Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(65,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.bn (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 114) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.65 |
Dual form | 912.2.bn.b.449.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.73205i | 1.00000i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.00000 | + | 1.73205i | 1.34164 | + | 0.774597i | 0.987048 | − | 0.160424i | \(-0.0512862\pi\) |
0.354593 | + | 0.935021i | \(0.384620\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.73205i | 0.522233i | 0.965307 | + | 0.261116i | \(0.0840907\pi\) | ||||
−0.965307 | + | 0.261116i | \(0.915909\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | + | 1.73205i | −0.832050 | + | 0.480384i | −0.854554 | − | 0.519362i | \(-0.826170\pi\) |
0.0225039 | + | 0.999747i | \(0.492836\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.00000 | + | 5.19615i | −0.774597 | + | 1.34164i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.00000 | + | 3.46410i | 1.45521 | + | 0.840168i | 0.998770 | − | 0.0495842i | \(-0.0157896\pi\) |
0.456444 | + | 0.889752i | \(0.349123\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | − | 4.33013i | −0.114708 | − | 0.993399i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.46410i | 0.755929i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.50000 | + | 6.06218i | 0.700000 | + | 1.21244i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | − | 5.19615i | −0.557086 | − | 0.964901i | −0.997738 | − | 0.0672232i | \(-0.978586\pi\) |
0.440652 | − | 0.897678i | \(-0.354747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.92820i | 1.24434i | 0.782881 | + | 0.622171i | \(0.213749\pi\) | ||||
−0.782881 | + | 0.622171i | \(0.786251\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.00000 | −0.522233 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.00000 | + | 3.46410i | 1.01419 | + | 0.585540i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.92820i | − | 1.13899i | −0.821995 | − | 0.569495i | \(-0.807139\pi\) | ||
0.821995 | − | 0.569495i | \(-0.192861\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.00000 | − | 5.19615i | −0.480384 | − | 0.832050i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | + | 2.59808i | −0.234261 | + | 0.405751i | −0.959058 | − | 0.283211i | \(-0.908600\pi\) |
0.724797 | + | 0.688963i | \(0.241934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | − | 6.92820i | 0.609994 | − | 1.05654i | −0.381246 | − | 0.924473i | \(-0.624505\pi\) |
0.991241 | − | 0.132068i | \(-0.0421616\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.00000 | − | 5.19615i | −1.34164 | − | 0.774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00000 | − | 1.73205i | 0.437595 | − | 0.252646i | −0.264982 | − | 0.964253i | \(-0.585366\pi\) |
0.702577 | + | 0.711608i | \(0.252033\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.00000 | + | 10.3923i | −0.840168 | + | 1.45521i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.00000 | + | 5.19615i | 0.412082 | + | 0.713746i | 0.995117 | − | 0.0987002i | \(-0.0314685\pi\) |
−0.583036 | + | 0.812447i | \(0.698135\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.00000 | + | 5.19615i | −0.404520 | + | 0.700649i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.50000 | − | 0.866025i | 0.993399 | − | 0.114708i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.50000 | + | 2.59808i | −0.195283 | + | 0.338241i | −0.946993 | − | 0.321253i | \(-0.895896\pi\) |
0.751710 | + | 0.659494i | \(0.229229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.00000 | − | 8.66025i | −0.640184 | − | 1.10883i | −0.985391 | − | 0.170305i | \(-0.945525\pi\) |
0.345207 | − | 0.938527i | \(-0.387809\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.00000 | −0.755929 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.0000 | −1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.50000 | + | 2.59808i | −0.549762 | + | 0.317406i | −0.749026 | − | 0.662540i | \(-0.769478\pi\) |
0.199264 | + | 0.979946i | \(0.436145\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | + | 5.19615i | −0.356034 | + | 0.616670i | −0.987294 | − | 0.158901i | \(-0.949205\pi\) |
0.631260 | + | 0.775571i | \(0.282538\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.50000 | + | 4.33013i | −0.292603 | + | 0.506803i | −0.974424 | − | 0.224716i | \(-0.927855\pi\) |
0.681822 | + | 0.731519i | \(0.261188\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.5000 | + | 6.06218i | −1.21244 | + | 0.700000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.46410i | 0.394771i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0000 | + | 6.92820i | 1.35011 | + | 0.779484i | 0.988264 | − | 0.152756i | \(-0.0488148\pi\) |
0.361842 | + | 0.932240i | \(0.382148\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.19615i | 0.570352i | 0.958475 | + | 0.285176i | \(0.0920520\pi\) | ||||
−0.958475 | + | 0.285176i | \(0.907948\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0000 | + | 20.7846i | 1.30158 | + | 2.25441i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.00000 | − | 5.19615i | 0.964901 | − | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | − | 5.19615i | −0.317999 | − | 0.550791i | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.980071 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | + | 3.46410i | −0.628971 | + | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.0000 | −1.24434 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.00000 | − | 13.8564i | 0.615587 | − | 1.42164i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.50000 | + | 4.33013i | 0.761510 | + | 0.439658i | 0.829837 | − | 0.558005i | \(-0.188433\pi\) |
−0.0683279 | + | 0.997663i | \(0.521766\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 5.19615i | − | 0.522233i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.00000 | − | 5.19615i | 0.895533 | − | 0.517036i | 0.0197851 | − | 0.999804i | \(-0.493702\pi\) |
0.875748 | + | 0.482768i | \(0.160368\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.3923i | − | 1.02398i | −0.858990 | − | 0.511992i | \(-0.828908\pi\) | ||
0.858990 | − | 0.511992i | \(-0.171092\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.00000 | + | 10.3923i | −0.585540 | + | 1.01419i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.0000 | 1.13899 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.0000 | −1.41108 | −0.705541 | − | 0.708669i | \(-0.749296\pi\) | ||||
−0.705541 | + | 0.708669i | \(0.749296\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.00000 | − | 5.19615i | 0.832050 | − | 0.480384i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.0000 | + | 6.92820i | 1.10004 | + | 0.635107i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.00000 | 0.727273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.50000 | − | 2.59808i | −0.405751 | − | 0.234261i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820i | 0.619677i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.00000 | − | 5.19615i | 0.798621 | − | 0.461084i | −0.0443678 | − | 0.999015i | \(-0.514127\pi\) |
0.842989 | + | 0.537931i | \(0.180794\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.0000 | + | 6.92820i | 1.05654 | + | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.5000 | − | 9.52628i | −1.44161 | − | 0.832315i | −0.443654 | − | 0.896198i | \(-0.646318\pi\) |
−0.997957 | + | 0.0638831i | \(0.979652\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | − | 8.66025i | −0.0867110 | − | 0.750939i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.00000 | − | 15.5885i | 0.774597 | − | 1.34164i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.50000 | − | 0.866025i | 0.128154 | − | 0.0739895i | −0.434553 | − | 0.900646i | \(-0.643094\pi\) |
0.562706 | + | 0.826657i | \(0.309760\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.500000 | + | 0.866025i | 0.0424094 | + | 0.0734553i | 0.886451 | − | 0.462822i | \(-0.153163\pi\) |
−0.844042 | + | 0.536278i | \(0.819830\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | + | 5.19615i | 0.252646 | + | 0.437595i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.00000 | − | 5.19615i | −0.250873 | − | 0.434524i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 20.7846i | − | 1.72607i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 5.19615i | − | 0.428571i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00000 | + | 3.46410i | 0.491539 | + | 0.283790i | 0.725213 | − | 0.688525i | \(-0.241741\pi\) |
−0.233674 | + | 0.972315i | \(0.575075\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.92820i | − | 0.563809i | −0.959442 | − | 0.281905i | \(-0.909034\pi\) | ||
0.959442 | − | 0.281905i | \(-0.0909662\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.0000 | − | 10.3923i | −1.45521 | − | 0.840168i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.0000 | + | 20.7846i | −0.963863 | + | 1.66946i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0000 | − | 17.3205i | 0.798087 | − | 1.38233i | −0.122774 | − | 0.992435i | \(-0.539179\pi\) |
0.920860 | − | 0.389892i | \(-0.127488\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.00000 | + | 5.19615i | −0.713746 | + | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.0000 | 1.33154 | 0.665771 | − | 0.746156i | \(-0.268103\pi\) | ||||
0.665771 | + | 0.746156i | \(0.268103\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.00000 | − | 5.19615i | −0.700649 | − | 0.404520i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.00000 | − | 10.3923i | −0.464294 | − | 0.804181i | 0.534875 | − | 0.844931i | \(-0.320359\pi\) |
−0.999169 | + | 0.0407502i | \(0.987025\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | + | 0.866025i | −0.0384615 | + | 0.0666173i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.50000 | + | 12.9904i | 0.114708 | + | 0.993399i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.00000 | − | 15.5885i | 0.684257 | − | 1.18517i | −0.289412 | − | 0.957205i | \(-0.593460\pi\) |
0.973670 | − | 0.227964i | \(-0.0732068\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.00000 | + | 12.1244i | 0.529150 | + | 0.916515i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.50000 | − | 2.59808i | −0.338241 | − | 0.195283i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.00000 | 0.224231 | 0.112115 | − | 0.993695i | \(-0.464237\pi\) | ||||
0.112115 | + | 0.993695i | \(0.464237\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | − | 3.46410i | 0.445976 | − | 0.257485i | −0.260153 | − | 0.965567i | \(-0.583773\pi\) |
0.706129 | + | 0.708083i | \(0.250440\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.0000 | − | 8.66025i | 1.10883 | − | 0.640184i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.0000 | − | 20.7846i | 0.882258 | − | 1.52811i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.00000 | + | 10.3923i | −0.438763 | + | 0.759961i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 10.3923i | − | 0.755929i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 6.92820i | − | 0.501307i | −0.968077 | − | 0.250654i | \(-0.919354\pi\) | ||
0.968077 | − | 0.250654i | \(-0.0806455\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.0000 | + | 10.3923i | 1.29567 | + | 0.748054i | 0.979653 | − | 0.200700i | \(-0.0643215\pi\) |
0.316016 | + | 0.948754i | \(0.397655\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 20.7846i | − | 1.48842i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.7846i | 1.48084i | 0.672143 | + | 0.740421i | \(0.265374\pi\) | ||||
−0.672143 | + | 0.740421i | \(0.734626\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.00000 | + | 12.1244i | 0.496217 | + | 0.859473i | 0.999990 | − | 0.00436292i | \(-0.00138876\pi\) |
−0.503774 | + | 0.863836i | \(0.668055\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.50000 | − | 7.79423i | −0.317406 | − | 0.549762i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.00000 | − | 10.3923i | −0.421117 | − | 0.729397i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00000 | + | 5.19615i | −0.628587 | + | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.50000 | − | 0.866025i | 0.518786 | − | 0.0599042i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.00000 | − | 5.19615i | −0.619586 | − | 0.357718i | 0.157122 | − | 0.987579i | \(-0.449778\pi\) |
−0.776708 | + | 0.629861i | \(0.783112\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.00000 | − | 5.19615i | −0.616670 | − | 0.356034i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 24.0000 | − | 13.8564i | 1.63679 | − | 0.944999i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.8564i | 0.940634i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.50000 | − | 4.33013i | −0.506803 | − | 0.292603i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.0000 | −1.61441 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.0000 | − | 6.92820i | −0.803579 | − | 0.463947i | 0.0411418 | − | 0.999153i | \(-0.486900\pi\) |
−0.844721 | + | 0.535207i | \(0.820234\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.5000 | − | 18.1865i | −0.700000 | − | 1.21244i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.0000 | 1.39382 | 0.696909 | − | 0.717159i | \(-0.254558\pi\) | ||||
0.696909 | + | 0.717159i | \(0.254558\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.00000 | 0.264327 | 0.132164 | − | 0.991228i | \(-0.457808\pi\) | ||||
0.132164 | + | 0.991228i | \(0.457808\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.00000 | −0.394771 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.50000 | + | 0.866025i | 0.0982683 | + | 0.0567352i | 0.548329 | − | 0.836263i | \(-0.315264\pi\) |
−0.450060 | + | 0.892998i | \(0.648598\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0000 | 0.782794 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.0000 | + | 20.7846i | −0.779484 | + | 1.35011i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6.92820i | − | 0.448148i | −0.974572 | − | 0.224074i | \(-0.928064\pi\) | ||
0.974572 | − | 0.224074i | \(-0.0719358\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.50000 | − | 2.59808i | 0.289870 | − | 0.167357i | −0.348013 | − | 0.937490i | \(-0.613143\pi\) |
0.637883 | + | 0.770133i | \(0.279810\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 1.00000i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.00000 | − | 5.19615i | −0.574989 | − | 0.331970i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.00000 | + | 12.1244i | 0.572656 | + | 0.771454i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.00000 | −0.570352 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.50000 | + | 4.33013i | −0.473396 | + | 0.273315i | −0.717660 | − | 0.696393i | \(-0.754787\pi\) |
0.244264 | + | 0.969709i | \(0.421454\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −36.0000 | + | 20.7846i | −2.25441 | + | 1.30158i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.50000 | − | 12.9904i | −0.467837 | − | 0.810318i | 0.531487 | − | 0.847066i | \(-0.321633\pi\) |
−0.999325 | + | 0.0367485i | \(0.988300\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 13.8564i | − | 0.860995i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.00000 | + | 15.5885i | 0.557086 | + | 0.964901i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.00000 | + | 1.73205i | 0.184988 | + | 0.106803i | 0.589634 | − | 0.807671i | \(-0.299272\pi\) |
−0.404646 | + | 0.914473i | \(0.632605\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.7846i | 1.27679i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.00000 | − | 5.19615i | 0.550791 | − | 0.317999i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.0000 | − | 22.5167i | 0.789694 | − | 1.36779i | −0.136461 | − | 0.990645i | \(-0.543573\pi\) |
0.926155 | − | 0.377144i | \(-0.123094\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.00000 | − | 10.3923i | −0.363137 | − | 0.628971i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.5000 | + | 6.06218i | −0.633174 | + | 0.365563i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00000 | −0.120168 | −0.0600842 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600842 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 20.7846i | − | 1.24434i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.50000 | + | 12.9904i | 0.447412 | + | 0.774941i | 0.998217 | − | 0.0596933i | \(-0.0190123\pi\) |
−0.550804 | + | 0.834634i | \(0.685679\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.500000 | + | 0.866025i | −0.0297219 | + | 0.0514799i | −0.880504 | − | 0.474039i | \(-0.842796\pi\) |
0.850782 | + | 0.525519i | \(0.176129\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 24.0000 | + | 10.3923i | 1.42164 | + | 0.615587i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.00000 | + | 5.19615i | −0.177084 | + | 0.306719i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.5000 | + | 26.8468i | 0.911765 | + | 1.57922i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.50000 | + | 12.9904i | −0.439658 | + | 0.761510i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.00000 | + | 5.19615i | −0.524000 | + | 0.302532i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.00000 | 0.522233 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | − | 13.8564i | 0.461112 | − | 0.798670i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.00000 | + | 15.5885i | 0.517036 | + | 0.895533i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 34.6410i | − | 1.98354i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.50000 | + | 2.59808i | 0.256829 | + | 0.148280i | 0.622887 | − | 0.782312i | \(-0.285960\pi\) |
−0.366058 | + | 0.930592i | \(0.619293\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.0000 | 1.02398 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.8564i | 0.785725i | 0.919597 | + | 0.392862i | \(0.128515\pi\) | ||||
−0.919597 | + | 0.392862i | \(0.871485\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.5000 | − | 26.8468i | −0.876112 | − | 1.51747i | −0.855574 | − | 0.517681i | \(-0.826795\pi\) |
−0.0205381 | − | 0.999789i | \(-0.506538\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −18.0000 | − | 10.3923i | −1.01419 | − | 0.585540i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.00000 | − | 5.19615i | −0.168497 | − | 0.291845i | 0.769395 | − | 0.638774i | \(-0.220558\pi\) |
−0.937892 | + | 0.346929i | \(0.887225\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.00000 | − | 5.19615i | 0.503903 | − | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 20.7846i | − | 1.16008i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.0000 | − | 27.7128i | 0.667698 | − | 1.54198i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.0000 | − | 12.1244i | −1.16487 | − | 0.672538i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.00000 | − | 3.46410i | 0.330791 | − | 0.190982i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.66025i | 0.476011i | 0.971264 | + | 0.238005i | \(0.0764936\pi\) | ||||
−0.971264 | + | 0.238005i | \(0.923506\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.7846i | 1.13899i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.0000 | −0.983445 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.5000 | − | 12.9904i | −1.22565 | − | 0.707631i | −0.259536 | − | 0.965734i | \(-0.583569\pi\) |
−0.966118 | + | 0.258102i | \(0.916903\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 25.9808i | − | 1.41108i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.50000 | − | 4.33013i | −0.402621 | − | 0.232453i | 0.284993 | − | 0.958530i | \(-0.408009\pi\) |
−0.687614 | + | 0.726076i | \(0.741342\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.00000 | 0.428230 | 0.214115 | − | 0.976808i | \(-0.431313\pi\) | ||||
0.214115 | + | 0.976808i | \(0.431313\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.00000 | + | 15.5885i | 0.480384 | + | 0.832050i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.9808i | 1.38282i | 0.722464 | + | 0.691408i | \(0.243009\pi\) | ||||
−0.722464 | + | 0.691408i | \(0.756991\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.0000 | + | 10.3923i | −0.955341 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.0000 | + | 20.7846i | −0.635107 | + | 1.10004i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.00000 | + | 3.46410i | 0.316668 | + | 0.182828i | 0.649906 | − | 0.760014i | \(-0.274808\pi\) |
−0.333238 | + | 0.942843i | \(0.608141\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5000 | + | 4.33013i | −0.973684 | + | 0.227901i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.8564i | 0.727273i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.0000 | + | 8.66025i | −0.785136 | + | 0.453298i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.00000 | − | 3.46410i | −0.104399 | − | 0.180825i | 0.809093 | − | 0.587680i | \(-0.199959\pi\) |
−0.913493 | + | 0.406855i | \(0.866625\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.50000 | − | 7.79423i | 0.234261 | − | 0.405751i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.00000 | + | 10.3923i | 0.311504 | + | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.92820i | 0.358729i | 0.983783 | + | 0.179364i | \(0.0574041\pi\) | ||||
−0.983783 | + | 0.179364i | \(0.942596\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.0000 | −0.619677 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.0000 | + | 10.3923i | 0.927047 | + | 0.535231i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 10.3923i | − | 0.533817i | −0.963722 | − | 0.266908i | \(-0.913998\pi\) | ||
0.963722 | − | 0.266908i | \(-0.0860021\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.00000 | + | 15.5885i | 0.461084 | + | 0.798621i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.00000 | − | 15.5885i | 0.459879 | − | 0.796533i | −0.539076 | − | 0.842257i | \(-0.681226\pi\) |
0.998954 | + | 0.0457244i | \(0.0145596\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | + | 10.3923i | −0.305788 | + | 0.529641i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.0000 | + | 20.7846i | −0.609994 | + | 1.05654i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.0000 | − | 17.3205i | 1.52106 | − | 0.878185i | 0.521369 | − | 0.853331i | \(-0.325421\pi\) |
0.999691 | − | 0.0248535i | \(-0.00791191\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.5000 | − | 28.5788i | 0.832315 | − | 1.44161i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.0000 | + | 41.5692i | 1.20757 | + | 2.09157i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.0000 | + | 17.3205i | −0.501886 | + | 0.869291i | 0.498112 | + | 0.867113i | \(0.334027\pi\) |
−0.999998 | + | 0.00217869i | \(0.999307\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.0000 | − | 1.73205i | 0.750939 | − | 0.0867110i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.50000 | + | 2.59808i | −0.0749064 | + | 0.129742i | −0.901046 | − | 0.433724i | \(-0.857199\pi\) |
0.826139 | + | 0.563466i | \(0.190532\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0000 | − | 20.7846i | −0.597763 | − | 1.03536i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 27.0000 | + | 15.5885i | 1.34164 | + | 0.774597i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0000 | 0.594818 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.5000 | + | 9.52628i | −0.815872 | + | 0.471044i | −0.848991 | − | 0.528407i | \(-0.822789\pi\) |
0.0331186 | + | 0.999451i | \(0.489456\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.50000 | + | 2.59808i | 0.0739895 | + | 0.128154i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.00000 | + | 5.19615i | −0.147620 | + | 0.255686i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.00000 | + | 15.5885i | −0.441793 | + | 0.765207i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.50000 | + | 0.866025i | −0.0734553 | + | 0.0424094i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 10.3923i | − | 0.507697i | −0.967244 | − | 0.253849i | \(-0.918303\pi\) | ||
0.967244 | − | 0.253849i | \(-0.0816965\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.0000 | − | 6.92820i | −0.584844 | − | 0.337660i | 0.178212 | − | 0.983992i | \(-0.442969\pi\) |
−0.763056 | + | 0.646332i | \(0.776302\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.00000 | + | 5.19615i | −0.437595 | + | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 48.4974i | 2.35247i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.0000 | − | 17.3205i | −0.483934 | − | 0.838198i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.00000 | − | 5.19615i | 0.434524 | − | 0.250873i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.00000 | + | 5.19615i | 0.144505 | + | 0.250290i | 0.929188 | − | 0.369607i | \(-0.120508\pi\) |
−0.784683 | + | 0.619897i | \(0.787174\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.0000 | + | 6.92820i | −0.576683 | + | 0.332948i | −0.759814 | − | 0.650140i | \(-0.774710\pi\) |
0.183131 | + | 0.983089i | \(0.441377\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 36.0000 | 1.72607 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.0000 | + | 6.92820i | 0.572729 | + | 0.330665i | 0.758238 | − | 0.651977i | \(-0.226060\pi\) |
−0.185510 | + | 0.982642i | \(0.559394\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.00000 | 0.428571 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.5000 | + | 6.06218i | −0.498870 | + | 0.288023i | −0.728247 | − | 0.685315i | \(-0.759665\pi\) |
0.229377 | + | 0.973338i | \(0.426331\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 20.7846i | − | 0.985285i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.00000 | + | 10.3923i | −0.283790 | + | 0.491539i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.00000 | −0.141579 | −0.0707894 | − | 0.997491i | \(-0.522552\pi\) | ||||
−0.0707894 | + | 0.997491i | \(0.522552\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.50000 | − | 2.59808i | −0.211897 | − | 0.122339i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.0000 | 0.563809 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −24.0000 | −1.12514 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.0000 | 0.795226 | 0.397613 | − | 0.917553i | \(-0.369839\pi\) | ||||
0.397613 | + | 0.917553i | \(0.369839\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.0000 | − | 31.1769i | 0.840168 | − | 1.45521i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.0000 | − | 12.1244i | −0.978068 | − | 0.564688i | −0.0763814 | − | 0.997079i | \(-0.524337\pi\) |
−0.901686 | + | 0.432391i | \(0.857670\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.0000 | −0.650635 | −0.325318 | − | 0.945605i | \(-0.605471\pi\) | ||||
−0.325318 | + | 0.945605i | \(0.605471\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −36.0000 | − | 20.7846i | −1.66946 | − | 0.963863i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.1244i | 0.561048i | 0.959847 | + | 0.280524i | \(0.0905083\pi\) | ||||
−0.959847 | + | 0.280524i | \(0.909492\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.00000 | + | 5.19615i | −0.415581 | + | 0.239936i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 30.0000 | + | 17.3205i | 1.38233 | + | 0.798087i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.0000 | + | 6.92820i | 0.551761 | + | 0.318559i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.5000 | − | 18.1865i | 1.12414 | − | 0.834455i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.00000 | − | 15.5885i | −0.412082 | − | 0.713746i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0000 | + | 20.7846i | 0.547153 | + | 0.947697i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.0000 | + | 25.9808i | 0.681115 | + | 1.17973i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.92820i | − | 0.313947i | −0.987603 | − | 0.156973i | \(-0.949826\pi\) | ||
0.987603 | − | 0.156973i | \(-0.0501737\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 29.4449i | 1.33154i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.0000 | + | 15.5885i | 1.21849 | + | 0.703497i | 0.964595 | − | 0.263734i | \(-0.0849541\pi\) |
0.253897 | + | 0.967231i | \(0.418287\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 41.5692i | − | 1.87218i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.00000 | − | 15.5885i | 0.404520 | − | 0.700649i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.00000 | + | 10.3923i | −0.269137 | + | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.5000 | + | 35.5070i | −0.917706 | + | 1.58951i | −0.114816 | + | 0.993387i | \(0.536628\pi\) |
−0.802890 | + | 0.596127i | \(0.796706\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.0000 | − | 10.3923i | 0.804181 | − | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.0000 | + | 10.3923i | −0.802580 | + | 0.463370i | −0.844373 | − | 0.535756i | \(-0.820027\pi\) |
0.0417923 | + | 0.999126i | \(0.486693\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.0000 | 1.60198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.50000 | − | 0.866025i | −0.0666173 | − | 0.0384615i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.0000 | − | 20.7846i | −0.531891 | − | 0.921262i | −0.999307 | − | 0.0372243i | \(-0.988148\pi\) |
0.467416 | − | 0.884037i | \(-0.345185\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.00000 | + | 8.66025i | −0.221187 | + | 0.383107i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −22.5000 | + | 2.59808i | −0.993399 | + | 0.114708i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.0000 | − | 31.1769i | 0.793175 | − | 1.37382i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.00000 | + | 5.19615i | 0.131940 | + | 0.228527i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.0000 | + | 15.5885i | 1.18517 | + | 0.684257i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.0000 | 0.920027 | 0.460013 | − | 0.887912i | \(-0.347845\pi\) | ||||
0.460013 | + | 0.887912i | \(0.347845\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.0000 | + | 8.66025i | −0.655904 | + | 0.378686i | −0.790715 | − | 0.612185i | \(-0.790291\pi\) |
0.134810 | + | 0.990871i | \(0.456957\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −21.0000 | + | 12.1244i | −0.916515 | + | 0.529150i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.0000 | + | 41.5692i | −1.04546 | + | 1.81078i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.5000 | + | 19.9186i | −0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.50000 | − | 7.79423i | 0.195283 | − | 0.338241i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 10.3923i | − | 0.450141i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −36.0000 | − | 20.7846i | −1.55642 | − | 0.898597i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.19615i | 0.224231i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 5.19615i | − | 0.223814i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0000 | − | 17.3205i | −0.429934 | − | 0.744667i | 0.566933 | − | 0.823764i | \(-0.308130\pi\) |
−0.996867 | + | 0.0790969i | \(0.974796\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.00000 | + | 10.3923i | 0.257485 | + | 0.445976i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.0000 | − | 12.1244i | 0.897895 | − | 0.518400i | 0.0213785 | − | 0.999771i | \(-0.493195\pi\) |
0.876517 | + | 0.481371i | \(0.159861\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.0000 | + | 25.9808i | 0.640184 | + | 1.10883i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.0000 | + | 15.5885i | −0.894630 | + | 0.664091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.0000 | + | 13.8564i | 1.02058 | + | 0.589234i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 36.0000 | + | 20.7846i | 1.52811 | + | 0.882258i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.0000 | + | 6.92820i | −0.508456 | + | 0.293557i | −0.732199 | − | 0.681091i | \(-0.761506\pi\) |
0.223743 | + | 0.974648i | \(0.428173\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.7128i | 1.17213i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.0000 | − | 10.3923i | −0.759961 | − | 0.438763i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.0000 | −0.885044 | −0.442522 | − | 0.896758i | \(-0.645916\pi\) | ||||
−0.442522 | + | 0.896758i | \(0.645916\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −45.0000 | − | 25.9808i | −1.89316 | − | 1.09302i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.0000 | 0.755929 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.00000 | −0.251533 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.0000 | 1.79949 | 0.899747 | − | 0.436412i | \(-0.143751\pi\) | ||||
0.899747 | + | 0.436412i | \(0.143751\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000 | 0.501307 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.0000 | −1.20729 | −0.603643 | − | 0.797255i | \(-0.706285\pi\) | ||||
−0.603643 | + | 0.797255i | \(0.706285\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.0000 | + | 31.1769i | −0.748054 | + | 1.29567i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.3923i | 0.431145i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.00000 | + | 5.19615i | −0.372742 | + | 0.215203i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 36.0000 | 1.48842 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.0000 | − | 19.0526i | −1.36206 | − | 0.786383i | −0.372158 | − | 0.928169i | \(-0.621382\pi\) |
−0.989897 | + | 0.141786i | \(0.954716\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.0000 | − | 3.46410i | 1.23613 | − | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −36.0000 | −1.48084 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.5000 | + | 12.9904i | −0.923964 | + | 0.533451i | −0.884898 | − | 0.465786i | \(-0.845772\pi\) |
−0.0390666 | + | 0.999237i | \(0.512438\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.0000 | + | 41.5692i | 0.983904 | + | 1.70417i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.0000 | + | 12.1244i | −0.859473 | + | 0.496217i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.0000 | + | 31.1769i | 0.735460 | + | 1.27385i | 0.954521 | + | 0.298143i | \(0.0963673\pi\) |
−0.219061 | + | 0.975711i | \(0.570299\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 8.66025i | − | 0.353259i | −0.984277 | − | 0.176630i | \(-0.943481\pi\) | ||
0.984277 | − | 0.176630i | \(-0.0565195\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.5000 | − | 7.79423i | 0.549762 | − | 0.317406i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.0000 | + | 13.8564i | 0.975739 | + | 0.563343i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 31.1769i | − | 1.26543i | −0.774384 | − | 0.632716i | \(-0.781940\pi\) | ||
0.774384 | − | 0.632716i | \(-0.218060\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.0000 | − | 10.3923i | 0.729397 | − | 0.421117i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.00000 | + | 10.3923i | −0.242734 | + | 0.420428i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.0000 | + | 29.4449i | −0.686624 | + | 1.18927i | 0.286300 | + | 0.958140i | \(0.407575\pi\) |
−0.972924 | + | 0.231127i | \(0.925759\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.00000 | − | 15.5885i | −0.362915 | − | 0.628587i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.50000 | − | 0.866025i | 0.0603877 | − | 0.0348649i | −0.469502 | − | 0.882931i | \(-0.655567\pi\) |
0.529890 | + | 0.848066i | \(0.322233\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.0000 | −1.60774 | −0.803868 | − | 0.594808i | \(-0.797228\pi\) | ||||
−0.803868 | + | 0.594808i | \(0.797228\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.00000 | − | 10.3923i | −0.240385 | − | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | − | 9.52628i | 0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.50000 | + | 12.9904i | 0.0599042 | + | 0.518786i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.0000 | − | 41.5692i | 0.956943 | − | 1.65747i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00000 | − | 1.73205i | −0.0398094 | − | 0.0689519i | 0.845434 | − | 0.534080i | \(-0.179342\pi\) |
−0.885244 | + | 0.465128i | \(0.846008\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.00000 | − | 15.5885i | 0.357718 | − | 0.619586i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 36.0000 | 1.42862 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.00000 | − | 5.19615i | 0.356593 | − | 0.205879i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.00000 | − | 15.5885i | 0.356034 | − | 0.616670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.5000 | + | 38.9711i | −0.888697 | + | 1.53927i | −0.0472793 | + | 0.998882i | \(0.515055\pi\) |
−0.841417 | + | 0.540386i | \(0.818278\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.5000 | + | 42.4352i | −0.966186 | + | 1.67348i | −0.259791 | + | 0.965665i | \(0.583654\pi\) |
−0.706395 | + | 0.707818i | \(0.749680\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.0000 | + | 41.5692i | 0.944999 | + | 1.63679i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 24.2487i | − | 0.953315i | −0.879089 | − | 0.476658i | \(-0.841848\pi\) | ||
0.879089 | − | 0.476658i | \(-0.158152\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.50000 | − | 2.59808i | −0.176640 | − | 0.101983i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.0000 | −0.940634 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.92820i | 0.271122i | 0.990769 | + | 0.135561i | \(0.0432836\pi\) | ||||
−0.990769 | + | 0.135561i | \(0.956716\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −33.0000 | − | 57.1577i | −1.28942 | − | 2.23334i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.50000 | − | 12.9904i | 0.292603 | − | 0.506803i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.0000 | − | 31.1769i | −0.701180 | − | 1.21448i | −0.968052 | − | 0.250748i | \(-0.919323\pi\) |
0.266872 | − | 0.963732i | \(-0.414010\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.0000 | + | 19.0526i | −1.28355 | + | 0.741059i | −0.977496 | − | 0.210955i | \(-0.932343\pi\) |
−0.306055 | + | 0.952014i | \(0.599009\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 41.5692i | − | 1.61441i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.0000 | − | 27.7128i | 0.465340 | − | 1.07466i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.0000 | − | 20.7846i | 0.463947 | − | 0.803579i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.0000 | − | 8.66025i | 0.579069 | − | 0.334325i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 20.7846i | − | 0.801188i | −0.916256 | − | 0.400594i | \(-0.868804\pi\) | ||
0.916256 | − | 0.400594i | \(-0.131196\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 31.5000 | − | 18.1865i | 1.21244 | − | 0.700000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.0000 | −1.61419 | −0.807096 | − | 0.590421i | \(-0.798962\pi\) | ||||
−0.807096 | + | 0.590421i | \(0.798962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.0000 | + | 8.66025i | 0.575647 | + | 0.332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 36.3731i | 1.39382i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −36.0000 | −1.37750 | −0.688751 | − | 0.724998i | \(-0.741841\pi\) | ||||
−0.688751 | + | 0.724998i | \(0.741841\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.00000 | 0.229248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.92820i | 0.264327i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.0000 | − | 10.3923i | −0.685745 | − | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.0000 | −0.760836 | −0.380418 | − | 0.924815i | \(-0.624220\pi\) | ||||
−0.380418 | + | 0.924815i | \(0.624220\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 10.3923i | − | 0.394771i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.46410i | 0.131401i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0000 | + | 10.3923i | −0.681799 | + | 0.393637i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.50000 | + | 2.59808i | −0.0567352 | + | 0.0982683i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.00000 | − | 5.19615i | −0.339925 | − | 0.196256i | 0.320314 | − | 0.947312i | \(-0.396212\pi\) |
−0.660239 | + | 0.751056i | \(0.729545\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.0000 | + | 3.46410i | −1.13147 | + | 0.130651i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 20.7846i | 0.782794i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.0000 | − | 10.3923i | 0.676960 | − | 0.390843i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.00000 | − | 6.92820i | −0.150223 | − | 0.260194i | 0.781086 | − | 0.624423i | \(-0.214666\pi\) |
−0.931309 | + | 0.364229i | \(0.881333\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −36.0000 | − | 20.7846i | −1.35011 | − | 0.779484i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 20.7846i | − | 0.777300i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.0000 | 0.448148 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.00000 | + | 1.73205i | 0.111881 | + | 0.0645946i | 0.554896 | − | 0.831919i | \(-0.312758\pi\) |
−0.443015 | + | 0.896514i | \(0.646091\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 20.7846i | − | 0.774059i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.50000 | + | 7.79423i | 0.167357 | + | 0.289870i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.0000 | − | 36.3731i | 0.779920 | − | 1.35086i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.00000 | − | 6.92820i | 0.148352 | − | 0.256953i | −0.782267 | − | 0.622944i | \(-0.785937\pi\) |
0.930618 | + | 0.365991i | \(0.119270\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 48.0000 | − | 27.7128i | 1.77534 | − | 1.02500i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.00000 | −0.147743 | −0.0738717 | − | 0.997268i | \(-0.523536\pi\) | ||||
−0.0738717 | + | 0.997268i | \(0.523536\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.00000 | − | 15.5885i | 0.331970 | − | 0.574989i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.50000 | − | 7.79423i | −0.165760 | − | 0.287104i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.50000 | + | 9.52628i | −0.202321 | + | 0.350430i | −0.949276 | − | 0.314445i | \(-0.898182\pi\) |
0.746955 | + | 0.664875i | \(0.231515\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.0000 | + | 15.5885i | −0.771454 | + | 0.572656i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.0000 | + | 20.7846i | 0.439646 | + | 0.761489i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 15.5885i | − | 0.570352i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.0000 | −0.876941 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.0000 | − | 19.0526i | 1.20419 | − | 0.695238i | 0.242704 | − | 0.970100i | \(-0.421966\pi\) |
0.961483 | + | 0.274863i | \(0.0886324\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.50000 | − | 12.9904i | −0.273315 | − | 0.473396i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000 | − | 20.7846i | 0.436725 | − | 0.756429i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.0000 | − | 32.9090i | 0.690567 | − | 1.19610i | −0.281086 | − | 0.959683i | \(-0.590695\pi\) |
0.971652 | − | 0.236414i | \(-0.0759722\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.66025i | 0.313934i | 0.987604 | + | 0.156967i | \(0.0501716\pi\) | ||||
−0.987604 | + | 0.156967i | \(0.949828\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −36.0000 | − | 62.3538i | −1.30158 | − | 2.25441i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 10.3923i | − | 0.375244i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.00000 | + | 12.1244i | 0.252426 | + | 0.437215i | 0.964193 | − | 0.265200i | \(-0.0854381\pi\) |
−0.711767 | + | 0.702416i | \(0.752105\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.5000 | − | 12.9904i | 0.810318 | − | 0.467837i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.00000 | + | 5.19615i | 0.107903 | + | 0.186893i | 0.914920 | − | 0.403634i | \(-0.132253\pi\) |
−0.807018 | + | 0.590527i | \(0.798920\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −42.0000 | + | 24.2487i | −1.50868 | + | 0.871039i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.0000 | 0.860995 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.0000 | + | 5.19615i | 0.429945 | + | 0.186171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.00000 | − | 5.19615i | −0.322045 | − | 0.185933i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −27.0000 | + | 15.5885i | −0.964901 | + | 0.557086i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 60.0000 | − | 34.6410i | 2.14149 | − | 1.23639i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.73205i | − | 0.0617409i | −0.999523 | − | 0.0308705i | \(-0.990172\pi\) | ||
0.999523 | − | 0.0308705i | \(-0.00982794\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.00000 | + | 5.19615i | −0.106803 | + | 0.184988i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.0000 | −1.06668 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.0000 | + | 17.3205i | 1.06533 | + | 0.615069i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −36.0000 | −1.27679 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.0000 | 0.425062 | 0.212531 | − | 0.977154i | \(-0.431829\pi\) | ||||
0.212531 | + | 0.977154i | \(0.431829\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.00000 | + | 15.5885i | 0.317999 | + | 0.550791i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.50000 | − | 4.33013i | −0.264669 | − | 0.152807i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 32.9090i | − | 1.15702i | −0.815676 | − | 0.578509i | \(-0.803635\pi\) | ||
0.815676 | − | 0.578509i | \(-0.196365\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.0000 | − | 15.5885i | 0.948098 | − | 0.547385i | 0.0556086 | − | 0.998453i | \(-0.482290\pi\) |
0.892490 | + | 0.451068i | \(0.148957\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 39.0000 | + | 22.5167i | 1.36779 | + | 0.789694i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 51.0000 | + | 29.4449i | 1.78645 | + | 1.03141i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.0000 | − | 13.8564i | −1.11954 | − | 0.484774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.0000 | − | 10.3923i | 0.628971 | − | 0.363137i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.0000 | − | 19.0526i | 1.15171 | − | 0.664939i | 0.202405 | − | 0.979302i | \(-0.435124\pi\) |
0.949303 | + | 0.314363i | \(0.101791\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.0000 | + | 19.0526i | 0.383436 | + | 0.664130i | 0.991551 | − | 0.129719i | \(-0.0414074\pi\) |
−0.608115 | + | 0.793849i | \(0.708074\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.5000 | − | 18.1865i | −0.365563 | − | 0.633174i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.50000 | + | 7.79423i | 0.156480 | + | 0.271032i | 0.933597 | − | 0.358325i | \(-0.116652\pi\) |
−0.777117 | + | 0.629356i | \(0.783319\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.7846i | 0.721879i | 0.932589 | + | 0.360940i | \(0.117544\pi\) | ||||
−0.932589 | + | 0.360940i | \(0.882456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 3.46410i | − | 0.120168i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.0000 | − | 10.3923i | −0.623663 | − | 0.360072i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 41.5692i | − | 1.43856i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.0000 | 1.24434 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.0000 | − | 36.3731i | 0.725001 | − | 1.25574i | −0.233973 | − | 0.972243i | \(-0.575173\pi\) |
0.958974 | − | 0.283495i | \(-0.0914938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.5000 | + | 12.9904i | −0.774941 | + | 0.447412i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.00000 | + | 1.73205i | −0.103203 | + | 0.0595844i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.0000 | 0.549767 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.50000 | − | 0.866025i | −0.0514799 | − | 0.0297219i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.00000 | − | 8.66025i | 0.171197 | − | 0.296521i | −0.767642 | − | 0.640879i | \(-0.778570\pi\) |
0.938839 | + | 0.344358i | \(0.111903\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.0000 | + | 41.5692i | −0.615587 | + | 1.42164i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.5000 | + | 18.1865i | −0.358673 | + | 0.621240i | −0.987739 | − | 0.156112i | \(-0.950104\pi\) |
0.629066 | + | 0.777352i | \(0.283437\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.5000 | + | 42.4352i | 0.835929 | + | 1.44787i | 0.893272 | + | 0.449517i | \(0.148404\pi\) |
−0.0573424 | + | 0.998355i | \(0.518263\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.00000 | − | 5.19615i | −0.306719 | − | 0.177084i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.0000 | −0.408485 | −0.204242 | − | 0.978920i | \(-0.565473\pi\) | ||||
−0.204242 | + | 0.978920i | \(0.565473\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 54.0000 | − | 31.1769i | 1.83606 | − | 1.06005i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −46.5000 | + | 26.8468i | −1.57922 | + | 0.911765i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0000 | + | 20.7846i | −0.407072 | + | 0.705070i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.00000 | − | 15.5885i | 0.304953 | − | 0.528195i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −22.5000 | − | 12.9904i | −0.761510 | − | 0.439658i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.8564i | 0.468432i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.0000 | − | 19.0526i | −1.11433 | − | 0.643359i | −0.174383 | − | 0.984678i | \(-0.555793\pi\) |
−0.939948 | + | 0.341319i | \(0.889126\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.3923i | 0.350524i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 19.0526i | − | 0.641897i | −0.947097 | − | 0.320949i | \(-0.895998\pi\) | ||
0.947097 | − | 0.320949i | \(-0.104002\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.50000 | − | 9.52628i | −0.185090 | − | 0.320585i | 0.758517 | − | 0.651653i | \(-0.225924\pi\) |
−0.943607 | + | 0.331068i | \(0.892591\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.00000 | − | 15.5885i | −0.302532 | − | 0.524000i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.0000 | + | 31.1769i | 0.604381 | + | 1.04682i | 0.992149 | + | 0.125061i | \(0.0399128\pi\) |
−0.387768 | + | 0.921757i | \(0.626754\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0000 | − | 10.3923i | 0.603701 | − | 0.348547i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.5885i | 0.522233i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.00000 | − | 12.1244i | −0.301174 | − | 0.405726i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.00000 | + | 5.19615i | 0.300837 | + | 0.173688i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 36.0000 | − | 20.7846i | 1.20067 | − | 0.693206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.5692i | 1.38487i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.0000 | + | 13.8564i | 0.798670 | + | 0.461112i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.0000 | 0.797787 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.50000 | − | 0.866025i | −0.0498067 | − | 0.0287559i | 0.474890 | − | 0.880045i | \(-0.342488\pi\) |
−0.524697 | + | 0.851289i | \(0.675821\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27.0000 | + | 15.5885i | −0.895533 | + | 0.517036i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.0000 | −1.19273 | −0.596367 | − | 0.802712i | \(-0.703390\pi\) | ||||
−0.596367 | + | 0.802712i | \(0.703390\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.00000 | −0.297857 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 60.0000 | 1.98354 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −33.0000 | − | 19.0526i | −1.08976 | − | 0.629171i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.0000 | 0.857661 | 0.428830 | − | 0.903385i | \(-0.358926\pi\) | ||||
0.428830 | + | 0.903385i | \(0.358926\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.50000 | + | 7.79423i | −0.148280 | + | 0.256829i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 20.7846i | − | 0.684134i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.0000 | − | 24.2487i | 1.38095 | − | 0.797293i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 31.1769i | 1.02398i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.5000 | − | 18.1865i | −1.03348 | − | 0.596681i | −0.115501 | − | 0.993307i | \(-0.536847\pi\) |
−0.917980 | + | 0.396627i | \(0.870181\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.50000 | + | 12.9904i | 0.0491605 | + | 0.425743i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.0000 | −0.785725 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −36.0000 | + | 20.7846i | −1.17733 | + | 0.679729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.50000 | + | 6.06218i | 0.114340 | + | 0.198043i | 0.917516 | − | 0.397699i | \(-0.130191\pi\) |
−0.803176 | + | 0.595742i | \(0.796858\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 46.5000 | − | 26.8468i | 1.51747 | − | 0.876112i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.0000 | + | 46.7654i | 0.880175 | + | 1.52451i | 0.851146 | + | 0.524929i | \(0.175908\pi\) |
0.0290288 | + | 0.999579i | \(0.490759\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.0000 | − | 31.1769i | 0.585540 | − | 1.01419i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.0000 | − | 25.9808i | −1.46230 | − | 0.844261i | −0.463186 | − | 0.886261i | \(-0.653294\pi\) |
−0.999118 | + | 0.0419998i | \(0.986627\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 17.3205i | − | 0.562247i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.00000 | − | 5.19615i | 0.291845 | − | 0.168497i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.5000 | + | 44.1673i | −0.826026 | + | 1.43072i | 0.0751066 | + | 0.997176i | \(0.476070\pi\) |
−0.901133 | + | 0.433544i | \(0.857263\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.0000 | − | 20.7846i | 0.388311 | − | 0.672574i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.00000 | + | 15.5885i | 0.290929 | + | 0.503903i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.00000 | − | 1.73205i | 0.0968751 | − | 0.0559308i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.0000 | −0.548387 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.0000 | 1.16008 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 36.0000 | + | 62.3538i | 1.15888 | + | 2.00724i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.0000 | + | 43.3013i | −0.803946 | + | 1.39247i | 0.113055 | + | 0.993589i | \(0.463936\pi\) |
−0.917000 | + | 0.398886i | \(0.869397\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 48.0000 | + | 20.7846i | 1.54198 | + | 0.667698i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.50000 | − | 7.79423i | 0.144412 | − | 0.250129i | −0.784741 | − | 0.619823i | \(-0.787204\pi\) |
0.929153 | + | 0.369694i | \(0.120538\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.00000 | + | 1.73205i | 0.0320585 | + | 0.0555270i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 21.0000 | − | 36.3731i | 0.672538 | − | 1.16487i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.0000 | 0.863807 | 0.431903 | − | 0.901920i | \(-0.357842\pi\) | ||||
0.431903 | + | 0.901920i | \(0.357842\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.00000 | − | 5.19615i | 0.287641 | − | 0.166070i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.0000 | + | 31.1769i | −0.574111 | + | 0.994389i | 0.422027 | + | 0.906583i | \(0.361319\pi\) |
−0.996138 | + | 0.0878058i | \(0.972015\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.0000 | + | 62.3538i | −1.14706 | + | 1.98676i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.00000 | + | 10.3923i | 0.190982 | + | 0.330791i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.00000 | − | 3.46410i | −0.190596 | − | 0.110041i | 0.401665 | − | 0.915786i | \(-0.368431\pi\) |
−0.592262 | + | 0.805746i | \(0.701765\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.0000 | −0.476011 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 48.4974i | 1.53747i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.0000 | + | 22.5167i | 0.411714 | + | 0.713110i | 0.995077 | − | 0.0991016i | \(-0.0315969\pi\) |
−0.583363 | + | 0.812211i | \(0.698264\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −36.0000 | −1.13899 |
(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 | 912.2.bn.b.65.1 | 2 | ||
3.2 | odd | 2 | 912.2.bn.d.65.1 | 2 | |||
4.3 | odd | 2 | 114.2.h.d.65.1 | yes | 2 | ||
12.11 | even | 2 | 114.2.h.a.65.1 | ✓ | 2 | ||
19.12 | odd | 6 | 912.2.bn.d.449.1 | 2 | |||
57.50 | even | 6 | inner | 912.2.bn.b.449.1 | 2 | ||
76.31 | even | 6 | 114.2.h.a.107.1 | yes | 2 | ||
228.107 | odd | 6 | 114.2.h.d.107.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.h.a.65.1 | ✓ | 2 | 12.11 | even | 2 | ||
114.2.h.a.107.1 | yes | 2 | 76.31 | even | 6 | ||
114.2.h.d.65.1 | yes | 2 | 4.3 | odd | 2 | ||
114.2.h.d.107.1 | yes | 2 | 228.107 | odd | 6 | ||
912.2.bn.b.65.1 | 2 | 1.1 | even | 1 | trivial | ||
912.2.bn.b.449.1 | 2 | 57.50 | even | 6 | inner | ||
912.2.bn.d.65.1 | 2 | 3.2 | odd | 2 | |||
912.2.bn.d.449.1 | 2 | 19.12 | odd | 6 |