| Orbit label |
Conrey labels |
Modulus |
Conductor |
Order |
Kernel field |
Value field |
Parity |
Real |
Primitive |
Minimal |
| 323.a |
\(\chi_{323}(1, \cdot)\)
|
$323$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
| 323.b |
\(\chi_{323}(18, \cdot)\)
|
$323$ |
$19$ |
$2$ |
\(\Q(\sqrt{-19}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 323.c |
\(\chi_{323}(322, \cdot)\)
|
$323$ |
$323$ |
$2$ |
\(\Q(\sqrt{-323}) \) |
\(\Q\) |
odd |
✓ |
✓ |
✓ |
| 323.d |
\(\chi_{323}(305, \cdot)\)
|
$323$ |
$17$ |
$2$ |
\(\Q(\sqrt{17}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 323.e |
\(\chi_{323}(239, \cdot)\)$,$ \(\chi_{323}(273, \cdot)\)
|
$323$ |
$19$ |
$3$ |
3.3.361.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
✓ |
| 323.f |
\(\chi_{323}(115, \cdot)\)$,$ \(\chi_{323}(191, \cdot)\)
|
$323$ |
$17$ |
$4$ |
4.4.4913.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
✓ |
| 323.g |
\(\chi_{323}(132, \cdot)\)$,$ \(\chi_{323}(208, \cdot)\)
|
$323$ |
$323$ |
$4$ |
4.0.1773593.2 |
\(\mathbb{Q}(i)\) |
odd |
|
✓ |
✓ |
| 323.h |
\(\chi_{323}(220, \cdot)\)$,$ \(\chi_{323}(254, \cdot)\)
|
$323$ |
$323$ |
$6$ |
6.6.640267073.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
✓ |
✓ |
| 323.i |
\(\chi_{323}(50, \cdot)\)$,$ \(\chi_{323}(84, \cdot)\)
|
$323$ |
$323$ |
$6$ |
6.0.12165074387.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
✓ |
✓ |
| 323.j |
\(\chi_{323}(69, \cdot)\)$,$ \(\chi_{323}(103, \cdot)\)
|
$323$ |
$19$ |
$6$ |
6.0.2476099.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
✓ |
| 323.k |
\(\chi_{323}(77, \cdot)\)$, \cdots ,$\(\chi_{323}(229, \cdot)\)
|
$323$ |
$17$ |
$8$ |
\(\Q(\zeta_{17})^+\) |
\(\Q(\zeta_{8})\) |
even |
|
|
✓ |
| 323.l |
\(\chi_{323}(94, \cdot)\)$, \cdots ,$\(\chi_{323}(246, \cdot)\)
|
$323$ |
$323$ |
$8$ |
8.0.53475746204033.2 |
\(\Q(\zeta_{8})\) |
odd |
|
✓ |
✓ |
| 323.m |
\(\chi_{323}(35, \cdot)\)$, \cdots ,$\(\chi_{323}(290, \cdot)\)
|
$323$ |
$19$ |
$9$ |
\(\Q(\zeta_{19})^+\) |
\(\Q(\zeta_{9})\) |
even |
|
|
✓ |
| 323.n |
\(\chi_{323}(183, \cdot)\)$, \cdots ,$\(\chi_{323}(293, \cdot)\)
|
$323$ |
$323$ |
$12$ |
12.0.727070128175028950803097.1 |
\(\Q(\zeta_{12})\) |
odd |
|
✓ |
✓ |
| 323.o |
\(\chi_{323}(30, \cdot)\)$, \cdots ,$\(\chi_{323}(140, \cdot)\)
|
$323$ |
$323$ |
$12$ |
12.12.2014044676385121747377.1 |
\(\Q(\zeta_{12})\) |
even |
|
✓ |
✓ |
| 323.p |
\(\chi_{323}(37, \cdot)\)$, \cdots ,$\(\chi_{323}(303, \cdot)\)
|
$323$ |
$323$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
even |
|
✓ |
✓ |
| 323.q |
\(\chi_{323}(20, \cdot)\)$, \cdots ,$\(\chi_{323}(286, \cdot)\)
|
$323$ |
$17$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
odd |
|
|
✓ |
| 323.r |
\(\chi_{323}(52, \cdot)\)$, \cdots ,$\(\chi_{323}(307, \cdot)\)
|
$323$ |
$19$ |
$18$ |
not computed |
\(\Q(\zeta_{9})\) |
odd |
|
|
✓ |
| 323.s |
\(\chi_{323}(16, \cdot)\)$, \cdots ,$\(\chi_{323}(271, \cdot)\)
|
$323$ |
$323$ |
$18$ |
not computed |
\(\Q(\zeta_{9})\) |
even |
|
✓ |
✓ |
| 323.t |
\(\chi_{323}(33, \cdot)\)$, \cdots ,$\(\chi_{323}(288, \cdot)\)
|
$323$ |
$323$ |
$18$ |
not computed |
\(\Q(\zeta_{9})\) |
odd |
|
✓ |
✓ |
| 323.u |
\(\chi_{323}(8, \cdot)\)$, \cdots ,$\(\chi_{323}(297, \cdot)\)
|
$323$ |
$323$ |
$24$ |
not computed |
\(\Q(\zeta_{24})\) |
odd |
|
✓ |
✓ |
| 323.v |
\(\chi_{323}(26, \cdot)\)$, \cdots ,$\(\chi_{323}(315, \cdot)\)
|
$323$ |
$323$ |
$24$ |
not computed |
\(\Q(\zeta_{24})\) |
even |
|
✓ |
✓ |
| 323.w |
\(\chi_{323}(13, \cdot)\)$, \cdots ,$\(\chi_{323}(319, \cdot)\)
|
$323$ |
$323$ |
$36$ |
not computed |
\(\Q(\zeta_{36})\) |
odd |
|
✓ |
✓ |
| 323.x |
\(\chi_{323}(4, \cdot)\)$, \cdots ,$\(\chi_{323}(310, \cdot)\)
|
$323$ |
$323$ |
$36$ |
not computed |
\(\Q(\zeta_{36})\) |
even |
|
✓ |
✓ |
| 323.y |
\(\chi_{323}(12, \cdot)\)$, \cdots ,$\(\chi_{323}(316, \cdot)\)
|
$323$ |
$323$ |
$48$ |
not computed |
\(\Q(\zeta_{48})\) |
even |
|
✓ |
✓ |
| 323.z |
\(\chi_{323}(7, \cdot)\)$, \cdots ,$\(\chi_{323}(311, \cdot)\)
|
$323$ |
$323$ |
$48$ |
not computed |
\(\Q(\zeta_{48})\) |
odd |
|
✓ |
✓ |
| 323.ba |
\(\chi_{323}(2, \cdot)\)$, \cdots ,$\(\chi_{323}(314, \cdot)\)
|
$323$ |
$323$ |
$72$ |
not computed |
$\Q(\zeta_{72})$ |
odd |
|
✓ |
✓ |
| 323.bb |
\(\chi_{323}(9, \cdot)\)$, \cdots ,$\(\chi_{323}(321, \cdot)\)
|
$323$ |
$323$ |
$72$ |
not computed |
$\Q(\zeta_{72})$ |
even |
|
✓ |
✓ |
| 323.bc |
\(\chi_{323}(3, \cdot)\)$, \cdots ,$\(\chi_{323}(318, \cdot)\)
|
$323$ |
$323$ |
$144$ |
not computed |
$\Q(\zeta_{144})$ |
even |
|
✓ |
✓ |
| 323.bd |
\(\chi_{323}(5, \cdot)\)$, \cdots ,$\(\chi_{323}(320, \cdot)\)
|
$323$ |
$323$ |
$144$ |
not computed |
$\Q(\zeta_{144})$ |
odd |
|
✓ |
✓ |
