| Orbit label |
Conrey labels |
Modulus |
Conductor |
Order |
Kernel field |
Value field |
Parity |
Real |
Primitive |
Minimal |
| 588.a |
\(\chi_{588}(1, \cdot)\)
|
$588$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
| 588.b |
\(\chi_{588}(391, \cdot)\)
|
$588$ |
$28$ |
$2$ |
\(\Q(\sqrt{7}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 588.c |
\(\chi_{588}(197, \cdot)\)
|
$588$ |
$3$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 588.d |
\(\chi_{588}(97, \cdot)\)
|
$588$ |
$7$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 588.e |
\(\chi_{588}(491, \cdot)\)
|
$588$ |
$12$ |
$2$ |
\(\Q(\sqrt{3}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 588.f |
\(\chi_{588}(293, \cdot)\)
|
$588$ |
$21$ |
$2$ |
\(\Q(\sqrt{21}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 588.g |
\(\chi_{588}(295, \cdot)\)
|
$588$ |
$4$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 588.h |
\(\chi_{588}(587, \cdot)\)
|
$588$ |
$84$ |
$2$ |
\(\Q(\sqrt{-21}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 588.i |
\(\chi_{588}(361, \cdot)\)$,$ \(\chi_{588}(373, \cdot)\)
|
$588$ |
$7$ |
$3$ |
\(\Q(\zeta_{7})^+\) |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
|
| 588.j |
\(\chi_{588}(215, \cdot)\)$,$ \(\chi_{588}(227, \cdot)\)
|
$588$ |
$84$ |
$6$ |
6.0.29042496.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
|
| 588.k |
\(\chi_{588}(509, \cdot)\)$,$ \(\chi_{588}(521, \cdot)\)
|
$588$ |
$21$ |
$6$ |
\(\Q(\zeta_{21})^+\) |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
|
| 588.l |
\(\chi_{588}(67, \cdot)\)$,$ \(\chi_{588}(79, \cdot)\)
|
$588$ |
$28$ |
$6$ |
6.0.153664.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
|
| 588.m |
\(\chi_{588}(313, \cdot)\)$,$ \(\chi_{588}(325, \cdot)\)
|
$588$ |
$7$ |
$6$ |
\(\Q(\zeta_{7})\) |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
|
| 588.n |
\(\chi_{588}(263, \cdot)\)$,$ \(\chi_{588}(275, \cdot)\)
|
$588$ |
$84$ |
$6$ |
6.6.4148928.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
|
| 588.o |
\(\chi_{588}(19, \cdot)\)$,$ \(\chi_{588}(31, \cdot)\)
|
$588$ |
$28$ |
$6$ |
\(\Q(\zeta_{28})^+\) |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
|
| 588.p |
\(\chi_{588}(557, \cdot)\)$,$ \(\chi_{588}(569, \cdot)\)
|
$588$ |
$21$ |
$6$ |
6.0.64827.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
|
| 588.q |
\(\chi_{588}(85, \cdot)\)$, \cdots ,$\(\chi_{588}(505, \cdot)\)
|
$588$ |
$49$ |
$7$ |
7.7.13841287201.1 |
\(\Q(\zeta_{7})\) |
even |
|
|
✓ |
| 588.r |
\(\chi_{588}(83, \cdot)\)$, \cdots ,$\(\chi_{588}(503, \cdot)\)
|
$588$ |
$588$ |
$14$ |
not computed |
\(\Q(\zeta_{7})\) |
odd |
|
✓ |
✓ |
| 588.s |
\(\chi_{588}(43, \cdot)\)$, \cdots ,$\(\chi_{588}(547, \cdot)\)
|
$588$ |
$196$ |
$14$ |
not computed |
\(\Q(\zeta_{7})\) |
odd |
|
|
✓ |
| 588.t |
\(\chi_{588}(41, \cdot)\)$, \cdots ,$\(\chi_{588}(545, \cdot)\)
|
$588$ |
$147$ |
$14$ |
not computed |
\(\Q(\zeta_{7})\) |
even |
|
|
✓ |
| 588.u |
\(\chi_{588}(71, \cdot)\)$, \cdots ,$\(\chi_{588}(575, \cdot)\)
|
$588$ |
$588$ |
$14$ |
not computed |
\(\Q(\zeta_{7})\) |
even |
|
✓ |
✓ |
| 588.v |
\(\chi_{588}(13, \cdot)\)$, \cdots ,$\(\chi_{588}(517, \cdot)\)
|
$588$ |
$49$ |
$14$ |
not computed |
\(\Q(\zeta_{7})\) |
odd |
|
|
✓ |
| 588.w |
\(\chi_{588}(29, \cdot)\)$, \cdots ,$\(\chi_{588}(533, \cdot)\)
|
$588$ |
$147$ |
$14$ |
not computed |
\(\Q(\zeta_{7})\) |
odd |
|
|
✓ |
| 588.x |
\(\chi_{588}(55, \cdot)\)$, \cdots ,$\(\chi_{588}(559, \cdot)\)
|
$588$ |
$196$ |
$14$ |
not computed |
\(\Q(\zeta_{7})\) |
even |
|
|
✓ |
| 588.y |
\(\chi_{588}(25, \cdot)\)$, \cdots ,$\(\chi_{588}(541, \cdot)\)
|
$588$ |
$49$ |
$21$ |
not computed |
\(\Q(\zeta_{21})\) |
even |
|
|
✓ |
| 588.z |
\(\chi_{588}(53, \cdot)\)$, \cdots ,$\(\chi_{588}(485, \cdot)\)
|
$588$ |
$147$ |
$42$ |
not computed |
\(\Q(\zeta_{21})\) |
odd |
|
|
✓ |
| 588.ba |
\(\chi_{588}(103, \cdot)\)$, \cdots ,$\(\chi_{588}(535, \cdot)\)
|
$588$ |
$196$ |
$42$ |
not computed |
\(\Q(\zeta_{21})\) |
even |
|
|
✓ |
| 588.bb |
\(\chi_{588}(11, \cdot)\)$, \cdots ,$\(\chi_{588}(527, \cdot)\)
|
$588$ |
$588$ |
$42$ |
not computed |
\(\Q(\zeta_{21})\) |
even |
|
✓ |
✓ |
| 588.bc |
\(\chi_{588}(61, \cdot)\)$, \cdots ,$\(\chi_{588}(577, \cdot)\)
|
$588$ |
$49$ |
$42$ |
not computed |
\(\Q(\zeta_{21})\) |
odd |
|
|
✓ |
| 588.bd |
\(\chi_{588}(151, \cdot)\)$, \cdots ,$\(\chi_{588}(583, \cdot)\)
|
$588$ |
$196$ |
$42$ |
not computed |
\(\Q(\zeta_{21})\) |
odd |
|
|
✓ |
| 588.be |
\(\chi_{588}(5, \cdot)\)$, \cdots ,$\(\chi_{588}(437, \cdot)\)
|
$588$ |
$147$ |
$42$ |
not computed |
\(\Q(\zeta_{21})\) |
even |
|
|
✓ |
| 588.bf |
\(\chi_{588}(47, \cdot)\)$, \cdots ,$\(\chi_{588}(563, \cdot)\)
|
$588$ |
$588$ |
$42$ |
not computed |
\(\Q(\zeta_{21})\) |
odd |
|
✓ |
✓ |
