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 | 667.4 | ||
Root | \(-1.62968 - 0.586627i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.667 |
Dual form | 2646.2.h.r.361.4 |
$q$-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 | ||||
\(5\) | 3.25937 | 1.45763 | 0.728817 | − | 0.684709i | \(-0.240071\pi\) | ||||
0.728817 | + | 0.684709i | \(0.240071\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.62968 | − | 2.82269i | −0.515351 | − | 0.892615i | ||||
\(11\) | −5.62348 | −1.69554 | −0.847771 | − | 0.530363i | \(-0.822056\pi\) | ||||
−0.847771 | + | 0.530363i | \(0.822056\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.613616 | + | 1.06281i | 0.170186 | + | 0.294772i | 0.938485 | − | 0.345320i | \(-0.112230\pi\) |
−0.768298 | + | 0.640092i | \(0.778896\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.95256 | − | 5.11398i | −0.716101 | − | 1.24032i | −0.962533 | − | 0.271163i | \(-0.912592\pi\) |
0.246433 | − | 0.969160i | \(-0.420742\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.32288 | + | 2.29129i | −0.303488 | + | 0.525657i | −0.976924 | − | 0.213589i | \(-0.931485\pi\) |
0.673435 | + | 0.739246i | \(0.264818\pi\) | |||||||
\(20\) | −1.62968 | + | 2.82269i | −0.364408 | + | 0.631174i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.81174 | + | 4.87007i | 0.599464 | + | 1.03830i | ||||
\(23\) | −6.62348 | −1.38109 | −0.690545 | − | 0.723289i | \(-0.742629\pi\) | ||||
−0.690545 | + | 0.723289i | \(0.742629\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.62348 | 1.12470 | ||||||||
\(26\) | 0.613616 | − | 1.06281i | 0.120340 | − | 0.208435i | ||||
\(27\) | 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 | ||||||||
\(31\) | −0.613616 | + | 1.06281i | −0.110209 | + | 0.190887i | −0.915854 | − | 0.401511i | \(-0.868485\pi\) |
0.805646 | + | 0.592398i | \(0.201819\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.95256 | + | 5.11398i | −0.506360 | + | 0.877041i | ||||
\(35\) | 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 | ||||||||
\(40\) | 3.25937 | 0.515351 | ||||||||
\(41\) | −2.95256 | − | 5.11398i | −0.461112 | − | 0.798670i | 0.537904 | − | 0.843006i | \(-0.319216\pi\) |
−0.999017 | + | 0.0443359i | \(0.985883\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.81174 | + | 6.60212i | −0.581285 | + | 1.00681i | 0.414043 | + | 0.910257i | \(0.364116\pi\) |
−0.995327 | + | 0.0965570i | \(0.969217\pi\) | |||||||
\(44\) | 2.81174 | − | 4.87007i | 0.423885 | − | 0.734191i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.31174 | + | 5.73610i | 0.488289 | + | 0.845742i | ||||
\(47\) | 5.29150 | + | 9.16515i | 0.771845 | + | 1.33687i | 0.936551 | + | 0.350532i | \(0.113999\pi\) |
−0.164706 | + | 0.986343i | \(0.552667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.81174 | − | 4.87007i | −0.397640 | − | 0.688732i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.22723 | −0.170186 | ||||||||
\(53\) | −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 | ||||||||
\(55\) | −18.3290 | −2.47148 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.00000 | 0.525226 | ||||||||
\(59\) | −7.43916 | + | 12.8850i | −0.968496 | + | 1.67748i | −0.268582 | + | 0.963257i | \(0.586555\pi\) |
−0.699914 | + | 0.714227i | \(0.746778\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.24330 | + | 3.88551i | 0.287225 | + | 0.497488i | 0.973146 | − | 0.230187i | \(-0.0739339\pi\) |
−0.685921 | + | 0.727676i | \(0.740601\pi\) | |||||||
\(62\) | 1.22723 | 0.155859 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.00000 | + | 3.46410i | 0.248069 | + | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.81174 | − | 4.87007i | 0.343508 | − | 0.594974i | −0.641573 | − | 0.767062i | \(-0.721718\pi\) |
0.985082 | + | 0.172088i | \(0.0550513\pi\) | |||||||
\(68\) | 5.90512 | 0.716101 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.6235 | 1.26077 | 0.630387 | − | 0.776281i | \(-0.282896\pi\) | ||||
0.630387 | + | 0.776281i | \(0.282896\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.59831 | − | 9.69656i | −0.655233 | − | 1.13490i | −0.981835 | − | 0.189735i | \(-0.939237\pi\) |
0.326603 | − | 0.945162i | \(-0.394096\pi\) | |||||||
\(74\) | 6.00000 | 0.697486 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.32288 | − | 2.29129i | −0.151744 | − | 0.262829i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.68826 | − | 2.92416i | −0.189944 | − | 0.328993i | 0.755287 | − | 0.655394i | \(-0.227497\pi\) |
−0.945231 | + | 0.326401i | \(0.894164\pi\) | |||||||
\(80\) | −1.62968 | − | 2.82269i | −0.182204 | − | 0.315587i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.95256 | + | 5.11398i | −0.326056 | + | 0.564745i | ||||
\(83\) | −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 | ||||||||
\(85\) | −9.62348 | − | 16.6683i | −1.04381 | − | 1.80794i | ||||
\(86\) | 7.62348 | 0.822060 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.62348 | −0.599464 | ||||||||
\(89\) | 4.48660 | − | 7.77102i | 0.475579 | − | 0.823726i | −0.524030 | − | 0.851700i | \(-0.675572\pi\) |
0.999609 | + | 0.0279735i | \(0.00890540\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.31174 | − | 5.73610i | 0.345273 | − | 0.598030i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.29150 | − | 9.16515i | 0.545777 | − | 0.945313i | ||||
\(95\) | −4.31174 | + | 7.46815i | −0.442375 | + | 0.766216i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.53404 | + | 2.65704i | −0.155758 | + | 0.269781i | −0.933335 | − | 0.359007i | \(-0.883115\pi\) |
0.777577 | + | 0.628788i | \(0.216449\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.81174 | + | 4.87007i | −0.281174 | + | 0.487007i | ||||
\(101\) | −12.6151 | −1.25525 | −0.627627 | − | 0.778514i | \(-0.715974\pi\) | ||||
−0.627627 | + | 0.778514i | \(0.715974\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.35577 | −0.921852 | −0.460926 | − | 0.887439i | \(-0.652483\pi\) | ||||
−0.460926 | + | 0.887439i | \(0.652483\pi\) | |||||||
\(104\) | 0.613616 | + | 1.06281i | 0.0601700 | + | 0.104217i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.00000 | + | 3.46410i | −0.194257 | + | 0.336463i | ||||
\(107\) | 0.188262 | − | 0.326080i | 0.0182000 | − | 0.0315233i | −0.856782 | − | 0.515679i | \(-0.827540\pi\) |
0.874982 | + | 0.484156i | \(0.160873\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.62348 | − | 9.74015i | −0.538631 | − | 0.932937i | −0.998978 | − | 0.0451975i | \(-0.985608\pi\) |
0.460347 | − | 0.887739i | \(-0.347725\pi\) | |||||||
\(110\) | 9.16449 | + | 15.8734i | 0.873799 | + | 1.51347i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.68826 | − | 6.38826i | −0.346963 | − | 0.600957i | 0.638746 | − | 0.769418i | \(-0.279454\pi\) |
−0.985708 | + | 0.168461i | \(0.946120\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −21.5883 | −2.01312 | ||||||||
\(116\) | −2.00000 | − | 3.46410i | −0.185695 | − | 0.321634i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.8783 | 1.36966 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.6235 | 1.87486 | ||||||||
\(122\) | 2.24330 | − | 3.88551i | 0.203099 | − | 0.351777i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.613616 | − | 1.06281i | −0.0551043 | − | 0.0954435i | ||||
\(125\) | 2.03214 | 0.181760 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.37652 | 0.122147 | 0.0610734 | − | 0.998133i | \(-0.480548\pi\) | ||||
0.0610734 | + | 0.998133i | \(0.480548\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | − | 3.46410i | 0.175412 | − | 0.303822i | ||||
\(131\) | 5.71383 | 0.499220 | 0.249610 | − | 0.968346i | \(-0.419698\pi\) | ||||
0.249610 | + | 0.968346i | \(0.419698\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.62348 | −0.485794 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.95256 | − | 5.11398i | −0.253180 | − | 0.438520i | ||||
\(137\) | 20.8704 | 1.78308 | 0.891540 | − | 0.452941i | \(-0.149625\pi\) | ||||
0.891540 | + | 0.452941i | \(0.149625\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.96863 | − | 6.87386i | −0.336615 | − | 0.583033i | 0.647179 | − | 0.762338i | \(-0.275949\pi\) |
−0.983794 | + | 0.179305i | \(0.942615\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.31174 | − | 9.20020i | −0.445751 | − | 0.772064i | ||||
\(143\) | −3.45065 | − | 5.97671i | −0.288558 | − | 0.499798i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.51873 | + | 11.2908i | −0.541351 | + | 0.937648i | ||||
\(146\) | −5.59831 | + | 9.69656i | −0.463319 | + | 0.802493i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.00000 | − | 5.19615i | −0.246598 | − | 0.427121i | ||||
\(149\) | 5.24695 | 0.429847 | 0.214923 | − | 0.976631i | \(-0.431050\pi\) | ||||
0.214923 | + | 0.976631i | \(0.431050\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.62348 | −0.701768 | −0.350884 | − | 0.936419i | \(-0.614119\pi\) | ||||
−0.350884 | + | 0.936419i | \(0.614119\pi\) | |||||||
\(152\) | −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 | ||||||||
\(157\) | −8.14842 | + | 14.1135i | −0.650315 | + | 1.12638i | 0.332732 | + | 0.943021i | \(0.392030\pi\) |
−0.983046 | + | 0.183356i | \(0.941304\pi\) | |||||||
\(158\) | −1.68826 | + | 2.92416i | −0.134311 | + | 0.232633i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.62968 | + | 2.82269i | −0.128838 | + | 0.223154i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.623475 | − | 1.07989i | 0.0488344 | − | 0.0845836i | −0.840575 | − | 0.541695i | \(-0.817783\pi\) |
0.889409 | + | 0.457112i | \(0.151116\pi\) | |||||||
\(164\) | 5.90512 | 0.461112 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.74597 | 0.601204 | ||||||||
\(167\) | −3.25937 | − | 5.64539i | −0.252217 | − | 0.436853i | 0.711919 | − | 0.702262i | \(-0.247826\pi\) |
−0.964136 | + | 0.265409i | \(0.914493\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.74695 | − | 9.95401i | 0.442073 | − | 0.765693i | ||||
\(170\) | −9.62348 | + | 16.6683i | −0.738087 | + | 1.27840i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.81174 | − | 6.60212i | −0.290642 | − | 0.503407i | ||||
\(173\) | 0.613616 | + | 1.06281i | 0.0466524 | + | 0.0808043i | 0.888409 | − | 0.459053i | \(-0.151811\pi\) |
−0.841756 | + | 0.539858i | \(0.818478\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.81174 | + | 4.87007i | 0.211943 | + | 0.367096i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.97320 | −0.672570 | ||||||||
\(179\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.48660 | −0.333486 | −0.166743 | − | 0.986000i | \(-0.553325\pi\) | ||||
−0.166743 | + | 0.986000i | \(0.553325\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.62348 | −0.488289 | ||||||||
\(185\) | −9.77810 | + | 16.9362i | −0.718900 | + | 1.24517i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.6036 | + | 28.7584i | 1.21418 | + | 2.10302i | ||||
\(188\) | −10.5830 | −0.771845 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.62348 | 0.625613 | ||||||||
\(191\) | 2.68826 | + | 4.65621i | 0.194516 | + | 0.336911i | 0.946742 | − | 0.321994i | \(-0.104353\pi\) |
−0.752226 | + | 0.658905i | \(0.771020\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.74695 | + | 11.6861i | −0.485656 | + | 0.841181i | −0.999864 | − | 0.0164844i | \(-0.994753\pi\) |
0.514208 | + | 0.857666i | \(0.328086\pi\) | |||||||
\(194\) | 3.06808 | 0.220275 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.24695 | −0.516324 | −0.258162 | − | 0.966102i | \(-0.583117\pi\) | ||||
−0.258162 | + | 0.966102i | \(0.583117\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.10022 | + | 8.83383i | 0.361545 | + | 0.626214i | 0.988215 | − | 0.153071i | \(-0.0489162\pi\) |
−0.626671 | + | 0.779284i | \(0.715583\pi\) | |||||||
\(200\) | 5.62348 | 0.397640 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.30757 | + | 10.9250i | 0.443799 | + | 0.768683i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.62348 | − | 16.6683i | −0.672133 | − | 1.16417i | ||||
\(206\) | 4.67789 | + | 8.10234i | 0.325924 | + | 0.564517i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.613616 | − | 1.06281i | 0.0425466 | − | 0.0736929i | ||||
\(209\) | 7.43916 | − | 12.8850i | 0.514577 | − | 0.891274i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.62348 | + | 4.54399i | 0.180607 | + | 0.312821i | 0.942088 | − | 0.335367i | \(-0.108860\pi\) |
−0.761480 | + | 0.648188i | \(0.775527\pi\) | |||||||
\(212\) | 4.00000 | 0.274721 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.376525 | −0.0257387 | ||||||||
\(215\) | −12.4239 | + | 21.5187i | −0.847300 | + | 1.46757i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −5.62348 | + | 9.74015i | −0.380870 | + | 0.659686i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.16449 | − | 15.8734i | 0.617870 | − | 1.07018i | ||||
\(221\) | 3.62348 | − | 6.27604i | 0.243741 | − | 0.422172i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.25937 | − | 5.64539i | 0.218263 | − | 0.378043i | −0.736014 | − | 0.676967i | \(-0.763294\pi\) |
0.954277 | + | 0.298923i | \(0.0966275\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.68826 | + | 6.38826i | −0.245340 | + | 0.424941i | ||||
\(227\) | −28.7207 | −1.90626 | −0.953130 | − | 0.302562i | \(-0.902158\pi\) | ||||
−0.953130 | + | 0.302562i | \(0.902158\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.8798 | −1.77627 | −0.888135 | − | 0.459583i | \(-0.847999\pi\) | ||||
−0.888135 | + | 0.459583i | \(0.847999\pi\) | |||||||
\(230\) | 10.7942 | + | 18.6961i | 0.711746 | + | 1.23278i | ||||
\(231\) | 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 | ||||||||
\(235\) | 17.2470 | + | 29.8726i | 1.12507 | + | 1.94867i | ||||
\(236\) | −7.43916 | − | 12.8850i | −0.484248 | − | 0.838742i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.31174 | + | 10.9323i | 0.408272 | + | 0.707148i | 0.994696 | − | 0.102856i | \(-0.0327980\pi\) |
−0.586424 | + | 0.810004i | \(0.699465\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.6886 | 1.71916 | 0.859580 | − | 0.511000i | \(-0.170725\pi\) | ||||
0.859580 | + | 0.511000i | \(0.170725\pi\) | |||||||
\(242\) | −10.3117 | − | 17.8605i | −0.662864 | − | 1.14811i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.48660 | −0.287225 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.24695 | −0.206599 | ||||||||
\(248\) | −0.613616 | + | 1.06281i | −0.0389647 | + | 0.0674888i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.01607 | − | 1.75988i | −0.0642618 | − | 0.111305i | ||||
\(251\) | 5.10022 | 0.321923 | 0.160961 | − | 0.986961i | \(-0.448541\pi\) | ||||
0.160961 | + | 0.986961i | \(0.448541\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.2470 | 2.34170 | ||||||||
\(254\) | −0.688262 | − | 1.19211i | −0.0431854 | − | 0.0747993i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 0.996190 | 0.0621407 | 0.0310703 | − | 0.999517i | \(-0.490108\pi\) | ||||
0.0310703 | + | 0.999517i | \(0.490108\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.00000 | −0.248069 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.85692 | − | 4.94832i | −0.176501 | − | 0.305708i | ||||
\(263\) | 3.37652 | 0.208205 | 0.104103 | − | 0.994567i | \(-0.466803\pi\) | ||||
0.104103 | + | 0.994567i | \(0.466803\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.51873 | − | 11.2908i | −0.400443 | − | 0.693587i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.81174 | + | 4.87007i | 0.171754 | + | 0.297487i | ||||
\(269\) | 12.0214 | + | 20.8217i | 0.732958 | + | 1.26952i | 0.955614 | + | 0.294623i | \(0.0951941\pi\) |
−0.222656 | + | 0.974897i | \(0.571473\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.41852 | + | 2.45695i | −0.0861689 | + | 0.149249i | −0.905889 | − | 0.423516i | \(-0.860796\pi\) |
0.819720 | + | 0.572765i | \(0.194129\pi\) | |||||||
\(272\) | −2.95256 | + | 5.11398i | −0.179025 | + | 0.310081i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.4352 | − | 18.0743i | −0.630414 | − | 1.09191i | ||||
\(275\) | −31.6235 | −1.90697 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.4939 | −1.71203 | −0.856016 | − | 0.516949i | \(-0.827068\pi\) | ||||
−0.856016 | + | 0.516949i | \(0.827068\pi\) | |||||||
\(278\) | −3.96863 | + | 6.87386i | −0.238022 | + | 0.412267i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.9352 | + | 22.4044i | −0.771650 | + | 1.33654i | 0.165008 | + | 0.986292i | \(0.447235\pi\) |
−0.936658 | + | 0.350245i | \(0.886098\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.66182 | + | 6.34246i | −0.217673 | + | 0.377020i | −0.954096 | − | 0.299501i | \(-0.903180\pi\) |
0.736423 | + | 0.676521i | \(0.236513\pi\) | |||||||
\(284\) | −5.31174 | + | 9.20020i | −0.315194 | + | 0.545931i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.45065 | + | 5.97671i | −0.204041 | + | 0.353410i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.93521 | + | 15.4762i | −0.525601 | + | 0.910367i | ||||
\(290\) | 13.0375 | 0.765587 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.1966 | 0.655233 | ||||||||
\(293\) | 12.8263 | + | 22.2158i | 0.749321 | + | 1.29786i | 0.948149 | + | 0.317827i | \(0.102953\pi\) |
−0.198828 | + | 0.980034i | \(0.563713\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.2470 | + | 41.9970i | −1.41171 | + | 2.44516i | ||||
\(296\) | −3.00000 | + | 5.19615i | −0.174371 | + | 0.302020i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.62348 | − | 4.54399i | −0.151974 | − | 0.263226i | ||||
\(299\) | −4.06427 | − | 7.03952i | −0.235043 | − | 0.407106i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.31174 | + | 7.46815i | 0.248113 | + | 0.429744i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.64575 | 0.151744 | ||||||||
\(305\) | 7.31174 | + | 12.6643i | 0.418669 | + | 0.725156i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.2288 | 0.755005 | 0.377503 | − | 0.926009i | \(-0.376783\pi\) | ||||
0.377503 | + | 0.926009i | \(0.376783\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.00000 | 0.227185 | ||||||||
\(311\) | 10.3917 | − | 17.9990i | 0.589260 | − | 1.02063i | −0.405069 | − | 0.914286i | \(-0.632753\pi\) |
0.994330 | − | 0.106343i | \(-0.0339141\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.8898 | − | 18.8617i | −0.615529 | − | 1.06613i | −0.990292 | − | 0.139006i | \(-0.955609\pi\) |
0.374763 | − | 0.927121i | \(-0.377724\pi\) | |||||||
\(314\) | 16.2968 | 0.919684 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.37652 | 0.189944 | ||||||||
\(317\) | 3.62348 | + | 6.27604i | 0.203515 | + | 0.352498i | 0.949658 | − | 0.313287i | \(-0.101430\pi\) |
−0.746144 | + | 0.665785i | \(0.768097\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.2470 | − | 19.4803i | 0.629708 | − | 1.09069i | ||||
\(320\) | 3.25937 | 0.182204 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.6235 | 0.869313 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.45065 | + | 5.97671i | 0.191408 | + | 0.331528i | ||||
\(326\) | −1.24695 | −0.0690622 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.95256 | − | 5.11398i | −0.163028 | − | 0.282372i | ||||
\(329\) | 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 | ||||||||
\(334\) | −3.25937 | + | 5.64539i | −0.178345 | + | 0.308902i | ||||
\(335\) | 9.16449 | − | 15.8734i | 0.500709 | − | 0.867254i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.56479 | − | 2.71029i | −0.0852394 | − | 0.147639i | 0.820254 | − | 0.572000i | \(-0.193832\pi\) |
−0.905493 | + | 0.424361i | \(0.860499\pi\) | |||||||
\(338\) | −11.4939 | −0.625186 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 19.2470 | 1.04381 | ||||||||
\(341\) | 3.45065 | − | 5.97671i | 0.186863 | − | 0.323657i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.81174 | + | 6.60212i | −0.205515 | + | 0.355963i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.613616 | − | 1.06281i | 0.0329882 | − | 0.0571372i | ||||
\(347\) | −1.81174 | + | 3.13802i | −0.0972592 | + | 0.168458i | −0.910549 | − | 0.413401i | \(-0.864341\pi\) |
0.813290 | + | 0.581858i | \(0.197674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.6511 | − | 23.6444i | 0.730726 | − | 1.26565i | −0.225848 | − | 0.974163i | \(-0.572515\pi\) |
0.956573 | − | 0.291492i | \(-0.0941515\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.81174 | − | 4.87007i | 0.149866 | − | 0.259576i | ||||
\(353\) | 5.90512 | 0.314298 | 0.157149 | − | 0.987575i | \(-0.449770\pi\) | ||||
0.157149 | + | 0.987575i | \(0.449770\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 34.6258 | 1.83775 | ||||||||
\(356\) | 4.48660 | + | 7.77102i | 0.237789 | + | 0.411863i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.5587 | − | 26.9484i | 0.821156 | − | 1.42228i | −0.0836657 | − | 0.996494i | \(-0.526663\pi\) |
0.904822 | − | 0.425790i | \(-0.140004\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | + | 10.3923i | 0.315789 | + | 0.546963i | ||||
\(362\) | 2.24330 | + | 3.88551i | 0.117905 | + | 0.204218i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.2470 | − | 31.6046i | −0.955089 | − | 1.65426i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.90131 | −0.360245 | −0.180123 | − | 0.983644i | \(-0.557649\pi\) | ||||
−0.180123 | + | 0.983644i | \(0.557649\pi\) | |||||||
\(368\) | 3.31174 | + | 5.73610i | 0.172636 | + | 0.299015i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 19.5562 | 1.01668 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.2470 | 0.582345 | 0.291173 | − | 0.956671i | \(-0.405955\pi\) | ||||
0.291173 | + | 0.956671i | \(0.405955\pi\) | |||||||
\(374\) | 16.6036 | − | 28.7584i | 0.858554 | − | 1.48706i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.29150 | + | 9.16515i | 0.272888 | + | 0.472657i | ||||
\(377\) | −4.90893 | −0.252823 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.6235 | 0.802524 | 0.401262 | − | 0.915963i | \(-0.368572\pi\) | ||||
0.401262 | + | 0.915963i | \(0.368572\pi\) | |||||||
\(380\) | −4.31174 | − | 7.46815i | −0.221187 | − | 0.383108i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.68826 | − | 4.65621i | 0.137543 | − | 0.238232i | ||||
\(383\) | −27.6847 | −1.41462 | −0.707312 | − | 0.706901i | \(-0.750092\pi\) | ||||
−0.707312 | + | 0.706901i | \(0.750092\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.4939 | 0.686822 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.53404 | − | 2.65704i | −0.0778791 | − | 0.134891i | ||||
\(389\) | −37.2470 | −1.88850 | −0.944248 | − | 0.329236i | \(-0.893209\pi\) | ||||
−0.944248 | + | 0.329236i | \(0.893209\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.5562 | + | 33.8723i | 0.989000 | + | 1.71300i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.62348 | + | 6.27604i | 0.182548 | + | 0.316183i | ||||
\(395\) | −5.50267 | − | 9.53090i | −0.276869 | − | 0.479552i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.67789 | − | 8.10234i | 0.234776 | − | 0.406645i | −0.724431 | − | 0.689347i | \(-0.757898\pi\) |
0.959208 | + | 0.282702i | \(0.0912309\pi\) | |||||||
\(398\) | 5.10022 | − | 8.83383i | 0.255651 | − | 0.442800i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.81174 | − | 4.87007i | −0.140587 | − | 0.243504i | ||||
\(401\) | 15.0000 | 0.749064 | 0.374532 | − | 0.927214i | \(-0.377803\pi\) | ||||
0.374532 | + | 0.927214i | \(0.377803\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.50610 | −0.0750241 | ||||||||
\(404\) | 6.30757 | − | 10.9250i | 0.313813 | − | 0.543541i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.8704 | − | 29.2204i | 0.836236 | − | 1.44840i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.11171 | + | 1.92554i | −0.0549706 | + | 0.0952118i | −0.892201 | − | 0.451638i | \(-0.850840\pi\) |
0.837231 | + | 0.546850i | \(0.184173\pi\) | |||||||
\(410\) | −9.62348 | + | 16.6683i | −0.475270 | + | 0.823191i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.67789 | − | 8.10234i | 0.230463 | − | 0.399174i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.6235 | + | 21.8645i | −0.619662 | + | 1.07329i | ||||
\(416\) | −1.22723 | −0.0601700 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −14.8783 | −0.727722 | ||||||||
\(419\) | 0.402452 | + | 0.697067i | 0.0196610 | + | 0.0340539i | 0.875689 | − | 0.482876i | \(-0.160408\pi\) |
−0.856027 | + | 0.516930i | \(0.827075\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(422\) | 2.62348 | − | 4.54399i | 0.127709 | − | 0.221198i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.00000 | − | 3.46410i | −0.0971286 | − | 0.168232i | ||||
\(425\) | −16.6036 | − | 28.7584i | −0.805395 | − | 1.39499i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.188262 | + | 0.326080i | 0.00910000 | + | 0.0157617i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 24.8477 | 1.19826 | ||||||||
\(431\) | −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 | ||||||||
\(433\) | −7.13235 | −0.342759 | −0.171379 | − | 0.985205i | \(-0.554822\pi\) | ||||
−0.171379 | + | 0.985205i | \(0.554822\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.2470 | 0.538631 | ||||||||
\(437\) | 8.76203 | − | 15.1763i | 0.419145 | − | 0.725980i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.4919 | − | 26.8328i | −0.739390 | − | 1.28066i | −0.952770 | − | 0.303691i | \(-0.901781\pi\) |
0.213381 | − | 0.976969i | \(-0.431552\pi\) | |||||||
\(440\) | −18.3290 | −0.873799 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.24695 | −0.344702 | ||||||||
\(443\) | 10.1883 | + | 17.6466i | 0.484059 | + | 0.838415i | 0.999832 | − | 0.0183103i | \(-0.00582869\pi\) |
−0.515773 | + | 0.856725i | \(0.672495\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.6235 | − | 25.3286i | 0.693219 | − | 1.20069i | ||||
\(446\) | −6.51873 | −0.308671 | ||||||||
\(447\) | 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 | ||||||||
\(451\) | 16.6036 | + | 28.7584i | 0.781835 | + | 1.35418i | ||||
\(452\) | 7.37652 | 0.346963 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.3603 | + | 24.8728i | 0.673964 | + | 1.16734i | ||||
\(455\) | 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 | \(0.916159\pi\) | |||||||
\(458\) | 13.4399 | + | 23.2786i | 0.628006 | + | 1.08774i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.7942 | − | 18.6961i | 0.503281 | − | 0.871708i | ||||
\(461\) | 4.88905 | − | 8.46808i | 0.227706 | − | 0.394398i | −0.729422 | − | 0.684064i | \(-0.760211\pi\) |
0.957128 | + | 0.289666i | \(0.0935442\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.6883 | − | 21.9767i | −0.589674 | − | 1.02134i | −0.994275 | − | 0.106851i | \(-0.965923\pi\) |
0.404601 | − | 0.914493i | \(-0.367410\pi\) | |||||||
\(464\) | 4.00000 | 0.185695 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.0000 | −0.787510 | ||||||||
\(467\) | 5.59831 | − | 9.69656i | 0.259059 | − | 0.448703i | −0.706931 | − | 0.707282i | \(-0.749921\pi\) |
0.965990 | + | 0.258579i | \(0.0832543\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 17.2470 | − | 29.8726i | 0.795543 | − | 1.37792i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.43916 | + | 12.8850i | −0.342415 | + | 0.593080i | ||||
\(473\) | 21.4352 | − | 37.1269i | 0.985592 | − | 1.70710i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.43916 | + | 12.8850i | −0.341332 | + | 0.591204i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.31174 | − | 10.9323i | 0.288692 | − | 0.500029i | ||||
\(479\) | −15.4919 | −0.707845 | −0.353922 | − | 0.935275i | \(-0.615152\pi\) | ||||
−0.353922 | + | 0.935275i | \(0.615152\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.36339 | −0.335742 | ||||||||
\(482\) | −13.3443 | − | 23.1130i | −0.607815 | − | 1.05277i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.3117 | + | 17.8605i | −0.468715 | + | 0.811839i | ||||
\(485\) | −5.00000 | + | 8.66025i | −0.227038 | + | 0.393242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.31174 | − | 4.00405i | −0.104755 | − | 0.181441i | 0.808883 | − | 0.587969i | \(-0.200072\pi\) |
−0.913638 | + | 0.406529i | \(0.866739\pi\) | |||||||
\(488\) | 2.24330 | + | 3.88551i | 0.101549 | + | 0.175889i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.0587 | − | 31.2786i | −0.814977 | − | 1.41158i | −0.909344 | − | 0.416044i | \(-0.863416\pi\) |
0.0943671 | − | 0.995537i | \(-0.469917\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.6205 | 1.06381 | ||||||||
\(494\) | 1.62348 | + | 2.81194i | 0.0730436 | + | 0.126515i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.22723 | 0.0551043 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.37652 | 0.374985 | 0.187492 | − | 0.982266i | \(-0.439964\pi\) | ||||
0.187492 | + | 0.982266i | \(0.439964\pi\) | |||||||
\(500\) | −1.01607 | + | 1.75988i | −0.0454399 | + | 0.0787043i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.55011 | − | 4.41692i | −0.113817 | − | 0.197137i | ||||
\(503\) | −20.7834 | −0.926688 | −0.463344 | − | 0.886179i | \(-0.653350\pi\) | ||||
−0.463344 | + | 0.886179i | \(0.653350\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −41.1174 | −1.82970 | ||||||||
\(506\) | −18.6235 | − | 32.2568i | −0.827914 | − | 1.43399i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.688262 | + | 1.19211i | −0.0305367 | + | 0.0528911i | ||||
\(509\) | −16.7192 | −0.741064 | −0.370532 | − | 0.928820i | \(-0.620825\pi\) | ||||
−0.370532 | + | 0.928820i | \(0.620825\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.498095 | − | 0.862726i | −0.0219700 | − | 0.0380532i | ||||
\(515\) | −30.4939 | −1.34372 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −29.7566 | − | 51.5400i | −1.30870 | − | 2.26673i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.00000 | + | 3.46410i | 0.0877058 | + | 0.151911i | ||||
\(521\) | 15.5677 | + | 26.9640i | 0.682033 | + | 1.18132i | 0.974359 | + | 0.224998i | \(0.0722374\pi\) |
−0.292326 | + | 0.956319i | \(0.594429\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.11628 | + | 10.5937i | −0.267446 | + | 0.463231i | −0.968202 | − | 0.250171i | \(-0.919513\pi\) |
0.700755 | + | 0.713402i | \(0.252846\pi\) | |||||||
\(524\) | −2.85692 | + | 4.94832i | −0.124805 | + | 0.216169i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.68826 | − | 2.92416i | −0.0736117 | − | 0.127499i | ||||
\(527\) | 7.24695 | 0.315682 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.8704 | 0.907410 | ||||||||
\(530\) | −6.51873 | + | 11.2908i | −0.283156 | + | 0.490440i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.62348 | − | 6.27604i | 0.156950 | − | 0.271846i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.613616 | − | 1.06281i | 0.0265289 | − | 0.0459495i | ||||
\(536\) | 2.81174 | − | 4.87007i | 0.121449 | − | 0.210355i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.0214 | − | 20.8217i | 0.518279 | − | 0.897686i | ||||
\(539\) | 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 | \(0.194071\pi\) | |||||||
\(542\) | 2.83704 | 0.121861 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.90512 | 0.253180 | ||||||||
\(545\) | −18.3290 | − | 31.7467i | −0.785127 | − | 1.35988i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.81174 | + | 16.9944i | −0.419520 | + | 0.726629i | −0.995891 | − | 0.0905585i | \(-0.971135\pi\) |
0.576372 | + | 0.817188i | \(0.304468\pi\) | |||||||
\(548\) | −10.4352 | + | 18.0743i | −0.445770 | + | 0.772097i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 15.8117 | + | 27.3867i | 0.674215 | + | 1.16777i | ||||
\(551\) | −5.29150 | − | 9.16515i | −0.225426 | − | 0.390449i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 14.2470 | + | 24.6764i | 0.605295 | + | 1.04840i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.93725 | 0.336615 | ||||||||
\(557\) | 11.3765 | + | 19.7047i | 0.482039 | + | 0.834916i | 0.999787 | − | 0.0206171i | \(-0.00656308\pi\) |
−0.517749 | + | 0.855533i | \(0.673230\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.35577 | −0.395707 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 25.8704 | 1.09128 | ||||||||
\(563\) | 2.74139 | − | 4.74824i | 0.115536 | − | 0.200114i | −0.802458 | − | 0.596709i | \(-0.796475\pi\) |
0.917994 | + | 0.396595i | \(0.129808\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.0214 | − | 20.8217i | −0.505744 | − | 0.875975i | ||||
\(566\) | 7.32364 | 0.307835 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.6235 | 0.445751 | ||||||||
\(569\) | 14.4352 | + | 25.0025i | 0.605156 | + | 1.04816i | 0.992027 | + | 0.126027i | \(0.0402224\pi\) |
−0.386871 | + | 0.922134i | \(0.626444\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.18826 | − | 7.25428i | 0.175273 | − | 0.303582i | −0.764983 | − | 0.644051i | \(-0.777252\pi\) |
0.940256 | + | 0.340469i | \(0.110586\pi\) | |||||||
\(572\) | 6.90131 | 0.288558 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −37.2470 | −1.55331 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.24406 | + | 14.2791i | 0.343205 | + | 0.594448i | 0.985026 | − | 0.172406i | \(-0.0551542\pi\) |
−0.641821 | + | 0.766854i | \(0.721821\pi\) | |||||||
\(578\) | 17.8704 | 0.743312 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.51873 | − | 11.2908i | −0.270676 | − | 0.468824i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.2470 | + | 19.4803i | 0.465801 | + | 0.806791i | ||||
\(584\) | −5.59831 | − | 9.69656i | −0.231660 | − | 0.401246i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.8263 | − | 22.2158i | 0.529850 | − | 0.917727i | ||||
\(587\) | 1.51416 | − | 2.62261i | 0.0624962 | − | 0.108247i | −0.833084 | − | 0.553146i | \(-0.813427\pi\) |
0.895581 | + | 0.444899i | \(0.146761\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.62348 | − | 2.81194i | −0.0668941 | − | 0.115864i | ||||
\(590\) | 48.4939 | 1.99646 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.00000 | 0.246598 | ||||||||
\(593\) | 6.09641 | − | 10.5593i | 0.250349 | − | 0.433618i | −0.713273 | − | 0.700887i | \(-0.752788\pi\) |
0.963622 | + | 0.267269i | \(0.0861212\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.62348 | + | 4.54399i | −0.107462 | + | 0.186129i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.06427 | + | 7.03952i | −0.166200 | + | 0.287868i | ||||
\(599\) | −1.24695 | + | 2.15978i | −0.0509490 | + | 0.0882463i | −0.890375 | − | 0.455227i | \(-0.849558\pi\) |
0.839426 | + | 0.543474i | \(0.182891\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.8630 | + | 34.4037i | −0.810229 | + | 1.40336i | 0.102474 | + | 0.994736i | \(0.467324\pi\) |
−0.912704 | + | 0.408622i | \(0.866009\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.31174 | − | 7.46815i | 0.175442 | − | 0.303875i | ||||
\(605\) | 67.2195 | 2.73286 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.6847 | 1.12369 | 0.561845 | − | 0.827243i | \(-0.310092\pi\) | ||||
0.561845 | + | 0.827243i | \(0.310092\pi\) | |||||||
\(608\) | −1.32288 | − | 2.29129i | −0.0536497 | − | 0.0929240i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.31174 | − | 12.6643i | 0.296044 | − | 0.512763i | ||||
\(611\) | −6.49390 | + | 11.2478i | −0.262715 | + | 0.455036i | ||||
\(612\) | 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 | ||||||||
\(617\) | 20.0587 | + | 34.7427i | 0.807532 | + | 1.39869i | 0.914568 | + | 0.404432i | \(0.132531\pi\) |
−0.107036 | + | 0.994255i | \(0.534136\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.0122 | −1.36707 | −0.683533 | − | 0.729920i | \(-0.739557\pi\) | ||||
−0.683533 | + | 0.729920i | \(0.739557\pi\) | |||||||
\(620\) | −2.00000 | − | 3.46410i | −0.0803219 | − | 0.139122i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −20.7834 | −0.833340 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.4939 | −0.859756 | ||||||||
\(626\) | −10.8898 | + | 18.8617i | −0.435244 | + | 0.753866i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.14842 | − | 14.1135i | −0.325157 | − | 0.563189i | ||||
\(629\) | 35.4307 | 1.41271 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.6235 | 1.21910 | 0.609551 | − | 0.792747i | \(-0.291350\pi\) | ||||
0.609551 | + | 0.792747i | \(0.291350\pi\) | |||||||
\(632\) | −1.68826 | − | 2.92416i | −0.0671555 | − | 0.116317i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.62348 | − | 6.27604i | 0.143907 | − | 0.249254i | ||||
\(635\) | 4.48660 | 0.178045 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −22.4939 | −0.890542 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.62968 | − | 2.82269i | −0.0644189 | − | 0.111577i | ||||
\(641\) | 25.4939 | 1.00695 | 0.503474 | − | 0.864010i | \(-0.332055\pi\) | ||||
0.503474 | + | 0.864010i | \(0.332055\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.82554 | + | 11.8222i | 0.269173 | + | 0.466222i | 0.968649 | − | 0.248435i | \(-0.0799163\pi\) |
−0.699475 | + | 0.714657i | \(0.746583\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.81174 | − | 13.5303i | −0.307349 | − | 0.532344i | ||||
\(647\) | −17.5241 | − | 30.3526i | −0.688942 | − | 1.19328i | −0.972180 | − | 0.234233i | \(-0.924742\pi\) |
0.283238 | − | 0.959050i | \(-0.408591\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 41.8339 | − | 72.4585i | 1.64213 | − | 2.84424i | ||||
\(650\) | 3.45065 | − | 5.97671i | 0.135346 | − | 0.234426i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.623475 | + | 1.07989i | 0.0244172 | + | 0.0422918i | ||||
\(653\) | −39.2470 | −1.53585 | −0.767926 | − | 0.640539i | \(-0.778711\pi\) | ||||
−0.767926 | + | 0.640539i | \(0.778711\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.6235 | 0.727679 | ||||||||
\(656\) | −2.95256 | + | 5.11398i | −0.115278 | + | 0.199667i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.24695 | + | 9.08799i | −0.204392 | + | 0.354018i | −0.949939 | − | 0.312436i | \(-0.898855\pi\) |
0.745547 | + | 0.666453i | \(0.232188\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.43840 | − | 2.49138i | 0.0559471 | − | 0.0969033i | −0.836695 | − | 0.547669i | \(-0.815516\pi\) |
0.892643 | + | 0.450765i | \(0.148849\pi\) | |||||||
\(662\) | −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 | ||||||||
\(667\) | 13.2470 | − | 22.9444i | 0.512924 | − | 0.888410i | ||||
\(668\) | 6.51873 | 0.252217 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −18.3290 | −0.708110 | ||||||||
\(671\) | −12.6151 | − | 21.8501i | −0.487002 | − | 0.843512i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.68826 | + | 16.7806i | −0.373455 | + | 0.646843i | −0.990095 | − | 0.140403i | \(-0.955160\pi\) |
0.616639 | + | 0.787246i | \(0.288494\pi\) | |||||||
\(674\) | −1.56479 | + | 2.71029i | −0.0602733 | + | 0.104396i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.74695 | + | 9.95401i | 0.221037 | + | 0.382847i | ||||
\(677\) | −21.3971 | − | 37.0608i | −0.822356 | − | 1.42436i | −0.903924 | − | 0.427694i | \(-0.859326\pi\) |
0.0815682 | − | 0.996668i | \(-0.474007\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9.62348 | − | 16.6683i | −0.369043 | − | 0.639202i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.90131 | −0.264265 | ||||||||
\(683\) | −13.6822 | − | 23.6982i | −0.523533 | − | 0.906787i | −0.999625 | − | 0.0273907i | \(-0.991280\pi\) |
0.476091 | − | 0.879396i | \(-0.342053\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 68.0244 | 2.59908 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.62348 | 0.290642 | ||||||||
\(689\) | 2.45446 | − | 4.25126i | 0.0935076 | − | 0.161960i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.34352 | − | 12.7193i | −0.279360 | − | 0.483867i | 0.691865 | − | 0.722026i | \(-0.256789\pi\) |
−0.971226 | + | 0.238160i | \(0.923456\pi\) | |||||||
\(692\) | −1.22723 | −0.0466524 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.62348 | 0.137545 | ||||||||
\(695\) | −12.9352 | − | 22.4044i | −0.490661 | − | 0.849849i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.4352 | + | 30.1987i | −0.660406 | + | 1.14386i | ||||
\(698\) | −27.3022 | −1.03340 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.2470 | 0.802486 | 0.401243 | − | 0.915972i | \(-0.368578\pi\) | ||||
0.401243 | + | 0.915972i | \(0.368578\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.93725 | − | 13.7477i | −0.299359 | − | 0.518505i | ||||
\(704\) | −5.62348 | −0.211943 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.95256 | − | 5.11398i | −0.111121 | − | 0.192467i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.24695 | − | 16.0162i | −0.347277 | − | 0.601501i | 0.638488 | − | 0.769632i | \(-0.279560\pi\) |
−0.985765 | + | 0.168131i | \(0.946227\pi\) | |||||||
\(710\) | −17.3129 | − | 29.9868i | −0.649742 | − | 1.12539i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.48660 | − | 7.77102i | 0.168142 | − | 0.291231i | ||||
\(713\) | 4.06427 | − | 7.03952i | 0.152208 | − | 0.263632i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.2470 | − | 19.4803i | −0.420612 | − | 0.728522i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −31.1174 | −1.16129 | ||||||||
\(719\) | −5.90512 | + | 10.2280i | −0.220224 | + | 0.381439i | −0.954876 | − | 0.297005i | \(-0.904012\pi\) |
0.734652 | + | 0.678444i | \(0.237345\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.00000 | − | 10.3923i | 0.223297 | − | 0.386762i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.24330 | − | 3.88551i | 0.0833716 | − | 0.144404i | ||||
\(725\) | −11.2470 | + | 19.4803i | −0.417701 | + | 0.723480i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.2020 | − | 38.4549i | 0.823425 | − | 1.42621i | −0.0796922 | − | 0.996820i | \(-0.525394\pi\) |
0.903117 | − | 0.429394i | \(-0.141273\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −18.2470 | + | 31.6046i | −0.675350 | + | 1.16974i | ||||
\(731\) | 45.0175 | 1.66503 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.16830 | −0.301703 | −0.150851 | − | 0.988556i | \(-0.548202\pi\) | ||||
−0.150851 | + | 0.988556i | \(0.548202\pi\) | |||||||
\(734\) | 3.45065 | + | 5.97671i | 0.127366 | + | 0.220604i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.31174 | − | 5.73610i | 0.122072 | − | 0.211435i | ||||
\(737\) | −15.8117 | + | 27.3867i | −0.582433 | + | 1.00880i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.4352 | − | 18.0743i | −0.383866 | − | 0.664875i | 0.607746 | − | 0.794132i | \(-0.292074\pi\) |
−0.991611 | + | 0.129257i | \(0.958741\pi\) | |||||||
\(740\) | −9.77810 | − | 16.9362i | −0.359450 | − | 0.622586i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.6235 | + | 27.0607i | 0.573170 | + | 0.992759i | 0.996238 | + | 0.0866612i | \(0.0276198\pi\) |
−0.423068 | + | 0.906098i | \(0.639047\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.1017 | 0.626559 | ||||||||
\(746\) | −5.62348 | − | 9.74015i | −0.205890 | − | 0.356612i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −33.2073 | −1.21418 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.3765 | −0.415135 | −0.207568 | − | 0.978221i | \(-0.566555\pi\) | ||||
−0.207568 | + | 0.978221i | \(0.566555\pi\) | |||||||
\(752\) | 5.29150 | − | 9.16515i | 0.192961 | − | 0.334219i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.45446 | + | 4.25126i | 0.0893863 | + | 0.154822i | ||||
\(755\) | −28.1071 | −1.02292 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.7409 | 1.58979 | 0.794894 | − | 0.606748i | \(-0.207526\pi\) | ||||
0.794894 | + | 0.606748i | \(0.207526\pi\) | |||||||
\(758\) | −7.81174 | − | 13.5303i | −0.283735 | − | 0.491444i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.31174 | + | 7.46815i | −0.156403 | + | 0.270898i | ||||
\(761\) | 5.67408 | 0.205685 | 0.102843 | − | 0.994698i | \(-0.467206\pi\) | ||||
0.102843 | + | 0.994698i | \(0.467206\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5.37652 | −0.194516 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.8424 | + | 23.9757i | 0.500145 | + | 0.866277i | ||||
\(767\) | −18.2591 | −0.659300 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.422329 | + | 0.731495i | 0.0152296 | + | 0.0263784i | 0.873540 | − | 0.486753i | \(-0.161819\pi\) |
−0.858310 | + | 0.513131i | \(0.828485\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.74695 | − | 11.6861i | −0.242828 | − | 0.420591i | ||||
\(773\) | −6.72990 | − | 11.6565i | −0.242058 | − | 0.419256i | 0.719243 | − | 0.694759i | \(-0.244489\pi\) |
−0.961300 | + | 0.275503i | \(0.911156\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.45065 | + | 5.97671i | −0.123951 | + | 0.214690i | ||||
\(776\) | −1.53404 | + | 2.65704i | −0.0550688 | + | 0.0953820i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.6235 | + | 32.2568i | 0.667684 | + | 1.15646i | ||||
\(779\) | 15.6235 | 0.559769 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −59.7409 | −2.13770 | ||||||||
\(782\) | 19.5562 | − | 33.8723i | 0.699328 | − | 1.21127i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26.5587 | + | 46.0010i | −0.947920 | + | 1.64185i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.2288 | − | 22.9129i | 0.471554 | − | 0.816756i | −0.527916 | − | 0.849296i | \(-0.677026\pi\) |
0.999470 | + | 0.0325406i | \(0.0103598\pi\) | |||||||
\(788\) | 3.62348 | − | 6.27604i | 0.129081 | − | 0.223575i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.50267 | + | 9.53090i | −0.195776 | + | 0.339094i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.75305 | + | 4.76842i | −0.0977636 | + | 0.169332i | ||||
\(794\) | −9.35577 | −0.332024 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.2004 | −0.361545 | ||||||||
\(797\) | −8.76203 | − | 15.1763i | −0.310367 | − | 0.537572i | 0.668075 | − | 0.744094i | \(-0.267119\pi\) |
−0.978442 | + | 0.206523i | \(0.933785\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.2470 | − | 54.1213i | 1.10544 | − | 1.91467i | ||||
\(800\) | −2.81174 | + | 4.87007i | −0.0994099 | + | 0.172183i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.50000 | − | 12.9904i | −0.264834 | − | 0.458706i | ||||
\(803\) | 31.4820 | + | 54.5284i | 1.11097 | + | 1.92426i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.753049 | + | 1.30432i | 0.0265250 | + | 0.0459427i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.6151 | −0.443799 | ||||||||
\(809\) | 12.0587 | + | 20.8863i | 0.423961 | + | 0.734322i | 0.996323 | − | 0.0856793i | \(-0.0273061\pi\) |
−0.572362 | + | 0.820001i | \(0.693973\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.51493 | −0.263885 | −0.131942 | − | 0.991257i | \(-0.542121\pi\) | ||||
−0.131942 | + | 0.991257i | \(0.542121\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −33.7409 | −1.18262 | ||||||||
\(815\) | 2.03214 | − | 3.51976i | 0.0711826 | − | 0.123292i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.0849 | − | 17.4676i | −0.352826 | − | 0.611113i | ||||
\(818\) | 2.22342 | 0.0777401 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19.2470 | 0.672133 | ||||||||
\(821\) | −18.8704 | − | 32.6845i | −0.658582 | − | 1.14070i | −0.980983 | − | 0.194095i | \(-0.937823\pi\) |
0.322400 | − | 0.946603i | \(-0.395510\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.8704 | + | 22.2922i | −0.448635 | + | 0.777058i | −0.998297 | − | 0.0583284i | \(-0.981423\pi\) |
0.549663 | + | 0.835387i | \(0.314756\pi\) | |||||||
\(824\) | −9.35577 | −0.325924 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.2470 | −0.877922 | −0.438961 | − | 0.898506i | \(-0.644653\pi\) | ||||
−0.438961 | + | 0.898506i | \(0.644653\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.45446 | − | 4.25126i | −0.0852471 | − | 0.147652i | 0.820249 | − | 0.572006i | \(-0.193835\pi\) |
−0.905496 | + | 0.424354i | \(0.860501\pi\) | |||||||
\(830\) | 25.2470 | 0.876334 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.613616 | + | 1.06281i | 0.0212733 | + | 0.0368465i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.6235 | − | 18.4004i | −0.367641 | − | 0.636772i | ||||
\(836\) | 7.43916 | + | 12.8850i | 0.257289 | + | 0.445637i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.402452 | − | 0.697067i | 0.0139025 | − | 0.0240798i | ||||
\(839\) | −17.9066 | + | 31.0152i | −0.618206 | + | 1.07076i | 0.371607 | + | 0.928390i | \(0.378807\pi\) |
−0.989813 | + | 0.142374i | \(0.954526\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.50000 | + | 11.2583i | 0.224138 | + | 0.388218i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.24695 | −0.180607 | ||||||||
\(845\) | 18.7314 | − | 32.4438i | 0.644381 | − | 1.11610i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.00000 | + | 3.46410i | −0.0686803 | + | 0.118958i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −16.6036 | + | 28.7584i | −0.569500 | + | 0.986403i | ||||
\(851\) | 19.8704 | − | 34.4166i | 0.681149 | − | 1.17979i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.0857 | + | 27.8612i | −0.550763 | + | 0.953949i | 0.447457 | + | 0.894306i | \(0.352330\pi\) |
−0.998220 | + | 0.0596438i | \(0.981004\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.188262 | − | 0.326080i | 0.00643467 | − | 0.0111452i | ||||
\(857\) | 12.1928 | 0.416499 | 0.208249 | − | 0.978076i | \(-0.433223\pi\) | ||||
0.208249 | + | 0.978076i | \(0.433223\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.96939 | 0.340151 | 0.170076 | − | 0.985431i | \(-0.445599\pi\) | ||||
0.170076 | + | 0.985431i | \(0.445599\pi\) | |||||||
\(860\) | −12.4239 | − | 21.5187i | −0.423650 | − | 0.733783i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.00000 | + | 6.92820i | −0.136241 | + | 0.235976i | ||||
\(863\) | 18.9352 | − | 32.7968i | 0.644562 | − | 1.11641i | −0.339840 | − | 0.940483i | \(-0.610373\pi\) |
0.984402 | − | 0.175931i | \(-0.0562936\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.00000 | + | 3.46410i | 0.0680020 | + | 0.117783i | ||||
\(866\) | 3.56618 | + | 6.17680i | 0.121184 | + | 0.209896i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.49390 | + | 16.4439i | 0.322059 | + | 0.557822i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.90131 | 0.233842 | ||||||||
\(872\) | −5.62348 | − | 9.74015i | −0.190435 | − | 0.329843i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −17.5241 | −0.592760 | ||||||||
\(875\) | 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 | ||||||||
\(880\) | 9.16449 | + | 15.8734i | 0.308935 | + | 0.535091i | ||||
\(881\) | 4.90893 | 0.165386 | 0.0826930 | − | 0.996575i | \(-0.473648\pi\) | ||||
0.0826930 | + | 0.996575i | \(0.473648\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.12957 | −0.105319 | −0.0526593 | − | 0.998613i | \(-0.516770\pi\) | ||||
−0.0526593 | + | 0.998613i | \(0.516770\pi\) | |||||||
\(884\) | 3.62348 | + | 6.27604i | 0.121871 | + | 0.211086i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.1883 | − | 17.6466i | 0.342281 | − | 0.592849i | ||||
\(887\) | 27.3022 | 0.916717 | 0.458359 | − | 0.888767i | \(-0.348438\pi\) | ||||
0.458359 | + | 0.888767i | \(0.348438\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −29.2470 | −0.980360 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.25937 | + | 5.64539i | 0.109132 | + | 0.189022i | ||||
\(893\) | −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 | ||||
\(899\) | −2.45446 | − | 4.25126i | −0.0818610 | − | 0.141787i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.8102 | + | 20.4559i | −0.393456 | + | 0.681486i | ||||
\(902\) | 16.6036 | − | 28.7584i | 0.552841 | − | 0.957549i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.68826 | − | 6.38826i | −0.122670 | − | 0.212470i | ||||
\(905\) | −14.6235 | −0.486101 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.3765 | 0.610182 | 0.305091 | − | 0.952323i | \(-0.401313\pi\) | ||||
0.305091 | + | 0.952323i | \(0.401313\pi\) | |||||||
\(908\) | 14.3603 | − | 24.8728i | 0.476565 | − | 0.825434i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.0648 | − | 17.4327i | 0.333461 | − | 0.577572i | −0.649727 | − | 0.760168i | \(-0.725117\pi\) |
0.983188 | + | 0.182596i | \(0.0584500\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.7796 | − | 37.7234i | 0.720800 | − | 1.24846i | ||||
\(914\) | −5.50000 | + | 9.52628i | −0.181924 | + | 0.315101i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.4399 | − | 23.2786i | 0.444067 | − | 0.769147i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.1822 | + | 19.3681i | −0.368866 | + | 0.638894i | −0.989388 | − | 0.145294i | \(-0.953587\pi\) |
0.620523 | + | 0.784188i | \(0.286920\pi\) | |||||||
\(920\) | −21.5883 | −0.711746 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9.77810 | −0.322025 | ||||||||
\(923\) | 6.51873 | + | 11.2908i | 0.214567 | + | 0.371641i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.8704 | + | 29.2204i | −0.554696 | + | 0.960762i | ||||
\(926\) | −12.6883 | + | 21.9767i | −0.416962 | + | 0.722200i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.00000 | − | 3.46410i | −0.0656532 | − | 0.113715i | ||||
\(929\) | 6.09641 | + | 10.5593i | 0.200017 | + | 0.346439i | 0.948533 | − | 0.316677i | \(-0.102567\pi\) |
−0.748517 | + | 0.663116i | \(0.769234\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8.50000 | + | 14.7224i | 0.278427 | + | 0.482249i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −11.1966 | −0.366365 | ||||||||
\(935\) | 54.1174 | + | 93.7340i | 1.76983 | + | 3.06543i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.12854 | 0.265548 | 0.132774 | − | 0.991146i | \(-0.457612\pi\) | ||||
0.132774 | + | 0.991146i | \(0.457612\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −34.4939 | −1.12507 | ||||||||
\(941\) | −9.14461 | + | 15.8389i | −0.298106 | + | 0.516334i | −0.975703 | − | 0.219099i | \(-0.929688\pi\) |
0.677597 | + | 0.735434i | \(0.263021\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.5562 | + | 33.8723i | 0.636838 | + | 1.10304i | ||||
\(944\) | 14.8783 | 0.484248 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −42.8704 | −1.39384 | ||||||||
\(947\) | 25.6822 | + | 44.4828i | 0.834558 | + | 1.44550i | 0.894390 | + | 0.447289i | \(0.147610\pi\) |
−0.0598315 | + | 0.998208i | \(0.519056\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.87043 | − | 11.8999i | 0.223023 | − | 0.386288i | ||||
\(950\) | 14.8783 | 0.482716 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.62348 | 0.311735 | 0.155867 | − | 0.987778i | \(-0.450183\pi\) | ||||
0.155867 | + | 0.987778i | \(0.450183\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.76203 | + | 15.1763i | 0.283533 | + | 0.491093i | ||||
\(956\) | −12.6235 | −0.408272 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.74597 | + | 13.4164i | 0.250261 | + | 0.433464i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.7470 | + | 25.5425i | 0.475708 | + | 0.823951i | ||||
\(962\) | 3.68170 | + | 6.37688i | 0.118703 | + | 0.205599i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13.3443 | + | 23.1130i | −0.429790 | + | 0.744419i | ||||
\(965\) | −21.9908 | + | 38.0892i | −0.707909 | + | 1.22613i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.55869 | − | 6.16383i | −0.114440 | − | 0.198215i | 0.803116 | − | 0.595823i | \(-0.203174\pi\) |
−0.917556 | + | 0.397607i | \(0.869841\pi\) | |||||||
\(968\) | 20.6235 | 0.662864 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.0000 | 0.321081 | ||||||||
\(971\) | −21.5685 | + | 37.3577i | −0.692165 | + | 1.19886i | 0.278962 | + | 0.960302i | \(0.410010\pi\) |
−0.971127 | + | 0.238563i | \(0.923324\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.31174 | + | 4.00405i | −0.0740729 | + | 0.128298i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.24330 | − | 3.88551i | 0.0718063 | − | 0.124372i | ||||
\(977\) | 20.8117 | − | 36.0470i | 0.665826 | − | 1.15325i | −0.313234 | − | 0.949676i | \(-0.601412\pi\) |
0.979061 | − | 0.203569i | \(-0.0652542\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.2303 | + | 43.7001i | −0.806363 | + | 1.39666i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −18.0587 | + | 31.2786i | −0.576276 | + | 0.998139i | ||||
\(983\) | −17.9464 | −0.572401 | −0.286201 | − | 0.958170i | \(-0.592392\pi\) | ||||
−0.286201 | + | 0.958170i | \(0.592392\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.6205 | −0.752611 | ||||||||
\(986\) | −11.8102 | − | 20.4559i | −0.376115 | − | 0.651450i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.62348 | − | 2.81194i | 0.0516496 | − | 0.0894598i | ||||
\(989\) | 25.2470 | − | 43.7290i | 0.802806 | − | 1.39050i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.4939 | − | 32.0324i | −0.587478 | − | 1.01754i | −0.994561 | − | 0.104151i | \(-0.966787\pi\) |
0.407083 | − | 0.913391i | \(-0.366546\pi\) | |||||||
\(992\) | −0.613616 | − | 1.06281i | −0.0194823 | − | 0.0337444i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.6235 | + | 28.7927i | 0.527000 | + | 0.912790i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.9173 | 1.26419 | 0.632097 | − | 0.774889i | \(-0.282194\pi\) | ||||
0.632097 | + | 0.774889i | \(0.282194\pi\) | |||||||
\(998\) | −4.18826 | − | 7.25428i | −0.132577 | − | 0.229630i | ||||
\(999\) | 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.667.4 | 8 | ||
3.2 | odd | 2 | 882.2.h.s.79.4 | 8 | |||
7.2 | even | 3 | 2646.2.f.p.883.1 | 8 | |||
7.3 | odd | 6 | 2646.2.e.s.2125.4 | 8 | |||
7.4 | even | 3 | 2646.2.e.s.2125.1 | 8 | |||
7.5 | odd | 6 | 2646.2.f.p.883.4 | 8 | |||
7.6 | odd | 2 | inner | 2646.2.h.r.667.1 | 8 | ||
9.4 | even | 3 | 2646.2.e.s.1549.1 | 8 | |||
9.5 | odd | 6 | 882.2.e.r.373.2 | 8 | |||
21.2 | odd | 6 | 882.2.f.r.295.2 | ✓ | 8 | ||
21.5 | even | 6 | 882.2.f.r.295.3 | yes | 8 | ||
21.11 | odd | 6 | 882.2.e.r.655.1 | 8 | |||
21.17 | even | 6 | 882.2.e.r.655.4 | 8 | |||
21.20 | even | 2 | 882.2.h.s.79.1 | 8 | |||
63.2 | odd | 6 | 7938.2.a.ch.1.1 | 4 | |||
63.4 | even | 3 | inner | 2646.2.h.r.361.4 | 8 | ||
63.5 | even | 6 | 882.2.f.r.589.3 | yes | 8 | ||
63.13 | odd | 6 | 2646.2.e.s.1549.4 | 8 | |||
63.16 | even | 3 | 7938.2.a.cq.1.4 | 4 | |||
63.23 | odd | 6 | 882.2.f.r.589.2 | yes | 8 | ||
63.31 | odd | 6 | inner | 2646.2.h.r.361.1 | 8 | ||
63.32 | odd | 6 | 882.2.h.s.67.4 | 8 | |||
63.40 | odd | 6 | 2646.2.f.p.1765.4 | 8 | |||
63.41 | even | 6 | 882.2.e.r.373.3 | 8 | |||
63.47 | even | 6 | 7938.2.a.ch.1.4 | 4 | |||
63.58 | even | 3 | 2646.2.f.p.1765.1 | 8 | |||
63.59 | even | 6 | 882.2.h.s.67.1 | 8 | |||
63.61 | odd | 6 | 7938.2.a.cq.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.2.e.r.373.2 | 8 | 9.5 | odd | 6 | |||
882.2.e.r.373.3 | 8 | 63.41 | even | 6 | |||
882.2.e.r.655.1 | 8 | 21.11 | odd | 6 | |||
882.2.e.r.655.4 | 8 | 21.17 | even | 6 | |||
882.2.f.r.295.2 | ✓ | 8 | 21.2 | odd | 6 | ||
882.2.f.r.295.3 | yes | 8 | 21.5 | even | 6 | ||
882.2.f.r.589.2 | yes | 8 | 63.23 | odd | 6 | ||
882.2.f.r.589.3 | yes | 8 | 63.5 | even | 6 | ||
882.2.h.s.67.1 | 8 | 63.59 | even | 6 | |||
882.2.h.s.67.4 | 8 | 63.32 | odd | 6 | |||
882.2.h.s.79.1 | 8 | 21.20 | even | 2 | |||
882.2.h.s.79.4 | 8 | 3.2 | odd | 2 | |||
2646.2.e.s.1549.1 | 8 | 9.4 | even | 3 | |||
2646.2.e.s.1549.4 | 8 | 63.13 | odd | 6 | |||
2646.2.e.s.2125.1 | 8 | 7.4 | even | 3 | |||
2646.2.e.s.2125.4 | 8 | 7.3 | odd | 6 | |||
2646.2.f.p.883.1 | 8 | 7.2 | even | 3 | |||
2646.2.f.p.883.4 | 8 | 7.5 | odd | 6 | |||
2646.2.f.p.1765.1 | 8 | 63.58 | even | 3 | |||
2646.2.f.p.1765.4 | 8 | 63.40 | odd | 6 | |||
2646.2.h.r.361.1 | 8 | 63.31 | odd | 6 | inner | ||
2646.2.h.r.361.4 | 8 | 63.4 | even | 3 | inner | ||
2646.2.h.r.667.1 | 8 | 7.6 | odd | 2 | inner | ||
2646.2.h.r.667.4 | 8 | 1.1 | even | 1 | trivial | ||
7938.2.a.ch.1.1 | 4 | 63.2 | odd | 6 | |||
7938.2.a.ch.1.4 | 4 | 63.47 | even | 6 | |||
7938.2.a.cq.1.1 | 4 | 63.61 | odd | 6 | |||
7938.2.a.cq.1.4 | 4 | 63.16 | even | 3 |