(0.183020\pi\) | ||||
−0.839206 | + | 0.543814i | \(0.816980\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.9534i | 1.29353i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 12.9791i | − | 0.507910i | −0.967216 | − | 0.253955i | \(-0.918269\pi\) | ||
0.967216 | − | 0.253955i | \(-0.0817314\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 13.1854i | − | 0.515195i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.1712 | 0.980532 | 0.490266 | − | 0.871573i | \(-0.336900\pi\) | ||||
0.490266 | + | 0.871573i | \(0.336900\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.49951i | 0.136115i | 0.997681 | + | 0.0680577i | \(0.0216802\pi\) | ||||
−0.997681 | + | 0.0680577i | \(0.978320\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.829593 | −0.0321702 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.11329 | − | 3.44095i | 0.0818270 | − | 0.133234i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 5.91810i | − | 0.228466i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.5139 | −1.79298 | −0.896489 | − | 0.443066i | \(-0.853891\pi\) | ||||
−0.896489 | + | 0.443066i | \(0.853891\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.2333 | −0.508598 | −0.254299 | − | 0.967126i | \(-0.581845\pi\) | ||||
−0.254299 | + | 0.967126i | \(0.581845\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.6256 | −0.407774 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.9323i | 1.06880i | 0.845232 | + | 0.534400i | \(0.179462\pi\) | ||||
−0.845232 | + | 0.534400i | \(0.820538\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.5459 | 0.479354 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.41672 | 0.320652 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.9018 | −0.490808 | −0.245404 | − | 0.969421i | \(-0.578921\pi\) | ||||
−0.245404 | + | 0.969421i | \(0.578921\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.0180 | 0.493799 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 45.5609i | − | 1.72574i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.822196 | −0.0310539 | −0.0155270 | − | 0.999879i | \(-0.504943\pi\) | ||||
−0.0155270 | + | 0.999879i | \(0.504943\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.17768 | −0.157564 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.76466 | −0.254411 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 3.99096i | − | 0.149883i | −0.997188 | − | 0.0749417i | \(-0.976123\pi\) | ||
0.997188 | − | 0.0749417i | \(-0.0238771\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.400992 | + | 0.246274i | 0.0150173 | + | 0.00922302i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.3810 | −0.537819 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 52.1805i | − | 1.94600i | −0.230800 | − | 0.973001i | \(-0.574134\pi\) | ||
0.230800 | − | 0.973001i | \(-0.425866\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.8052 | 0.402407 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 0.841999i | − | 0.0312710i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.5482i | 1.20715i | 0.797308 | + | 0.603573i | \(0.206257\pi\) | ||||
−0.797308 | + | 0.603573i | \(0.793743\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 2.02753i | − | 0.0749909i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 3.25906i | − | 0.120376i | −0.998187 | − | 0.0601881i | \(-0.980830\pi\) | ||
0.998187 | − | 0.0601881i | \(-0.0191701\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 30.9711i | − | 1.14084i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.9443 | 0.402593 | 0.201296 | − | 0.979530i | \(-0.435485\pi\) | ||||
0.201296 | + | 0.979530i | \(0.435485\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.7242 | −0.650236 | −0.325118 | − | 0.945673i | \(-0.605404\pi\) | ||||
−0.325118 | + | 0.945673i | \(0.605404\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.638019 | −0.0233752 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 8.68482i | − | 0.317336i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.88536i | − | 0.0687978i | −0.999408 | − | 0.0343989i | \(-0.989048\pi\) | ||
0.999408 | − | 0.0343989i | \(-0.0109517\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.8378 | 0.394427 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 13.7509i | − | 0.499783i | −0.968274 | − | 0.249892i | \(-0.919605\pi\) | ||
0.968274 | − | 0.249892i | \(-0.0803950\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 41.2184i | − | 1.49417i | −0.664731 | − | 0.747083i | \(-0.731454\pi\) | ||
0.664731 | − | 0.747083i | \(-0.268546\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.5512 | 0.635397 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 87.4017i | 3.15589i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.0574i | 1.22814i | 0.789252 | + | 0.614070i | \(0.210469\pi\) | ||||
−0.789252 | + | 0.614070i | \(0.789531\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.13234 | −0.184597 | −0.0922987 | − | 0.995731i | \(-0.529421\pi\) | ||||
−0.0922987 | + | 0.995731i | \(0.529421\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.0981227 | 0.00352467 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.01414 | −0.143822 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 11.3616i | − | 0.406549i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.59811i | − | 0.0570390i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 15.3569i | − | 0.547415i | −0.961813 | − | 0.273707i | \(-0.911750\pi\) | ||
0.961813 | − | 0.273707i | \(-0.0882500\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.93225i | 0.175371i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 15.6965i | − | 0.557397i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.7015 | −1.19377 | −0.596884 | − | 0.802328i | \(-0.703595\pi\) | ||||
−0.596884 | + | 0.802328i | \(0.703595\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.4377i | 0.935300i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.96082 | 0.280931 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.41593 | − | 5.56195i | 0.120396 | − | 0.196033i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.2530i | 0.465951i | 0.972483 | + | 0.232976i | \(0.0748462\pi\) | ||||
−0.972483 | + | 0.232976i | \(0.925154\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.21633 | −0.288514 | −0.144257 | − | 0.989540i | \(-0.546079\pi\) | ||||
−0.144257 | + | 0.989540i | \(0.546079\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.2578 | 0.499428 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.178635 | −0.00624966 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.6343i | 1.45305i | 0.687141 | + | 0.726524i | \(0.258865\pi\) | ||||
−0.687141 | + | 0.726524i | \(0.741135\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.7235 | −0.582944 | −0.291472 | − | 0.956579i | \(-0.594145\pi\) | ||||
−0.291472 | + | 0.956579i | \(0.594145\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.03443 | 0.105518 | 0.0527588 | − | 0.998607i | \(-0.483199\pi\) | ||||
0.0527588 | + | 0.998607i | \(0.483199\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.1045 | 0.837183 | 0.418592 | − | 0.908175i | \(-0.362524\pi\) | ||||
0.418592 | + | 0.908175i | \(0.362524\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35.6135 | 1.23393 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 2.30317i | − | 0.0797044i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 54.4402 | 1.87948 | 0.939742 | − | 0.341886i | \(-0.111066\pi\) | ||||
0.939742 | + | 0.341886i | \(0.111066\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.2910 | 0.975553 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.1425 | −0.864927 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.59152i | − | 0.260848i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.2020 | − | 28.0089i | 0.589676 | − | 0.960134i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.4941 | 1.11258 | 0.556288 | − | 0.830990i | \(-0.312225\pi\) | ||||
0.556288 | + | 0.830990i | \(0.312225\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.7047i | 0.468145i | 0.972219 | + | 0.234072i | \(0.0752053\pi\) | ||||
−0.972219 | + | 0.234072i | \(0.924795\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.1773 | −1.40495 | −0.702476 | − | 0.711708i | \(-0.747922\pi\) | ||||
−0.702476 | + | 0.711708i | \(0.747922\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.1059i | 1.39926i | 0.714506 | + | 0.699630i | \(0.246652\pi\) | ||||
−0.714506 | + | 0.699630i | \(0.753348\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.9985i | 0.475964i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 5.58472i | − | 0.189449i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 82.1441i | − | 2.78335i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 1.36101i | − | 0.0460104i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.93361 | −0.200364 | −0.100182 | − | 0.994969i | \(-0.531942\pi\) | ||||
−0.100182 | + | 0.994969i | \(0.531942\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.7778 | −0.497877 | −0.248939 | − | 0.968519i | \(-0.580082\pi\) | ||||
−0.248939 | + | 0.968519i | \(0.580082\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.65523 | 0.223966 | 0.111983 | − | 0.993710i | \(-0.464280\pi\) | ||||
0.111983 | + | 0.993710i | \(0.464280\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.4121i | 0.752523i | 0.926513 | + | 0.376262i | \(0.122791\pi\) | ||||
−0.926513 | + | 0.376262i | \(0.877209\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.8033i | 0.530025i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.32930 | 0.0779469 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.9442i | 0.566382i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 0.0826192i | − | 0.00275550i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.42852 | 0.314109 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 3.00241i | − | 0.0998035i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 31.1572i | − | 1.03456i | −0.855817 | − | 0.517278i | \(-0.826945\pi\) | ||
0.855817 | − | 0.517278i | \(-0.173055\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.0796 | −0.565873 | −0.282936 | − | 0.959139i | \(-0.591309\pi\) | ||||
−0.282936 | + | 0.959139i | \(0.591309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.89008 | 0.161838 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.9454 | −0.592608 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 11.0423i | − | 0.364252i | −0.983275 | − | 0.182126i | \(-0.941702\pi\) | ||
0.983275 | − | 0.182126i | \(-0.0582979\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 30.1341i | − | 0.991874i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 6.85378i | − | 0.225351i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52.9143i | 1.73606i | 0.496509 | + | 0.868032i | \(0.334615\pi\) | ||||
−0.496509 | + | 0.868032i | \(0.665385\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 3.13772i | − | 0.102835i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.1098 | −0.526846 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8.17719i | − | 0.267137i | −0.991040 | − | 0.133569i | \(-0.957356\pi\) | ||
0.991040 | − | 0.133569i | \(-0.0426436\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.0012 | −0.978011 | −0.489005 | − | 0.872281i | \(-0.662640\pi\) | ||||
−0.489005 | + | 0.872281i | \(0.662640\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.5286 | − | 26.9125i | 0.538245 | − | 0.876393i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.5736i | 0.571067i | 0.958369 | + | 0.285533i | \(0.0921707\pi\) | ||||
−0.958369 | + | 0.285533i | \(0.907829\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.1143 | 0.685400 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.1688 | 1.75470 | 0.877350 | − | 0.479851i | \(-0.159309\pi\) | ||||
0.877350 | + | 0.479851i | \(0.159309\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.1388 | 0.360442 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 17.0750i | − | 0.551382i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9904 | −0.999689 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −24.7159 | −0.795634 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.8381 | −1.40974 | −0.704869 | − | 0.709338i | \(-0.748994\pi\) | ||||
−0.704869 | + | 0.709338i | \(0.748994\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.2808 | 0.490384 | 0.245192 | − | 0.969475i | \(-0.421149\pi\) | ||||
0.245192 | + | 0.969475i | \(0.421149\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 17.7175i | − | 0.567998i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.6814 | −0.917598 | −0.458799 | − | 0.888540i | \(-0.651720\pi\) | ||||
−0.458799 | + | 0.888540i | \(0.651720\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.5810 | −0.977374 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42.3387 | −1.35040 | −0.675198 | − | 0.737637i | \(-0.735942\pi\) | ||||
−0.675198 | + | 0.737637i | \(0.735942\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 2.21643i | − | 0.0706213i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.735548 | − | 1.19765i | 0.0233891 | − | 0.0380830i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.0587 | 0.573654 | 0.286827 | − | 0.957982i | \(-0.407400\pi\) | ||||
0.286827 | + | 0.957982i | \(0.407400\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.02768i | 0.191090i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.0287 | 1.29939 | 0.649697 | − | 0.760194i | \(-0.274896\pi\) | ||||
0.649697 | + | 0.760194i | \(0.274896\pi\) | |||||||
\(998\) | 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 | 8280.2.p.a.1241.30 | yes | 48 | |
3.2 | odd | 2 | 8280.2.p.b.1241.30 | yes | 48 | ||
23.22 | odd | 2 | 8280.2.p.b.1241.19 | yes | 48 | ||
69.68 | even | 2 | inner | 8280.2.p.a.1241.19 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8280.2.p.a.1241.19 | ✓ | 48 | 69.68 | even | 2 | inner | |
8280.2.p.a.1241.30 | yes | 48 | 1.1 | even | 1 | trivial | |
8280.2.p.b.1241.19 | yes | 48 | 23.22 | odd | 2 | ||
8280.2.p.b.1241.30 | yes | 48 | 3.2 | odd | 2 |