| Orbit label |
Conrey labels |
Modulus |
Conductor |
Order |
Kernel field |
Value field |
Parity |
Real |
Primitive |
Minimal |
| 117.a |
\(\chi_{117}(1, \cdot)\)
|
$117$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
| 117.b |
\(\chi_{117}(64, \cdot)\)
|
$117$ |
$13$ |
$2$ |
\(\Q(\sqrt{13}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 117.c |
\(\chi_{117}(53, \cdot)\)
|
$117$ |
$3$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 117.d |
\(\chi_{117}(116, \cdot)\)
|
$117$ |
$39$ |
$2$ |
\(\Q(\sqrt{-39}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 117.e |
\(\chi_{117}(40, \cdot)\)$,$ \(\chi_{117}(79, \cdot)\)
|
$117$ |
$9$ |
$3$ |
\(\Q(\zeta_{9})^+\) |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
✓ |
| 117.f |
\(\chi_{117}(61, \cdot)\)$,$ \(\chi_{117}(94, \cdot)\)
|
$117$ |
$117$ |
$3$ |
3.3.13689.2 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
✓ |
✓ |
| 117.g |
\(\chi_{117}(55, \cdot)\)$,$ \(\chi_{117}(100, \cdot)\)
|
$117$ |
$13$ |
$3$ |
3.3.169.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
✓ |
| 117.h |
\(\chi_{117}(16, \cdot)\)$,$ \(\chi_{117}(22, \cdot)\)
|
$117$ |
$117$ |
$3$ |
3.3.13689.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
✓ |
✓ |
| 117.i |
\(\chi_{117}(8, \cdot)\)$,$ \(\chi_{117}(44, \cdot)\)
|
$117$ |
$39$ |
$4$ |
4.4.19773.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
✓ |
| 117.j |
\(\chi_{117}(73, \cdot)\)$,$ \(\chi_{117}(109, \cdot)\)
|
$117$ |
$13$ |
$4$ |
4.0.2197.1 |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
| 117.k |
\(\chi_{117}(29, \cdot)\)$,$ \(\chi_{117}(113, \cdot)\)
|
$117$ |
$117$ |
$6$ |
6.0.562166163.2 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
✓ |
✓ |
| 117.l |
\(\chi_{117}(4, \cdot)\)$,$ \(\chi_{117}(88, \cdot)\)
|
$117$ |
$117$ |
$6$ |
6.6.2436053373.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
✓ |
✓ |
| 117.m |
\(\chi_{117}(23, \cdot)\)$,$ \(\chi_{117}(56, \cdot)\)
|
$117$ |
$117$ |
$6$ |
6.0.7308160119.2 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
✓ |
✓ |
| 117.n |
\(\chi_{117}(38, \cdot)\)$,$ \(\chi_{117}(77, \cdot)\)
|
$117$ |
$117$ |
$6$ |
6.0.43243551.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
✓ |
✓ |
| 117.o |
\(\chi_{117}(17, \cdot)\)$,$ \(\chi_{117}(62, \cdot)\)
|
$117$ |
$39$ |
$6$ |
6.0.10024911.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
✓ |
| 117.p |
\(\chi_{117}(35, \cdot)\)$,$ \(\chi_{117}(107, \cdot)\)
|
$117$ |
$39$ |
$6$ |
6.0.771147.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
✓ |
| 117.q |
\(\chi_{117}(10, \cdot)\)$,$ \(\chi_{117}(82, \cdot)\)
|
$117$ |
$13$ |
$6$ |
\(\Q(\zeta_{13})^+\) |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
✓ |
| 117.r |
\(\chi_{117}(43, \cdot)\)$,$ \(\chi_{117}(49, \cdot)\)
|
$117$ |
$117$ |
$6$ |
6.6.2436053373.2 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
✓ |
✓ |
| 117.s |
\(\chi_{117}(14, \cdot)\)$,$ \(\chi_{117}(92, \cdot)\)
|
$117$ |
$9$ |
$6$ |
\(\Q(\zeta_{9})\) |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
✓ |
| 117.t |
\(\chi_{117}(25, \cdot)\)$,$ \(\chi_{117}(103, \cdot)\)
|
$117$ |
$117$ |
$6$ |
6.6.14414517.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
✓ |
✓ |
| 117.u |
\(\chi_{117}(68, \cdot)\)$,$ \(\chi_{117}(74, \cdot)\)
|
$117$ |
$117$ |
$6$ |
6.0.562166163.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
✓ |
✓ |
| 117.v |
\(\chi_{117}(95, \cdot)\)$,$ \(\chi_{117}(101, \cdot)\)
|
$117$ |
$117$ |
$6$ |
6.0.7308160119.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
✓ |
✓ |
| 117.w |
\(\chi_{117}(58, \cdot)\)$, \cdots ,$\(\chi_{117}(115, \cdot)\)
|
$117$ |
$117$ |
$12$ |
12.0.77146628469360802677.2 |
\(\Q(\zeta_{12})\) |
odd |
|
✓ |
✓ |
| 117.x |
\(\chi_{117}(2, \cdot)\)$, \cdots ,$\(\chi_{117}(59, \cdot)\)
|
$117$ |
$117$ |
$12$ |
12.12.694319656224247224093.2 |
\(\Q(\zeta_{12})\) |
even |
|
✓ |
✓ |
| 117.y |
\(\chi_{117}(31, \cdot)\)$, \cdots ,$\(\chi_{117}(112, \cdot)\)
|
$117$ |
$117$ |
$12$ |
12.0.456488925854205933.1 |
\(\Q(\zeta_{12})\) |
odd |
|
✓ |
✓ |
| 117.z |
\(\chi_{117}(5, \cdot)\)$, \cdots ,$\(\chi_{117}(86, \cdot)\)
|
$117$ |
$117$ |
$12$ |
12.12.4108400332687853397.1 |
\(\Q(\zeta_{12})\) |
even |
|
✓ |
✓ |
| 117.ba |
\(\chi_{117}(71, \cdot)\)$, \cdots ,$\(\chi_{117}(98, \cdot)\)
|
$117$ |
$39$ |
$12$ |
\(\Q(\zeta_{39})^+\) |
\(\Q(\zeta_{12})\) |
even |
|
|
✓ |
| 117.bb |
\(\chi_{117}(7, \cdot)\)$, \cdots ,$\(\chi_{117}(97, \cdot)\)
|
$117$ |
$117$ |
$12$ |
12.0.77146628469360802677.1 |
\(\Q(\zeta_{12})\) |
odd |
|
✓ |
✓ |
| 117.bc |
\(\chi_{117}(20, \cdot)\)$, \cdots ,$\(\chi_{117}(110, \cdot)\)
|
$117$ |
$117$ |
$12$ |
12.12.694319656224247224093.1 |
\(\Q(\zeta_{12})\) |
even |
|
✓ |
✓ |
| 117.bd |
\(\chi_{117}(19, \cdot)\)$, \cdots ,$\(\chi_{117}(46, \cdot)\)
|
$117$ |
$13$ |
$12$ |
\(\Q(\zeta_{13})\) |
\(\Q(\zeta_{12})\) |
odd |
|
|
✓ |
