Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(185,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.185");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.cx (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 185.13 | ||
Character | \(\chi\) | \(=\) | 504.185 |
Dual form | 504.2.cx.a.425.13 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | 0 | ||||||||
\(3\) | 0.149059 | − | 1.72562i | 0.0860590 | − | 0.996290i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.22094 | −0.993234 | −0.496617 | − | 0.867970i | \(-0.665425\pi\) | ||||
−0.496617 | + | 0.867970i | \(0.665425\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.45091 | − | 0.996507i | −0.926358 | − | 0.376644i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.95556 | − | 0.514438i | −0.985188 | − | 0.171479i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.17296i | 0.353662i | 0.984241 | + | 0.176831i | \(0.0565846\pi\) | ||||
−0.984241 | + | 0.176831i | \(0.943415\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.12404 | + | 1.80366i | 0.866453 | + | 0.500247i | 0.866168 | − | 0.499753i | \(-0.166576\pi\) |
0.000284763 | 1.00000i | \(0.499909\pi\) | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.331050 | + | 3.83251i | −0.0854767 | + | 0.989549i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.71178 | + | 6.42899i | −0.900238 | + | 1.55926i | −0.0730533 | + | 0.997328i | \(0.523274\pi\) |
−0.827185 | + | 0.561930i | \(0.810059\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.05231 | + | 1.76225i | −0.700249 | + | 0.404289i | −0.807440 | − | 0.589950i | \(-0.799148\pi\) |
0.107191 | + | 0.994238i | \(0.465814\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.08493 | + | 4.08082i | −0.454969 | + | 0.890508i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.81246i | − | 1.21198i | −0.795472 | − | 0.605991i | \(-0.792777\pi\) | ||
0.795472 | − | 0.605991i | \(-0.207223\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.0674336 | −0.0134867 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.32828 | + | 5.02351i | −0.255628 | + | 0.966775i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.04430 | + | 3.48968i | −1.12240 | + | 0.648017i | −0.942012 | − | 0.335579i | \(-0.891068\pi\) |
−0.180387 | + | 0.983596i | \(0.557735\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.88517 | − | 3.97516i | 1.23661 | − | 0.713959i | 0.268213 | − | 0.963360i | \(-0.413567\pi\) |
0.968400 | + | 0.249400i | \(0.0802335\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.02410 | + | 0.174840i | 0.352350 | + | 0.0304358i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.44333 | + | 2.21318i | 0.920090 | + | 0.374096i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.54350 | − | 9.60163i | −0.911346 | − | 1.57850i | −0.812164 | − | 0.583429i | \(-0.801711\pi\) |
−0.0991818 | − | 0.995069i | \(-0.531623\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.57811 | − | 5.12207i | 0.572957 | − | 0.820187i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.809022 | + | 1.40127i | −0.126348 | + | 0.218841i | −0.922259 | − | 0.386572i | \(-0.873659\pi\) |
0.795911 | + | 0.605414i | \(0.206992\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.904302 | + | 1.56630i | 0.137905 | + | 0.238858i | 0.926703 | − | 0.375794i | \(-0.122630\pi\) |
−0.788799 | + | 0.614652i | \(0.789297\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.56412 | + | 1.14254i | 0.978522 | + | 0.170319i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.26476 | + | 7.38679i | −0.622080 | + | 1.07747i | 0.367018 | + | 0.930214i | \(0.380379\pi\) |
−0.989098 | + | 0.147260i | \(0.952955\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.01395 | + | 4.88471i | 0.716278 | + | 0.697815i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.5407 | + | 7.36343i | 1.47600 | + | 1.03109i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.62611 | − | 5.55764i | −1.32225 | − | 0.763400i | −0.338161 | − | 0.941088i | \(-0.609805\pi\) |
−0.984087 | + | 0.177688i | \(0.943138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.60508i | − | 0.351269i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.58602 | + | 5.52983i | 0.342526 | + | 0.732444i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00138 | − | 3.46649i | −0.260557 | − | 0.451298i | 0.705833 | − | 0.708378i | \(-0.250573\pi\) |
−0.966390 | + | 0.257080i | \(0.917240\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.09004 | − | 4.09344i | −0.907787 | − | 0.524111i | −0.0280684 | − | 0.999606i | \(-0.508936\pi\) |
−0.879718 | + | 0.475495i | \(0.842269\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.73119 | + | 4.20608i | 0.848050 | + | 0.529917i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.93830 | − | 4.00583i | −0.860590 | − | 0.496862i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.96334 | − | 8.59676i | −0.606369 | − | 1.05026i | −0.991834 | − | 0.127539i | \(-0.959292\pi\) |
0.385465 | − | 0.922723i | \(-0.374041\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.0301 | − | 0.866397i | −1.20749 | − | 0.104302i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.67194i | − | 0.435779i | −0.975973 | − | 0.217890i | \(-0.930083\pi\) | ||
0.975973 | − | 0.217890i | \(-0.0699172\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.92803 | + | 3.99990i | 0.810865 | + | 0.468153i | 0.847256 | − | 0.531185i | \(-0.178253\pi\) |
−0.0363913 | + | 0.999338i | \(0.511586\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.0100516 | + | 0.116365i | −0.00116065 | + | 0.0134367i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.16887 | − | 2.87483i | 0.133205 | − | 0.327618i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.25993 | − | 3.91432i | 0.254262 | − | 0.440395i | −0.710433 | − | 0.703765i | \(-0.751501\pi\) |
0.964695 | + | 0.263370i | \(0.0848340\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.47071 | + | 3.04091i | 0.941190 | + | 0.337879i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.390969 | − | 0.677179i | −0.0429145 | − | 0.0743300i | 0.843770 | − | 0.536704i | \(-0.180331\pi\) |
−0.886685 | + | 0.462374i | \(0.846998\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.24363 | − | 14.2784i | 0.894147 | − | 1.54871i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.12092 | + | 10.9504i | 0.549021 | + | 1.17400i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.75440 | + | 3.03870i | 0.185966 | + | 0.322102i | 0.943901 | − | 0.330227i | \(-0.107125\pi\) |
−0.757936 | + | 0.652329i | \(0.773792\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.85938 | − | 7.53375i | −0.614230 | − | 0.789752i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.83334 | − | 12.4738i | −0.604889 | − | 1.29347i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.77900 | − | 3.91386i | 0.695511 | − | 0.401553i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.49226 | + | 2.01626i | −0.354585 | + | 0.204720i | −0.666703 | − | 0.745324i | \(-0.732295\pi\) |
0.312118 | + | 0.950043i | \(0.398962\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.603418 | − | 3.46677i | 0.0606458 | − | 0.348424i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.27809 | 0.226678 | 0.113339 | − | 0.993556i | \(-0.463845\pi\) | ||||
0.113339 | + | 0.993556i | \(0.463845\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.87303i | − | 0.874285i | −0.899392 | − | 0.437143i | \(-0.855990\pi\) | ||
0.899392 | − | 0.437143i | \(-0.144010\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.63050 | − | 9.06324i | 0.451890 | − | 0.884482i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.574764 | + | 0.331840i | −0.0555646 | + | 0.0320802i | −0.527525 | − | 0.849540i | \(-0.676880\pi\) |
0.471960 | + | 0.881620i | \(0.343547\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.03435 | + | 13.9159i | −0.769551 | + | 1.33290i | 0.168256 | + | 0.985743i | \(0.446187\pi\) |
−0.937807 | + | 0.347158i | \(0.887147\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.3951 | + | 8.13480i | −1.65107 | + | 0.772121i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.86666 | − | 2.80977i | −0.457817 | − | 0.264321i | 0.253309 | − | 0.967385i | \(-0.418481\pi\) |
−0.711126 | + | 0.703065i | \(0.751814\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.9091i | 1.20378i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.30542 | − | 6.93797i | −0.767836 | − | 0.641416i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.5038 | − | 12.0581i | 1.42123 | − | 1.10536i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.62415 | 0.874923 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.29747 | + | 1.60494i | 0.207156 | + | 0.144713i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.2545 | 1.00663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.74425 | 0.687191 | 0.343595 | − | 0.939118i | \(-0.388355\pi\) | ||||
0.343595 | + | 0.939118i | \(0.388355\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.83764 | − | 1.32702i | 0.249840 | − | 0.116837i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.6259 | −1.36524 | −0.682619 | − | 0.730774i | \(-0.739159\pi\) | ||||
−0.682619 | + | 0.730774i | \(0.739159\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.23705 | − | 1.27748i | 0.800954 | − | 0.110771i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.95003 | − | 11.1569i | 0.253898 | − | 0.960234i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1.07565i | − | 0.0918991i | −0.998944 | − | 0.0459496i | \(-0.985369\pi\) | ||
0.998944 | − | 0.0459496i | \(-0.0146313\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.81776 | + | 3.35889i | 0.493456 | + | 0.284897i | 0.726007 | − | 0.687687i | \(-0.241374\pi\) |
−0.232551 | + | 0.972584i | \(0.574707\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.1111 | + | 8.46045i | 1.01994 | + | 0.712498i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.11563 | + | 3.66439i | −0.176918 | + | 0.306431i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.4240 | − | 7.75036i | 1.11480 | − | 0.643633i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.17654 | − | 7.92408i | 0.756868 | − | 0.653567i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.5635i | 1.43886i | 0.694565 | + | 0.719430i | \(0.255597\pi\) | ||||
−0.694565 | + | 0.719430i | \(0.744403\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.69606 | 0.138023 | 0.0690115 | − | 0.997616i | \(-0.478015\pi\) | ||||
0.0690115 | + | 0.997616i | \(0.478015\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.2777 | − | 17.0918i | 1.15428 | − | 1.38179i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.2915 | + | 8.82858i | −1.22825 | + | 0.709128i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.82630 | − | 3.94116i | 0.544798 | − | 0.314539i | −0.202223 | − | 0.979339i | \(-0.564817\pi\) |
0.747021 | + | 0.664800i | \(0.231483\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.0253 | + | 15.7826i | −0.874360 | + | 1.25165i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.79216 | + | 14.2458i | −0.456486 | + | 1.12273i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.69385 | − | 9.86204i | −0.445977 | − | 0.772455i | 0.552143 | − | 0.833750i | \(-0.313810\pi\) |
−0.998120 | + | 0.0612949i | \(0.980477\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.49539 | − | 0.388310i | −0.349966 | − | 0.0302299i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.05638 | − | 13.9541i | 0.623422 | − | 1.07980i | −0.365422 | − | 0.930842i | \(-0.619075\pi\) |
0.988844 | − | 0.148956i | \(-0.0475913\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.00641296 | + | 0.0111076i | 0.000493305 | + | 0.000854429i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.92788 | − | 3.63823i | 0.759204 | − | 0.278222i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.45182 | − | 5.97872i | 0.262437 | − | 0.454554i | −0.704452 | − | 0.709752i | \(-0.748807\pi\) |
0.966889 | + | 0.255198i | \(0.0821405\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.165274 | + | 0.0671981i | 0.0124935 | + | 0.00507970i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.28018 | + | 2.93692i | −0.472047 | + | 0.220752i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.28759 | − | 3.05279i | −0.395213 | − | 0.228176i | 0.289203 | − | 0.957268i | \(-0.406610\pi\) |
−0.684416 | + | 0.729091i | \(0.739943\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.46329i | 0.406083i | 0.979170 | + | 0.203041i | \(0.0650826\pi\) | ||||
−0.979170 | + | 0.203041i | \(0.934917\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.12057 | + | 11.6246i | −0.600290 | + | 0.859315i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.3118 | + | 21.3246i | 0.905180 | + | 1.56782i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.54097 | − | 4.35378i | −0.551451 | − | 0.318380i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.26147 | − | 10.9885i | 0.600933 | − | 0.799299i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.21032 | + | 3.00818i | 0.377005 | + | 0.217664i | 0.676515 | − | 0.736429i | \(-0.263490\pi\) |
−0.299509 | + | 0.954093i | \(0.596823\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.89017 | + | 5.00592i | 0.208039 | + | 0.360334i | 0.951097 | − | 0.308893i | \(-0.0999586\pi\) |
−0.743058 | + | 0.669227i | \(0.766625\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.94677 | + | 11.3758i | −0.569080 | + | 0.814638i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 7.95354i | − | 0.566666i | −0.959022 | − | 0.283333i | \(-0.908560\pi\) | ||
0.959022 | − | 0.283333i | \(-0.0914402\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.5229 | − | 8.96214i | −1.10039 | − | 0.635309i | −0.164065 | − | 0.986450i | \(-0.552461\pi\) |
−0.936323 | + | 0.351141i | \(0.885794\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.5746 | + | 7.28345i | −1.09855 | + | 0.513735i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.2915 | − | 2.52971i | 1.28382 | − | 0.177551i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.79679 | − | 3.11213i | 0.125493 | − | 0.217360i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.99015 | + | 17.1791i | −0.207830 | + | 1.19403i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.06706 | − | 3.58026i | −0.142982 | − | 0.247651i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00200 | + | 6.93166i | −0.275509 | + | 0.477195i | −0.970263 | − | 0.242052i | \(-0.922180\pi\) |
0.694755 | + | 0.719247i | \(0.255513\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.33639 | − | 0.547334i | −0.434162 | − | 0.0375027i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.00840 | − | 3.47865i | −0.136972 | − | 0.237242i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.8362 | + | 2.88164i | −1.41446 | + | 0.195618i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.93501 | − | 11.3590i | 0.536198 | − | 0.767568i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.1915 | + | 13.3896i | −1.56003 | + | 0.900682i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.2405 | + | 8.22177i | −0.953616 | + | 0.550570i | −0.894202 | − | 0.447663i | \(-0.852256\pi\) |
−0.0594134 | + | 0.998233i | \(0.518923\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.199304 | + | 0.0346904i | 0.0132869 | + | 0.00231269i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.9930 | −1.06149 | −0.530746 | − | 0.847531i | \(-0.678088\pi\) | ||||
−0.530746 | + | 0.847531i | \(0.678088\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.4612i | 1.02170i | 0.859669 | + | 0.510851i | \(0.170670\pi\) | ||||
−0.859669 | + | 0.510851i | \(0.829330\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.78665 | − | 2.44555i | −0.314939 | − | 0.160905i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.5268 | − | 9.54175i | 1.08271 | − | 0.625101i | 0.151081 | − | 0.988521i | \(-0.451725\pi\) |
0.931625 | + | 0.363421i | \(0.118391\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.47178 | − | 16.4056i | 0.617871 | − | 1.07018i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.41778 | − | 4.48326i | −0.416880 | − | 0.291219i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.37626 | + | 4.25868i | 0.477130 | + | 0.275471i | 0.719220 | − | 0.694783i | \(-0.244499\pi\) |
−0.242089 | + | 0.970254i | \(0.577833\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.6376i | 1.45821i | 0.684400 | + | 0.729107i | \(0.260064\pi\) | ||||
−0.684400 | + | 0.729107i | \(0.739936\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.51010 | − | 14.1640i | 0.417623 | − | 0.908620i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.1357 | − | 10.8486i | −0.711431 | − | 0.693093i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.7141 | −0.808976 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.22683 | + | 0.573727i | −0.0777474 | + | 0.0363585i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.74235 | 0.488693 | 0.244346 | − | 0.969688i | \(-0.421427\pi\) | ||||
0.244346 | + | 0.969688i | \(0.421427\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.81781 | 0.428632 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −23.4103 | − | 16.3537i | −1.46601 | − | 1.02411i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.7890 | −1.48392 | −0.741958 | − | 0.670447i | \(-0.766103\pi\) | ||||
−0.741958 | + | 0.670447i | \(0.766103\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.01855 | + | 29.0569i | 0.249700 | + | 1.80551i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.6595 | − | 7.20455i | 1.21690 | − | 0.445950i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.5341i | 1.26619i | 0.774075 | + | 0.633094i | \(0.218215\pi\) | ||||
−0.774075 | + | 0.633094i | \(0.781785\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.3790 | + | 12.3432i | 1.31330 | + | 0.758235i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.50517 | − | 2.57448i | 0.336911 | − | 0.157556i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.17188 | − | 10.6900i | 0.376306 | − | 0.651782i | −0.614215 | − | 0.789138i | \(-0.710527\pi\) |
0.990522 | + | 0.137357i | \(0.0438607\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.3900 | + | 14.6589i | −1.54233 | + | 0.890467i | −0.543643 | + | 0.839317i | \(0.682955\pi\) |
−0.998691 | + | 0.0511505i | \(0.983711\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.8738 | + | 8.98812i | −0.839682 | + | 0.543986i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 0.0790972i | − | 0.00476974i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.48230 | −0.149147 | −0.0745735 | − | 0.997216i | \(-0.523760\pi\) | ||||
−0.0745735 | + | 0.997216i | \(0.523760\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −22.3945 | + | 8.20683i | −1.34073 | + | 0.491330i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.0970 | − | 11.6030i | 1.19889 | − | 0.692178i | 0.238581 | − | 0.971123i | \(-0.423318\pi\) |
0.960307 | + | 0.278944i | \(0.0899845\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.6425 | + | 13.6500i | −1.40540 | + | 0.811408i | −0.994940 | − | 0.100471i | \(-0.967965\pi\) |
−0.410460 | + | 0.911879i | \(0.634632\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.74338 | − | 12.2814i | −0.340209 | − | 0.727488i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.37922 | − | 2.62819i | 0.199469 | − | 0.155137i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −19.0546 | − | 33.0035i | −1.12086 | − | 1.94138i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.95875 | + | 6.32687i | 0.173445 | + | 0.370888i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.15628 | − | 7.19888i | 0.242812 | − | 0.420563i | −0.718702 | − | 0.695318i | \(-0.755263\pi\) |
0.961514 | + | 0.274755i | \(0.0885968\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.44494 | + | 7.69886i | 0.258794 | + | 0.448245i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.89240 | − | 1.55803i | −0.341912 | − | 0.0904058i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.4837 | − | 18.1584i | 0.606290 | − | 1.05012i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.655539 | − | 4.74000i | −0.0377846 | − | 0.273209i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.339569 | − | 3.93113i | 0.0195077 | − | 0.225837i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.7465 | + | 9.09127i | 0.901645 | + | 0.520565i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.4908i | 1.28362i | 0.766864 | + | 0.641810i | \(0.221816\pi\) | ||||
−0.766864 | + | 0.641810i | \(0.778184\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.3115 | − | 1.32260i | −0.871042 | − | 0.0752401i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.83900 | + | 8.38139i | 0.274394 | + | 0.475265i | 0.969982 | − | 0.243176i | \(-0.0781893\pi\) |
−0.695588 | + | 0.718441i | \(0.744856\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.2150 | + | 12.2485i | 1.19914 | + | 0.692324i | 0.960363 | − | 0.278751i | \(-0.0899204\pi\) |
0.238776 | + | 0.971075i | \(0.423254\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −14.9495 | − | 9.34145i | −0.842312 | − | 0.526331i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.95548 | + | 4.59310i | 0.446824 | + | 0.257974i | 0.706488 | − | 0.707725i | \(-0.250278\pi\) |
−0.259664 | + | 0.965699i | \(0.583612\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.09327 | − | 7.08975i | −0.229179 | − | 0.396950i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.486958 | + | 1.04129i | 0.0271794 | + | 0.0581192i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 26.1644i | − | 1.45582i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.210665 | − | 0.121628i | −0.0116856 | − | 0.00674668i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 22.8160 | + | 15.9386i | 1.26173 | + | 0.881404i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.8136 | − | 13.8545i | 0.982093 | − | 0.763823i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.8599 | + | 22.2739i | −0.706842 | + | 1.22429i | 0.259181 | + | 0.965829i | \(0.416547\pi\) |
−0.966023 | + | 0.258457i | \(0.916786\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.4447 | + | 31.2300i | 0.627167 | + | 1.71139i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.0233 | + | 19.0929i | 0.602266 | + | 1.04316i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.80657 | − | 15.2534i | 0.479724 | − | 0.830907i | −0.520005 | − | 0.854163i | \(-0.674070\pi\) |
0.999730 | + | 0.0232560i | \(0.00740329\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.57402 | + | 7.97921i | −0.302739 | + | 0.433371i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.66272 | + | 8.07606i | 0.252500 | + | 0.437343i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.42110 | − | 16.9684i | −0.400702 | − | 0.916209i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 22.2763 | + | 1.92421i | 1.19932 | + | 0.103596i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.23389 | − | 4.17649i | 0.388335 | − | 0.224206i | −0.293103 | − | 0.956081i | \(-0.594688\pi\) |
0.681439 | + | 0.731875i | \(0.261355\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.4062 | + | 9.47211i | −0.878203 | + | 0.507031i | −0.870065 | − | 0.492936i | \(-0.835924\pi\) |
−0.00813729 | + | 0.999967i | \(0.502590\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.2103 | + | 13.2979i | −0.705115 | + | 0.709788i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.4971 | 1.35707 | 0.678537 | − | 0.734566i | \(-0.262614\pi\) | ||||
0.678537 | + | 0.734566i | \(0.262614\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.15515i | 0.432830i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.4967 | − | 28.5511i | −0.978951 | − | 1.51108i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.4128 | + | 10.0533i | −0.919013 | + | 0.530592i | −0.883320 | − | 0.468771i | \(-0.844697\pi\) |
−0.0356928 | + | 0.999363i | \(0.511364\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.28892 | + | 5.69658i | −0.173101 | + | 0.299820i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.43456 | − | 16.6077i | 0.0752950 | − | 0.871677i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.3867 | − | 8.88353i | −0.805378 | − | 0.464985i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 23.2850i | − | 1.21547i | −0.794140 | − | 0.607735i | \(-0.792078\pi\) | ||
0.794140 | − | 0.607735i | \(-0.207922\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.11198 | − | 3.72534i | 0.162003 | − | 0.193934i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.0545 | + | 23.2138i | 0.937345 | + | 1.20520i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.1249 | −1.30092 | −0.650460 | − | 0.759540i | \(-0.725424\pi\) | ||||
−0.650460 | + | 0.759540i | \(0.725424\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.67757 | − | 19.4210i | 0.0866295 | − | 1.00289i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −25.1768 | −1.29667 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.3000 | 1.65914 | 0.829569 | − | 0.558404i | \(-0.188586\pi\) | ||||
0.829569 | + | 0.558404i | \(0.188586\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.15435 | − | 13.3637i | 0.0591390 | − | 0.684641i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.54363 | 0.487657 | 0.243828 | − | 0.969818i | \(-0.421597\pi\) | ||||
0.243828 | + | 0.969818i | \(0.421597\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.59598 | + | 6.38483i | −0.132304 | + | 0.325401i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.86696 | − | 5.09450i | −0.0949028 | − | 0.258968i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 13.6201i | − | 0.690566i | −0.938499 | − | 0.345283i | \(-0.887783\pi\) | ||
0.938499 | − | 0.345283i | \(-0.112217\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.3682 | + | 21.5746i | 1.88979 | + | 1.09107i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.32917 | + | 26.9644i | −0.117491 | + | 1.36017i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.01917 | + | 8.69346i | −0.252542 | + | 0.437415i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.59589 | − | 1.49874i | 0.130284 | − | 0.0752196i | −0.433441 | − | 0.901182i | \(-0.642701\pi\) |
0.563726 | + | 0.825962i | \(0.309368\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.827585 | − | 16.1301i | −0.0414311 | − | 0.807516i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.0336i | 0.650869i | 0.945565 | + | 0.325434i | \(0.105511\pi\) | ||||
−0.945565 | + | 0.325434i | \(0.894489\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.6794 | 1.42862 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.8129 | − | 6.75367i | −0.934821 | − | 0.335593i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.2624 | − | 6.50233i | 0.558255 | − | 0.322309i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.4682 | + | 16.4361i | −1.40766 | + | 0.812714i | −0.995162 | − | 0.0982431i | \(-0.968678\pi\) |
−0.412500 | + | 0.910958i | \(0.635344\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.85617 | − | 0.160335i | −0.0915582 | − | 0.00790875i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.45082 | + | 10.4905i | 0.0713903 | + | 0.516201i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.868319 | + | 1.50397i | 0.0426241 | + | 0.0738271i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.66337 | − | 9.53861i | 0.326307 | − | 0.467108i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.0687 | − | 19.1716i | 0.540742 | − | 0.936593i | −0.458119 | − | 0.888891i | \(-0.651477\pi\) |
0.998862 | − | 0.0477024i | \(-0.0151899\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.1963 | + | 21.1245i | 0.594409 | + | 1.02955i | 0.993630 | + | 0.112692i | \(0.0359472\pi\) |
−0.399221 | + | 0.916855i | \(0.630719\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 16.4048 | − | 19.6382i | 0.797630 | − | 0.954840i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.250298 | − | 0.433529i | 0.0121413 | − | 0.0210293i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.2979 | + | 17.0979i | 0.643532 | + | 0.827427i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.00800 | + | 4.19700i | 0.290069 | + | 0.202633i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.2611 | − | 7.07897i | −0.590598 | − | 0.340982i | 0.174736 | − | 0.984615i | \(-0.444093\pi\) |
−0.765334 | + | 0.643634i | \(0.777426\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8.90220i | − | 0.427813i | −0.976854 | − | 0.213906i | \(-0.931381\pi\) | ||
0.976854 | − | 0.213906i | \(-0.0686187\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.3733 | − | 24.3201i | −0.545306 | − | 1.16606i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.2430 | + | 17.7415i | 0.489991 | + | 0.848689i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.9971 | − | 8.08120i | −0.668043 | − | 0.385695i | 0.127292 | − | 0.991865i | \(-0.459372\pi\) |
−0.795335 | + | 0.606171i | \(0.792705\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.3062 | − | 17.0164i | −0.586007 | − | 0.810306i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.1101 | − | 8.72383i | −0.717903 | − | 0.414482i | 0.0960772 | − | 0.995374i | \(-0.469370\pi\) |
−0.813980 | + | 0.580892i | \(0.802704\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.89640 | − | 6.74877i | −0.184707 | − | 0.319922i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 30.3080 | + | 2.61799i | 1.43352 | + | 0.123827i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.14988i | 0.431809i | 0.976414 | + | 0.215905i | \(0.0692700\pi\) | ||||
−0.976414 | + | 0.215905i | \(0.930730\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.64364 | − | 0.948954i | −0.0773958 | − | 0.0446845i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.252812 | − | 2.92676i | 0.0118781 | − | 0.137511i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.0133 | + | 16.7320i | 0.610074 | + | 0.784408i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.05757 | + | 12.2241i | −0.330139 | + | 0.571818i | −0.982539 | − | 0.186057i | \(-0.940429\pi\) |
0.652400 | + | 0.757875i | \(0.273762\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −27.3658 | − | 27.1856i | −1.27733 | − | 1.26892i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.5323 | − | 30.3668i | −0.816561 | − | 1.41432i | −0.908202 | − | 0.418532i | \(-0.862545\pi\) |
0.0916412 | − | 0.995792i | \(-0.470789\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.9985 | − | 27.7103i | 0.743515 | − | 1.28781i | −0.207370 | − | 0.978263i | \(-0.566490\pi\) |
0.950885 | − | 0.309543i | \(-0.100176\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.9555 | + | 27.7034i | 0.600796 | + | 1.28472i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.02671 | − | 13.9027i | −0.371432 | − | 0.643339i | 0.618354 | − | 0.785899i | \(-0.287800\pi\) |
−0.989786 | + | 0.142561i | \(0.954466\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.59798 | + | 26.0159i | 0.166139 | + | 1.20130i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.78345 | − | 12.3671i | −0.266487 | − | 0.569846i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.83721 | + | 1.06071i | −0.0844751 | + | 0.0487717i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.205828 | − | 0.118835i | 0.00944406 | − | 0.00545253i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 25.5915 | + | 21.3780i | 1.17176 | + | 0.978831i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.4961 | 1.43909 | 0.719547 | − | 0.694443i | \(-0.244349\pi\) | ||||
0.719547 | + | 0.694443i | \(0.244349\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 39.9945i | − | 1.82359i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 23.7196 | + | 12.1186i | 1.07928 | + | 0.551413i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.75609 | − | 4.47798i | 0.352186 | − | 0.203335i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.7924 | − | 18.6930i | 0.489052 | − | 0.847062i | −0.510869 | − | 0.859659i | \(-0.670676\pi\) |
0.999921 | + | 0.0125963i | \(0.00400964\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.8669 | + | 8.35543i | −0.807969 | + | 0.377846i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.9290 | − | 16.7022i | −1.30555 | − | 0.753758i | −0.324197 | − | 0.945990i | \(-0.605094\pi\) |
−0.981349 | + | 0.192232i | \(0.938427\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 51.8116i | − | 2.33348i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.34015 | + | 7.69948i | −0.0602355 | + | 0.346066i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.65911 | + | 8.99960i | −0.164134 | + | 0.403687i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.1443 | 1.43898 | 0.719489 | − | 0.694504i | \(-0.244376\pi\) | ||||
0.719489 | + | 0.694504i | \(0.244376\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22.8786 | − | 15.9823i | −1.02214 | − | 0.714035i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.7295 | −0.968872 | −0.484436 | − | 0.874827i | \(-0.660975\pi\) | ||||
−0.484436 | + | 0.874827i | \(0.660975\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.05949 | −0.225145 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.0201234 | − | 0.00941069i | 0.000893713 | − | 0.000417943i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.8864 | 1.05875 | 0.529373 | − | 0.848389i | \(-0.322427\pi\) | ||||
0.529373 | + | 0.848389i | \(0.322427\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.9941 | − | 16.7072i | −0.574824 | − | 0.739085i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.79838 | − | 17.6741i | −0.211854 | − | 0.780331i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.7064i | 0.868370i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.66444 | − | 5.00242i | −0.381062 | − | 0.220006i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.80251 | − | 6.84772i | −0.430283 | − | 0.300582i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.5098 | − | 23.3996i | 0.591874 | − | 1.02516i | −0.402106 | − | 0.915593i | \(-0.631722\pi\) |
0.993980 | − | 0.109562i | \(-0.0349449\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.2136 | − | 15.7118i | 1.18997 | − | 0.687028i | 0.231669 | − | 0.972795i | \(-0.425582\pi\) |
0.958299 | + | 0.285766i | \(0.0922482\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.140594 | − | 0.275184i | 0.00613603 | − | 0.0120100i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 59.0196i | 2.57093i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.7847 | −0.468899 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.13190 | + | 11.2750i | 0.179309 | + | 0.489294i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.05483 | + | 2.91841i | −0.218949 | + | 0.126410i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.27652 | − | 0.736997i | 0.0551886 | − | 0.0318632i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.05613 | + | 8.66935i | −0.261341 | + | 0.374110i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.72959 | + | 5.88118i | −0.246791 | + | 0.253320i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.0969057 | − | 0.167846i | −0.00416630 | − | 0.00721624i | 0.863935 | − | 0.503604i | \(-0.167993\pi\) |
−0.868101 | + | 0.496388i | \(0.834660\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.42758 | + | 0.814350i | 0.404576 | + | 0.0349471i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.8438 | − | 30.9064i | 0.764344 | − | 1.32388i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.987053 | + | 1.70963i | 0.0422033 | + | 0.0730983i | 0.886355 | − | 0.463005i | \(-0.153229\pi\) |
−0.844152 | + | 0.536104i | \(0.819896\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18.8492 | + | 15.7458i | 0.804466 | + | 0.672015i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.2994 | − | 21.3032i | 0.523972 | − | 0.907547i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.43955 | + | 7.34161i | −0.401410 | + | 0.312197i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 38.6335 | − | 18.0669i | 1.63990 | − | 0.766897i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.3383 | − | 10.5876i | −0.777018 | − | 0.448612i | 0.0583543 | − | 0.998296i | \(-0.481415\pi\) |
−0.835373 | + | 0.549684i | \(0.814748\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.52423i | 0.275946i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.63704 | + | 12.3639i | −0.364656 | + | 0.522005i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.0645 | − | 29.5565i | −0.719182 | − | 1.24566i | −0.961324 | − | 0.275419i | \(-0.911183\pi\) |
0.242142 | − | 0.970241i | \(-0.422150\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.8085 | + | 6.24032i | 0.454719 | + | 0.262532i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.7307 | − | 15.8941i | −0.744618 | − | 0.667491i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.55993 | + | 5.51943i | 0.400773 | + | 0.231387i | 0.686818 | − | 0.726830i | \(-0.259007\pi\) |
−0.286044 | + | 0.958216i | \(0.592340\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.6616 | − | 35.7870i | −0.864663 | − | 1.49764i | −0.867382 | − | 0.497644i | \(-0.834199\pi\) |
0.00271871 | − | 0.999996i | \(-0.499135\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.96763 | − | 8.54266i | 0.249301 | − | 0.356875i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.391955i | 0.0163456i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.5253 | + | 7.23151i | 0.521437 | + | 0.301052i | 0.737522 | − | 0.675323i | \(-0.235996\pi\) |
−0.216085 | + | 0.976374i | \(0.569329\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.06915 | − | 4.24117i | 0.376901 | − | 0.176257i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.283418 | + | 2.04931i | 0.0117582 | + | 0.0850197i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.51891 | − | 11.2911i | 0.269986 | − | 0.467629i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.4458 | + | 15.4088i | 0.762641 | + | 0.637076i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.248251 | − | 0.429983i | −0.0102464 | − | 0.0177473i | 0.860857 | − | 0.508847i | \(-0.169928\pi\) |
−0.871103 | + | 0.491100i | \(0.836595\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.0105 | + | 24.2669i | −0.577292 | + | 0.999898i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.7248 | − | 1.18554i | −0.564564 | − | 0.0487667i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.2302 | + | 21.1834i | 0.502236 | + | 0.869898i | 0.999997 | + | 0.00258345i | \(0.000822338\pi\) |
−0.497761 | + | 0.867314i | \(0.665844\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −34.4329 | + | 26.7802i | −1.41161 | + | 1.09788i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.7791 | + | 25.4508i | −0.727650 | + | 1.04163i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.3114 | − | 9.41741i | 0.666467 | − | 0.384785i | −0.128270 | − | 0.991739i | \(-0.540942\pi\) |
0.794737 | + | 0.606954i | \(0.207609\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.37572 | + | 3.68102i | −0.260071 | + | 0.150152i | −0.624367 | − | 0.781131i | \(-0.714643\pi\) |
0.364296 | + | 0.931283i | \(0.381310\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.2470 | + | 27.9616i | 0.417289 | + | 1.13868i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21.3747 | −0.869003 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.9923i | 1.17676i | 0.808584 | + | 0.588380i | \(0.200234\pi\) | ||||
−0.808584 | + | 0.588380i | \(0.799766\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.63881 | − | 31.9414i | −0.0664081 | − | 1.29433i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.6466 | + | 15.3844i | −1.07801 | + | 0.622387i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.4334 | − | 21.5352i | 0.502179 | − | 0.869799i | −0.497818 | − | 0.867282i | \(-0.665865\pi\) |
0.999997 | − | 0.00251771i | \(-0.000801413\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.10254 | − | 3.56447i | −0.205754 | − | 0.143733i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −37.4629 | − | 21.6292i | −1.50820 | − | 0.870759i | −0.999954 | − | 0.00954684i | \(-0.996961\pi\) |
−0.508245 | − | 0.861213i | \(-0.669706\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 7.45221i | − | 0.299529i | −0.988722 | − | 0.149765i | \(-0.952148\pi\) | ||
0.988722 | − | 0.149765i | \(-0.0478516\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 29.1990 | + | 7.72057i | 1.17171 | + | 0.309816i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.27178 | − | 9.19586i | −0.0509528 | − | 0.368424i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.6583 | −0.986331 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.48629 | + | 3.03331i | −0.259038 | + | 0.121139i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 82.3050 | 3.28171 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.67068 | −0.384984 | −0.192492 | − | 0.981299i | \(-0.561657\pi\) | ||||
−0.192492 | + | 0.981299i | \(0.561657\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.3649 | + | 7.93917i | 0.451715 | + | 0.315554i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.1995 | −0.682541 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.85339 | + | 24.3035i | 0.271541 | + | 0.962939i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.88899 | + | 10.8526i | −0.0747272 | + | 0.429324i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.9590i | 1.22281i | 0.791318 | + | 0.611404i | \(0.209395\pi\) | ||||
−0.791318 | + | 0.611404i | \(0.790605\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.99262 | + | 4.03719i | 0.275762 | + | 0.159211i | 0.631503 | − | 0.775373i | \(-0.282438\pi\) |
−0.355741 | + | 0.934585i | \(0.615772\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.30221 | + | 2.94722i | −0.248149 | + | 0.116047i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.54355 | − | 7.86966i | 0.178625 | − | 0.309388i | −0.762785 | − | 0.646653i | \(-0.776168\pi\) |
0.941410 | + | 0.337265i | \(0.109502\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.06607 | − | 2.34755i | 0.159607 | − | 0.0921492i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.86680 | + | 36.3851i | 0.0731658 | + | 1.42604i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.5913i | 0.805800i | 0.915244 | + | 0.402900i | \(0.131998\pi\) | ||||
−0.915244 | + | 0.402900i | \(0.868002\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.7041 | 1.35600 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −18.4185 | − | 15.3860i | −0.718575 | − | 0.600265i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.7687 | + | 24.1152i | −1.62708 | + | 0.939395i | −0.642121 | + | 0.766604i | \(0.721945\pi\) |
−0.984959 | + | 0.172791i | \(0.944722\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.8342 | + | 13.7607i | −0.927042 | + | 0.535228i | −0.885875 | − | 0.463924i | \(-0.846441\pi\) |
−0.0411674 | + | 0.999152i | \(0.513108\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 19.6485 | + | 42.0156i | 0.763086 | + | 1.63175i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.5149 | + | 2.83720i | −0.795535 | + | 0.110022i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.2836 | + | 35.1323i | 0.785385 | + | 1.36033i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.0650 | + | 25.7993i | 0.466460 | + | 0.997459i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.80146 | − | 8.31637i | 0.185358 | − | 0.321050i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.5734 | − | 30.4380i | −0.677404 | − | 1.17330i | −0.975760 | − | 0.218844i | \(-0.929771\pi\) |
0.298355 | − | 0.954455i | \(-0.403562\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.0895707 | − | 0.338753i | 0.00344758 | − | 0.0130386i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.9428 | + | 38.0060i | −0.843329 | + | 1.46069i | 0.0437349 | + | 0.999043i | \(0.486074\pi\) |
−0.887064 | + | 0.461646i | \(0.847259\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.5684 | − | 1.46161i | 0.405579 | − | 0.0560913i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.38389 | + | 27.5979i | −0.0913510 | + | 1.05755i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.9331 | + | 10.3537i | 0.686190 | + | 0.396172i | 0.802183 | − | 0.597078i | \(-0.203672\pi\) |
−0.115993 | + | 0.993250i | \(0.537005\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.38896i | 0.0912773i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.6802 | + | 2.30462i | 1.01791 | + | 0.0879267i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.0482 | − | 34.7246i | −0.763777 | − | 1.32290i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.8678 | − | 9.16129i | −0.603640 | − | 0.348512i | 0.166832 | − | 0.985985i | \(-0.446646\pi\) |
−0.770472 | + | 0.637474i | \(0.779980\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.93359 | + | 7.89544i | −0.187412 | + | 0.299923i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.9209 | − | 7.45988i | −0.490117 | − | 0.282969i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.00582 | − | 10.4024i | −0.227487 | − | 0.394018i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.0020 | − | 29.9413i | −0.529605 | − | 1.13248i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.62840i | − | 0.0992734i | −0.998767 | − | 0.0496367i | \(-0.984194\pi\) | ||
0.998767 | − | 0.0496367i | \(-0.0158064\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.8410 | + | 19.5381i | 1.27634 | + | 0.736894i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −26.8981 | − | 18.7901i | −1.01304 | − | 0.707677i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.58340 | − | 2.27013i | −0.209985 | − | 0.0853771i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.16634 | − | 14.1445i | 0.306693 | − | 0.531208i | −0.670944 | − | 0.741508i | \(-0.734111\pi\) |
0.977637 | + | 0.210300i | \(0.0674441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.69305 | + | 10.4064i | −0.326015 | + | 0.390271i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −23.1054 | − | 40.0198i | −0.865305 | − | 1.49875i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.69869 | − | 8.13838i | 0.175721 | − | 0.304358i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.44839 | − | 12.0939i | 0.315511 | − | 0.451654i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.15485 | + | 5.46436i | 0.117656 | + | 0.203786i | 0.918838 | − | 0.394634i | \(-0.129129\pi\) |
−0.801182 | + | 0.598420i | \(0.795795\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.84204 | + | 21.7470i | −0.329295 | + | 0.809901i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 39.0640 | + | 3.37432i | 1.45280 | + | 0.125492i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.407589 | − | 0.235322i | 0.0151375 | − | 0.00873962i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.3318 | − | 8.27447i | 0.531537 | − | 0.306883i | −0.210105 | − | 0.977679i | \(-0.567381\pi\) |
0.741642 | + | 0.670796i | \(0.234047\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.4713 | − | 13.3453i | −0.869309 | − | 0.494269i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.4263 | −0.496589 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 19.9109i | − | 0.735425i | −0.929939 | − | 0.367713i | \(-0.880141\pi\) | ||
0.929939 | − | 0.367713i | \(-0.119859\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −20.3805 | + | 17.5989i | −0.751747 | + | 0.649145i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.0837 | − | 5.82183i | 0.371438 | − | 0.214450i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.1545 | + | 41.8368i | −0.888536 | + | 1.53899i | −0.0469307 | + | 0.998898i | \(0.514944\pi\) |
−0.841606 | + | 0.540092i | \(0.818389\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.89514 | + | 21.9397i | −0.0696197 | + | 0.805975i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.17819 | − | 4.14433i | −0.263342 | − | 0.152041i | 0.362516 | − | 0.931978i | \(-0.381918\pi\) |
−0.625858 | + | 0.779937i | \(0.715251\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 39.0075i | − | 1.42912i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.807168 | + | 2.20257i | 0.0295327 | + | 0.0805880i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.73938 | − | 0.240555i | 0.0635555 | − | 0.00878968i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.0229 | −0.913099 | −0.456549 | − | 0.889698i | \(-0.650915\pi\) | ||||
−0.456549 | + | 0.889698i | \(0.650915\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.15406 | − | 13.3604i | 0.0420564 | − | 0.486879i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.76683 | −0.137089 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.7744 | −0.682368 | −0.341184 | − | 0.939997i | \(-0.610828\pi\) | ||||
−0.341184 | + | 0.939997i | \(0.610828\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.01625 | − | 11.7650i | 0.0368876 | − | 0.427042i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.1927 | 0.840733 | 0.420367 | − | 0.907354i | \(-0.361901\pi\) | ||||
0.420367 | + | 0.907354i | \(0.361901\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.5588 | − | 26.1004i | 1.21491 | − | 0.944897i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −31.7099 | + | 37.9598i | −1.14647 | + | 1.37244i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 14.4393i | − | 0.521372i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.8202 | + | 16.0620i | 1.00322 | + | 0.579210i | 0.909200 | − | 0.416360i | \(-0.136695\pi\) |
0.0940211 | + | 0.995570i | \(0.470028\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.54595 | + | 41.0509i | −0.127704 | + | 1.47841i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.14023 | + | 14.0993i | −0.292784 | + | 0.507116i | −0.974467 | − | 0.224531i | \(-0.927915\pi\) |
0.681683 | + | 0.731647i | \(0.261248\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.464292 | + | 0.268059i | −0.0166779 | + | 0.00962896i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 50.7403 | − | 2.60332i | 1.82030 | − | 0.0933938i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 5.70281i | − | 0.204324i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.30705 | 0.154119 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.50192 | − | 34.9989i | −0.339571 | − | 1.25076i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.1608 | + | 8.75308i | −0.541112 | + | 0.312411i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.799139 | + | 0.461383i | −0.0284862 | + | 0.0164465i | −0.514175 | − | 0.857685i | \(-0.671902\pi\) |
0.485689 | + | 0.874132i | \(0.338569\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 35.4342 | + | 3.06079i | 1.26149 | + | 0.108967i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.12780 | + | 11.7362i | 0.324547 | + | 0.417290i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.7664 | − | 25.5761i | −0.524369 | − | 0.908235i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 24.4864 | − | 35.0523i | 0.868443 | − | 1.24318i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.98084 | + | 5.16296i | −0.105587 | + | 0.182881i | −0.913978 | − | 0.405764i | \(-0.867005\pi\) |
0.808391 | + | 0.588646i | \(0.200339\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.6597 | − | 54.8362i | −1.12004 | − | 1.93997i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.62200 | − | 9.88360i | −0.127977 | − | 0.349220i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.69174 | + | 8.12634i | −0.165568 | + | 0.286772i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.8640 | − | 31.6391i | 0.453397 | − | 1.11513i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.5270 | − | 12.2438i | −0.616979 | − | 0.431002i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.0267 | − | 10.4077i | −0.633784 | − | 0.365916i | 0.148432 | − | 0.988923i | \(-0.452577\pi\) |
−0.782216 | + | 0.623007i | \(0.785911\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 11.7101i | − | 0.411198i | −0.978636 | − | 0.205599i | \(-0.934086\pi\) | ||
0.978636 | − | 0.205599i | \(-0.0659142\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.5112 | + | 45.9987i | 0.754432 | + | 1.61324i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.6457 | + | 21.9030i | 0.442959 | + | 0.767228i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.52043 | − | 3.18722i | −0.193135 | − | 0.111507i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.4421 | + | 25.2808i | 0.469706 | + | 0.883382i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.483490 | + | 0.279143i | 0.0168739 | + | 0.00974215i | 0.508413 | − | 0.861113i | \(-0.330232\pi\) |
−0.491539 | + | 0.870855i | \(0.663566\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.7043 | − | 35.8609i | −0.721707 | − | 1.25003i | −0.960315 | − | 0.278918i | \(-0.910024\pi\) |
0.238607 | − | 0.971116i | \(-0.423309\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.136492 | − | 0.0117901i | −0.00475204 | − | 0.000410479i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.83309i | 0.307157i | 0.988136 | + | 0.153578i | \(0.0490797\pi\) | ||||
−0.988136 | + | 0.153578i | \(0.950920\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.60753 | − | 4.39221i | −0.264220 | − | 0.152548i | 0.362038 | − | 0.932163i | \(-0.382081\pi\) |
−0.626258 | + | 0.779616i | \(0.715414\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.370008 | + | 4.28352i | −0.0128355 | + | 0.148594i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −50.0143 | + | 14.1037i | −1.73289 | + | 0.488663i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.8927 | + | 30.9911i | −0.619204 | + | 1.07249i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.8238 | + | 39.8679i | 0.374126 | + | 1.37804i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.6778 | + | 20.2265i | 0.403161 | + | 0.698295i | 0.994106 | − | 0.108417i | \(-0.0345781\pi\) |
−0.590944 | + | 0.806712i | \(0.701245\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.85573 | − | 17.0706i | 0.339853 | − | 0.588642i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.0268 | − | 36.4095i | −0.586435 | − | 1.25401i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.0142428 | − | 0.0246693i | −0.000489967 | − | 0.000848648i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.5880 | − | 9.59054i | −0.810492 | − | 0.329535i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.0307 | + | 42.8327i | 0.687450 | + | 1.47001i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −55.8091 | + | 32.2214i | −1.91311 | + | 1.10453i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.8754 | + | 8.01099i | −0.475086 | + | 0.274291i | −0.718366 | − | 0.695665i | \(-0.755110\pi\) |
0.243280 | + | 0.969956i | \(0.421777\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.0492 | + | 8.08027i | −0.754067 | + | 0.276340i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.8241 | −0.574700 | −0.287350 | − | 0.957826i | \(-0.592774\pi\) | ||||
−0.287350 | + | 0.957826i | \(0.592774\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.5953i | 1.62393i | 0.583705 | + | 0.811966i | \(0.301603\pi\) | ||||
−0.583705 | + | 0.811966i | \(0.698397\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.03156 | − | 6.22301i | −0.137395 | − | 0.212080i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44.7300 | + | 25.8249i | −1.52263 | + | 0.879089i | −0.522985 | + | 0.852342i | \(0.675182\pi\) |
−0.999642 | + | 0.0267477i | \(0.991485\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.66628 | + | 13.2784i | −0.260661 | + | 0.451478i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −59.7919 | + | 27.9616i | −2.03064 | + | 0.949625i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.59136 | + | 2.65082i | 0.155751 | + | 0.0899230i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 35.8088i | − | 1.21334i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.3588 | − | 4.16262i | 0.384438 | − | 0.140883i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.5837 | − | 11.2151i | −0.932499 | − | 0.379141i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.3056 | 0.483066 | 0.241533 | − | 0.970393i | \(-0.422350\pi\) | ||||
0.241533 | + | 0.970393i | \(0.422350\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.8030 | − | 8.24523i | −0.398107 | − | 0.278105i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.4054 | −0.350566 | −0.175283 | − | 0.984518i | \(-0.556084\pi\) | ||||
−0.175283 | + | 0.984518i | \(0.556084\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.9042 | 1.51115 | 0.755574 | − | 0.655064i | \(-0.227358\pi\) | ||||
0.755574 | + | 0.655064i | \(0.227358\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.9479 | − | 6.52271i | 0.468853 | − | 0.219259i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.948519 | 0.0318482 | 0.0159241 | − | 0.999873i | \(-0.494931\pi\) | ||||
0.0159241 | + | 0.999873i | \(0.494931\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.9805 | − | 7.71720i | −0.636585 | − | 0.258827i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.56688 | + | 9.93584i | −0.119495 | + | 0.332863i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 30.0624i | − | 1.00600i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.7434 | + | 6.78006i | 0.392539 | + | 0.226632i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −29.7718 | − | 20.7976i | −0.994052 | − | 0.694413i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.7440 | + | 48.0541i | −0.925316 | + | 1.60269i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 71.4600 | − | 41.2574i | 2.38068 | − | 1.37448i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.27718 | + | 0.424676i | −0.275447 | + | 0.0141323i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 12.1336i | − | 0.403335i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.0550 | 1.16398 | 0.581990 | − | 0.813196i | \(-0.302274\pi\) | ||||
0.581990 | + | 0.813196i | \(0.302274\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.73303 | − | 1.17194i | −0.223321 | − | 0.0388707i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.8316 | + | 24.7288i | −1.41907 | + | 0.819303i | −0.996218 | − | 0.0868934i | \(-0.972306\pi\) |
−0.422857 | + | 0.906196i | \(0.638973\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.794307 | − | 0.458593i | 0.0262877 | − | 0.0151772i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 18.0353 | − | 25.8175i | 0.596228 | − | 0.853500i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 38.2976 | + | 15.5713i | 1.26470 | + | 0.514209i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.34526 | + | 14.4544i | 0.275285 | + | 0.476807i | 0.970207 | − | 0.242278i | \(-0.0778945\pi\) |
−0.694922 | + | 0.719085i | \(0.744561\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 38.8107 | + | 3.35245i | 1.27886 | + | 0.110467i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.62295 | − | 11.4713i | 0.217997 | − | 0.377582i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.373818 | + | 0.647472i | 0.0122911 | + | 0.0212888i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.56463 | + | 26.2248i | −0.149922 | + | 0.861335i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.31860 | + | 9.21208i | −0.174498 | + | 0.302239i | −0.939987 | − | 0.341209i | \(-0.889163\pi\) |
0.765490 | + | 0.643448i | \(0.222497\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.9122 | − | 6.07381i | −0.783692 | − | 0.199061i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.1844 | − | 7.10097i | 0.497116 | − | 0.232475i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.7480 | + | 9.66948i | 0.547719 | + | 0.316226i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.7085i | 0.872528i | 0.899819 | + | 0.436264i | \(0.143699\pi\) | ||||
−0.899819 | + | 0.436264i | \(0.856301\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.2985 | − | 34.7833i | 0.792952 | − | 1.13511i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.29534 | + | 5.70769i | 0.107425 | + | 0.186065i | 0.914726 | − | 0.404074i | \(-0.132406\pi\) |
−0.807301 | + | 0.590139i | \(0.799073\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.14481 | + | 4.70241i | 0.265232 | + | 0.153131i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −18.3482 | + | 24.4049i | −0.596867 | + | 0.793891i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.8907 | + | 14.3706i | 0.808838 | + | 0.466983i | 0.846552 | − | 0.532306i | \(-0.178674\pi\) |
−0.0377144 | + | 0.999289i | \(0.512008\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.4290 | + | 24.9917i | 0.468384 | + | 0.811265i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.11179 | − | 13.0435i | 0.295470 | − | 0.422965i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 18.2616i | − | 0.591550i | −0.955258 | − | 0.295775i | \(-0.904422\pi\) | ||
0.955258 | − | 0.295775i | \(-0.0955778\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.5718 | − | 6.68098i | −0.374455 | − | 0.216191i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.8444 | + | 6.00666i | −0.415200 | + | 0.194168i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.07189 | + | 2.63633i | −0.0346133 | + | 0.0851315i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.1037 | − | 27.8925i | 0.519476 | − | 0.899758i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.86946 | − | 0.685094i | 0.0602426 | − | 0.0220769i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.41889 | − | 11.1178i | −0.206631 | − | 0.357896i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.5899 | − | 21.8064i | 0.404865 | − | 0.701247i | −0.589441 | − | 0.807812i | \(-0.700652\pi\) |
0.994306 | + | 0.106565i | \(0.0339851\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −45.1499 | − | 3.90003i | −1.45042 | − | 0.125287i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.7214 | − | 41.0866i | −0.761255 | − | 1.31853i | −0.942204 | − | 0.335040i | \(-0.891250\pi\) |
0.180949 | − | 0.983492i | \(-0.442083\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.9117 | − | 14.0298i | −0.349812 | − | 0.449774i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.241285 | + | 0.345399i | −0.00772730 | + | 0.0110616i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47.9278 | − | 27.6711i | 1.53334 | − | 0.885277i | 0.534141 | − | 0.845396i | \(-0.320635\pi\) |
0.999204 | − | 0.0398814i | \(-0.0126980\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.56429 | + | 2.05784i | −0.113915 | + | 0.0657690i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.9049 | − | 36.9961i | 0.986717 | − | 1.18120i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.3499 | −0.808537 | −0.404268 | − | 0.914640i | \(-0.632474\pi\) | ||||
−0.404268 | + | 0.914640i | \(0.632474\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.6643i | 0.562832i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.2524 | − | 32.8046i | −0.676472 | − | 1.04418i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.10404 | − | 5.25622i | 0.289492 | − | 0.167138i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.9683 | + | 22.4618i | −0.411953 | + | 0.713523i | −0.995103 | − | 0.0988413i | \(-0.968486\pi\) |
0.583151 | + | 0.812364i | \(0.301820\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 36.5196 | + | 25.5114i | 1.15891 | + | 0.809580i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34.4753 | + | 19.9043i | 1.09294 | + | 0.631010i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 15.9283i | − | 0.504453i | −0.967668 | − | 0.252227i | \(-0.918837\pi\) | ||
0.967668 | − | 0.252227i | \(-0.0811629\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 55.5972 | − | 15.0942i | 1.75902 | − | 0.477559i |
(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 | 504.2.cx.a.185.13 | yes | 48 | |
3.2 | odd | 2 | 1512.2.cx.a.17.20 | 48 | |||
4.3 | odd | 2 | 1008.2.df.e.689.12 | 48 | |||
7.5 | odd | 6 | 504.2.bs.a.257.5 | ✓ | 48 | ||
9.2 | odd | 6 | 504.2.bs.a.353.5 | yes | 48 | ||
9.7 | even | 3 | 1512.2.bs.a.521.20 | 48 | |||
12.11 | even | 2 | 3024.2.df.e.17.20 | 48 | |||
21.5 | even | 6 | 1512.2.bs.a.1097.20 | 48 | |||
28.19 | even | 6 | 1008.2.ca.e.257.20 | 48 | |||
36.7 | odd | 6 | 3024.2.ca.e.2033.20 | 48 | |||
36.11 | even | 6 | 1008.2.ca.e.353.20 | 48 | |||
63.47 | even | 6 | inner | 504.2.cx.a.425.13 | yes | 48 | |
63.61 | odd | 6 | 1512.2.cx.a.89.20 | 48 | |||
84.47 | odd | 6 | 3024.2.ca.e.2609.20 | 48 | |||
252.47 | odd | 6 | 1008.2.df.e.929.12 | 48 | |||
252.187 | even | 6 | 3024.2.df.e.1601.20 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bs.a.257.5 | ✓ | 48 | 7.5 | odd | 6 | ||
504.2.bs.a.353.5 | yes | 48 | 9.2 | odd | 6 | ||
504.2.cx.a.185.13 | yes | 48 | 1.1 | even | 1 | trivial | |
504.2.cx.a.425.13 | yes | 48 | 63.47 | even | 6 | inner | |
1008.2.ca.e.257.20 | 48 | 28.19 | even | 6 | |||
1008.2.ca.e.353.20 | 48 | 36.11 | even | 6 | |||
1008.2.df.e.689.12 | 48 | 4.3 | odd | 2 | |||
1008.2.df.e.929.12 | 48 | 252.47 | odd | 6 | |||
1512.2.bs.a.521.20 | 48 | 9.7 | even | 3 | |||
1512.2.bs.a.1097.20 | 48 | 21.5 | even | 6 | |||
1512.2.cx.a.17.20 | 48 | 3.2 | odd | 2 | |||
1512.2.cx.a.89.20 | 48 | 63.61 | odd | 6 | |||
3024.2.ca.e.2033.20 | 48 | 36.7 | odd | 6 | |||
3024.2.ca.e.2609.20 | 48 | 84.47 | odd | 6 | |||
3024.2.df.e.17.20 | 48 | 12.11 | even | 2 | |||
3024.2.df.e.1601.20 | 48 | 252.187 | even | 6 |