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 | 449.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.449 |
Dual form | 912.2.bn.b.65.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
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 | 0.354593 | − | 0.935021i | \(-0.384620\pi\) |
0.987048 | + | 0.160424i | \(0.0512862\pi\) | |||||||
\(6\) | 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 | \(-0.915909\pi\) | ||
0.965307 | − | 0.261116i | \(-0.0840907\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | − | 1.73205i | −0.832050 | − | 0.480384i | 0.0225039 | − | 0.999747i | \(-0.492836\pi\) |
−0.854554 | + | 0.519362i | \(0.826170\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.00000 | − | 5.19615i | −0.774597 | − | 1.34164i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.00000 | − | 3.46410i | 1.45521 | − | 0.840168i | 0.456444 | − | 0.889752i | \(-0.349123\pi\) |
0.998770 | + | 0.0495842i | \(0.0157896\pi\) | |||||||
\(18\) | 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 | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 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 | 0.440652 | + | 0.897678i | \(0.354747\pi\) |
−0.997738 | + | 0.0672232i | \(0.978586\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.92820i | − | 1.24434i | −0.782881 | − | 0.622171i | \(-0.786251\pi\) | ||
0.782881 | − | 0.622171i | \(-0.213749\pi\) | |||||||
\(32\) | 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 | \(0.192861\pi\) | ||||
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.00000 | + | 5.19615i | −0.480384 | + | 0.832050i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | − | 2.59808i | −0.234261 | − | 0.405751i | 0.724797 | − | 0.688963i | \(-0.241934\pi\) |
−0.959058 | + | 0.283211i | \(0.908600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | + | 6.92820i | 0.609994 | + | 1.05654i | 0.991241 | + | 0.132068i | \(0.0421616\pi\) |
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.00000 | + | 5.19615i | −1.34164 | + | 0.774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00000 | + | 1.73205i | 0.437595 | + | 0.252646i | 0.702577 | − | 0.711608i | \(-0.252033\pi\) |
−0.264982 | + | 0.964253i | \(0.585366\pi\) | |||||||
\(48\) | 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 | −0.583036 | − | 0.812447i | \(-0.698135\pi\) |
0.995117 | + | 0.0987002i | \(0.0314685\pi\) | |||||||
\(54\) | 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 | 0.751710 | − | 0.659494i | \(-0.229229\pi\) |
−0.946993 | + | 0.321253i | \(0.895896\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.00000 | + | 8.66025i | −0.640184 | + | 1.10883i | 0.345207 | + | 0.938527i | \(0.387809\pi\) |
−0.985391 | + | 0.170305i | \(0.945525\pi\) | |||||||
\(62\) | 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 | 0.199264 | − | 0.979946i | \(-0.436145\pi\) |
−0.749026 | + | 0.662540i | \(0.769478\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | − | 5.19615i | −0.356034 | − | 0.616670i | 0.631260 | − | 0.775571i | \(-0.282538\pi\) |
−0.987294 | + | 0.158901i | \(0.949205\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.50000 | − | 4.33013i | −0.292603 | − | 0.506803i | 0.681822 | − | 0.731519i | \(-0.261188\pi\) |
−0.974424 | + | 0.224716i | \(0.927855\pi\) | |||||||
\(74\) | 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 | 0.361842 | − | 0.932240i | \(-0.382148\pi\) |
0.988264 | + | 0.152756i | \(0.0488148\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.19615i | − | 0.570352i | −0.958475 | − | 0.285176i | \(-0.907948\pi\) | ||
0.958475 | − | 0.285176i | \(-0.0920520\pi\) | |||||||
\(84\) | 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 | −0.980071 | − | 0.198650i | \(-0.936344\pi\) |
0.662071 | + | 0.749441i | \(0.269678\pi\) | |||||||
\(90\) | 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 | −0.0683279 | − | 0.997663i | \(-0.521766\pi\) |
0.829837 | + | 0.558005i | \(0.188433\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.19615i | 0.522233i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.00000 | + | 5.19615i | 0.895533 | + | 0.517036i | 0.875748 | − | 0.482768i | \(-0.160368\pi\) |
0.0197851 | + | 0.999804i | \(0.493702\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.3923i | 1.02398i | 0.858990 | + | 0.511992i | \(0.171092\pi\) | ||||
−0.858990 | + | 0.511992i | \(0.828908\pi\) | |||||||
\(104\) | 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 | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(110\) | 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 | 0.842989 | − | 0.537931i | \(-0.180794\pi\) |
−0.0443678 | + | 0.999015i | \(0.514127\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.0000 | − | 6.92820i | 1.05654 | − | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.5000 | + | 9.52628i | −1.44161 | + | 0.832315i | −0.997957 | − | 0.0638831i | \(-0.979652\pi\) |
−0.443654 | + | 0.896198i | \(0.646318\pi\) | |||||||
\(132\) | 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 | 0.562706 | − | 0.826657i | \(-0.309760\pi\) |
−0.434553 | + | 0.900646i | \(0.643094\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.500000 | − | 0.866025i | 0.0424094 | − | 0.0734553i | −0.844042 | − | 0.536278i | \(-0.819830\pi\) |
0.886451 | + | 0.462822i | \(0.153163\pi\) | |||||||
\(140\) | 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 | −0.233674 | − | 0.972315i | \(-0.575075\pi\) |
0.725213 | + | 0.688525i | \(0.241741\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.92820i | 0.563809i | 0.959442 | + | 0.281905i | \(0.0909662\pi\) | ||||
−0.959442 | + | 0.281905i | \(0.909034\pi\) | |||||||
\(152\) | 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 | 0.920860 | + | 0.389892i | \(0.127488\pi\) |
−0.122774 | + | 0.992435i | \(0.539179\pi\) | |||||||
\(158\) | 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 | −0.999169 | − | 0.0407502i | \(-0.987025\pi\) |
0.534875 | + | 0.844931i | \(0.320359\pi\) | |||||||
\(168\) | 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 | 0.973670 | + | 0.227964i | \(0.0732068\pi\) |
−0.289412 | + | 0.957205i | \(0.593460\pi\) | |||||||
\(174\) | 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 | 0.706129 | − | 0.708083i | \(-0.250440\pi\) |
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | 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 | \(0.0806455\pi\) | ||||
−0.968077 | + | 0.250654i | \(0.919354\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.0000 | − | 10.3923i | 1.29567 | − | 0.748054i | 0.316016 | − | 0.948754i | \(-0.397655\pi\) |
0.979653 | + | 0.200700i | \(0.0643215\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 20.7846i | 1.48842i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 20.7846i | − | 1.48084i | −0.672143 | − | 0.740421i | \(-0.734626\pi\) | ||
0.672143 | − | 0.740421i | \(-0.265374\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.00000 | − | 12.1244i | 0.496217 | − | 0.859473i | −0.503774 | − | 0.863836i | \(-0.668055\pi\) |
0.999990 | + | 0.00436292i | \(0.00138876\pi\) | |||||||
\(200\) | 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 | −0.776708 | − | 0.629861i | \(-0.783112\pi\) |
0.157122 | + | 0.987579i | \(0.449778\pi\) | |||||||
\(212\) | 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 | −0.844721 | − | 0.535207i | \(-0.820234\pi\) |
0.0411418 | + | 0.999153i | \(0.486900\pi\) | |||||||
\(224\) | 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 | −0.450060 | − | 0.892998i | \(-0.648598\pi\) |
0.548329 | + | 0.836263i | \(0.315264\pi\) | |||||||
\(234\) | 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 | \(0.0719358\pi\) | ||||
−0.974572 | + | 0.224074i | \(0.928064\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.50000 | + | 2.59808i | 0.289870 | + | 0.167357i | 0.637883 | − | 0.770133i | \(-0.279810\pi\) |
−0.348013 | + | 0.937490i | \(0.613143\pi\) | |||||||
\(242\) | 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 | 0.244264 | − | 0.969709i | \(-0.421454\pi\) |
−0.717660 | + | 0.696393i | \(0.754787\pi\) | |||||||
\(252\) | 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 | −0.999325 | − | 0.0367485i | \(-0.988300\pi\) |
0.531487 | + | 0.847066i | \(0.321633\pi\) | |||||||
\(258\) | 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 | −0.404646 | − | 0.914473i | \(-0.632605\pi\) |
0.589634 | + | 0.807671i | \(0.299272\pi\) | |||||||
\(264\) | 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 | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.0000 | + | 22.5167i | 0.789694 | + | 1.36779i | 0.926155 | + | 0.377144i | \(0.123094\pi\) |
−0.136461 | + | 0.990645i | \(0.543573\pi\) | |||||||
\(272\) | 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 | −0.550804 | − | 0.834634i | \(-0.685679\pi\) |
0.998217 | + | 0.0596933i | \(0.0190123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.500000 | − | 0.866025i | −0.0297219 | − | 0.0514799i | 0.850782 | − | 0.525519i | \(-0.176129\pi\) |
−0.880504 | + | 0.474039i | \(0.842796\pi\) | |||||||
\(284\) | 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 | −0.366058 | − | 0.930592i | \(-0.619293\pi\) |
0.622887 | + | 0.782312i | \(0.285960\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.0000 | 1.02398 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 13.8564i | − | 0.785725i | −0.919597 | − | 0.392862i | \(-0.871485\pi\) | ||
0.919597 | − | 0.392862i | \(-0.128515\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.5000 | + | 26.8468i | −0.876112 | + | 1.51747i | −0.0205381 | + | 0.999789i | \(0.506538\pi\) |
−0.855574 | + | 0.517681i | \(0.826795\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −18.0000 | + | 10.3923i | −1.01419 | + | 0.585540i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.00000 | + | 5.19615i | −0.168497 | + | 0.291845i | −0.937892 | − | 0.346929i | \(-0.887225\pi\) |
0.769395 | + | 0.638774i | \(0.220558\pi\) | |||||||
\(318\) | 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 | \(-0.923506\pi\) | ||
0.971264 | − | 0.238005i | \(-0.0764936\pi\) | |||||||
\(332\) | 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 | −0.966118 | − | 0.258102i | \(-0.916903\pi\) |
−0.259536 | + | 0.965734i | \(0.583569\pi\) | |||||||
\(338\) | 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 | −0.687614 | − | 0.726076i | \(-0.741342\pi\) |
0.284993 | + | 0.958530i | \(0.408009\pi\) | |||||||
\(348\) | 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 | \(-0.756991\pi\) | ||
0.722464 | − | 0.691408i | \(-0.243009\pi\) | |||||||
\(354\) | 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 | −0.333238 | − | 0.942843i | \(-0.608141\pi\) |
0.649906 | + | 0.760014i | \(0.274808\pi\) | |||||||
\(360\) | 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 | −0.913493 | − | 0.406855i | \(-0.866625\pi\) |
0.809093 | + | 0.587680i | \(0.199959\pi\) | |||||||
\(368\) | 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 | \(-0.942596\pi\) | ||
0.983783 | − | 0.179364i | \(-0.0574041\pi\) | |||||||
\(374\) | 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 | \(0.0860021\pi\) | ||||
−0.963722 | + | 0.266908i | \(0.913998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.00000 | − | 15.5885i | 0.461084 | − | 0.798621i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.00000 | + | 15.5885i | 0.459879 | + | 0.796533i | 0.998954 | − | 0.0457244i | \(-0.0145596\pi\) |
−0.539076 | + | 0.842257i | \(0.681226\pi\) | |||||||
\(384\) | 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 | 0.999691 | + | 0.0248535i | \(0.00791191\pi\) |
0.521369 | + | 0.853331i | \(0.325421\pi\) | |||||||
\(390\) | 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 | −0.999998 | − | 0.00217869i | \(-0.999307\pi\) |
0.498112 | − | 0.867113i | \(-0.334027\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.0000 | + | 1.73205i | 0.750939 | + | 0.0867110i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.50000 | − | 2.59808i | −0.0749064 | − | 0.129742i | 0.826139 | − | 0.563466i | \(-0.190532\pi\) |
−0.901046 | + | 0.433724i | \(0.857199\pi\) | |||||||
\(402\) | 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 | 0.0331186 | − | 0.999451i | \(-0.489456\pi\) |
−0.848991 | + | 0.528407i | \(0.822789\pi\) | |||||||
\(410\) | 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 | \(0.0816965\pi\) | ||||
−0.967244 | + | 0.253849i | \(0.918303\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.0000 | + | 6.92820i | −0.584844 | + | 0.337660i | −0.763056 | − | 0.646332i | \(-0.776302\pi\) |
0.178212 | + | 0.983992i | \(0.442969\pi\) | |||||||
\(422\) | 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 | −0.784683 | − | 0.619897i | \(-0.787174\pi\) |
0.929188 | + | 0.369607i | \(0.120508\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.0000 | − | 6.92820i | −0.576683 | − | 0.332948i | 0.183131 | − | 0.983089i | \(-0.441377\pi\) |
−0.759814 | + | 0.650140i | \(0.774710\pi\) | |||||||
\(434\) | 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 | −0.185510 | − | 0.982642i | \(-0.559394\pi\) |
0.758238 | + | 0.651977i | \(0.226060\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.00000 | 0.428571 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.5000 | − | 6.06218i | −0.498870 | − | 0.288023i | 0.229377 | − | 0.973338i | \(-0.426331\pi\) |
−0.728247 | + | 0.685315i | \(0.759665\pi\) | |||||||
\(444\) | 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 | −0.901686 | − | 0.432391i | \(-0.857670\pi\) |
−0.0763814 | + | 0.997079i | \(0.524337\pi\) | |||||||
\(462\) | 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 | \(-0.909492\pi\) | ||
0.959847 | − | 0.280524i | \(-0.0905083\pi\) | |||||||
\(468\) | 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 | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(480\) | 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 | \(0.0501737\pi\) | ||||
−0.987603 | + | 0.156973i | \(0.949826\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 29.4449i | − | 1.33154i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.0000 | − | 15.5885i | 1.21849 | − | 0.703497i | 0.253897 | − | 0.967231i | \(-0.418287\pi\) |
0.964595 | + | 0.263734i | \(0.0849541\pi\) | |||||||
\(492\) | 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 | −0.802890 | − | 0.596127i | \(-0.796706\pi\) |
−0.114816 | − | 0.993387i | \(-0.536628\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.0000 | + | 10.3923i | 0.804181 | + | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.0000 | − | 10.3923i | −0.802580 | − | 0.463370i | 0.0417923 | − | 0.999126i | \(-0.486693\pi\) |
−0.844373 | + | 0.535756i | \(0.820027\pi\) | |||||||
\(504\) | 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 | 0.467416 | + | 0.884037i | \(0.345185\pi\) |
−0.999307 | + | 0.0372243i | \(0.988148\pi\) | |||||||
\(510\) | 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 | 0.134810 | − | 0.990871i | \(-0.456957\pi\) |
−0.790715 | + | 0.612185i | \(0.790291\pi\) | |||||||
\(524\) | 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 | −0.996867 | − | 0.0790969i | \(-0.974796\pi\) |
0.566933 | + | 0.823764i | \(0.308130\pi\) | |||||||
\(542\) | 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 | 0.876517 | − | 0.481371i | \(-0.159861\pi\) |
0.0213785 | + | 0.999771i | \(0.493195\pi\) | |||||||
\(548\) | 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 | 0.223743 | − | 0.974648i | \(-0.428173\pi\) |
−0.732199 | + | 0.681091i | \(0.761506\pi\) | |||||||
\(558\) | 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 | −0.989897 | − | 0.141786i | \(-0.954716\pi\) |
−0.372158 | + | 0.928169i | \(0.621382\pi\) | |||||||
\(588\) | 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 | −0.0390666 | − | 0.999237i | \(-0.512438\pi\) |
−0.884898 | + | 0.465786i | \(0.845772\pi\) | |||||||
\(594\) | 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 | −0.219061 | − | 0.975711i | \(-0.570299\pi\) |
0.954521 | − | 0.298143i | \(-0.0963673\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.66025i | 0.353259i | 0.984277 | + | 0.176630i | \(0.0565195\pi\) | ||||
−0.984277 | + | 0.176630i | \(0.943481\pi\) | |||||||
\(602\) | 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 | \(0.218060\pi\) | ||||
−0.774384 | + | 0.632716i | \(0.781940\pi\) | |||||||
\(608\) | 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 | −0.972924 | − | 0.231127i | \(-0.925759\pi\) |
0.286300 | − | 0.958140i | \(-0.407575\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.00000 | + | 15.5885i | −0.362915 | + | 0.628587i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.50000 | + | 0.866025i | 0.0603877 | + | 0.0348649i | 0.529890 | − | 0.848066i | \(-0.322233\pi\) |
−0.469502 | + | 0.882931i | \(0.655567\pi\) | |||||||
\(618\) | 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 | −0.885244 | − | 0.465128i | \(-0.846008\pi\) |
0.845434 | + | 0.534080i | \(0.179342\pi\) | |||||||
\(632\) | 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 | −0.841417 | − | 0.540386i | \(-0.818278\pi\) |
−0.0472793 | − | 0.998882i | \(-0.515055\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.5000 | − | 42.4352i | −0.966186 | − | 1.67348i | −0.706395 | − | 0.707818i | \(-0.749680\pi\) |
−0.259791 | − | 0.965665i | \(-0.583654\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.0000 | − | 41.5692i | 0.944999 | − | 1.63679i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.2487i | 0.953315i | 0.879089 | + | 0.476658i | \(0.158152\pi\) | ||||
−0.879089 | + | 0.476658i | \(0.841848\pi\) | |||||||
\(648\) | 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 | \(-0.956716\pi\) | ||
0.990769 | − | 0.135561i | \(-0.0432836\pi\) | |||||||
\(654\) | 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 | 0.266872 | + | 0.963732i | \(0.414010\pi\) |
−0.968052 | + | 0.250748i | \(0.919323\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.0000 | − | 19.0526i | −1.28355 | − | 0.741059i | −0.306055 | − | 0.952014i | \(-0.599009\pi\) |
−0.977496 | + | 0.210955i | \(0.932343\pi\) | |||||||
\(662\) | 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 | \(0.131196\pi\) | ||||
−0.916256 | + | 0.400594i | \(0.868804\pi\) | |||||||
\(674\) | 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 | −0.660239 | − | 0.751056i | \(-0.729545\pi\) |
0.320314 | + | 0.947312i | \(0.396212\pi\) | |||||||
\(702\) | 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 | −0.931309 | − | 0.364229i | \(-0.881333\pi\) |
0.781086 | + | 0.624423i | \(0.214666\pi\) | |||||||
\(710\) | 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 | −0.443015 | − | 0.896514i | \(-0.646091\pi\) |
0.554896 | + | 0.831919i | \(0.312758\pi\) | |||||||
\(720\) | 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 | 0.930618 | − | 0.365991i | \(-0.119270\pi\) |
−0.782267 | + | 0.622944i | \(0.785937\pi\) | |||||||
\(728\) | 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 | 0.746955 | − | 0.664875i | \(-0.231515\pi\) |
−0.949276 | + | 0.314445i | \(0.898182\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.0000 | − | 15.5885i | −0.771454 | − | 0.572656i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(744\) | 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 | 0.961483 | − | 0.274863i | \(-0.0886324\pi\) |
0.242704 | + | 0.970100i | \(0.421966\pi\) | |||||||
\(752\) | 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 | 0.971652 | + | 0.236414i | \(0.0759722\pi\) |
−0.281086 | + | 0.959683i | \(0.590695\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 8.66025i | − | 0.313934i | −0.987604 | − | 0.156967i | \(-0.949828\pi\) | ||
0.987604 | − | 0.156967i | \(-0.0501716\pi\) | |||||||
\(762\) | 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 | −0.711767 | − | 0.702416i | \(-0.752105\pi\) |
0.964193 | + | 0.265200i | \(0.0854381\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.5000 | + | 12.9904i | 0.810318 | + | 0.467837i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.00000 | − | 5.19615i | 0.107903 | − | 0.186893i | −0.807018 | − | 0.590527i | \(-0.798920\pi\) |
0.914920 | + | 0.403634i | \(0.132253\pi\) | |||||||
\(774\) | 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 | \(0.00982794\pi\) | ||||
−0.999523 | + | 0.0308705i | \(0.990172\pi\) | |||||||
\(788\) | 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 | \(0.196365\pi\) | ||||
−0.815676 | + | 0.578509i | \(0.803635\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.0000 | + | 15.5885i | 0.948098 | + | 0.547385i | 0.892490 | − | 0.451068i | \(-0.148957\pi\) |
0.0556086 | + | 0.998453i | \(0.482290\pi\) | |||||||
\(812\) | 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 | 0.949303 | − | 0.314363i | \(-0.101791\pi\) |
0.202405 | + | 0.979302i | \(0.435124\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.0000 | − | 19.0526i | 0.383436 | − | 0.664130i | −0.608115 | − | 0.793849i | \(-0.708074\pi\) |
0.991551 | + | 0.129719i | \(0.0414074\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.5000 | + | 18.1865i | −0.365563 | + | 0.633174i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.50000 | − | 7.79423i | 0.156480 | − | 0.271032i | −0.777117 | − | 0.629356i | \(-0.783319\pi\) |
0.933597 | + | 0.358325i | \(0.116652\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 20.7846i | − | 0.721879i | −0.932589 | − | 0.360940i | \(-0.882456\pi\) | ||
0.932589 | − | 0.360940i | \(-0.117544\pi\) | |||||||
\(830\) | 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 | 0.958974 | + | 0.283495i | \(0.0914938\pi\) |
−0.233973 | + | 0.972243i | \(0.575173\pi\) | |||||||
\(840\) | 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 | 0.938839 | − | 0.344358i | \(-0.111903\pi\) |
−0.767642 | + | 0.640879i | \(0.778570\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.0000 | − | 41.5692i | −0.615587 | − | 1.42164i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.5000 | − | 18.1865i | −0.358673 | − | 0.621240i | 0.629066 | − | 0.777352i | \(-0.283437\pi\) |
−0.987739 | + | 0.156112i | \(0.950104\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.5000 | − | 42.4352i | 0.835929 | − | 1.44787i | −0.0573424 | − | 0.998355i | \(-0.518263\pi\) |
0.893272 | − | 0.449517i | \(-0.148404\pi\) | |||||||
\(860\) | 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 | −0.939948 | − | 0.341319i | \(-0.889126\pi\) |
−0.174383 | + | 0.984678i | \(0.555793\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 10.3923i | − | 0.350524i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.0526i | 0.641897i | 0.947097 | + | 0.320949i | \(0.104002\pi\) | ||||
−0.947097 | + | 0.320949i | \(0.895998\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.50000 | + | 9.52628i | −0.185090 | + | 0.320585i | −0.943607 | − | 0.331068i | \(-0.892591\pi\) |
0.758517 | + | 0.651653i | \(0.225924\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.00000 | + | 15.5885i | −0.302532 | + | 0.524000i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.0000 | − | 31.1769i | 0.604381 | − | 1.04682i | −0.387768 | − | 0.921757i | \(-0.626754\pi\) |
0.992149 | − | 0.125061i | \(-0.0399128\pi\) | |||||||
\(888\) | 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 | −0.524697 | − | 0.851289i | \(-0.675821\pi\) |
0.474890 | + | 0.880045i | \(0.342488\pi\) | |||||||
\(908\) | 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 | −0.917980 | − | 0.396627i | \(-0.870181\pi\) |
−0.115501 | + | 0.993307i | \(0.536847\pi\) | |||||||
\(930\) | 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 | −0.803176 | − | 0.595742i | \(-0.796858\pi\) |
0.917516 | + | 0.397699i | \(0.130191\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 46.5000 | + | 26.8468i | 1.51747 | + | 0.876112i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.0000 | − | 46.7654i | 0.880175 | − | 1.52451i | 0.0290288 | − | 0.999579i | \(-0.490759\pi\) |
0.851146 | − | 0.524929i | \(-0.175908\pi\) | |||||||
\(942\) | 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 | −0.999118 | − | 0.0419998i | \(-0.986627\pi\) |
−0.463186 | + | 0.886261i | \(0.653294\pi\) | |||||||
\(948\) | 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 | −0.901133 | − | 0.433544i | \(-0.857263\pi\) |
0.0751066 | − | 0.997176i | \(-0.476070\pi\) | |||||||
\(954\) | 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 | −0.917000 | − | 0.398886i | \(-0.869397\pi\) |
0.113055 | − | 0.993589i | \(-0.463936\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 48.0000 | − | 20.7846i | 1.54198 | − | 0.667698i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.50000 | + | 7.79423i | 0.144412 | + | 0.250129i | 0.929153 | − | 0.369694i | \(-0.120538\pi\) |
−0.784741 | + | 0.619823i | \(0.787204\pi\) | |||||||
\(972\) | 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 | −0.996138 | − | 0.0878058i | \(-0.972015\pi\) |
0.422027 | − | 0.906583i | \(-0.361319\pi\) | |||||||
\(984\) | 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 | −0.592262 | − | 0.805746i | \(-0.701765\pi\) |
0.401665 | + | 0.915786i | \(0.368431\pi\) | |||||||
\(992\) | 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 | −0.583363 | − | 0.812211i | \(-0.698264\pi\) |
0.995077 | + | 0.0991016i | \(0.0315969\pi\) | |||||||
\(998\) | 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.449.1 | 2 | ||
3.2 | odd | 2 | 912.2.bn.d.449.1 | 2 | |||
4.3 | odd | 2 | 114.2.h.d.107.1 | yes | 2 | ||
12.11 | even | 2 | 114.2.h.a.107.1 | yes | 2 | ||
19.8 | odd | 6 | 912.2.bn.d.65.1 | 2 | |||
57.8 | even | 6 | inner | 912.2.bn.b.65.1 | 2 | ||
76.27 | even | 6 | 114.2.h.a.65.1 | ✓ | 2 | ||
228.179 | odd | 6 | 114.2.h.d.65.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.h.a.65.1 | ✓ | 2 | 76.27 | even | 6 | ||
114.2.h.a.107.1 | yes | 2 | 12.11 | even | 2 | ||
114.2.h.d.65.1 | yes | 2 | 228.179 | odd | 6 | ||
114.2.h.d.107.1 | yes | 2 | 4.3 | odd | 2 | ||
912.2.bn.b.65.1 | 2 | 57.8 | even | 6 | inner | ||
912.2.bn.b.449.1 | 2 | 1.1 | even | 1 | trivial | ||
912.2.bn.d.65.1 | 2 | 19.8 | odd | 6 | |||
912.2.bn.d.449.1 | 2 | 3.2 | odd | 2 |