| Orbit label |
Conrey labels |
Modulus |
Conductor |
Order |
Kernel field |
Value field |
Parity |
Real |
Primitive |
Minimal |
| 340.a |
\(\chi_{340}(1, \cdot)\)
|
$340$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
| 340.b |
\(\chi_{340}(171, \cdot)\)
|
$340$ |
$4$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 340.c |
\(\chi_{340}(101, \cdot)\)
|
$340$ |
$17$ |
$2$ |
\(\Q(\sqrt{17}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 340.d |
\(\chi_{340}(339, \cdot)\)
|
$340$ |
$340$ |
$2$ |
\(\Q(\sqrt{-85}) \) |
\(\Q\) |
odd |
✓ |
✓ |
✓ |
| 340.e |
\(\chi_{340}(69, \cdot)\)
|
$340$ |
$5$ |
$2$ |
\(\Q(\sqrt{5}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 340.f |
\(\chi_{340}(239, \cdot)\)
|
$340$ |
$20$ |
$2$ |
\(\Q(\sqrt{-5}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 340.g |
\(\chi_{340}(169, \cdot)\)
|
$340$ |
$85$ |
$2$ |
\(\Q(\sqrt{85}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 340.h |
\(\chi_{340}(271, \cdot)\)
|
$340$ |
$68$ |
$2$ |
\(\Q(\sqrt{-17}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 340.i |
\(\chi_{340}(47, \cdot)\)$,$ \(\chi_{340}(123, \cdot)\)
|
$340$ |
$340$ |
$4$ |
4.4.9826000.1 |
\(\mathbb{Q}(i)\) |
even |
|
✓ |
✓ |
| 340.j |
\(\chi_{340}(13, \cdot)\)$,$ \(\chi_{340}(157, \cdot)\)
|
$340$ |
$85$ |
$4$ |
4.0.614125.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
| 340.k |
\(\chi_{340}(33, \cdot)\)$,$ \(\chi_{340}(237, \cdot)\)
|
$340$ |
$85$ |
$4$ |
4.0.36125.1 |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
| 340.l |
\(\chi_{340}(103, \cdot)\)$,$ \(\chi_{340}(307, \cdot)\)
|
$340$ |
$20$ |
$4$ |
\(\Q(\zeta_{20})^+\) |
\(\mathbb{Q}(i)\) |
even |
|
|
✓ |
| 340.m |
\(\chi_{340}(89, \cdot)\)$,$ \(\chi_{340}(149, \cdot)\)
|
$340$ |
$85$ |
$4$ |
4.4.122825.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
✓ |
| 340.n |
\(\chi_{340}(259, \cdot)\)$,$ \(\chi_{340}(319, \cdot)\)
|
$340$ |
$340$ |
$4$ |
4.0.1965200.1 |
\(\mathbb{Q}(i)\) |
odd |
|
✓ |
✓ |
| 340.o |
\(\chi_{340}(21, \cdot)\)$,$ \(\chi_{340}(81, \cdot)\)
|
$340$ |
$17$ |
$4$ |
4.4.4913.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
✓ |
| 340.p |
\(\chi_{340}(191, \cdot)\)$,$ \(\chi_{340}(251, \cdot)\)
|
$340$ |
$68$ |
$4$ |
4.0.78608.1 |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
| 340.q |
\(\chi_{340}(137, \cdot)\)$,$ \(\chi_{340}(273, \cdot)\)
|
$340$ |
$5$ |
$4$ |
\(\Q(\zeta_{5})\) |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
| 340.r |
\(\chi_{340}(67, \cdot)\)$,$ \(\chi_{340}(203, \cdot)\)
|
$340$ |
$340$ |
$4$ |
4.4.578000.1 |
\(\mathbb{Q}(i)\) |
even |
|
✓ |
✓ |
| 340.s |
\(\chi_{340}(183, \cdot)\)$,$ \(\chi_{340}(327, \cdot)\)
|
$340$ |
$340$ |
$4$ |
4.4.9826000.2 |
\(\mathbb{Q}(i)\) |
even |
|
✓ |
✓ |
| 340.t |
\(\chi_{340}(217, \cdot)\)$,$ \(\chi_{340}(293, \cdot)\)
|
$340$ |
$85$ |
$4$ |
4.0.614125.1 |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
| 340.u |
\(\chi_{340}(121, \cdot)\)$, \cdots ,$\(\chi_{340}(321, \cdot)\)
|
$340$ |
$17$ |
$8$ |
\(\Q(\zeta_{17})^+\) |
\(\Q(\zeta_{8})\) |
even |
|
|
✓ |
| 340.v |
\(\chi_{340}(111, \cdot)\)$, \cdots ,$\(\chi_{340}(331, \cdot)\)
|
$340$ |
$68$ |
$8$ |
8.0.105046700288.1 |
\(\Q(\zeta_{8})\) |
odd |
|
|
✓ |
| 340.w |
\(\chi_{340}(83, \cdot)\)$, \cdots ,$\(\chi_{340}(247, \cdot)\)
|
$340$ |
$340$ |
$8$ |
8.8.1641354692000000.2 |
\(\Q(\zeta_{8})\) |
even |
|
✓ |
✓ |
| 340.x |
\(\chi_{340}(93, \cdot)\)$, \cdots ,$\(\chi_{340}(257, \cdot)\)
|
$340$ |
$85$ |
$8$ |
8.0.6411541765625.1 |
\(\Q(\zeta_{8})\) |
odd |
|
|
✓ |
| 340.y |
\(\chi_{340}(53, \cdot)\)$, \cdots ,$\(\chi_{340}(297, \cdot)\)
|
$340$ |
$85$ |
$8$ |
8.0.6411541765625.2 |
\(\Q(\zeta_{8})\) |
odd |
|
|
✓ |
| 340.z |
\(\chi_{340}(43, \cdot)\)$, \cdots ,$\(\chi_{340}(287, \cdot)\)
|
$340$ |
$340$ |
$8$ |
8.8.1641354692000000.1 |
\(\Q(\zeta_{8})\) |
even |
|
✓ |
✓ |
| 340.ba |
\(\chi_{340}(19, \cdot)\)$, \cdots ,$\(\chi_{340}(219, \cdot)\)
|
$340$ |
$340$ |
$8$ |
8.0.65654187680000.2 |
\(\Q(\zeta_{8})\) |
odd |
|
✓ |
✓ |
| 340.bb |
\(\chi_{340}(9, \cdot)\)$, \cdots ,$\(\chi_{340}(229, \cdot)\)
|
$340$ |
$85$ |
$8$ |
8.8.256461670625.1 |
\(\Q(\zeta_{8})\) |
even |
|
|
✓ |
| 340.bc |
\(\chi_{340}(3, \cdot)\)$, \cdots ,$\(\chi_{340}(303, \cdot)\)
|
$340$ |
$340$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
odd |
|
✓ |
✓ |
| 340.bd |
\(\chi_{340}(57, \cdot)\)$, \cdots ,$\(\chi_{340}(317, \cdot)\)
|
$340$ |
$85$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
even |
|
|
✓ |
| 340.be |
\(\chi_{340}(41, \cdot)\)$, \cdots ,$\(\chi_{340}(301, \cdot)\)
|
$340$ |
$17$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
odd |
|
|
✓ |
| 340.bf |
\(\chi_{340}(11, \cdot)\)$, \cdots ,$\(\chi_{340}(311, \cdot)\)
|
$340$ |
$68$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
even |
|
|
✓ |
| 340.bg |
\(\chi_{340}(39, \cdot)\)$, \cdots ,$\(\chi_{340}(299, \cdot)\)
|
$340$ |
$340$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
even |
|
✓ |
✓ |
| 340.bh |
\(\chi_{340}(29, \cdot)\)$, \cdots ,$\(\chi_{340}(329, \cdot)\)
|
$340$ |
$85$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
odd |
|
|
✓ |
| 340.bi |
\(\chi_{340}(37, \cdot)\)$, \cdots ,$\(\chi_{340}(337, \cdot)\)
|
$340$ |
$85$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
even |
|
|
✓ |
| 340.bj |
\(\chi_{340}(23, \cdot)\)$, \cdots ,$\(\chi_{340}(283, \cdot)\)
|
$340$ |
$340$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
odd |
|
✓ |
✓ |
