Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(361,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.h (of order \(3\), 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: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.31116960000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} - 8x^{4} + 9x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 882) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.3 | ||
Root | \(-0.306808 + 1.70466i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.667 |
Dual form | 2646.2.h.r.361.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.613616 | 0.274417 | 0.137209 | − | 0.990542i | \(-0.456187\pi\) | ||||
0.137209 | + | 0.990542i | \(0.456187\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.306808 | − | 0.531407i | −0.0970212 | − | 0.168046i | ||||
\(11\) | 4.62348 | 1.39403 | 0.697015 | − | 0.717056i | \(-0.254511\pi\) | ||||
0.697015 | + | 0.717056i | \(0.254511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.25937 | + | 5.64539i | 0.903986 | + | 1.56575i | 0.822273 | + | 0.569094i | \(0.192706\pi\) |
0.0817130 | + | 0.996656i | \(0.473961\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.01607 | + | 1.75988i | 0.246433 | + | 0.426834i | 0.962533 | − | 0.271163i | \(-0.0874083\pi\) |
−0.716101 | + | 0.697997i | \(0.754075\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.32288 | − | 2.29129i | 0.303488 | − | 0.525657i | −0.673435 | − | 0.739246i | \(-0.735182\pi\) |
0.976924 | + | 0.213589i | \(0.0685153\pi\) | |||||||
\(20\) | −0.306808 | + | 0.531407i | −0.0686044 | + | 0.118826i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.31174 | − | 4.00405i | −0.492864 | − | 0.853666i | ||||
\(23\) | 3.62348 | 0.755547 | 0.377773 | − | 0.925898i | \(-0.376690\pi\) | ||||
0.377773 | + | 0.925898i | \(0.376690\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.62348 | −0.924695 | ||||||||
\(26\) | 3.25937 | − | 5.64539i | 0.639215 | − | 1.10715i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | + | 3.46410i | −0.371391 | + | 0.643268i | −0.989780 | − | 0.142605i | \(-0.954452\pi\) |
0.618389 | + | 0.785872i | \(0.287786\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.25937 | + | 5.64539i | −0.585400 | + | 1.01394i | 0.409426 | + | 0.912343i | \(0.365729\pi\) |
−0.994825 | + | 0.101599i | \(0.967604\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.01607 | − | 1.75988i | 0.174254 | − | 0.301817i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | + | 5.19615i | −0.493197 | + | 0.854242i | −0.999969 | − | 0.00783774i | \(-0.997505\pi\) |
0.506772 | + | 0.862080i | \(0.330838\pi\) | |||||||
\(38\) | −2.64575 | −0.429198 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.613616 | 0.0970212 | ||||||||
\(41\) | 1.01607 | + | 1.75988i | 0.158683 | + | 0.274847i | 0.934394 | − | 0.356241i | \(-0.115942\pi\) |
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.31174 | − | 2.27200i | 0.200038 | − | 0.346476i | −0.748502 | − | 0.663132i | \(-0.769227\pi\) |
0.948540 | + | 0.316656i | \(0.102560\pi\) | |||||||
\(44\) | −2.31174 | + | 4.00405i | −0.348508 | + | 0.603633i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.81174 | − | 3.13802i | −0.267126 | − | 0.462676i | ||||
\(47\) | −5.29150 | − | 9.16515i | −0.771845 | − | 1.33687i | −0.936551 | − | 0.350532i | \(-0.886001\pi\) |
0.164706 | − | 0.986343i | \(-0.447333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.31174 | + | 4.00405i | 0.326929 | + | 0.566258i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.51873 | −0.903986 | ||||||||
\(53\) | −2.00000 | − | 3.46410i | −0.274721 | − | 0.475831i | 0.695344 | − | 0.718677i | \(-0.255252\pi\) |
−0.970065 | + | 0.242846i | \(0.921919\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.83704 | 0.382546 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.00000 | 0.525226 | ||||||||
\(59\) | −6.11628 | + | 10.5937i | −0.796272 | + | 1.37918i | 0.125756 | + | 0.992061i | \(0.459864\pi\) |
−0.922028 | + | 0.387123i | \(0.873469\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.56618 | + | 6.17680i | 0.456602 | + | 0.790858i | 0.998779 | − | 0.0494066i | \(-0.0157330\pi\) |
−0.542177 | + | 0.840264i | \(0.682400\pi\) | |||||||
\(62\) | 6.51873 | 0.827880 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.00000 | + | 3.46410i | 0.248069 | + | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.31174 | + | 4.00405i | −0.282424 | + | 0.489172i | −0.971981 | − | 0.235059i | \(-0.924472\pi\) |
0.689557 | + | 0.724231i | \(0.257805\pi\) | |||||||
\(68\) | −2.03214 | −0.246433 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.376525 | 0.0446853 | 0.0223426 | − | 0.999750i | \(-0.492888\pi\) | ||||
0.0223426 | + | 0.999750i | \(0.492888\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.66182 | + | 6.34246i | 0.428583 | + | 0.742328i | 0.996748 | − | 0.0805869i | \(-0.0256795\pi\) |
−0.568164 | + | 0.822915i | \(0.692346\pi\) | |||||||
\(74\) | 6.00000 | 0.697486 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.32288 | + | 2.29129i | 0.151744 | + | 0.262829i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.81174 | − | 11.7983i | −0.766380 | − | 1.32741i | −0.939514 | − | 0.342511i | \(-0.888722\pi\) |
0.173133 | − | 0.984898i | \(-0.444611\pi\) | |||||||
\(80\) | −0.306808 | − | 0.531407i | −0.0343022 | − | 0.0594131i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.01607 | − | 1.75988i | 0.112206 | − | 0.194346i | ||||
\(83\) | −3.87298 | + | 6.70820i | −0.425115 | + | 0.736321i | −0.996431 | − | 0.0844091i | \(-0.973100\pi\) |
0.571316 | + | 0.820730i | \(0.306433\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.623475 | + | 1.07989i | 0.0676254 | + | 0.117131i | ||||
\(86\) | −2.62348 | −0.282897 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.62348 | 0.492864 | ||||||||
\(89\) | 7.13235 | − | 12.3536i | 0.756028 | − | 1.30948i | −0.188834 | − | 0.982009i | \(-0.560471\pi\) |
0.944862 | − | 0.327469i | \(-0.106196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.81174 | + | 3.13802i | −0.188887 | + | 0.327161i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.29150 | + | 9.16515i | −0.545777 | + | 0.945313i | ||||
\(95\) | 0.811738 | − | 1.40597i | 0.0832825 | − | 0.144250i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.14842 | + | 14.1135i | −0.827347 | + | 1.43301i | 0.0727661 | + | 0.997349i | \(0.476817\pi\) |
−0.900113 | + | 0.435657i | \(0.856516\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.31174 | − | 4.00405i | 0.231174 | − | 0.400405i | ||||
\(101\) | 16.4881 | 1.64063 | 0.820315 | − | 0.571912i | \(-0.193798\pi\) | ||||
0.820315 | + | 0.571912i | \(0.193798\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.1017 | 1.68508 | 0.842542 | − | 0.538630i | \(-0.181058\pi\) | ||||
0.842542 | + | 0.538630i | \(0.181058\pi\) | |||||||
\(104\) | 3.25937 | + | 5.64539i | 0.319607 | + | 0.553576i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.00000 | + | 3.46410i | −0.194257 | + | 0.336463i | ||||
\(107\) | 5.31174 | − | 9.20020i | 0.513505 | − | 0.889417i | −0.486372 | − | 0.873752i | \(-0.661680\pi\) |
0.999877 | − | 0.0156651i | \(-0.00498658\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.62348 | + | 8.00809i | 0.442849 | + | 0.767036i | 0.997900 | − | 0.0647800i | \(-0.0206346\pi\) |
−0.555051 | + | 0.831816i | \(0.687301\pi\) | |||||||
\(110\) | −1.41852 | − | 2.45695i | −0.135251 | − | 0.234261i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.81174 | − | 15.2624i | −0.828939 | − | 1.43576i | −0.898872 | − | 0.438212i | \(-0.855612\pi\) |
0.0699331 | − | 0.997552i | \(-0.477721\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.22342 | 0.207335 | ||||||||
\(116\) | −2.00000 | − | 3.46410i | −0.185695 | − | 0.321634i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.2326 | 1.12610 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3765 | 0.943320 | ||||||||
\(122\) | 3.56618 | − | 6.17680i | 0.322866 | − | 0.559221i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.25937 | − | 5.64539i | −0.292700 | − | 0.506971i | ||||
\(125\) | −5.90512 | −0.528170 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6235 | 1.03142 | 0.515708 | − | 0.856764i | \(-0.327529\pi\) | ||||
0.515708 | + | 0.856764i | \(0.327529\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | − | 3.46410i | 0.175412 | − | 0.303822i | ||||
\(131\) | 13.6511 | 1.19270 | 0.596350 | − | 0.802724i | \(-0.296617\pi\) | ||||
0.596350 | + | 0.802724i | \(0.296617\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.62348 | 0.399407 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.01607 | + | 1.75988i | 0.0871271 | + | 0.150909i | ||||
\(137\) | −9.87043 | −0.843287 | −0.421644 | − | 0.906762i | \(-0.638547\pi\) | ||||
−0.421644 | + | 0.906762i | \(0.638547\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.96863 | + | 6.87386i | 0.336615 | + | 0.583033i | 0.983794 | − | 0.179305i | \(-0.0573847\pi\) |
−0.647179 | + | 0.762338i | \(0.724051\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.188262 | − | 0.326080i | −0.0157986 | − | 0.0273640i | ||||
\(143\) | 15.0696 | + | 26.1013i | 1.26018 | + | 2.18270i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.22723 | + | 2.12563i | −0.101916 | + | 0.176524i | ||||
\(146\) | 3.66182 | − | 6.34246i | 0.303054 | − | 0.524905i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.00000 | − | 5.19615i | −0.246598 | − | 0.427121i | ||||
\(149\) | −15.2470 | −1.24908 | −0.624539 | − | 0.780993i | \(-0.714713\pi\) | ||||
−0.624539 | + | 0.780993i | \(0.714713\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.62348 | 0.132117 | 0.0660583 | − | 0.997816i | \(-0.478958\pi\) | ||||
0.0660583 | + | 0.997816i | \(0.478958\pi\) | |||||||
\(152\) | 1.32288 | − | 2.29129i | 0.107299 | − | 0.185848i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | + | 3.46410i | −0.160644 | + | 0.278243i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.53404 | + | 2.65704i | −0.122430 | + | 0.212055i | −0.920725 | − | 0.390211i | \(-0.872402\pi\) |
0.798296 | + | 0.602266i | \(0.205735\pi\) | |||||||
\(158\) | −6.81174 | + | 11.7983i | −0.541913 | + | 0.938620i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.306808 | + | 0.531407i | −0.0242553 | + | 0.0420114i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.62348 | + | 16.6683i | −0.753769 | + | 1.30557i | 0.192215 | + | 0.981353i | \(0.438433\pi\) |
−0.945984 | + | 0.324213i | \(0.894901\pi\) | |||||||
\(164\) | −2.03214 | −0.158683 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.74597 | 0.601204 | ||||||||
\(167\) | −0.613616 | − | 1.06281i | −0.0474830 | − | 0.0822430i | 0.841307 | − | 0.540558i | \(-0.181787\pi\) |
−0.888790 | + | 0.458315i | \(0.848453\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.7470 | + | 25.5425i | −1.13438 | + | 1.96481i | ||||
\(170\) | 0.623475 | − | 1.07989i | 0.0478184 | − | 0.0828239i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.31174 | + | 2.27200i | 0.100019 | + | 0.173238i | ||||
\(173\) | 3.25937 | + | 5.64539i | 0.247805 | + | 0.429211i | 0.962917 | − | 0.269799i | \(-0.0869574\pi\) |
−0.715111 | + | 0.699010i | \(0.753624\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.31174 | − | 4.00405i | −0.174254 | − | 0.301816i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −14.2647 | −1.06918 | ||||||||
\(179\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.13235 | −0.530143 | −0.265072 | − | 0.964229i | \(-0.585396\pi\) | ||||
−0.265072 | + | 0.964229i | \(0.585396\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.62348 | 0.267126 | ||||||||
\(185\) | −1.84085 | + | 3.18844i | −0.135342 | + | 0.234419i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.69776 | + | 8.13677i | 0.343535 | + | 0.595019i | ||||
\(188\) | 10.5830 | 0.771845 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.62348 | −0.117779 | ||||||||
\(191\) | 7.81174 | + | 13.5303i | 0.565238 | + | 0.979020i | 0.997028 | + | 0.0770459i | \(0.0245488\pi\) |
−0.431790 | + | 0.901974i | \(0.642118\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.7470 | − | 23.8104i | 0.989527 | − | 1.71391i | 0.369756 | − | 0.929129i | \(-0.379441\pi\) |
0.619772 | − | 0.784782i | \(-0.287225\pi\) | |||||||
\(194\) | 16.2968 | 1.17004 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.2470 | 0.943806 | 0.471903 | − | 0.881650i | \(-0.343567\pi\) | ||||
0.471903 | + | 0.881650i | \(0.343567\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.3917 | + | 17.9990i | 0.736649 | + | 1.27591i | 0.953996 | + | 0.299820i | \(0.0969265\pi\) |
−0.217347 | + | 0.976095i | \(0.569740\pi\) | |||||||
\(200\) | −4.62348 | −0.326929 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.24406 | − | 14.2791i | −0.580050 | − | 1.00468i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.623475 | + | 1.07989i | 0.0435454 | + | 0.0754229i | ||||
\(206\) | −8.55087 | − | 14.8105i | −0.595767 | − | 1.03190i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.25937 | − | 5.64539i | 0.225996 | − | 0.391437i | ||||
\(209\) | 6.11628 | − | 10.5937i | 0.423072 | − | 0.732782i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.62348 | − | 13.2042i | −0.524822 | − | 0.909018i | −0.999582 | − | 0.0289028i | \(-0.990799\pi\) |
0.474761 | − | 0.880115i | \(-0.342535\pi\) | |||||||
\(212\) | 4.00000 | 0.274721 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −10.6235 | −0.726206 | ||||||||
\(215\) | 0.804903 | − | 1.39413i | 0.0548939 | − | 0.0950791i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.62348 | − | 8.00809i | 0.313141 | − | 0.542377i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.41852 | + | 2.45695i | −0.0956366 | + | 0.165647i | ||||
\(221\) | −6.62348 | + | 11.4722i | −0.445543 | + | 0.771703i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.613616 | − | 1.06281i | 0.0410908 | − | 0.0711713i | −0.844749 | − | 0.535163i | \(-0.820250\pi\) |
0.885839 | + | 0.463992i | \(0.153583\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.81174 | + | 15.2624i | −0.586148 | + | 1.01524i | ||||
\(227\) | −2.26318 | −0.150212 | −0.0751062 | − | 0.997176i | \(-0.523930\pi\) | ||||
−0.0751062 | + | 0.997176i | \(0.523930\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.51493 | 0.496600 | 0.248300 | − | 0.968683i | \(-0.420128\pi\) | ||||
0.248300 | + | 0.968683i | \(0.420128\pi\) | |||||||
\(230\) | −1.11171 | − | 1.92554i | −0.0733041 | − | 0.126966i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.00000 | + | 3.46410i | −0.131306 | + | 0.227429i | ||||
\(233\) | 8.50000 | − | 14.7224i | 0.556854 | − | 0.964499i | −0.440903 | − | 0.897555i | \(-0.645342\pi\) |
0.997757 | − | 0.0669439i | \(-0.0213249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.24695 | − | 5.62388i | −0.211808 | − | 0.366862i | ||||
\(236\) | −6.11628 | − | 10.5937i | −0.398136 | − | 0.689592i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.18826 | + | 2.05813i | 0.0768623 | + | 0.133129i | 0.901895 | − | 0.431956i | \(-0.142176\pi\) |
−0.825032 | + | 0.565086i | \(0.808843\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.16830 | 0.526166 | 0.263083 | − | 0.964773i | \(-0.415261\pi\) | ||||
0.263083 | + | 0.964773i | \(0.415261\pi\) | |||||||
\(242\) | −5.18826 | − | 8.98633i | −0.333514 | − | 0.577663i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.13235 | −0.456602 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.2470 | 1.09740 | ||||||||
\(248\) | −3.25937 | + | 5.64539i | −0.206970 | + | 0.358483i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.95256 | + | 5.11398i | 0.186736 | + | 0.323437i | ||||
\(251\) | 10.3917 | 0.655919 | 0.327960 | − | 0.944692i | \(-0.393639\pi\) | ||||
0.327960 | + | 0.944692i | \(0.393639\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.7530 | 1.05326 | ||||||||
\(254\) | −5.81174 | − | 10.0662i | −0.364661 | − | 0.631611i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −28.1071 | −1.75327 | −0.876636 | − | 0.481155i | \(-0.840217\pi\) | ||||
−0.876636 | + | 0.481155i | \(0.840217\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.00000 | −0.248069 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.82554 | − | 11.8222i | −0.421683 | − | 0.730377i | ||||
\(263\) | 13.6235 | 0.840059 | 0.420030 | − | 0.907510i | \(-0.362020\pi\) | ||||
0.420030 | + | 0.907510i | \(0.362020\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.22723 | − | 2.12563i | −0.0753883 | − | 0.130576i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.31174 | − | 4.00405i | −0.141212 | − | 0.244586i | ||||
\(269\) | 5.40702 | + | 9.36524i | 0.329672 | + | 0.571009i | 0.982447 | − | 0.186543i | \(-0.0597285\pi\) |
−0.652775 | + | 0.757552i | \(0.726395\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.16449 | − | 15.8734i | 0.556703 | − | 0.964238i | −0.441066 | − | 0.897475i | \(-0.645400\pi\) |
0.997769 | − | 0.0667630i | \(-0.0212671\pi\) | |||||||
\(272\) | 1.01607 | − | 1.75988i | 0.0616082 | − | 0.106708i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.93521 | + | 8.54804i | 0.298147 | + | 0.516406i | ||||
\(275\) | −21.3765 | −1.28905 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.4939 | 0.750686 | 0.375343 | − | 0.926886i | \(-0.377525\pi\) | ||||
0.375343 | + | 0.926886i | \(0.377525\pi\) | |||||||
\(278\) | 3.96863 | − | 6.87386i | 0.238022 | − | 0.412267i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.43521 | − | 4.21791i | 0.145273 | − | 0.251620i | −0.784202 | − | 0.620506i | \(-0.786927\pi\) |
0.929475 | + | 0.368886i | \(0.120261\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.59831 | − | 9.69656i | 0.332785 | − | 0.576401i | −0.650272 | − | 0.759702i | \(-0.725345\pi\) |
0.983057 | + | 0.183301i | \(0.0586783\pi\) | |||||||
\(284\) | −0.188262 | + | 0.326080i | −0.0111713 | + | 0.0193493i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.0696 | − | 26.1013i | 0.891084 | − | 1.54340i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.43521 | − | 11.1461i | 0.378542 | − | 0.655654i | ||||
\(290\) | 2.45446 | 0.144131 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.32364 | −0.428583 | ||||||||
\(293\) | −7.01683 | − | 12.1535i | −0.409928 | − | 0.710015i | 0.584954 | − | 0.811067i | \(-0.301113\pi\) |
−0.994881 | + | 0.101051i | \(0.967779\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.75305 | + | 6.50047i | −0.218511 | + | 0.378472i | ||||
\(296\) | −3.00000 | + | 5.19615i | −0.174371 | + | 0.302020i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.62348 | + | 13.2042i | 0.441616 | + | 0.764901i | ||||
\(299\) | 11.8102 | + | 20.4559i | 0.683004 | + | 1.18300i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.811738 | − | 1.40597i | −0.0467103 | − | 0.0809045i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.64575 | −0.151744 | ||||||||
\(305\) | 2.18826 | + | 3.79018i | 0.125300 | + | 0.217025i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.2288 | −0.755005 | −0.377503 | − | 0.926009i | \(-0.623217\pi\) | ||||
−0.377503 | + | 0.926009i | \(0.623217\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.00000 | 0.227185 | ||||||||
\(311\) | 5.10022 | − | 8.83383i | 0.289207 | − | 0.500921i | −0.684414 | − | 0.729094i | \(-0.739942\pi\) |
0.973621 | + | 0.228173i | \(0.0732752\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.95332 | + | 15.5076i | 0.506072 | + | 0.876542i | 0.999975 | + | 0.00702519i | \(0.00223621\pi\) |
−0.493904 | + | 0.869517i | \(0.664430\pi\) | |||||||
\(314\) | 3.06808 | 0.173142 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.6235 | 0.766380 | ||||||||
\(317\) | −6.62348 | − | 11.4722i | −0.372011 | − | 0.644343i | 0.617863 | − | 0.786285i | \(-0.287998\pi\) |
−0.989875 | + | 0.141943i | \(0.954665\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.24695 | + | 16.0162i | −0.517730 | + | 0.896734i | ||||
\(320\) | 0.613616 | 0.0343022 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.37652 | 0.299158 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.0696 | − | 26.1013i | −0.835911 | − | 1.44784i | ||||
\(326\) | 19.2470 | 1.06599 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.01607 | + | 1.75988i | 0.0561030 | + | 0.0971732i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | − | 6.92820i | −0.219860 | − | 0.380808i | 0.734905 | − | 0.678170i | \(-0.237227\pi\) |
−0.954765 | + | 0.297361i | \(0.903893\pi\) | |||||||
\(332\) | −3.87298 | − | 6.70820i | −0.212558 | − | 0.368161i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.613616 | + | 1.06281i | −0.0335756 | + | 0.0581546i | ||||
\(335\) | −1.41852 | + | 2.45695i | −0.0775020 | + | 0.134237i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.9352 | − | 29.3326i | −0.922520 | − | 1.59785i | −0.795502 | − | 0.605951i | \(-0.792793\pi\) |
−0.127018 | − | 0.991900i | \(-0.540541\pi\) | |||||||
\(338\) | 29.4939 | 1.60426 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.24695 | −0.0676254 | ||||||||
\(341\) | −15.0696 | + | 26.1013i | −0.816065 | + | 1.41347i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.31174 | − | 2.27200i | 0.0707242 | − | 0.122498i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.25937 | − | 5.64539i | 0.175225 | − | 0.303498i | ||||
\(347\) | 3.31174 | − | 5.73610i | 0.177783 | − | 0.307930i | −0.763338 | − | 0.646000i | \(-0.776441\pi\) |
0.941121 | + | 0.338070i | \(0.109774\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.71383 | − | 9.89665i | 0.305854 | − | 0.529755i | −0.671597 | − | 0.740917i | \(-0.734391\pi\) |
0.977451 | + | 0.211161i | \(0.0677246\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.31174 | + | 4.00405i | −0.123216 | + | 0.213416i | ||||
\(353\) | −2.03214 | −0.108160 | −0.0540798 | − | 0.998537i | \(-0.517223\pi\) | ||||
−0.0540798 | + | 0.998537i | \(0.517223\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.231042 | 0.0122624 | ||||||||
\(356\) | 7.13235 | + | 12.3536i | 0.378014 | + | 0.654739i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.0587 | + | 17.4222i | −0.530877 | + | 0.919506i | 0.468473 | + | 0.883478i | \(0.344804\pi\) |
−0.999351 | + | 0.0360288i | \(0.988529\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | + | 10.3923i | 0.315789 | + | 0.546963i | ||||
\(362\) | 3.56618 | + | 6.17680i | 0.187434 | + | 0.324645i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.24695 | + | 3.89183i | 0.117611 | + | 0.203708i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.1392 | 1.57325 | 0.786627 | − | 0.617429i | \(-0.211826\pi\) | ||||
0.786627 | + | 0.617429i | \(0.211826\pi\) | |||||||
\(368\) | −1.81174 | − | 3.13802i | −0.0944434 | − | 0.163581i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.68170 | 0.191402 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.24695 | −0.478789 | −0.239394 | − | 0.970922i | \(-0.576949\pi\) | ||||
−0.239394 | + | 0.970922i | \(0.576949\pi\) | |||||||
\(374\) | 4.69776 | − | 8.13677i | 0.242916 | − | 0.420742i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.29150 | − | 9.16515i | −0.272888 | − | 0.472657i | ||||
\(377\) | −26.0749 | −1.34293 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.37652 | 0.276174 | 0.138087 | − | 0.990420i | \(-0.455905\pi\) | ||||
0.138087 | + | 0.990420i | \(0.455905\pi\) | |||||||
\(380\) | 0.811738 | + | 1.40597i | 0.0416413 | + | 0.0721248i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.81174 | − | 13.5303i | 0.399683 | − | 0.692272i | ||||
\(383\) | 19.9388 | 1.01882 | 0.509412 | − | 0.860523i | \(-0.329863\pi\) | ||||
0.509412 | + | 0.860523i | \(0.329863\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −27.4939 | −1.39940 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.14842 | − | 14.1135i | −0.413673 | − | 0.716503i | ||||
\(389\) | −16.7530 | −0.849413 | −0.424707 | − | 0.905331i | \(-0.639623\pi\) | ||||
−0.424707 | + | 0.905331i | \(0.639623\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.68170 | + | 6.37688i | 0.186191 | + | 0.322493i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.62348 | − | 11.4722i | −0.333686 | − | 0.577961i | ||||
\(395\) | −4.17979 | − | 7.23961i | −0.210308 | − | 0.364264i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.55087 | + | 14.8105i | −0.429156 | + | 0.743320i | −0.996798 | − | 0.0799553i | \(-0.974522\pi\) |
0.567643 | + | 0.823275i | \(0.307856\pi\) | |||||||
\(398\) | 10.3917 | − | 17.9990i | 0.520890 | − | 0.902208i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.31174 | + | 4.00405i | 0.115587 | + | 0.200202i | ||||
\(401\) | 15.0000 | 0.749064 | 0.374532 | − | 0.927214i | \(-0.377803\pi\) | ||||
0.374532 | + | 0.927214i | \(0.377803\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −42.4939 | −2.11677 | ||||||||
\(404\) | −8.24406 | + | 14.2791i | −0.410157 | + | 0.710413i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.8704 | + | 24.0243i | −0.687531 | + | 1.19084i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.7942 | − | 18.6961i | 0.533737 | − | 0.924460i | −0.465486 | − | 0.885055i | \(-0.654120\pi\) |
0.999223 | − | 0.0394049i | \(-0.0125462\pi\) | |||||||
\(410\) | 0.623475 | − | 1.07989i | 0.0307913 | − | 0.0533320i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.55087 | + | 14.8105i | −0.421271 | + | 0.729663i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.37652 | + | 4.11626i | −0.116659 | + | 0.202059i | ||||
\(416\) | −6.51873 | −0.319607 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −12.2326 | −0.598314 | ||||||||
\(419\) | −6.21193 | − | 10.7594i | −0.303472 | − | 0.525630i | 0.673448 | − | 0.739235i | \(-0.264813\pi\) |
−0.976920 | + | 0.213605i | \(0.931479\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(422\) | −7.62348 | + | 13.2042i | −0.371105 | + | 0.642773i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.00000 | − | 3.46410i | −0.0971286 | − | 0.168232i | ||||
\(425\) | −4.69776 | − | 8.13677i | −0.227875 | − | 0.394691i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.31174 | + | 9.20020i | 0.256753 | + | 0.444708i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.60981 | −0.0776318 | ||||||||
\(431\) | −4.00000 | − | 6.92820i | −0.192673 | − | 0.333720i | 0.753462 | − | 0.657491i | \(-0.228382\pi\) |
−0.946135 | + | 0.323772i | \(0.895049\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.48660 | −0.215612 | −0.107806 | − | 0.994172i | \(-0.534383\pi\) | ||||
−0.107806 | + | 0.994172i | \(0.534383\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.24695 | −0.442849 | ||||||||
\(437\) | 4.79341 | − | 8.30243i | 0.229300 | − | 0.397159i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.4919 | − | 26.8328i | −0.739390 | − | 1.28066i | −0.952770 | − | 0.303691i | \(-0.901781\pi\) |
0.213381 | − | 0.976969i | \(-0.431552\pi\) | |||||||
\(440\) | 2.83704 | 0.135251 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.2470 | 0.630093 | ||||||||
\(443\) | 15.3117 | + | 26.5207i | 0.727483 | + | 1.26004i | 0.957944 | + | 0.286955i | \(0.0926431\pi\) |
−0.230461 | + | 0.973081i | \(0.574024\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.37652 | − | 7.58036i | 0.207467 | − | 0.359344i | ||||
\(446\) | −1.22723 | −0.0581111 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.0000 | 0.707894 | 0.353947 | − | 0.935266i | \(-0.384839\pi\) | ||||
0.353947 | + | 0.935266i | \(0.384839\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.69776 | + | 8.13677i | 0.221209 | + | 0.383145i | ||||
\(452\) | 17.6235 | 0.828939 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.13159 | + | 1.95997i | 0.0531081 | + | 0.0919859i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.50000 | − | 9.52628i | −0.257279 | − | 0.445621i | 0.708233 | − | 0.705979i | \(-0.249493\pi\) |
−0.965512 | + | 0.260358i | \(0.916159\pi\) | |||||||
\(458\) | −3.75746 | − | 6.50812i | −0.175575 | − | 0.304104i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.11171 | + | 1.92554i | −0.0518338 | + | 0.0897788i | ||||
\(461\) | 0.920424 | − | 1.59422i | 0.0428684 | − | 0.0742503i | −0.843795 | − | 0.536666i | \(-0.819684\pi\) |
0.886664 | + | 0.462415i | \(0.153017\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.8117 | − | 30.8508i | −0.827782 | − | 1.43376i | −0.899775 | − | 0.436355i | \(-0.856269\pi\) |
0.0719931 | − | 0.997405i | \(-0.477064\pi\) | |||||||
\(464\) | 4.00000 | 0.185695 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.0000 | −0.787510 | ||||||||
\(467\) | −3.66182 | + | 6.34246i | −0.169449 | + | 0.293494i | −0.938226 | − | 0.346023i | \(-0.887532\pi\) |
0.768777 | + | 0.639516i | \(0.220865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.24695 | + | 5.62388i | −0.149771 | + | 0.259410i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.11628 | + | 10.5937i | −0.281525 | + | 0.487615i | ||||
\(473\) | 6.06479 | − | 10.5045i | 0.278859 | − | 0.482998i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.11628 | + | 10.5937i | −0.280634 | + | 0.486073i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.18826 | − | 2.05813i | 0.0543499 | − | 0.0941367i | ||||
\(479\) | −15.4919 | −0.707845 | −0.353922 | − | 0.935275i | \(-0.615152\pi\) | ||||
−0.353922 | + | 0.935275i | \(0.615152\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −39.1124 | −1.78337 | ||||||||
\(482\) | −4.08415 | − | 7.07395i | −0.186028 | − | 0.322210i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.18826 | + | 8.98633i | −0.235830 | + | 0.408470i | ||||
\(485\) | −5.00000 | + | 8.66025i | −0.227038 | + | 0.393242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.81174 | + | 4.87007i | 0.127412 | + | 0.220684i | 0.922673 | − | 0.385583i | \(-0.126000\pi\) |
−0.795261 | + | 0.606267i | \(0.792666\pi\) | |||||||
\(488\) | 3.56618 | + | 6.17680i | 0.161433 | + | 0.279610i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.55869 | + | 13.0920i | 0.341119 | + | 0.590835i | 0.984641 | − | 0.174593i | \(-0.0558608\pi\) |
−0.643522 | + | 0.765428i | \(0.722527\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.12854 | −0.366091 | ||||||||
\(494\) | −8.62348 | − | 14.9363i | −0.387989 | − | 0.672016i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.51873 | 0.292700 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.6235 | 0.833701 | 0.416851 | − | 0.908975i | \(-0.363134\pi\) | ||||
0.416851 | + | 0.908975i | \(0.363134\pi\) | |||||||
\(500\) | 2.95256 | − | 5.11398i | 0.132042 | − | 0.228704i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.19586 | − | 8.99949i | −0.231903 | − | 0.401667i | ||||
\(503\) | −10.2004 | −0.454815 | −0.227407 | − | 0.973800i | \(-0.573025\pi\) | ||||
−0.227407 | + | 0.973800i | \(0.573025\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.1174 | 0.450217 | ||||||||
\(506\) | −8.37652 | − | 14.5086i | −0.372382 | − | 0.644984i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.81174 | + | 10.0662i | −0.257854 | + | 0.446617i | ||||
\(509\) | −22.0107 | −0.975606 | −0.487803 | − | 0.872954i | \(-0.662202\pi\) | ||||
−0.487803 | + | 0.872954i | \(0.662202\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.0535 | + | 24.3414i | 0.619875 | + | 1.07365i | ||||
\(515\) | 10.4939 | 0.462417 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.4651 | − | 42.3749i | −1.07598 | − | 1.86364i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.00000 | + | 3.46410i | 0.0877058 | + | 0.151911i | ||||
\(521\) | −17.5042 | − | 30.3181i | −0.766873 | − | 1.32826i | −0.939251 | − | 0.343231i | \(-0.888478\pi\) |
0.172378 | − | 0.985031i | \(-0.444855\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.43916 | + | 12.8850i | −0.325292 | + | 0.563422i | −0.981571 | − | 0.191096i | \(-0.938796\pi\) |
0.656280 | + | 0.754518i | \(0.272129\pi\) | |||||||
\(524\) | −6.82554 | + | 11.8222i | −0.298175 | + | 0.516455i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.81174 | − | 11.7983i | −0.297006 | − | 0.514429i | ||||
\(527\) | −13.2470 | −0.577046 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.87043 | −0.429149 | ||||||||
\(530\) | −1.22723 | + | 2.12563i | −0.0533076 | + | 0.0923314i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.62348 | + | 11.4722i | −0.286895 | + | 0.496916i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.25937 | − | 5.64539i | 0.140915 | − | 0.244071i | ||||
\(536\) | −2.31174 | + | 4.00405i | −0.0998519 | + | 0.172948i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.40702 | − | 9.36524i | 0.233113 | − | 0.403764i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | + | 3.46410i | −0.0859867 | + | 0.148933i | −0.905811 | − | 0.423681i | \(-0.860738\pi\) |
0.819825 | + | 0.572615i | \(0.194071\pi\) | |||||||
\(542\) | −18.3290 | −0.787297 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.03214 | −0.0871271 | ||||||||
\(545\) | 2.83704 | + | 4.91389i | 0.121525 | + | 0.210488i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.68826 | + | 8.12031i | −0.200456 | + | 0.347199i | −0.948675 | − | 0.316252i | \(-0.897576\pi\) |
0.748220 | + | 0.663451i | \(0.230909\pi\) | |||||||
\(548\) | 4.93521 | − | 8.54804i | 0.210822 | − | 0.365154i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10.6883 | + | 18.5126i | 0.455749 | + | 0.789380i | ||||
\(551\) | 5.29150 | + | 9.16515i | 0.225426 | + | 0.390449i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.24695 | − | 10.8200i | −0.265408 | − | 0.459699i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.93725 | −0.336615 | ||||||||
\(557\) | 21.6235 | + | 37.4530i | 0.916216 | + | 1.58693i | 0.805111 | + | 0.593124i | \(0.202106\pi\) |
0.111105 | + | 0.993809i | \(0.464561\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.1017 | 0.723327 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.87043 | −0.205447 | ||||||||
\(563\) | −10.4874 | + | 18.1646i | −0.441990 | + | 0.765548i | −0.997837 | − | 0.0657359i | \(-0.979061\pi\) |
0.555847 | + | 0.831284i | \(0.312394\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.40702 | − | 9.36524i | −0.227475 | − | 0.393999i | ||||
\(566\) | −11.1966 | −0.470629 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.376525 | 0.0157986 | ||||||||
\(569\) | −0.935213 | − | 1.61984i | −0.0392062 | − | 0.0679071i | 0.845756 | − | 0.533569i | \(-0.179150\pi\) |
−0.884963 | + | 0.465662i | \(0.845816\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.31174 | − | 16.1284i | 0.389684 | − | 0.674953i | −0.602723 | − | 0.797951i | \(-0.705918\pi\) |
0.992407 | + | 0.122998i | \(0.0392509\pi\) | |||||||
\(572\) | −30.1392 | −1.26018 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.7530 | −0.698650 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.30757 | − | 10.9250i | −0.262588 | − | 0.454815i | 0.704341 | − | 0.709862i | \(-0.251243\pi\) |
−0.966929 | + | 0.255047i | \(0.917909\pi\) | |||||||
\(578\) | −12.8704 | −0.535339 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.22723 | − | 2.12563i | −0.0509580 | − | 0.0882619i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.24695 | − | 16.0162i | −0.382970 | − | 0.663323i | ||||
\(584\) | 3.66182 | + | 6.34246i | 0.151527 | + | 0.262453i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.01683 | + | 12.1535i | −0.289863 | + | 0.502057i | ||||
\(587\) | −17.0061 | + | 29.4554i | −0.701917 | + | 1.21576i | 0.265876 | + | 0.964007i | \(0.414339\pi\) |
−0.967793 | + | 0.251748i | \(0.918995\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.62348 | + | 14.9363i | 0.355324 | + | 0.615439i | ||||
\(590\) | 7.50610 | 0.309021 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.00000 | 0.246598 | ||||||||
\(593\) | −17.7154 | + | 30.6839i | −0.727482 | + | 1.26004i | 0.230462 | + | 0.973081i | \(0.425976\pi\) |
−0.957944 | + | 0.286955i | \(0.907357\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.62348 | − | 13.2042i | 0.312270 | − | 0.540867i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 11.8102 | − | 20.4559i | 0.482957 | − | 0.836505i | ||||
\(599\) | 19.2470 | − | 33.3367i | 0.786409 | − | 1.36210i | −0.141745 | − | 0.989903i | \(-0.545271\pi\) |
0.928154 | − | 0.372197i | \(-0.121396\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.31138 | + | 9.19958i | −0.216656 | + | 0.375259i | −0.953783 | − | 0.300495i | \(-0.902848\pi\) |
0.737128 | + | 0.675753i | \(0.236182\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.811738 | + | 1.40597i | −0.0330291 | + | 0.0572081i | ||||
\(605\) | 6.36720 | 0.258864 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.9388 | −0.809290 | −0.404645 | − | 0.914474i | \(-0.632605\pi\) | ||||
−0.404645 | + | 0.914474i | \(0.632605\pi\) | |||||||
\(608\) | 1.32288 | + | 2.29129i | 0.0536497 | + | 0.0929240i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.18826 | − | 3.79018i | 0.0886002 | − | 0.153460i | ||||
\(611\) | 34.4939 | − | 59.7452i | 1.39547 | − | 2.41703i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.00000 | − | 1.73205i | −0.0403896 | − | 0.0699569i | 0.845124 | − | 0.534570i | \(-0.179527\pi\) |
−0.885514 | + | 0.464614i | \(0.846193\pi\) | |||||||
\(614\) | 6.61438 | + | 11.4564i | 0.266935 | + | 0.462344i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.55869 | − | 9.62793i | −0.223784 | − | 0.387606i | 0.732170 | − | 0.681122i | \(-0.238508\pi\) |
−0.955954 | + | 0.293516i | \(0.905174\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.02833 | 0.121719 | 0.0608593 | − | 0.998146i | \(-0.480616\pi\) | ||||
0.0608593 | + | 0.998146i | \(0.480616\pi\) | |||||||
\(620\) | −2.00000 | − | 3.46410i | −0.0803219 | − | 0.139122i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.2004 | −0.409000 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.4939 | 0.779756 | ||||||||
\(626\) | 8.95332 | − | 15.5076i | 0.357847 | − | 0.619809i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.53404 | − | 2.65704i | −0.0612149 | − | 0.106027i | ||||
\(629\) | −12.1928 | −0.486159 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.3765 | 0.811177 | 0.405588 | − | 0.914056i | \(-0.367067\pi\) | ||||
0.405588 | + | 0.914056i | \(0.367067\pi\) | |||||||
\(632\) | −6.81174 | − | 11.7983i | −0.270956 | − | 0.469310i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.62348 | + | 11.4722i | −0.263052 | + | 0.455619i | ||||
\(635\) | 7.13235 | 0.283039 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 18.4939 | 0.732181 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.306808 | − | 0.531407i | −0.0121277 | − | 0.0210057i | ||||
\(641\) | −15.4939 | −0.611972 | −0.305986 | − | 0.952036i | \(-0.598986\pi\) | ||||
−0.305986 | + | 0.952036i | \(0.598986\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.85692 | + | 4.94832i | 0.112666 | + | 0.195143i | 0.916844 | − | 0.399245i | \(-0.130728\pi\) |
−0.804178 | + | 0.594388i | \(0.797394\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.68826 | − | 4.65621i | −0.105768 | − | 0.183196i | ||||
\(647\) | −9.58681 | − | 16.6049i | −0.376897 | − | 0.652804i | 0.613712 | − | 0.789530i | \(-0.289675\pi\) |
−0.990609 | + | 0.136726i | \(0.956342\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.2785 | + | 48.9798i | −1.11003 | + | 1.92262i | ||||
\(650\) | −15.0696 | + | 26.1013i | −0.591079 | + | 1.02378i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.62348 | − | 16.6683i | −0.376884 | − | 0.652783i | ||||
\(653\) | −18.7530 | −0.733864 | −0.366932 | − | 0.930248i | \(-0.619592\pi\) | ||||
−0.366932 | + | 0.930248i | \(0.619592\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.37652 | 0.327298 | ||||||||
\(656\) | 1.01607 | − | 1.75988i | 0.0396708 | − | 0.0687118i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.2470 | − | 26.4085i | 0.593937 | − | 1.02873i | −0.399759 | − | 0.916620i | \(-0.630906\pi\) |
0.993696 | − | 0.112109i | \(-0.0357605\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.9900 | − | 27.6955i | 0.621940 | − | 1.07723i | −0.367184 | − | 0.930148i | \(-0.619678\pi\) |
0.989124 | − | 0.147083i | \(-0.0469886\pi\) | |||||||
\(662\) | −4.00000 | + | 6.92820i | −0.155464 | + | 0.269272i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.87298 | + | 6.70820i | −0.150301 | + | 0.260329i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.24695 | + | 12.5521i | −0.280603 | + | 0.486019i | ||||
\(668\) | 1.22723 | 0.0474830 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.83704 | 0.109604 | ||||||||
\(671\) | 16.4881 | + | 28.5583i | 0.636517 | + | 1.10248i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.8117 | + | 25.6547i | −0.570951 | + | 0.988915i | 0.425518 | + | 0.904950i | \(0.360092\pi\) |
−0.996469 | + | 0.0839654i | \(0.973241\pi\) | |||||||
\(674\) | −16.9352 | + | 29.3326i | −0.652320 | + | 1.12985i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −14.7470 | − | 25.5425i | −0.567190 | − | 0.982403i | ||||
\(677\) | −13.4598 | − | 23.3131i | −0.517302 | − | 0.895993i | −0.999798 | − | 0.0200953i | \(-0.993603\pi\) |
0.482496 | − | 0.875898i | \(-0.339730\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.623475 | + | 1.07989i | 0.0239092 | + | 0.0414119i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 30.1392 | 1.15409 | ||||||||
\(683\) | 22.1822 | + | 38.4206i | 0.848777 | + | 1.47012i | 0.882300 | + | 0.470687i | \(0.155994\pi\) |
−0.0335235 | + | 0.999438i | \(0.510673\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.05665 | −0.231413 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.62348 | −0.100019 | ||||||||
\(689\) | 13.0375 | − | 22.5816i | 0.496688 | − | 0.860289i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.9579 | − | 24.1758i | −0.530983 | − | 0.919690i | −0.999346 | − | 0.0361539i | \(-0.988489\pi\) |
0.468363 | − | 0.883536i | \(-0.344844\pi\) | |||||||
\(692\) | −6.51873 | −0.247805 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.62348 | −0.251424 | ||||||||
\(695\) | 2.43521 | + | 4.21791i | 0.0923729 | + | 0.159995i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.06479 | + | 3.57632i | −0.0782094 | + | 0.135463i | ||||
\(698\) | −11.4277 | −0.432543 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.753049 | 0.0284423 | 0.0142211 | − | 0.999899i | \(-0.495473\pi\) | ||||
0.0142211 | + | 0.999899i | \(0.495473\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.93725 | + | 13.7477i | 0.299359 | + | 0.518505i | ||||
\(704\) | 4.62348 | 0.174254 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.01607 | + | 1.75988i | 0.0382402 | + | 0.0662340i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.2470 | + | 19.4803i | 0.422388 | + | 0.731598i | 0.996173 | − | 0.0874087i | \(-0.0278586\pi\) |
−0.573784 | + | 0.819006i | \(0.694525\pi\) | |||||||
\(710\) | −0.115521 | − | 0.200088i | −0.00433542 | − | 0.00750916i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.13235 | − | 12.3536i | 0.267296 | − | 0.462970i | ||||
\(713\) | −11.8102 | + | 20.4559i | −0.442297 | + | 0.766081i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.24695 | + | 16.0162i | 0.345816 | + | 0.598971i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 20.1174 | 0.750774 | ||||||||
\(719\) | 2.03214 | − | 3.51976i | 0.0757859 | − | 0.131265i | −0.825642 | − | 0.564195i | \(-0.809187\pi\) |
0.901428 | + | 0.432930i | \(0.142520\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.00000 | − | 10.3923i | 0.223297 | − | 0.386762i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.56618 | − | 6.17680i | 0.132536 | − | 0.229559i | ||||
\(725\) | 9.24695 | − | 16.0162i | 0.343423 | − | 0.594826i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.03594 | − | 1.79431i | 0.0384211 | − | 0.0665472i | −0.846175 | − | 0.532904i | \(-0.821101\pi\) |
0.884596 | + | 0.466357i | \(0.154434\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.24695 | − | 3.89183i | 0.0831634 | − | 0.144043i | ||||
\(731\) | 5.33126 | 0.197184 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.6886 | −0.985764 | −0.492882 | − | 0.870096i | \(-0.664057\pi\) | ||||
−0.492882 | + | 0.870096i | \(0.664057\pi\) | |||||||
\(734\) | −15.0696 | − | 26.1013i | −0.556229 | − | 0.963417i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.81174 | + | 3.13802i | −0.0667815 | + | 0.115669i | ||||
\(737\) | −10.6883 | + | 18.5126i | −0.393707 | + | 0.681921i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.93521 | + | 8.54804i | 0.181545 | + | 0.314445i | 0.942407 | − | 0.334469i | \(-0.108557\pi\) |
−0.760862 | + | 0.648914i | \(0.775224\pi\) | |||||||
\(740\) | −1.84085 | − | 3.18844i | −0.0676709 | − | 0.117209i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.37652 | + | 9.31241i | 0.197246 | + | 0.341639i | 0.947634 | − | 0.319357i | \(-0.103467\pi\) |
−0.750389 | + | 0.660997i | \(0.770134\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.35577 | −0.342769 | ||||||||
\(746\) | 4.62348 | + | 8.00809i | 0.169277 | + | 0.293197i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.39553 | −0.343535 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.6235 | −0.789052 | −0.394526 | − | 0.918885i | \(-0.629091\pi\) | ||||
−0.394526 | + | 0.918885i | \(0.629091\pi\) | |||||||
\(752\) | −5.29150 | + | 9.16515i | −0.192961 | + | 0.334219i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13.0375 | + | 22.5816i | 0.474797 | + | 0.822372i | ||||
\(755\) | 0.996190 | 0.0362551 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.7409 | −0.644802 | −0.322401 | − | 0.946603i | \(-0.604490\pi\) | ||||
−0.322401 | + | 0.946603i | \(0.604490\pi\) | |||||||
\(758\) | −2.68826 | − | 4.65621i | −0.0976421 | − | 0.169121i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.811738 | − | 1.40597i | 0.0294448 | − | 0.0509999i | ||||
\(761\) | −36.6579 | −1.32885 | −0.664425 | − | 0.747355i | \(-0.731323\pi\) | ||||
−0.664425 | + | 0.747355i | \(0.731323\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −15.6235 | −0.565238 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.96939 | − | 17.2675i | −0.360209 | − | 0.623900i | ||||
\(767\) | −79.7409 | −2.87928 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.9426 | + | 32.8095i | 0.683087 | + | 1.18314i | 0.974034 | + | 0.226402i | \(0.0726964\pi\) |
−0.290947 | + | 0.956739i | \(0.593970\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.7470 | + | 23.8104i | 0.494764 | + | 0.856956i | ||||
\(773\) | −10.6985 | − | 18.5304i | −0.384799 | − | 0.666492i | 0.606942 | − | 0.794746i | \(-0.292396\pi\) |
−0.991741 | + | 0.128254i | \(0.959063\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.0696 | − | 26.1013i | 0.541316 | − | 0.937587i | ||||
\(776\) | −8.14842 | + | 14.1135i | −0.292511 | + | 0.506644i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.37652 | + | 14.5086i | 0.300313 | + | 0.520157i | ||||
\(779\) | 5.37652 | 0.192634 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.74085 | 0.0622926 | ||||||||
\(782\) | 3.68170 | − | 6.37688i | 0.131657 | − | 0.228037i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.941312 | + | 1.63040i | −0.0335968 | + | 0.0581915i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.2288 | + | 22.9129i | −0.471554 | + | 0.816756i | −0.999470 | − | 0.0325406i | \(-0.989640\pi\) |
0.527916 | + | 0.849296i | \(0.322974\pi\) | |||||||
\(788\) | −6.62348 | + | 11.4722i | −0.235952 | + | 0.408680i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.17979 | + | 7.23961i | −0.148710 | + | 0.257574i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.2470 | + | 40.2649i | −0.825523 | + | 1.42985i | ||||
\(794\) | 17.1017 | 0.606918 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.7834 | −0.736649 | ||||||||
\(797\) | −4.79341 | − | 8.30243i | −0.169791 | − | 0.294087i | 0.768555 | − | 0.639784i | \(-0.220976\pi\) |
−0.938346 | + | 0.345697i | \(0.887643\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.7530 | − | 18.6248i | 0.380416 | − | 0.658899i | ||||
\(800\) | 2.31174 | − | 4.00405i | 0.0817323 | − | 0.141564i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.50000 | − | 12.9904i | −0.264834 | − | 0.458706i | ||||
\(803\) | 16.9303 | + | 29.3242i | 0.597458 | + | 1.03483i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21.2470 | + | 36.8008i | 0.748392 | + | 1.29625i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.4881 | 0.580050 | ||||||||
\(809\) | −13.5587 | − | 23.4843i | −0.476698 | − | 0.825665i | 0.522945 | − | 0.852366i | \(-0.324833\pi\) |
−0.999643 | + | 0.0267009i | \(0.991500\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.8798 | 0.943879 | 0.471939 | − | 0.881631i | \(-0.343554\pi\) | ||||
0.471939 | + | 0.881631i | \(0.343554\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 27.7409 | 0.972316 | ||||||||
\(815\) | −5.90512 | + | 10.2280i | −0.206847 | + | 0.358270i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.47053 | − | 6.01114i | −0.121419 | − | 0.210303i | ||||
\(818\) | −21.5883 | −0.754819 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.24695 | −0.0435454 | ||||||||
\(821\) | 11.8704 | + | 20.5602i | 0.414281 | + | 0.717555i | 0.995353 | − | 0.0962969i | \(-0.0306998\pi\) |
−0.581072 | + | 0.813852i | \(0.697367\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.8704 | − | 30.9525i | 0.622924 | − | 1.07894i | −0.366015 | − | 0.930609i | \(-0.619278\pi\) |
0.988938 | − | 0.148327i | \(-0.0473887\pi\) | |||||||
\(824\) | 17.1017 | 0.595767 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.75305 | −0.165280 | −0.0826399 | − | 0.996579i | \(-0.526335\pi\) | ||||
−0.0826399 | + | 0.996579i | \(0.526335\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.0375 | − | 22.5816i | −0.452810 | − | 0.784290i | 0.545749 | − | 0.837948i | \(-0.316245\pi\) |
−0.998559 | + | 0.0536585i | \(0.982912\pi\) | |||||||
\(830\) | 4.75305 | 0.164981 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.25937 | + | 5.64539i | 0.112998 | + | 0.195719i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.376525 | − | 0.652160i | −0.0130302 | − | 0.0225689i | ||||
\(836\) | 6.11628 | + | 10.5937i | 0.211536 | + | 0.366391i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.21193 | + | 10.7594i | −0.214587 | + | 0.371676i | ||||
\(839\) | 21.7796 | − | 37.7234i | 0.751916 | − | 1.30236i | −0.194977 | − | 0.980808i | \(-0.562463\pi\) |
0.946893 | − | 0.321549i | \(-0.104204\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.50000 | + | 11.2583i | 0.224138 | + | 0.388218i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.2470 | 0.524822 | ||||||||
\(845\) | −9.04897 | + | 15.6733i | −0.311294 | + | 0.539177i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.00000 | + | 3.46410i | −0.0686803 | + | 0.118958i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.69776 | + | 8.13677i | −0.161132 | + | 0.279089i | ||||
\(851\) | −10.8704 | + | 18.8281i | −0.372633 | + | 0.645420i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.40321 | − | 11.0907i | 0.219242 | − | 0.379738i | −0.735335 | − | 0.677704i | \(-0.762975\pi\) |
0.954576 | + | 0.297966i | \(0.0963083\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.31174 | − | 9.20020i | 0.181551 | − | 0.314456i | ||||
\(857\) | −35.4307 | −1.21029 | −0.605145 | − | 0.796115i | \(-0.706885\pi\) | ||||
−0.605145 | + | 0.796115i | \(0.706885\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.8424 | −0.472296 | −0.236148 | − | 0.971717i | \(-0.575885\pi\) | ||||
−0.236148 | + | 0.971717i | \(0.575885\pi\) | |||||||
\(860\) | 0.804903 | + | 1.39413i | 0.0274470 | + | 0.0475396i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.00000 | + | 6.92820i | −0.136241 | + | 0.235976i | ||||
\(863\) | 3.56479 | − | 6.17439i | 0.121347 | − | 0.210179i | −0.798952 | − | 0.601394i | \(-0.794612\pi\) |
0.920299 | + | 0.391216i | \(0.127945\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.00000 | + | 3.46410i | 0.0680020 | + | 0.117783i | ||||
\(866\) | 2.24330 | + | 3.88551i | 0.0762304 | + | 0.132035i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.4939 | − | 54.5490i | −1.06836 | − | 1.85045i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.1392 | −1.02123 | ||||||||
\(872\) | 4.62348 | + | 8.00809i | 0.156571 | + | 0.271188i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.58681 | −0.324279 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.0000 | 0.405211 | 0.202606 | − | 0.979260i | \(-0.435059\pi\) | ||||
0.202606 | + | 0.979260i | \(0.435059\pi\) | |||||||
\(878\) | −15.4919 | + | 26.8328i | −0.522827 | + | 0.905564i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.41852 | − | 2.45695i | −0.0478183 | − | 0.0828237i | ||||
\(881\) | 26.0749 | 0.878487 | 0.439244 | − | 0.898368i | \(-0.355247\pi\) | ||||
0.439244 | + | 0.898368i | \(0.355247\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.8704 | −1.13983 | −0.569915 | − | 0.821703i | \(-0.693024\pi\) | ||||
−0.569915 | + | 0.821703i | \(0.693024\pi\) | |||||||
\(884\) | −6.62348 | − | 11.4722i | −0.222772 | − | 0.385852i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.3117 | − | 26.5207i | 0.514408 | − | 0.890981i | ||||
\(887\) | 11.4277 | 0.383703 | 0.191852 | − | 0.981424i | \(-0.438551\pi\) | ||||
0.191852 | + | 0.981424i | \(0.438551\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8.75305 | −0.293403 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.613616 | + | 1.06281i | 0.0205454 | + | 0.0355856i | ||||
\(893\) | −28.0000 | −0.936984 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.50000 | − | 12.9904i | −0.250278 | − | 0.433495i | ||||
\(899\) | −13.0375 | − | 22.5816i | −0.434824 | − | 0.753137i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.06427 | − | 7.03952i | 0.135400 | − | 0.234521i | ||||
\(902\) | 4.69776 | − | 8.13677i | 0.156418 | − | 0.270925i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.81174 | − | 15.2624i | −0.293074 | − | 0.507619i | ||||
\(905\) | −4.37652 | −0.145481 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.6235 | 0.950427 | 0.475213 | − | 0.879871i | \(-0.342371\pi\) | ||||
0.475213 | + | 0.879871i | \(0.342371\pi\) | |||||||
\(908\) | 1.13159 | − | 1.95997i | 0.0375531 | − | 0.0650438i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.4352 | − | 44.0551i | 0.842706 | − | 1.45961i | −0.0448922 | − | 0.998992i | \(-0.514294\pi\) |
0.887598 | − | 0.460618i | \(-0.152372\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.9066 | + | 31.0152i | −0.592623 | + | 1.02645i | ||||
\(914\) | −5.50000 | + | 9.52628i | −0.181924 | + | 0.315101i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.75746 | + | 6.50812i | −0.124150 | + | 0.215034i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.6822 | − | 42.7508i | 0.814189 | − | 1.41022i | −0.0957190 | − | 0.995408i | \(-0.530515\pi\) |
0.909908 | − | 0.414809i | \(-0.136152\pi\) | |||||||
\(920\) | 2.22342 | 0.0733041 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.84085 | −0.0606251 | ||||||||
\(923\) | 1.22723 | + | 2.12563i | 0.0403948 | + | 0.0699659i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.8704 | − | 24.0243i | 0.456057 | − | 0.789914i | ||||
\(926\) | −17.8117 | + | 30.8508i | −0.585330 | + | 1.01382i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.00000 | − | 3.46410i | −0.0656532 | − | 0.113715i | ||||
\(929\) | −17.7154 | − | 30.6839i | −0.581222 | − | 1.00671i | −0.995335 | − | 0.0964805i | \(-0.969241\pi\) |
0.414113 | − | 0.910226i | \(-0.364092\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8.50000 | + | 14.7224i | 0.278427 | + | 0.482249i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.32364 | 0.239637 | ||||||||
\(935\) | 2.88262 | + | 4.99285i | 0.0942719 | + | 0.163284i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.6205 | −0.771647 | −0.385824 | − | 0.922573i | \(-0.626083\pi\) | ||||
−0.385824 | + | 0.922573i | \(0.626083\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.49390 | 0.211808 | ||||||||
\(941\) | 26.5730 | − | 46.0258i | 0.866256 | − | 1.50040i | 0.000461671 | − | 1.00000i | \(-0.499853\pi\) |
0.865794 | − | 0.500400i | \(-0.166814\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.68170 | + | 6.37688i | 0.119893 | + | 0.207660i | ||||
\(944\) | 12.2326 | 0.398136 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.1296 | −0.394366 | ||||||||
\(947\) | −10.1822 | − | 17.6360i | −0.330876 | − | 0.573094i | 0.651808 | − | 0.758384i | \(-0.274011\pi\) |
−0.982684 | + | 0.185290i | \(0.940677\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.8704 | + | 41.3448i | −0.774867 | + | 1.34211i | ||||
\(950\) | 12.2326 | 0.396877 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.623475 | −0.0201963 | −0.0100982 | − | 0.999949i | \(-0.503214\pi\) | ||||
−0.0100982 | + | 0.999949i | \(0.503214\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.79341 | + | 8.30243i | 0.155111 | + | 0.268660i | ||||
\(956\) | −2.37652 | −0.0768623 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.74597 | + | 13.4164i | 0.250261 | + | 0.433464i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.74695 | − | 9.95401i | −0.185386 | − | 0.321097i | ||||
\(962\) | 19.5562 | + | 33.8723i | 0.630517 | + | 1.09209i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.08415 | + | 7.07395i | −0.131542 | + | 0.227837i | ||||
\(965\) | 8.43535 | − | 14.6105i | 0.271543 | − | 0.470327i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.0587 | + | 38.2068i | 0.709360 | + | 1.22865i | 0.965095 | + | 0.261900i | \(0.0843491\pi\) |
−0.255735 | + | 0.966747i | \(0.582318\pi\) | |||||||
\(968\) | 10.3765 | 0.333514 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.0000 | 0.321081 | ||||||||
\(971\) | 27.3779 | − | 47.4200i | 0.878600 | − | 1.52178i | 0.0257219 | − | 0.999669i | \(-0.491812\pi\) |
0.852878 | − | 0.522110i | \(-0.174855\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.81174 | − | 4.87007i | 0.0900939 | − | 0.156047i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.56618 | − | 6.17680i | 0.114150 | − | 0.197714i | ||||
\(977\) | 15.6883 | − | 27.1729i | 0.501912 | − | 0.869337i | −0.498086 | − | 0.867128i | \(-0.665963\pi\) |
0.999998 | − | 0.00220917i | \(-0.000703202\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.9762 | − | 57.1165i | 1.05393 | − | 1.82545i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.55869 | − | 13.0920i | 0.241207 | − | 0.417784i | ||||
\(983\) | −28.5294 | −0.909947 | −0.454973 | − | 0.890505i | \(-0.650351\pi\) | ||||
−0.454973 | + | 0.890505i | \(0.650351\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.12854 | 0.258997 | ||||||||
\(986\) | 4.06427 | + | 7.03952i | 0.129433 | + | 0.224184i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.62348 | + | 14.9363i | −0.274349 | + | 0.475187i | ||||
\(989\) | 4.75305 | − | 8.23252i | 0.151138 | − | 0.261779i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.4939 | + | 38.9606i | 0.714542 | + | 1.23762i | 0.963136 | + | 0.269016i | \(0.0866984\pi\) |
−0.248593 | + | 0.968608i | \(0.579968\pi\) | |||||||
\(992\) | −3.25937 | − | 5.64539i | −0.103485 | − | 0.179241i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.37652 | + | 11.0445i | 0.202149 | + | 0.350133i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.06046 | −0.160266 | −0.0801332 | − | 0.996784i | \(-0.525535\pi\) | ||||
−0.0801332 | + | 0.996784i | \(0.525535\pi\) | |||||||
\(998\) | −9.31174 | − | 16.1284i | −0.294758 | − | 0.510536i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2646.2.h.r.667.3 | 8 | ||
3.2 | odd | 2 | 882.2.h.s.79.3 | 8 | |||
7.2 | even | 3 | 2646.2.f.p.883.2 | 8 | |||
7.3 | odd | 6 | 2646.2.e.s.2125.3 | 8 | |||
7.4 | even | 3 | 2646.2.e.s.2125.2 | 8 | |||
7.5 | odd | 6 | 2646.2.f.p.883.3 | 8 | |||
7.6 | odd | 2 | inner | 2646.2.h.r.667.2 | 8 | ||
9.4 | even | 3 | 2646.2.e.s.1549.2 | 8 | |||
9.5 | odd | 6 | 882.2.e.r.373.4 | 8 | |||
21.2 | odd | 6 | 882.2.f.r.295.1 | ✓ | 8 | ||
21.5 | even | 6 | 882.2.f.r.295.4 | yes | 8 | ||
21.11 | odd | 6 | 882.2.e.r.655.3 | 8 | |||
21.17 | even | 6 | 882.2.e.r.655.2 | 8 | |||
21.20 | even | 2 | 882.2.h.s.79.2 | 8 | |||
63.2 | odd | 6 | 7938.2.a.ch.1.2 | 4 | |||
63.4 | even | 3 | inner | 2646.2.h.r.361.3 | 8 | ||
63.5 | even | 6 | 882.2.f.r.589.4 | yes | 8 | ||
63.13 | odd | 6 | 2646.2.e.s.1549.3 | 8 | |||
63.16 | even | 3 | 7938.2.a.cq.1.3 | 4 | |||
63.23 | odd | 6 | 882.2.f.r.589.1 | yes | 8 | ||
63.31 | odd | 6 | inner | 2646.2.h.r.361.2 | 8 | ||
63.32 | odd | 6 | 882.2.h.s.67.3 | 8 | |||
63.40 | odd | 6 | 2646.2.f.p.1765.3 | 8 | |||
63.41 | even | 6 | 882.2.e.r.373.1 | 8 | |||
63.47 | even | 6 | 7938.2.a.ch.1.3 | 4 | |||
63.58 | even | 3 | 2646.2.f.p.1765.2 | 8 | |||
63.59 | even | 6 | 882.2.h.s.67.2 | 8 | |||
63.61 | odd | 6 | 7938.2.a.cq.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.2.e.r.373.1 | 8 | 63.41 | even | 6 | |||
882.2.e.r.373.4 | 8 | 9.5 | odd | 6 | |||
882.2.e.r.655.2 | 8 | 21.17 | even | 6 | |||
882.2.e.r.655.3 | 8 | 21.11 | odd | 6 | |||
882.2.f.r.295.1 | ✓ | 8 | 21.2 | odd | 6 | ||
882.2.f.r.295.4 | yes | 8 | 21.5 | even | 6 | ||
882.2.f.r.589.1 | yes | 8 | 63.23 | odd | 6 | ||
882.2.f.r.589.4 | yes | 8 | 63.5 | even | 6 | ||
882.2.h.s.67.2 | 8 | 63.59 | even | 6 | |||
882.2.h.s.67.3 | 8 | 63.32 | odd | 6 | |||
882.2.h.s.79.2 | 8 | 21.20 | even | 2 | |||
882.2.h.s.79.3 | 8 | 3.2 | odd | 2 | |||
2646.2.e.s.1549.2 | 8 | 9.4 | even | 3 | |||
2646.2.e.s.1549.3 | 8 | 63.13 | odd | 6 | |||
2646.2.e.s.2125.2 | 8 | 7.4 | even | 3 | |||
2646.2.e.s.2125.3 | 8 | 7.3 | odd | 6 | |||
2646.2.f.p.883.2 | 8 | 7.2 | even | 3 | |||
2646.2.f.p.883.3 | 8 | 7.5 | odd | 6 | |||
2646.2.f.p.1765.2 | 8 | 63.58 | even | 3 | |||
2646.2.f.p.1765.3 | 8 | 63.40 | odd | 6 | |||
2646.2.h.r.361.2 | 8 | 63.31 | odd | 6 | inner | ||
2646.2.h.r.361.3 | 8 | 63.4 | even | 3 | inner | ||
2646.2.h.r.667.2 | 8 | 7.6 | odd | 2 | inner | ||
2646.2.h.r.667.3 | 8 | 1.1 | even | 1 | trivial | ||
7938.2.a.ch.1.2 | 4 | 63.2 | odd | 6 | |||
7938.2.a.ch.1.3 | 4 | 63.47 | even | 6 | |||
7938.2.a.cq.1.2 | 4 | 63.61 | odd | 6 | |||
7938.2.a.cq.1.3 | 4 | 63.16 | even | 3 |