| Orbit label |
Conrey labels |
Modulus |
Conductor |
Order |
Kernel field |
Value field |
Parity |
Real |
Primitive |
Minimal |
| 312.a |
\(\chi_{312}(1, \cdot)\)
|
$312$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
| 312.b |
\(\chi_{312}(77, \cdot)\)
|
$312$ |
$312$ |
$2$ |
\(\Q(\sqrt{-78}) \) |
\(\Q\) |
odd |
✓ |
✓ |
✓ |
| 312.c |
\(\chi_{312}(25, \cdot)\)
|
$312$ |
$13$ |
$2$ |
\(\Q(\sqrt{13}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 312.d |
\(\chi_{312}(287, \cdot)\)
|
$312$ |
$12$ |
$2$ |
\(\Q(\sqrt{3}) \) |
\(\Q\) |
even |
✓ |
|
|
| 312.e |
\(\chi_{312}(235, \cdot)\)
|
$312$ |
$8$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 312.f |
\(\chi_{312}(209, \cdot)\)
|
$312$ |
$3$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 312.g |
\(\chi_{312}(157, \cdot)\)
|
$312$ |
$8$ |
$2$ |
\(\Q(\sqrt{2}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 312.h |
\(\chi_{312}(155, \cdot)\)
|
$312$ |
$312$ |
$2$ |
\(\Q(\sqrt{78}) \) |
\(\Q\) |
even |
✓ |
✓ |
✓ |
| 312.i |
\(\chi_{312}(103, \cdot)\)
|
$312$ |
$52$ |
$2$ |
\(\Q(\sqrt{-13}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 312.j |
\(\chi_{312}(131, \cdot)\)
|
$312$ |
$24$ |
$2$ |
\(\Q(\sqrt{6}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 312.k |
\(\chi_{312}(79, \cdot)\)
|
$312$ |
$4$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 312.l |
\(\chi_{312}(233, \cdot)\)
|
$312$ |
$39$ |
$2$ |
\(\Q(\sqrt{-39}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 312.m |
\(\chi_{312}(181, \cdot)\)
|
$312$ |
$104$ |
$2$ |
\(\Q(\sqrt{26}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 312.n |
\(\chi_{312}(311, \cdot)\)
|
$312$ |
$156$ |
$2$ |
\(\Q(\sqrt{39}) \) |
\(\Q\) |
even |
✓ |
|
|
| 312.o |
\(\chi_{312}(259, \cdot)\)
|
$312$ |
$104$ |
$2$ |
\(\Q(\sqrt{-26}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 312.p |
\(\chi_{312}(53, \cdot)\)
|
$312$ |
$24$ |
$2$ |
\(\Q(\sqrt{-6}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 312.q |
\(\chi_{312}(217, \cdot)\)$,$ \(\chi_{312}(289, \cdot)\)
|
$312$ |
$13$ |
$3$ |
3.3.169.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
✓ |
| 312.r |
\(\chi_{312}(109, \cdot)\)$,$ \(\chi_{312}(229, \cdot)\)
|
$312$ |
$104$ |
$4$ |
4.0.140608.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
| 312.s |
\(\chi_{312}(73, \cdot)\)$,$ \(\chi_{312}(265, \cdot)\)
|
$312$ |
$13$ |
$4$ |
4.0.2197.1 |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
| 312.t |
\(\chi_{312}(187, \cdot)\)$,$ \(\chi_{312}(307, \cdot)\)
|
$312$ |
$104$ |
$4$ |
4.4.140608.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
✓ |
| 312.u |
\(\chi_{312}(31, \cdot)\)$,$ \(\chi_{312}(151, \cdot)\)
|
$312$ |
$52$ |
$4$ |
4.4.35152.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 312.v |
\(\chi_{312}(47, \cdot)\)$,$ \(\chi_{312}(239, \cdot)\)
|
$312$ |
$156$ |
$4$ |
4.0.316368.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 312.w |
\(\chi_{312}(83, \cdot)\)$,$ \(\chi_{312}(203, \cdot)\)
|
$312$ |
$312$ |
$4$ |
4.0.1265472.2 |
\(\mathbb{Q}(i)\) |
odd |
|
✓ |
✓ |
| 312.x |
\(\chi_{312}(161, \cdot)\)$,$ \(\chi_{312}(281, \cdot)\)
|
$312$ |
$39$ |
$4$ |
4.4.19773.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
✓ |
| 312.y |
\(\chi_{312}(5, \cdot)\)$,$ \(\chi_{312}(125, \cdot)\)
|
$312$ |
$312$ |
$4$ |
4.4.1265472.2 |
\(\mathbb{Q}(i)\) |
even |
|
✓ |
✓ |
| 312.z |
\(\chi_{312}(127, \cdot)\)$,$ \(\chi_{312}(199, \cdot)\)
|
$312$ |
$52$ |
$6$ |
6.0.23762752.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
|
| 312.ba |
\(\chi_{312}(179, \cdot)\)$,$ \(\chi_{312}(251, \cdot)\)
|
$312$ |
$312$ |
$6$ |
6.6.5132754432.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
✓ |
✓ |
| 312.bb |
\(\chi_{312}(61, \cdot)\)$,$ \(\chi_{312}(133, \cdot)\)
|
$312$ |
$104$ |
$6$ |
6.6.14623232.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
✓ |
| 312.bc |
\(\chi_{312}(113, \cdot)\)$,$ \(\chi_{312}(185, \cdot)\)
|
$312$ |
$39$ |
$6$ |
6.0.771147.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
✓ |
| 312.bd |
\(\chi_{312}(139, \cdot)\)$,$ \(\chi_{312}(211, \cdot)\)
|
$312$ |
$104$ |
$6$ |
6.0.14623232.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
✓ |
| 312.be |
\(\chi_{312}(191, \cdot)\)$,$ \(\chi_{312}(263, \cdot)\)
|
$312$ |
$156$ |
$6$ |
6.6.49353408.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
|
| 312.bf |
\(\chi_{312}(49, \cdot)\)$,$ \(\chi_{312}(121, \cdot)\)
|
$312$ |
$13$ |
$6$ |
\(\Q(\zeta_{13})^+\) |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
✓ |
| 312.bg |
\(\chi_{312}(101, \cdot)\)$,$ \(\chi_{312}(173, \cdot)\)
|
$312$ |
$312$ |
$6$ |
6.0.5132754432.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
✓ |
✓ |
| 312.bh |
\(\chi_{312}(29, \cdot)\)$,$ \(\chi_{312}(269, \cdot)\)
|
$312$ |
$312$ |
$6$ |
6.0.394827264.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
✓ |
✓ |
| 312.bi |
\(\chi_{312}(43, \cdot)\)$,$ \(\chi_{312}(283, \cdot)\)
|
$312$ |
$104$ |
$6$ |
6.0.190102016.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
✓ |
| 312.bj |
\(\chi_{312}(23, \cdot)\)$,$ \(\chi_{312}(95, \cdot)\)
|
$312$ |
$156$ |
$6$ |
6.6.641594304.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
|
| 312.bk |
\(\chi_{312}(205, \cdot)\)$,$ \(\chi_{312}(277, \cdot)\)
|
$312$ |
$104$ |
$6$ |
6.6.190102016.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
✓ |
| 312.bl |
\(\chi_{312}(17, \cdot)\)$,$ \(\chi_{312}(257, \cdot)\)
|
$312$ |
$39$ |
$6$ |
6.0.10024911.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
✓ |
| 312.bm |
\(\chi_{312}(55, \cdot)\)$,$ \(\chi_{312}(295, \cdot)\)
|
$312$ |
$52$ |
$6$ |
6.0.1827904.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
|
| 312.bn |
\(\chi_{312}(35, \cdot)\)$,$ \(\chi_{312}(107, \cdot)\)
|
$312$ |
$312$ |
$6$ |
6.6.394827264.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
✓ |
✓ |
| 312.bo |
\(\chi_{312}(149, \cdot)\)$, \cdots ,$\(\chi_{312}(293, \cdot)\)
|
$312$ |
$312$ |
$12$ |
12.12.342487184769803354112.1 |
\(\Q(\zeta_{12})\) |
even |
|
✓ |
✓ |
| 312.bp |
\(\chi_{312}(41, \cdot)\)$, \cdots ,$\(\chi_{312}(305, \cdot)\)
|
$312$ |
$39$ |
$12$ |
\(\Q(\zeta_{39})^+\) |
\(\Q(\zeta_{12})\) |
even |
|
|
✓ |
| 312.bq |
\(\chi_{312}(11, \cdot)\)$, \cdots ,$\(\chi_{312}(275, \cdot)\)
|
$312$ |
$312$ |
$12$ |
12.0.342487184769803354112.1 |
\(\Q(\zeta_{12})\) |
odd |
|
✓ |
✓ |
| 312.br |
\(\chi_{312}(71, \cdot)\)$, \cdots ,$\(\chi_{312}(215, \cdot)\)
|
$312$ |
$156$ |
$12$ |
12.0.5351362262028177408.1 |
\(\Q(\zeta_{12})\) |
odd |
|
|
|
| 312.bs |
\(\chi_{312}(7, \cdot)\)$, \cdots ,$\(\chi_{312}(271, \cdot)\)
|
$312$ |
$52$ |
$12$ |
\(\Q(\zeta_{52})^+\) |
\(\Q(\zeta_{12})\) |
even |
|
|
|
| 312.bt |
\(\chi_{312}(19, \cdot)\)$, \cdots ,$\(\chi_{312}(163, \cdot)\)
|
$312$ |
$104$ |
$12$ |
12.12.469804094334435328.1 |
\(\Q(\zeta_{12})\) |
even |
|
|
✓ |
| 312.bu |
\(\chi_{312}(97, \cdot)\)$, \cdots ,$\(\chi_{312}(241, \cdot)\)
|
$312$ |
$13$ |
$12$ |
\(\Q(\zeta_{13})\) |
\(\Q(\zeta_{12})\) |
odd |
|
|
✓ |
| 312.bv |
\(\chi_{312}(37, \cdot)\)$, \cdots ,$\(\chi_{312}(301, \cdot)\)
|
$312$ |
$104$ |
$12$ |
12.0.469804094334435328.1 |
\(\Q(\zeta_{12})\) |
odd |
|
|
✓ |
