Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2016,2,Mod(289,2016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2016, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2016.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2016.s (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.0978410475\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1156923.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 27x^{2} - 18x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 672) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.3 | ||
Root | \(0.500000 + 0.0585812i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2016.289 |
Dual form | 2016.2.s.v.865.3 |
$q$-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 \(\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1765\) | \(1793\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.37328 | − | 2.37860i | 0.614151 | − | 1.06374i | −0.376381 | − | 0.926465i | \(-0.622832\pi\) |
0.990533 | − | 0.137277i | \(-0.0438349\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64510 | − | 0.0585812i | 0.999755 | − | 0.0221416i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.771819 | − | 1.33683i | −0.232712 | − | 0.403069i | 0.725893 | − | 0.687807i | \(-0.241427\pi\) |
−0.958605 | + | 0.284738i | \(0.908093\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.03677 | 1.67430 | 0.837150 | − | 0.546974i | \(-0.184220\pi\) | ||||
0.837150 | + | 0.546974i | \(0.184220\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.74657 | + | 6.48925i | 0.908676 | + | 1.57387i | 0.815905 | + | 0.578186i | \(0.196239\pi\) |
0.0927713 | + | 0.995687i | \(0.470427\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.01839 | + | 5.22800i | −0.692465 | + | 1.19939i | 0.278562 | + | 0.960418i | \(0.410142\pi\) |
−0.971028 | + | 0.238967i | \(0.923191\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.74657 | − | 6.48925i | 0.781213 | − | 1.35310i | −0.150022 | − | 0.988683i | \(-0.547934\pi\) |
0.931235 | − | 0.364419i | \(-0.118732\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.27182 | − | 2.20285i | −0.254364 | − | 0.440571i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.25343 | −0.232756 | −0.116378 | − | 0.993205i | \(-0.537128\pi\) | ||||
−0.116378 | + | 0.993205i | \(0.537128\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.64510 | + | 4.58145i | 0.475074 | + | 0.822853i | 0.999592 | − | 0.0285462i | \(-0.00908778\pi\) |
−0.524518 | + | 0.851399i | \(0.675754\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.49314 | − | 6.37208i | 0.590448 | − | 1.07708i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.47475 | + | 4.28639i | −0.406846 | + | 0.704679i | −0.994534 | − | 0.104409i | \(-0.966705\pi\) |
0.587688 | + | 0.809088i | \(0.300038\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.08727 | 0.794499 | 0.397249 | − | 0.917711i | \(-0.369965\pi\) | ||||
0.397249 | + | 0.917711i | \(0.369965\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.45636 | −0.527090 | −0.263545 | − | 0.964647i | \(-0.584892\pi\) | ||||
−0.263545 | + | 0.964647i | \(0.584892\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.74657 | + | 8.22130i | −0.692358 | + | 1.19920i | 0.278705 | + | 0.960377i | \(0.410095\pi\) |
−0.971063 | + | 0.238823i | \(0.923239\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.99314 | − | 0.309906i | 0.999019 | − | 0.0442723i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.91692 | − | 3.32021i | −0.263309 | − | 0.456065i | 0.703810 | − | 0.710388i | \(-0.251481\pi\) |
−0.967119 | + | 0.254323i | \(0.918147\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.23970 | −0.571682 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.77182 | − | 4.80093i | −0.360860 | − | 0.625028i | 0.627243 | − | 0.778824i | \(-0.284183\pi\) |
−0.988103 | + | 0.153796i | \(0.950850\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.29021 | − | 12.6270i | 0.933415 | − | 1.61672i | 0.155979 | − | 0.987760i | \(-0.450147\pi\) |
0.777436 | − | 0.628962i | \(-0.216520\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.29021 | − | 14.3591i | 1.02827 | − | 1.78102i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.01839 | − | 3.49595i | −0.246585 | − | 0.427098i | 0.715991 | − | 0.698110i | \(-0.245975\pi\) |
−0.962576 | + | 0.271012i | \(0.912642\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.49314 | −0.651915 | −0.325958 | − | 0.945384i | \(-0.605687\pi\) | ||||
−0.325958 | + | 0.945384i | \(0.605687\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.27182 | − | 10.8631i | −0.734061 | − | 1.27143i | −0.955134 | − | 0.296173i | \(-0.904289\pi\) |
0.221073 | − | 0.975257i | \(-0.429044\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.11985 | − | 3.49084i | −0.241580 | − | 0.397818i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.89853 | + | 6.75246i | −0.438619 | + | 0.759711i | −0.997583 | − | 0.0694809i | \(-0.977866\pi\) |
0.558964 | + | 0.829192i | \(0.311199\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.52991 | −0.716751 | −0.358375 | − | 0.933578i | \(-0.616669\pi\) | ||||
−0.358375 | + | 0.933578i | \(0.616669\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.5804 | 2.23226 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.74657 | + | 8.22130i | −0.503135 | + | 0.871456i | 0.496858 | + | 0.867832i | \(0.334487\pi\) |
−0.999993 | + | 0.00362404i | \(0.998846\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.9679 | − | 0.353641i | 1.67389 | − | 0.0370717i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.29021 | + | 14.3591i | 0.850557 | + | 1.47321i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.54364 | 0.156733 | 0.0783663 | − | 0.996925i | \(-0.475030\pi\) | ||||
0.0783663 | + | 0.996925i | \(0.475030\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.29021 | − | 2.23470i | −0.128380 | − | 0.222361i | 0.794669 | − | 0.607043i | \(-0.207644\pi\) |
−0.923049 | + | 0.384682i | \(0.874311\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.27182 | − | 5.66696i | 0.322382 | − | 0.558382i | −0.658597 | − | 0.752496i | \(-0.728850\pi\) |
0.980979 | + | 0.194114i | \(0.0621832\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.26496 | − | 3.92302i | 0.218961 | − | 0.379252i | −0.735529 | − | 0.677493i | \(-0.763066\pi\) |
0.954491 | + | 0.298241i | \(0.0963998\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.22132 | + | 5.57949i | 0.308546 | + | 0.534418i | 0.978045 | − | 0.208396i | \(-0.0668242\pi\) |
−0.669498 | + | 0.742814i | \(0.733491\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.00000 | −0.752577 | −0.376288 | − | 0.926503i | \(-0.622800\pi\) | ||||
−0.376288 | + | 0.926503i | \(0.622800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.2902 | − | 17.8232i | −0.959567 | − | 1.66202i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.2902 | + | 16.9452i | 0.943302 | + | 1.55337i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.30859 | − | 7.46270i | 0.391690 | − | 0.678427i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.74657 | 0.603431 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.79707 | −0.336935 | −0.168468 | − | 0.985707i | \(-0.553882\pi\) | ||||
−0.168468 | + | 0.985707i | \(0.553882\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.771819 | + | 1.33683i | −0.0674341 | + | 0.116799i | −0.897771 | − | 0.440462i | \(-0.854815\pi\) |
0.830337 | + | 0.557262i | \(0.188148\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.67768 | + | 14.0054i | −0.665739 | + | 1.21442i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.746568 | + | 1.29309i | 0.0637836 | + | 0.110476i | 0.896154 | − | 0.443744i | \(-0.146350\pi\) |
−0.832370 | + | 0.554220i | \(0.813017\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.94950 | 0.250173 | 0.125087 | − | 0.992146i | \(-0.460079\pi\) | ||||
0.125087 | + | 0.992146i | \(0.460079\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.65929 | − | 8.07013i | −0.389630 | − | 0.674858i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.72132 | + | 2.98141i | −0.142948 | + | 0.247593i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.746568 | + | 1.29309i | −0.0611613 | + | 0.105934i | −0.894985 | − | 0.446097i | \(-0.852814\pi\) |
0.833823 | + | 0.552031i | \(0.186147\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.86642 | + | 8.42889i | 0.396024 | + | 0.685933i | 0.993231 | − | 0.116154i | \(-0.0370565\pi\) |
−0.597208 | + | 0.802087i | \(0.703723\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.5299 | 1.16707 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.54364 | − | 7.86981i | −0.362622 | − | 0.628079i | 0.625770 | − | 0.780008i | \(-0.284785\pi\) |
−0.988391 | + | 0.151929i | \(0.951452\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.52991 | − | 17.3842i | 0.751062 | − | 1.37007i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.78334 | − | 16.9452i | 0.766290 | − | 1.32725i | −0.173271 | − | 0.984874i | \(-0.555434\pi\) |
0.939562 | − | 0.342380i | \(-0.111233\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.8990 | −0.920772 | −0.460386 | − | 0.887719i | \(-0.652289\pi\) | ||||
−0.460386 | + | 0.887719i | \(0.652289\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.4426 | 1.80328 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.29021 | − | 2.23470i | 0.0980925 | − | 0.169901i | −0.812803 | − | 0.582539i | \(-0.802059\pi\) |
0.910895 | + | 0.412638i | \(0.135393\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.49314 | − | 5.75227i | −0.264056 | − | 0.434831i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.49314 | + | 2.58619i | 0.111602 | + | 0.193301i | 0.916416 | − | 0.400226i | \(-0.131068\pi\) |
−0.804814 | + | 0.593527i | \(0.797735\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.5436 | −0.783702 | −0.391851 | − | 0.920029i | \(-0.628165\pi\) | ||||
−0.391851 | + | 0.920029i | \(0.628165\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.79707 | + | 11.7729i | 0.499730 | + | 0.865559i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.78334 | − | 10.0170i | 0.422920 | − | 0.732519i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.58041 | + | 14.8617i | −0.620857 | + | 1.07536i | 0.368470 | + | 0.929640i | \(0.379882\pi\) |
−0.989327 | + | 0.145716i | \(0.953452\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.44950 | − | 9.43881i | −0.392264 | − | 0.679420i | 0.600484 | − | 0.799637i | \(-0.294975\pi\) |
−0.992748 | + | 0.120216i | \(0.961641\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.41959 | −0.386130 | −0.193065 | − | 0.981186i | \(-0.561843\pi\) | ||||
−0.193065 | + | 0.981186i | \(0.561843\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.4931 | − | 19.9067i | −0.814727 | − | 1.41115i | −0.909524 | − | 0.415652i | \(-0.863554\pi\) |
0.0947970 | − | 0.995497i | \(-0.469780\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.31546 | + | 0.0734275i | −0.232699 | + | 0.00515360i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.98627 | − | 12.1006i | 0.487942 | − | 0.845141i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.31859 | 0.644580 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.08727 | −0.212537 | −0.106268 | − | 0.994337i | \(-0.533890\pi\) | ||||
−0.106268 | + | 0.994337i | \(0.533890\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.74657 | + | 8.22130i | −0.323713 | + | 0.560688i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.26496 | + | 11.9635i | 0.493177 | + | 0.812132i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.6172 | + | 39.1741i | 1.52140 | + | 2.63514i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.7466 | 1.52322 | 0.761611 | − | 0.648034i | \(-0.224409\pi\) | ||||
0.761611 | + | 0.648034i | \(0.224409\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.3017 | − | 19.5752i | −0.750122 | − | 1.29925i | −0.947763 | − | 0.318975i | \(-0.896661\pi\) |
0.197641 | − | 0.980274i | \(-0.436672\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.67768 | − | 9.83403i | 0.375192 | − | 0.649851i | −0.615164 | − | 0.788399i | \(-0.710910\pi\) |
0.990356 | + | 0.138548i | \(0.0442435\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.70979 | − | 2.96145i | 0.112012 | − | 0.194011i | −0.804569 | − | 0.593859i | \(-0.797604\pi\) |
0.916582 | + | 0.399848i | \(0.130937\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.0368 | + | 22.5804i | 0.850425 | + | 1.47298i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.49314 | −0.484691 | −0.242345 | − | 0.970190i | \(-0.577917\pi\) | ||||
−0.242345 | + | 0.970190i | \(0.577917\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.30173 | + | 16.1111i | 0.599177 | + | 1.03781i | 0.992943 | + | 0.118594i | \(0.0378388\pi\) |
−0.393766 | + | 0.919211i | \(0.628828\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.86642 | − | 17.0594i | 0.566455 | − | 1.08989i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.2213 | + | 31.5602i | −1.15939 | + | 2.00813i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.5299 | 1.54831 | 0.774157 | − | 0.632994i | \(-0.218174\pi\) | ||||
0.774157 | + | 0.632994i | \(0.218174\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.5667 | −0.727191 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.74657 | + | 15.1495i | −0.545596 | + | 0.945000i | 0.452973 | + | 0.891524i | \(0.350363\pi\) |
−0.998569 | + | 0.0534758i | \(0.982970\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.29487 | + | 11.4829i | −0.391144 | + | 0.713514i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.74657 | + | 11.6854i | 0.416011 | + | 0.720553i | 0.995534 | − | 0.0944035i | \(-0.0300944\pi\) |
−0.579523 | + | 0.814956i | \(0.696761\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.5299 | −0.646847 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.17035 | + | 5.49121i | 0.193300 | + | 0.334805i | 0.946342 | − | 0.323167i | \(-0.104748\pi\) |
−0.753042 | + | 0.657972i | \(0.771414\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.1199 | + | 17.5281i | −0.614737 | + | 1.06476i | 0.375693 | + | 0.926744i | \(0.377405\pi\) |
−0.990431 | + | 0.138012i | \(0.955929\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.96323 | + | 3.40041i | −0.118387 | + | 0.205052i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.27182 | + | 2.20285i | 0.0764162 | + | 0.132357i | 0.901701 | − | 0.432360i | \(-0.142319\pi\) |
−0.825285 | + | 0.564716i | \(0.808986\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.5804 | −1.58565 | −0.792827 | − | 0.609447i | \(-0.791392\pi\) | ||||
−0.792827 | + | 0.609447i | \(0.791392\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.2718 | − | 17.7913i | −0.610596 | − | 1.05758i | −0.991140 | − | 0.132821i | \(-0.957597\pi\) |
0.380544 | − | 0.924763i | \(-0.375737\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.4564 | − | 0.298018i | 0.794304 | − | 0.0175915i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −19.5735 | + | 33.9024i | −1.15139 | + | 1.99426i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.25343 | −0.306909 | −0.153454 | − | 0.988156i | \(-0.549040\pi\) | ||||
−0.153454 | + | 0.988156i | \(0.549040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.2260 | −0.886491 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 22.6172 | − | 39.1741i | 1.30799 | − | 2.26550i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.14243 | + | 0.202478i | −0.526961 | + | 0.0116706i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −20.0230 | − | 34.6809i | −1.14652 | − | 1.98582i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.8485 | −0.847449 | −0.423724 | − | 0.905791i | \(-0.639277\pi\) | ||||
−0.423724 | + | 0.905791i | \(0.639277\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.949499 | + | 1.64458i | 0.0538412 | + | 0.0932556i | 0.891690 | − | 0.452647i | \(-0.149520\pi\) |
−0.837849 | + | 0.545903i | \(0.816187\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.0436371 | − | 0.0755817i | 0.00246652 | − | 0.00427213i | −0.864790 | − | 0.502135i | \(-0.832548\pi\) |
0.867256 | + | 0.497862i | \(0.165882\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.11985 | − | 7.13579i | 0.231394 | − | 0.400786i | −0.726825 | − | 0.686823i | \(-0.759005\pi\) |
0.958219 | + | 0.286037i | \(0.0923380\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.967422 | + | 1.67562i | 0.0541652 | + | 0.0938169i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −45.2344 | −2.51691 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.67768 | − | 13.2981i | −0.425881 | − | 0.737648i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.0735 | + | 22.0242i | −0.665636 | + | 1.21424i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.76496 | + | 4.78904i | −0.151976 | + | 0.263230i | −0.931954 | − | 0.362577i | \(-0.881897\pi\) |
0.779978 | + | 0.625807i | \(0.215230\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.0873 | −0.605763 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.17455 | 0.390823 | 0.195411 | − | 0.980721i | \(-0.437396\pi\) | ||||
0.195411 | + | 0.980721i | \(0.437396\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.08308 | − | 7.07210i | 0.221111 | − | 0.382976i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4794 | − | 1.22940i | 0.997794 | − | 0.0663814i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.0368 | − | 20.8483i | −0.646168 | − | 1.11920i | −0.984030 | − | 0.178000i | \(-0.943037\pi\) |
0.337863 | − | 0.941195i | \(-0.390296\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.1608 | −1.66800 | −0.834000 | − | 0.551764i | \(-0.813955\pi\) | ||||
−0.834000 | + | 0.551764i | \(0.813955\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.08727 | − | 8.81142i | −0.270768 | − | 0.468984i | 0.698290 | − | 0.715814i | \(-0.253944\pi\) |
−0.969059 | + | 0.246830i | \(0.920611\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.54364 | + | 13.0660i | −0.400375 | + | 0.693469i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.1240 | − | 27.9277i | 0.850995 | − | 1.47397i | −0.0293169 | − | 0.999570i | \(-0.509333\pi\) |
0.880312 | − | 0.474396i | \(-0.157333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.72132 | − | 15.1058i | −0.459017 | − | 0.795040i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −34.4520 | −1.80330 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.93531 | + | 3.35205i | 0.101022 | + | 0.174976i | 0.912106 | − | 0.409954i | \(-0.134455\pi\) |
−0.811084 | + | 0.584930i | \(0.801122\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.26496 | − | 8.66999i | −0.273343 | − | 0.450123i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.3454 | + | 30.0431i | −0.898109 | + | 1.55557i | −0.0682000 | + | 0.997672i | \(0.521726\pi\) |
−0.829909 | + | 0.557899i | \(0.811608\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.56668 | −0.389704 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.4564 | −0.691207 | −0.345603 | − | 0.938381i | \(-0.612326\pi\) | ||||
−0.345603 | + | 0.938381i | \(0.612326\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.08727 | + | 3.61527i | −0.106655 | + | 0.184731i | −0.914413 | − | 0.404782i | \(-0.867347\pi\) |
0.807758 | + | 0.589514i | \(0.200681\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.2145 | + | 0.248367i | −0.571542 | + | 0.0126579i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.32698 | − | 16.1548i | −0.472897 | − | 0.819081i | 0.526622 | − | 0.850099i | \(-0.323458\pi\) |
−0.999519 | + | 0.0310185i | \(0.990125\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 56.1471 | 2.83948 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.7076 | + | 18.5461i | 0.538757 | + | 0.933155i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.728181 | − | 1.26125i | 0.0365464 | − | 0.0633002i | −0.847174 | − | 0.531316i | \(-0.821698\pi\) |
0.883720 | + | 0.468016i | \(0.155031\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.6172 | + | 25.3177i | −0.729947 | + | 1.26431i | 0.226958 | + | 0.973905i | \(0.427122\pi\) |
−0.956905 | + | 0.290401i | \(0.906211\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.9679 | + | 27.6572i | 0.795417 | + | 1.37770i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.64023 | 0.378712 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.0299 | − | 22.5685i | −0.644288 | − | 1.11594i | −0.984466 | − | 0.175578i | \(-0.943821\pi\) |
0.340178 | − | 0.940361i | \(-0.389513\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.61299 | − | 12.5366i | −0.374611 | − | 0.616885i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.96742 | + | 15.5320i | −0.440193 | + | 0.762437i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.8853 | 1.60655 | 0.803275 | − | 0.595608i | \(-0.203089\pi\) | ||||
0.803275 | + | 0.595608i | \(0.203089\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.1976 | −0.838160 | −0.419080 | − | 0.907949i | \(-0.637647\pi\) | ||||
−0.419080 | + | 0.907949i | \(0.637647\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.52991 | − | 16.5063i | 0.462269 | − | 0.800673i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.5436 | − | 33.8268i | 0.897389 | − | 1.63699i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.49314 | − | 2.58619i | −0.0719219 | − | 0.124572i | 0.827822 | − | 0.560991i | \(-0.189580\pi\) |
−0.899744 | + | 0.436419i | \(0.856247\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.4426 | 0.886297 | 0.443148 | − | 0.896448i | \(-0.353862\pi\) | ||||
0.443148 | + | 0.896448i | \(0.353862\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.6172 | + | 39.1741i | 1.08193 | + | 1.87395i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.286010 | − | 0.495384i | 0.0136505 | − | 0.0236434i | −0.859119 | − | 0.511775i | \(-0.828988\pi\) |
0.872770 | + | 0.488132i | \(0.162321\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.2650 | + | 31.6358i | −0.867794 | + | 1.50306i | −0.00354850 | + | 0.999994i | \(0.501130\pi\) |
−0.864246 | + | 0.503070i | \(0.832204\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.0368 | + | 22.5804i | 0.618002 | + | 1.07041i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.5530 | 1.06434 | 0.532170 | − | 0.846638i | \(-0.321377\pi\) | ||||
0.532170 | + | 0.846638i | \(0.321377\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.92645 | − | 6.80082i | −0.184889 | − | 0.320238i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 21.0873 | − | 38.4668i | 0.988587 | − | 1.80335i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.1172 | + | 17.5235i | −0.473262 | + | 0.819714i | −0.999532 | − | 0.0306040i | \(-0.990257\pi\) |
0.526270 | + | 0.850318i | \(0.323590\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.4931 | −1.18733 | −0.593667 | − | 0.804711i | \(-0.702320\pi\) | ||||
−0.593667 | + | 0.804711i | \(0.702320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.70446 | 0.358057 | 0.179028 | − | 0.983844i | \(-0.442705\pi\) | ||||
0.179028 | + | 0.983844i | \(0.442705\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.0735 | + | 31.3043i | −0.836344 | + | 1.44859i | 0.0565874 | + | 0.998398i | \(0.481978\pi\) |
−0.892931 | + | 0.450193i | \(0.851355\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.54364 | − | 9.12890i | −0.255981 | − | 0.421534i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.66769 | + | 4.62057i | 0.122660 | + | 0.212454i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.3554 | 0.704552 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.2902 | − | 23.0193i | −0.607245 | − | 1.05178i | −0.991692 | − | 0.128632i | \(-0.958941\pi\) |
0.384447 | − | 0.923147i | \(-0.374392\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.9395 | + | 25.8760i | −0.681183 | + | 1.17984i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.11985 | − | 3.67169i | 0.0962575 | − | 0.166723i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.2118 | − | 35.0078i | −0.915883 | − | 1.58636i | −0.805603 | − | 0.592456i | \(-0.798158\pi\) |
−0.110281 | − | 0.993900i | \(-0.535175\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.6309 | 0.660284 | 0.330142 | − | 0.943931i | \(-0.392903\pi\) | ||||
0.330142 | + | 0.943931i | \(0.392903\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.69607 | − | 8.13383i | −0.211500 | − | 0.366329i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.5299 | + | 0.321794i | −0.651756 | + | 0.0144344i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.0552 | + | 31.2725i | −0.808260 | + | 1.39995i | 0.105808 | + | 0.994387i | \(0.466257\pi\) |
−0.914068 | + | 0.405561i | \(0.867076\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.4931 | 0.869156 | 0.434578 | − | 0.900634i | \(-0.356898\pi\) | ||||
0.434578 | + | 0.900634i | \(0.356898\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.08727 | −0.315380 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.9537 | + | 20.7044i | −0.529838 | + | 0.917707i | 0.469556 | + | 0.882903i | \(0.344414\pi\) |
−0.999394 | + | 0.0348040i | \(0.988919\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.2260 | − | 28.3666i | −0.762032 | − | 1.25487i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.98627 | − | 15.5647i | −0.395982 | − | 0.685862i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.6540 | 0.644480 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.54364 | − | 6.13776i | −0.155250 | − | 0.268900i | 0.777900 | − | 0.628388i | \(-0.216285\pi\) |
−0.933150 | + | 0.359488i | \(0.882952\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.3737 | + | 24.8961i | −0.628520 | + | 1.08863i | 0.359329 | + | 0.933211i | \(0.383006\pi\) |
−0.987849 | + | 0.155418i | \(0.950328\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.8201 | + | 34.3294i | −0.863378 | + | 1.49541i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.5735 | − | 28.7062i | −0.720589 | − | 1.24810i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.7107 | 1.33023 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.22085 | − | 10.7748i | −0.268951 | − | 0.465837i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.81172 | − | 9.10944i | −0.250329 | − | 0.392371i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.51152 | − | 6.08214i | 0.150972 | − | 0.261491i | −0.780613 | − | 0.625015i | \(-0.785093\pi\) |
0.931585 | + | 0.363523i | \(0.118426\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.6951 | 0.757976 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.59414 | −0.239188 | −0.119594 | − | 0.992823i | \(-0.538159\pi\) | ||||
−0.119594 | + | 0.992823i | \(0.538159\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.78334 | − | 6.55294i | 0.161176 | − | 0.279165i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.91646 | + | 18.0893i | −0.421691 | + | 0.769237i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.3228 | + | 24.8078i | 0.606876 | + | 1.05114i | 0.991752 | + | 0.128172i | \(0.0409108\pi\) |
−0.384876 | + | 0.922968i | \(0.625756\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.8653 | −0.882507 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.94637 | + | 17.2276i | 0.419189 | + | 0.726057i | 0.995858 | − | 0.0909207i | \(-0.0289810\pi\) |
−0.576669 | + | 0.816978i | \(0.695648\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.9863 | + | 19.0288i | −0.462196 | + | 0.800547i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.8201 | − | 30.8653i | 0.747058 | − | 1.29394i | −0.202169 | − | 0.979351i | \(-0.564799\pi\) |
0.949227 | − | 0.314592i | \(-0.101868\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.8385 | − | 23.9690i | −0.579123 | − | 1.00307i | −0.995580 | − | 0.0939155i | \(-0.970062\pi\) |
0.416457 | − | 0.909155i | \(-0.363272\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.0598 | −0.794849 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.00686 | + | 5.20804i | 0.125177 | + | 0.216814i | 0.921802 | − | 0.387660i | \(-0.126717\pi\) |
−0.796625 | + | 0.604474i | \(0.793383\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.2723 | + | 0.382530i | −0.716575 | + | 0.0158700i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.95903 | + | 5.12519i | −0.122551 | + | 0.212264i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.5436 | 0.641555 | 0.320777 | − | 0.947155i | \(-0.396056\pi\) | ||||
0.320777 | + | 0.947155i | \(0.396056\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.9358 | −1.31589 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.3270 | + | 42.1356i | −0.998989 | + | 1.73030i | −0.460568 | + | 0.887624i | \(0.652354\pi\) |
−0.538421 | + | 0.842676i | \(0.680979\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 54.4373 | − | 1.20562i | 2.23171 | − | 0.0494258i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.4564 | + | 18.1110i | 0.427235 | + | 0.739993i | 0.996626 | − | 0.0820735i | \(-0.0261542\pi\) |
−0.569391 | + | 0.822067i | \(0.692821\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.98627 | −0.325767 | −0.162883 | − | 0.986645i | \(-0.552079\pi\) | ||||
−0.162883 | + | 0.986645i | \(0.552079\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.8338 | − | 20.4968i | −0.481114 | − | 0.833314i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.35490 | − | 2.34675i | 0.0549936 | − | 0.0952517i | −0.837218 | − | 0.546869i | \(-0.815819\pi\) |
0.892212 | + | 0.451618i | \(0.149153\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.6540 | + | 49.6301i | −1.15922 | + | 2.00782i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.25343 | + | 14.2954i | 0.333353 | + | 0.577384i | 0.983167 | − | 0.182709i | \(-0.0584866\pi\) |
−0.649814 | + | 0.760093i | \(0.725153\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.1608 | 0.932420 | 0.466210 | − | 0.884674i | \(-0.345619\pi\) | ||||
0.466210 | + | 0.884674i | \(0.345619\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.7145 | − | 25.4862i | −0.591424 | − | 1.02438i | −0.994041 | − | 0.109008i | \(-0.965233\pi\) |
0.402617 | − | 0.915369i | \(-0.368101\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.0735 | + | 22.0242i | −0.483716 | + | 0.882382i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.6240 | − | 27.0616i | 0.624962 | − | 1.08247i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37.0873 | −1.47877 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.7054 | 1.42141 | 0.710705 | − | 0.703491i | \(-0.248376\pi\) | ||||
0.710705 | + | 0.703491i | \(0.248376\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.21445 | + | 9.03170i | −0.206929 | + | 0.358412i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 42.2160 | − | 1.87083i | 1.67266 | − | 0.0741252i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.68141 | − | 2.91229i | −0.0664118 | − | 0.115029i | 0.830908 | − | 0.556410i | \(-0.187822\pi\) |
−0.897319 | + | 0.441382i | \(0.854488\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.2113 | −0.402695 | −0.201348 | − | 0.979520i | \(-0.564532\pi\) | ||||
−0.201348 | + | 0.979520i | \(0.564532\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.2765 | + | 17.7994i | 0.404010 | + | 0.699766i | 0.994206 | − | 0.107494i | \(-0.0342827\pi\) |
−0.590196 | + | 0.807260i | \(0.700949\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.27868 | + | 7.41089i | −0.167953 | + | 0.290903i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.67722 | + | 9.83323i | −0.222167 | + | 0.384804i | −0.955466 | − | 0.295102i | \(-0.904646\pi\) |
0.733299 | + | 0.679906i | \(0.237980\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.11985 | + | 3.67169i | 0.0828295 | + | 0.143465i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.2344 | 0.827174 | 0.413587 | − | 0.910465i | \(-0.364276\pi\) | ||||
0.413587 | + | 0.910465i | \(0.364276\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.4610 | + | 25.0472i | 0.562469 | + | 0.974224i | 0.997280 | + | 0.0737028i | \(0.0234816\pi\) |
−0.434812 | + | 0.900521i | \(0.643185\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22.7696 | + | 37.4955i | 0.882968 | + | 1.45401i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.69607 | + | 8.13383i | −0.181832 | + | 0.314943i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.5069 | −0.868868 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.2618 | −1.32070 | −0.660348 | − | 0.750960i | \(-0.729591\pi\) | ||||
−0.660348 | + | 0.750960i | \(0.729591\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.3733 | − | 30.0914i | 0.667710 | − | 1.15651i | −0.310833 | − | 0.950464i | \(-0.600608\pi\) |
0.978543 | − | 0.206042i | \(-0.0660585\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.08308 | − | 0.0904281i | 0.156694 | − | 0.00347031i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.140907 | − | 0.244058i | −0.00539166 | − | 0.00933863i | 0.863317 | − | 0.504662i | \(-0.168383\pi\) |
−0.868709 | + | 0.495323i | \(0.835050\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.10100 | 0.156691 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.5720 | − | 20.0433i | −0.440859 | − | 0.763590i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.2076 | − | 29.8044i | 0.654608 | − | 1.13381i | −0.327384 | − | 0.944891i | \(-0.606167\pi\) |
0.981992 | − | 0.188922i | \(-0.0604995\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.05050 | − | 7.01567i | 0.153644 | − | 0.266120i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.0598 | + | 33.0126i | 0.721942 | + | 1.25044i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.498472 | 0.0188270 | 0.00941352 | − | 0.999956i | \(-0.497004\pi\) | ||||
0.00941352 | + | 0.999956i | \(0.497004\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.9395 | − | 25.8760i | −0.563454 | − | 0.975931i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.54364 | − | 5.83543i | −0.133272 | − | 0.219464i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.08727 | − | 3.61527i | 0.0783892 | − | 0.135774i | −0.824166 | − | 0.566348i | \(-0.808356\pi\) |
0.902555 | + | 0.430574i | \(0.141689\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 39.6402 | 1.48454 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −25.5941 | −0.957166 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.493136 | − | 0.854137i | 0.0183909 | − | 0.0318540i | −0.856683 | − | 0.515842i | \(-0.827479\pi\) |
0.875074 | + | 0.483988i | \(0.160812\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.32232 | − | 15.1813i | 0.309939 | − | 0.565383i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.59414 | + | 2.76113i | 0.0592048 | + | 0.102546i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.9304 | 1.29550 | 0.647749 | − | 0.761854i | \(-0.275711\pi\) | ||||
0.647749 | + | 0.761854i | \(0.275711\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.9495 | − | 22.4292i | −0.478955 | − | 0.829574i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.56202 | + | 4.43756i | −0.0946305 | + | 0.163905i | −0.909454 | − | 0.415804i | \(-0.863500\pi\) |
0.814824 | + | 0.579709i | \(0.196834\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.11566 | + | 5.39648i | −0.114767 | + | 0.198782i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.46102 | − | 14.6549i | −0.311244 | − | 0.539090i | 0.667388 | − | 0.744710i | \(-0.267412\pi\) |
−0.978632 | + | 0.205620i | \(0.934079\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.81172 | 0.249898 | 0.124949 | − | 0.992163i | \(-0.460123\pi\) | ||||
0.124949 | + | 0.992163i | \(0.460123\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.05050 | + | 3.55157i | 0.0751245 | + | 0.130120i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.76122 | − | 10.5095i | 0.210511 | − | 0.384008i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.0877 | + | 22.6686i | −0.477578 | + | 0.827190i | −0.999670 | − | 0.0256996i | \(-0.991819\pi\) |
0.522091 | + | 0.852890i | \(0.325152\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26.7319 | 0.972874 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.7138 | 1.80688 | 0.903439 | − | 0.428717i | \(-0.141034\pi\) | ||||
0.903439 | + | 0.428717i | \(0.141034\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.32698 | + | 10.9586i | −0.229353 | + | 0.397251i | −0.957616 | − | 0.288046i | \(-0.906994\pi\) |
0.728264 | + | 0.685297i | \(0.240328\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.84757 | + | 14.5696i | 0.320304 | + | 0.527455i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.7328 | − | 28.9821i | −0.604188 | − | 1.04648i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.2344 | −0.729670 | −0.364835 | − | 0.931072i | \(-0.618875\pi\) | ||||
−0.364835 | + | 0.931072i | \(0.618875\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.87062 | − | 17.0964i | −0.355021 | − | 0.614915i | 0.632100 | − | 0.774887i | \(-0.282193\pi\) |
−0.987122 | + | 0.159972i | \(0.948860\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.72818 | − | 11.6536i | 0.241683 | − | 0.418608i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.3554 | + | 26.5963i | −0.550163 | + | 0.952910i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.23970 | + | 7.34338i | 0.151709 | + | 0.262767i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.9588 | −0.890818 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.45636 | − | 14.6469i | −0.301437 | − | 0.522104i | 0.675025 | − | 0.737795i | \(-0.264133\pi\) |
−0.976462 | + | 0.215691i | \(0.930800\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.1608 | + | 0.468649i | −0.752392 | + | 0.0166633i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 44.0093 | − | 76.2264i | 1.56282 | − | 2.70688i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.48475 | −0.123436 | −0.0617180 | − | 0.998094i | \(-0.519658\pi\) | ||||
−0.0617180 | + | 0.998094i | \(0.519658\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −71.1334 | −2.51652 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.68141 | + | 16.7687i | −0.341650 | + | 0.591754i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28.2628 | − | 46.5413i | −0.996131 | − | 1.64036i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.59414 | − | 16.6175i | −0.337312 | − | 0.584241i | 0.646614 | − | 0.762817i | \(-0.276184\pi\) |
−0.983926 | + | 0.178576i | \(0.942851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.8285 | 1.71460 | 0.857300 | − | 0.514817i | \(-0.172140\pi\) | ||||
0.857300 | + | 0.514817i | \(0.172140\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −26.8706 | − | 46.5413i | −0.941237 | − | 1.63027i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.4326 | − | 18.0699i | 0.364992 | − | 0.632184i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.2723 | + | 22.9883i | −0.463206 | + | 0.802296i | −0.999119 | − | 0.0419773i | \(-0.986634\pi\) |
0.535913 | + | 0.844273i | \(0.319968\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.47941 | + | 14.6868i | 0.295574 | + | 0.511949i | 0.975118 | − | 0.221686i | \(-0.0711559\pi\) |
−0.679545 | + | 0.733634i | \(0.737823\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.4289 | 1.47540 | 0.737699 | − | 0.675130i | \(-0.235912\pi\) | ||||
0.737699 | + | 0.675130i | \(0.235912\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.9679 | + | 27.6572i | 0.554588 | + | 0.960574i | 0.997935 | + | 0.0642243i | \(0.0204573\pi\) |
−0.443348 | + | 0.896350i | \(0.646209\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.2113 | + | 44.2191i | 0.977464 | + | 1.53210i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.3407 | + | 28.3029i | −0.565493 | + | 0.979463i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 49.5392 | 1.71028 | 0.855142 | − | 0.518394i | \(-0.173470\pi\) | ||||
0.855142 | + | 0.518394i | \(0.173470\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.4289 | −0.945824 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 32.1934 | − | 55.7606i | 1.10749 | − | 1.91822i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9595 | − | 19.9920i | 0.376573 | − | 0.686934i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.5436 | + | 32.1185i | 0.635668 | + | 1.10101i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.4564 | 0.392258 | 0.196129 | − | 0.980578i | \(-0.437163\pi\) | ||||
0.196129 | + | 0.980578i | \(0.437163\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.1240 | − | 27.9277i | −0.550787 | − | 0.953991i | −0.998218 | − | 0.0596726i | \(-0.980994\pi\) |
0.447431 | − | 0.894318i | \(-0.352339\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.54364 | + | 2.67366i | −0.0526682 | + | 0.0912240i | −0.891158 | − | 0.453694i | \(-0.850106\pi\) |
0.838489 | + | 0.544918i | \(0.183439\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.07355 | − | 15.7158i | 0.308867 | − | 0.534974i | −0.669248 | − | 0.743039i | \(-0.733383\pi\) |
0.978115 | + | 0.208066i | \(0.0667168\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.54364 | − | 6.13776i | −0.120487 | − | 0.208690i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.0358 | 0.408288 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.1845 | − | 21.1042i | −0.412858 | − | 0.715090i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.8454 | − | 0.395222i | 0.603283 | − | 0.0133609i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.44264 | + | 7.69487i | −0.150017 | + | 0.259837i | −0.931234 | − | 0.364423i | \(-0.881266\pi\) |
0.781216 | + | 0.624260i | \(0.214600\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.5667 | 1.40042 | 0.700209 | − | 0.713938i | \(-0.253090\pi\) | ||||
0.700209 | + | 0.713938i | \(0.253090\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.7182 | 0.966444 | 0.483222 | − | 0.875498i | \(-0.339466\pi\) | ||||
0.483222 | + | 0.875498i | \(0.339466\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.9074 | − | 36.2127i | 0.702001 | − | 1.21590i | −0.265761 | − | 0.964039i | \(-0.585623\pi\) |
0.967763 | − | 0.251863i | \(-0.0810433\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.0436 | + | 0.222437i | −0.336853 | + | 0.00746029i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.6540 | − | 49.6301i | −0.958868 | − | 1.66081i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.20200 | 0.274163 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.31546 | − | 5.74254i | −0.110577 | − | 0.191524i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.3638 | − | 24.8787i | 0.478526 | − | 0.828831i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.4794 | + | 25.0791i | −0.481312 | + | 0.833657i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.5851 | + | 49.5108i | 0.949152 | + | 1.64398i | 0.747217 | + | 0.664580i | \(0.231389\pi\) |
0.201935 | + | 0.979399i | \(0.435277\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.4059 | 0.808602 | 0.404301 | − | 0.914626i | \(-0.367515\pi\) | ||||
0.404301 | + | 0.914626i | \(0.367515\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.03991 | + | 8.72937i | 0.166797 | + | 0.288900i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.96323 | + | 3.58126i | −0.0648314 | + | 0.118264i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.8522 | + | 41.3133i | −0.786812 | + | 1.36280i | 0.141098 | + | 0.989996i | \(0.454937\pi\) |
−0.927910 | + | 0.372803i | \(0.878397\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.1608 | −1.09150 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.5897 | 0.413948 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.6172 | − | 33.9780i | 0.643619 | − | 1.11478i | −0.341000 | − | 0.940063i | \(-0.610766\pi\) |
0.984619 | − | 0.174717i | \(-0.0559012\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.4878 | + | 37.4955i | −0.638687 | + | 1.22887i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.8843 | − | 27.5125i | −0.519474 | − | 0.899755i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.3491 | 0.501433 | 0.250717 | − | 0.968061i | \(-0.419334\pi\) | ||||
0.250717 | + | 0.968061i | \(0.419334\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.08308 | − | 10.5362i | −0.198303 | − | 0.343470i | 0.749676 | − | 0.661806i | \(-0.230210\pi\) |
−0.947978 | + | 0.318335i | \(0.896876\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.0598 | − | 33.0126i | 0.620673 | − | 1.07504i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.52991 | + | 16.5063i | −0.309680 | + | 0.536382i | −0.978292 | − | 0.207229i | \(-0.933555\pi\) |
0.668612 | + | 0.743611i | \(0.266889\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37.8615 | − | 65.5781i | −1.22904 | − | 2.12876i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.1334 | −0.555004 | −0.277502 | − | 0.960725i | \(-0.589507\pi\) | ||||
−0.277502 | + | 0.960725i | \(0.589507\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.5667 | + | 40.8187i | 0.762600 | + | 1.32086i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.05050 | + | 3.37663i | 0.0662141 | + | 0.109037i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.50686 | − | 2.60996i | 0.0486085 | − | 0.0841924i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −29.9348 | −0.963637 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.7833 | 0.861294 | 0.430647 | − | 0.902520i | \(-0.358285\pi\) | ||||
0.430647 | + | 0.902520i | \(0.358285\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.75809 | − | 9.97331i | 0.184786 | − | 0.320059i | −0.758718 | − | 0.651419i | \(-0.774174\pi\) |
0.943504 | + | 0.331360i | \(0.107507\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.80173 | − | 0.172785i | 0.250112 | − | 0.00553924i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.6677 | + | 18.4770i | 0.341289 | + | 0.591131i | 0.984672 | − | 0.174414i | \(-0.0558030\pi\) |
−0.643383 | + | 0.765544i | \(0.722470\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.6540 | 0.468343 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.1976 | − | 43.6435i | −0.803678 | − | 1.39201i | −0.917180 | − | 0.398474i | \(-0.869540\pi\) |
0.113501 | − | 0.993538i | \(-0.463793\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.44264 | + | 12.8910i | −0.237142 | + | 0.410742i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.9495 | + | 22.4292i | −0.411770 | + | 0.713207i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.34117 | − | 10.9832i | −0.201434 | − | 0.348894i | 0.747557 | − | 0.664198i | \(-0.231227\pi\) |
−0.948991 | + | 0.315304i | \(0.897893\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −63.1334 | −2.00146 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.1708 | + | 34.9369i | 0.638816 | + | 1.10646i | 0.985693 | + | 0.168551i | \(0.0539089\pi\) |
−0.346877 | + | 0.937911i | \(0.612758\pi\) | |||||||
\(998\) | 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 | 2016.2.s.v.289.3 | 6 | ||
3.2 | odd | 2 | 672.2.q.l.289.1 | yes | 6 | ||
4.3 | odd | 2 | 2016.2.s.u.289.3 | 6 | |||
7.4 | even | 3 | inner | 2016.2.s.v.865.3 | 6 | ||
12.11 | even | 2 | 672.2.q.k.289.1 | yes | 6 | ||
21.2 | odd | 6 | 4704.2.a.bs.1.3 | 3 | |||
21.5 | even | 6 | 4704.2.a.bv.1.1 | 3 | |||
21.11 | odd | 6 | 672.2.q.l.193.1 | yes | 6 | ||
24.5 | odd | 2 | 1344.2.q.y.961.3 | 6 | |||
24.11 | even | 2 | 1344.2.q.z.961.3 | 6 | |||
28.11 | odd | 6 | 2016.2.s.u.865.3 | 6 | |||
84.11 | even | 6 | 672.2.q.k.193.1 | ✓ | 6 | ||
84.23 | even | 6 | 4704.2.a.bu.1.3 | 3 | |||
84.47 | odd | 6 | 4704.2.a.bt.1.1 | 3 | |||
168.5 | even | 6 | 9408.2.a.eg.1.3 | 3 | |||
168.11 | even | 6 | 1344.2.q.z.193.3 | 6 | |||
168.53 | odd | 6 | 1344.2.q.y.193.3 | 6 | |||
168.107 | even | 6 | 9408.2.a.eh.1.1 | 3 | |||
168.131 | odd | 6 | 9408.2.a.ei.1.3 | 3 | |||
168.149 | odd | 6 | 9408.2.a.ej.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.q.k.193.1 | ✓ | 6 | 84.11 | even | 6 | ||
672.2.q.k.289.1 | yes | 6 | 12.11 | even | 2 | ||
672.2.q.l.193.1 | yes | 6 | 21.11 | odd | 6 | ||
672.2.q.l.289.1 | yes | 6 | 3.2 | odd | 2 | ||
1344.2.q.y.193.3 | 6 | 168.53 | odd | 6 | |||
1344.2.q.y.961.3 | 6 | 24.5 | odd | 2 | |||
1344.2.q.z.193.3 | 6 | 168.11 | even | 6 | |||
1344.2.q.z.961.3 | 6 | 24.11 | even | 2 | |||
2016.2.s.u.289.3 | 6 | 4.3 | odd | 2 | |||
2016.2.s.u.865.3 | 6 | 28.11 | odd | 6 | |||
2016.2.s.v.289.3 | 6 | 1.1 | even | 1 | trivial | ||
2016.2.s.v.865.3 | 6 | 7.4 | even | 3 | inner | ||
4704.2.a.bs.1.3 | 3 | 21.2 | odd | 6 | |||
4704.2.a.bt.1.1 | 3 | 84.47 | odd | 6 | |||
4704.2.a.bu.1.3 | 3 | 84.23 | even | 6 | |||
4704.2.a.bv.1.1 | 3 | 21.5 | even | 6 | |||
9408.2.a.eg.1.3 | 3 | 168.5 | even | 6 | |||
9408.2.a.eh.1.1 | 3 | 168.107 | even | 6 | |||
9408.2.a.ei.1.3 | 3 | 168.131 | odd | 6 | |||
9408.2.a.ej.1.1 | 3 | 168.149 | odd | 6 |