| Orbit label |
Conrey labels |
Modulus |
Conductor |
Order |
Kernel field |
Value field |
Parity |
Real |
Primitive |
Minimal |
| 384.a |
\(\chi_{384}(1, \cdot)\)
|
$384$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
| 384.b |
\(\chi_{384}(319, \cdot)\)
|
$384$ |
$8$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 384.c |
\(\chi_{384}(383, \cdot)\)
|
$384$ |
$12$ |
$2$ |
\(\Q(\sqrt{3}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 384.d |
\(\chi_{384}(193, \cdot)\)
|
$384$ |
$8$ |
$2$ |
\(\Q(\sqrt{2}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 384.e |
\(\chi_{384}(257, \cdot)\)
|
$384$ |
$3$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 384.f |
\(\chi_{384}(191, \cdot)\)
|
$384$ |
$24$ |
$2$ |
\(\Q(\sqrt{6}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 384.g |
\(\chi_{384}(127, \cdot)\)
|
$384$ |
$4$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 384.h |
\(\chi_{384}(65, \cdot)\)
|
$384$ |
$24$ |
$2$ |
\(\Q(\sqrt{-6}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 384.i |
\(\chi_{384}(161, \cdot)\)$,$ \(\chi_{384}(353, \cdot)\)
|
$384$ |
$48$ |
$4$ |
4.0.18432.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 384.j |
\(\chi_{384}(97, \cdot)\)$,$ \(\chi_{384}(289, \cdot)\)
|
$384$ |
$16$ |
$4$ |
\(\Q(\zeta_{16})^+\) |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 384.k |
\(\chi_{384}(95, \cdot)\)$,$ \(\chi_{384}(287, \cdot)\)
|
$384$ |
$48$ |
$4$ |
4.4.18432.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 384.l |
\(\chi_{384}(31, \cdot)\)$,$ \(\chi_{384}(223, \cdot)\)
|
$384$ |
$16$ |
$4$ |
4.0.2048.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 384.m |
\(\chi_{384}(79, \cdot)\)$, \cdots ,$\(\chi_{384}(367, \cdot)\)
|
$384$ |
$32$ |
$8$ |
8.0.2147483648.1 |
\(\Q(\zeta_{8})\) |
odd |
|
|
|
| 384.n |
\(\chi_{384}(49, \cdot)\)$, \cdots ,$\(\chi_{384}(337, \cdot)\)
|
$384$ |
$32$ |
$8$ |
\(\Q(\zeta_{32})^+\) |
\(\Q(\zeta_{8})\) |
even |
|
|
|
| 384.o |
\(\chi_{384}(47, \cdot)\)$, \cdots ,$\(\chi_{384}(335, \cdot)\)
|
$384$ |
$96$ |
$8$ |
8.8.173946175488.1 |
\(\Q(\zeta_{8})\) |
even |
|
|
|
| 384.p |
\(\chi_{384}(17, \cdot)\)$, \cdots ,$\(\chi_{384}(305, \cdot)\)
|
$384$ |
$96$ |
$8$ |
8.0.173946175488.1 |
\(\Q(\zeta_{8})\) |
odd |
|
|
|
| 384.q |
\(\chi_{384}(41, \cdot)\)$, \cdots ,$\(\chi_{384}(377, \cdot)\)
|
$384$ |
$192$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
odd |
|
|
|
| 384.r |
\(\chi_{384}(25, \cdot)\)$, \cdots ,$\(\chi_{384}(361, \cdot)\)
|
$384$ |
$64$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
even |
|
|
|
| 384.s |
\(\chi_{384}(23, \cdot)\)$, \cdots ,$\(\chi_{384}(359, \cdot)\)
|
$384$ |
$192$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
even |
|
|
|
| 384.t |
\(\chi_{384}(7, \cdot)\)$, \cdots ,$\(\chi_{384}(343, \cdot)\)
|
$384$ |
$64$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
odd |
|
|
|
| 384.u |
\(\chi_{384}(19, \cdot)\)$, \cdots ,$\(\chi_{384}(379, \cdot)\)
|
$384$ |
$128$ |
$32$ |
not computed |
\(\Q(\zeta_{32})\) |
odd |
|
|
✓ |
| 384.v |
\(\chi_{384}(13, \cdot)\)$, \cdots ,$\(\chi_{384}(373, \cdot)\)
|
$384$ |
$128$ |
$32$ |
not computed |
\(\Q(\zeta_{32})\) |
even |
|
|
✓ |
| 384.w |
\(\chi_{384}(11, \cdot)\)$, \cdots ,$\(\chi_{384}(371, \cdot)\)
|
$384$ |
$384$ |
$32$ |
not computed |
\(\Q(\zeta_{32})\) |
even |
|
✓ |
✓ |
| 384.x |
\(\chi_{384}(5, \cdot)\)$, \cdots ,$\(\chi_{384}(365, \cdot)\)
|
$384$ |
$384$ |
$32$ |
not computed |
\(\Q(\zeta_{32})\) |
odd |
|
✓ |
✓ |
