| Orbit label |
Conrey labels |
Modulus |
Conductor |
Order |
Kernel field |
Value field |
Parity |
Real |
Primitive |
Minimal |
| 864.a |
\(\chi_{864}(1, \cdot)\)
|
$864$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
| 864.b |
\(\chi_{864}(271, \cdot)\)
|
$864$ |
$8$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 864.c |
\(\chi_{864}(863, \cdot)\)
|
$864$ |
$12$ |
$2$ |
\(\Q(\sqrt{3}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 864.d |
\(\chi_{864}(433, \cdot)\)
|
$864$ |
$8$ |
$2$ |
\(\Q(\sqrt{2}) \) |
\(\Q\) |
even |
✓ |
|
|
| 864.e |
\(\chi_{864}(161, \cdot)\)
|
$864$ |
$3$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 864.f |
\(\chi_{864}(431, \cdot)\)
|
$864$ |
$24$ |
$2$ |
\(\Q(\sqrt{6}) \) |
\(\Q\) |
even |
✓ |
|
|
| 864.g |
\(\chi_{864}(703, \cdot)\)
|
$864$ |
$4$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 864.h |
\(\chi_{864}(593, \cdot)\)
|
$864$ |
$24$ |
$2$ |
\(\Q(\sqrt{-6}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 864.i |
\(\chi_{864}(289, \cdot)\)$,$ \(\chi_{864}(577, \cdot)\)
|
$864$ |
$9$ |
$3$ |
\(\Q(\zeta_{9})^+\) |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
|
| 864.j |
\(\chi_{864}(377, \cdot)\)$,$ \(\chi_{864}(809, \cdot)\)
|
$864$ |
$48$ |
$4$ |
4.0.18432.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 864.k |
\(\chi_{864}(217, \cdot)\)$,$ \(\chi_{864}(649, \cdot)\)
|
$864$ |
$16$ |
$4$ |
\(\Q(\zeta_{16})^+\) |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 864.l |
\(\chi_{864}(215, \cdot)\)$,$ \(\chi_{864}(647, \cdot)\)
|
$864$ |
$48$ |
$4$ |
4.4.18432.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 864.m |
\(\chi_{864}(55, \cdot)\)$,$ \(\chi_{864}(487, \cdot)\)
|
$864$ |
$16$ |
$4$ |
4.0.2048.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 864.n |
\(\chi_{864}(17, \cdot)\)$,$ \(\chi_{864}(305, \cdot)\)
|
$864$ |
$72$ |
$6$ |
6.0.10077696.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
|
| 864.o |
\(\chi_{864}(127, \cdot)\)$,$ \(\chi_{864}(415, \cdot)\)
|
$864$ |
$36$ |
$6$ |
6.0.419904.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
|
| 864.p |
\(\chi_{864}(143, \cdot)\)$,$ \(\chi_{864}(719, \cdot)\)
|
$864$ |
$72$ |
$6$ |
6.6.10077696.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
|
| 864.q |
\(\chi_{864}(449, \cdot)\)$,$ \(\chi_{864}(737, \cdot)\)
|
$864$ |
$9$ |
$6$ |
\(\Q(\zeta_{9})\) |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
|
| 864.r |
\(\chi_{864}(145, \cdot)\)$,$ \(\chi_{864}(721, \cdot)\)
|
$864$ |
$72$ |
$6$ |
6.6.3359232.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
|
| 864.s |
\(\chi_{864}(287, \cdot)\)$,$ \(\chi_{864}(575, \cdot)\)
|
$864$ |
$36$ |
$6$ |
\(\Q(\zeta_{36})^+\) |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
|
| 864.t |
\(\chi_{864}(559, \cdot)\)$,$ \(\chi_{864}(847, \cdot)\)
|
$864$ |
$72$ |
$6$ |
6.0.3359232.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
|
| 864.u |
\(\chi_{864}(163, \cdot)\)$, \cdots ,$\(\chi_{864}(811, \cdot)\)
|
$864$ |
$32$ |
$8$ |
8.0.2147483648.1 |
\(\Q(\zeta_{8})\) |
odd |
|
|
✓ |
| 864.v |
\(\chi_{864}(109, \cdot)\)$, \cdots ,$\(\chi_{864}(757, \cdot)\)
|
$864$ |
$32$ |
$8$ |
\(\Q(\zeta_{32})^+\) |
\(\Q(\zeta_{8})\) |
even |
|
|
✓ |
| 864.w |
\(\chi_{864}(107, \cdot)\)$, \cdots ,$\(\chi_{864}(755, \cdot)\)
|
$864$ |
$96$ |
$8$ |
8.8.173946175488.1 |
\(\Q(\zeta_{8})\) |
even |
|
|
✓ |
| 864.x |
\(\chi_{864}(53, \cdot)\)$, \cdots ,$\(\chi_{864}(701, \cdot)\)
|
$864$ |
$96$ |
$8$ |
8.0.173946175488.1 |
\(\Q(\zeta_{8})\) |
odd |
|
|
✓ |
| 864.y |
\(\chi_{864}(97, \cdot)\)$, \cdots ,$\(\chi_{864}(769, \cdot)\)
|
$864$ |
$27$ |
$9$ |
\(\Q(\zeta_{27})^+\) |
\(\Q(\zeta_{9})\) |
even |
|
|
✓ |
| 864.z |
\(\chi_{864}(71, \cdot)\)$, \cdots ,$\(\chi_{864}(791, \cdot)\)
|
$864$ |
$144$ |
$12$ |
12.12.3327916660110655488.1 |
\(\Q(\zeta_{12})\) |
even |
|
|
|
| 864.ba |
\(\chi_{864}(199, \cdot)\)$, \cdots ,$\(\chi_{864}(775, \cdot)\)
|
$864$ |
$144$ |
$12$ |
12.0.369768517790072832.1 |
\(\Q(\zeta_{12})\) |
odd |
|
|
|
| 864.bb |
\(\chi_{864}(89, \cdot)\)$, \cdots ,$\(\chi_{864}(665, \cdot)\)
|
$864$ |
$144$ |
$12$ |
12.0.3327916660110655488.1 |
\(\Q(\zeta_{12})\) |
odd |
|
|
|
| 864.bc |
\(\chi_{864}(73, \cdot)\)$, \cdots ,$\(\chi_{864}(793, \cdot)\)
|
$864$ |
$144$ |
$12$ |
12.12.369768517790072832.1 |
\(\Q(\zeta_{12})\) |
even |
|
|
|
| 864.bd |
\(\chi_{864}(79, \cdot)\)$, \cdots ,$\(\chi_{864}(751, \cdot)\)
|
$864$ |
$216$ |
$18$ |
not computed |
\(\Q(\zeta_{9})\) |
odd |
|
|
|
| 864.be |
\(\chi_{864}(31, \cdot)\)$, \cdots ,$\(\chi_{864}(799, \cdot)\)
|
$864$ |
$108$ |
$18$ |
not computed |
\(\Q(\zeta_{9})\) |
odd |
|
|
✓ |
| 864.bf |
\(\chi_{864}(49, \cdot)\)$, \cdots ,$\(\chi_{864}(817, \cdot)\)
|
$864$ |
$216$ |
$18$ |
not computed |
\(\Q(\zeta_{9})\) |
even |
|
|
|
| 864.bg |
\(\chi_{864}(65, \cdot)\)$, \cdots ,$\(\chi_{864}(833, \cdot)\)
|
$864$ |
$27$ |
$18$ |
not computed |
\(\Q(\zeta_{9})\) |
odd |
|
|
✓ |
| 864.bh |
\(\chi_{864}(47, \cdot)\)$, \cdots ,$\(\chi_{864}(815, \cdot)\)
|
$864$ |
$216$ |
$18$ |
not computed |
\(\Q(\zeta_{9})\) |
even |
|
|
|
| 864.bi |
\(\chi_{864}(95, \cdot)\)$, \cdots ,$\(\chi_{864}(767, \cdot)\)
|
$864$ |
$108$ |
$18$ |
not computed |
\(\Q(\zeta_{9})\) |
even |
|
|
✓ |
| 864.bj |
\(\chi_{864}(113, \cdot)\)$, \cdots ,$\(\chi_{864}(785, \cdot)\)
|
$864$ |
$216$ |
$18$ |
not computed |
\(\Q(\zeta_{9})\) |
odd |
|
|
|
| 864.bk |
\(\chi_{864}(37, \cdot)\)$, \cdots ,$\(\chi_{864}(829, \cdot)\)
|
$864$ |
$288$ |
$24$ |
not computed |
\(\Q(\zeta_{24})\) |
even |
|
|
|
| 864.bl |
\(\chi_{864}(19, \cdot)\)$, \cdots ,$\(\chi_{864}(739, \cdot)\)
|
$864$ |
$288$ |
$24$ |
not computed |
\(\Q(\zeta_{24})\) |
odd |
|
|
|
| 864.bm |
\(\chi_{864}(125, \cdot)\)$, \cdots ,$\(\chi_{864}(845, \cdot)\)
|
$864$ |
$288$ |
$24$ |
not computed |
\(\Q(\zeta_{24})\) |
odd |
|
|
|
| 864.bn |
\(\chi_{864}(35, \cdot)\)$, \cdots ,$\(\chi_{864}(827, \cdot)\)
|
$864$ |
$288$ |
$24$ |
not computed |
\(\Q(\zeta_{24})\) |
even |
|
|
|
| 864.bo |
\(\chi_{864}(25, \cdot)\)$, \cdots ,$\(\chi_{864}(841, \cdot)\)
|
$864$ |
$432$ |
$36$ |
not computed |
\(\Q(\zeta_{36})\) |
even |
|
|
|
| 864.bp |
\(\chi_{864}(7, \cdot)\)$, \cdots ,$\(\chi_{864}(823, \cdot)\)
|
$864$ |
$432$ |
$36$ |
not computed |
\(\Q(\zeta_{36})\) |
odd |
|
|
|
| 864.bq |
\(\chi_{864}(41, \cdot)\)$, \cdots ,$\(\chi_{864}(857, \cdot)\)
|
$864$ |
$432$ |
$36$ |
not computed |
\(\Q(\zeta_{36})\) |
odd |
|
|
|
| 864.br |
\(\chi_{864}(23, \cdot)\)$, \cdots ,$\(\chi_{864}(839, \cdot)\)
|
$864$ |
$432$ |
$36$ |
not computed |
\(\Q(\zeta_{36})\) |
even |
|
|
|
| 864.bs |
\(\chi_{864}(5, \cdot)\)$, \cdots ,$\(\chi_{864}(821, \cdot)\)
|
$864$ |
$864$ |
$72$ |
not computed |
$\Q(\zeta_{72})$ |
odd |
|
✓ |
✓ |
| 864.bt |
\(\chi_{864}(11, \cdot)\)$, \cdots ,$\(\chi_{864}(851, \cdot)\)
|
$864$ |
$864$ |
$72$ |
not computed |
$\Q(\zeta_{72})$ |
even |
|
✓ |
✓ |
| 864.bu |
\(\chi_{864}(13, \cdot)\)$, \cdots ,$\(\chi_{864}(853, \cdot)\)
|
$864$ |
$864$ |
$72$ |
not computed |
$\Q(\zeta_{72})$ |
even |
|
✓ |
✓ |
| 864.bv |
\(\chi_{864}(43, \cdot)\)$, \cdots ,$\(\chi_{864}(859, \cdot)\)
|
$864$ |
$864$ |
$72$ |
not computed |
$\Q(\zeta_{72})$ |
odd |
|
✓ |
✓ |
