| Orbit label |
Conrey labels |
Modulus |
Conductor |
Order |
Kernel field |
Value field |
Parity |
Real |
Primitive |
Minimal |
| 1309.a |
\(\chi_{1309}(1, \cdot)\)
|
$1309$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
| 1309.b |
\(\chi_{1309}(1121, \cdot)\)
|
$1309$ |
$187$ |
$2$ |
\(\Q(\sqrt{-187}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 1309.c |
\(\chi_{1309}(307, \cdot)\)
|
$1309$ |
$77$ |
$2$ |
\(\Q(\sqrt{77}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 1309.d |
\(\chi_{1309}(120, \cdot)\)
|
$1309$ |
$11$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 1309.e |
\(\chi_{1309}(1308, \cdot)\)
|
$1309$ |
$1309$ |
$2$ |
\(\Q(\sqrt{1309}) \) |
\(\Q\) |
even |
✓ |
✓ |
✓ |
| 1309.f |
\(\chi_{1309}(188, \cdot)\)
|
$1309$ |
$7$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 1309.g |
\(\chi_{1309}(1002, \cdot)\)
|
$1309$ |
$17$ |
$2$ |
\(\Q(\sqrt{17}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 1309.h |
\(\chi_{1309}(1189, \cdot)\)
|
$1309$ |
$119$ |
$2$ |
\(\Q(\sqrt{-119}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 1309.i |
\(\chi_{1309}(375, \cdot)\)$,$ \(\chi_{1309}(562, \cdot)\)
|
$1309$ |
$7$ |
$3$ |
\(\Q(\zeta_{7})^+\) |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
✓ |
| 1309.j |
\(\chi_{1309}(650, \cdot)\)$,$ \(\chi_{1309}(727, \cdot)\)
|
$1309$ |
$119$ |
$4$ |
4.0.240737.1 |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
| 1309.k |
\(\chi_{1309}(463, \cdot)\)$,$ \(\chi_{1309}(540, \cdot)\)
|
$1309$ |
$17$ |
$4$ |
4.4.4913.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
✓ |
| 1309.l |
\(\chi_{1309}(582, \cdot)\)$,$ \(\chi_{1309}(659, \cdot)\)
|
$1309$ |
$187$ |
$4$ |
4.0.594473.1 |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
| 1309.m |
\(\chi_{1309}(769, \cdot)\)$,$ \(\chi_{1309}(846, \cdot)\)
|
$1309$ |
$1309$ |
$4$ |
4.4.29129177.2 |
\(\mathbb{Q}(i)\) |
even |
|
✓ |
✓ |
| 1309.n |
\(\chi_{1309}(477, \cdot)\)$, \cdots ,$\(\chi_{1309}(1191, \cdot)\)
|
$1309$ |
$11$ |
$5$ |
\(\Q(\zeta_{11})^+\) |
\(\Q(\zeta_{5})\) |
even |
|
|
✓ |
| 1309.o |
\(\chi_{1309}(628, \cdot)\)$,$ \(\chi_{1309}(815, \cdot)\)
|
$1309$ |
$119$ |
$6$ |
6.0.82572791.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
✓ |
| 1309.p |
\(\chi_{1309}(936, \cdot)\)$,$ \(\chi_{1309}(1123, \cdot)\)
|
$1309$ |
$7$ |
$6$ |
\(\Q(\zeta_{7})\) |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
✓ |
| 1309.q |
\(\chi_{1309}(67, \cdot)\)$,$ \(\chi_{1309}(254, \cdot)\)
|
$1309$ |
$119$ |
$6$ |
6.6.11796113.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
✓ |
| 1309.r |
\(\chi_{1309}(494, \cdot)\)$,$ \(\chi_{1309}(681, \cdot)\)
|
$1309$ |
$77$ |
$6$ |
6.0.3195731.1 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
✓ |
| 1309.s |
\(\chi_{1309}(747, \cdot)\)$,$ \(\chi_{1309}(934, \cdot)\)
|
$1309$ |
$1309$ |
$6$ |
6.6.109904384821.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
✓ |
✓ |
| 1309.t |
\(\chi_{1309}(186, \cdot)\)$,$ \(\chi_{1309}(373, \cdot)\)
|
$1309$ |
$1309$ |
$6$ |
6.0.15700626403.5 |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
✓ |
✓ |
| 1309.u |
\(\chi_{1309}(1055, \cdot)\)$,$ \(\chi_{1309}(1242, \cdot)\)
|
$1309$ |
$77$ |
$6$ |
6.6.22370117.1 |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
✓ |
| 1309.v |
\(\chi_{1309}(76, \cdot)\)$, \cdots ,$\(\chi_{1309}(1154, \cdot)\)
|
$1309$ |
$1309$ |
$8$ |
8.8.14424652195854593.1 |
\(\Q(\zeta_{8})\) |
even |
|
✓ |
✓ |
| 1309.w |
\(\chi_{1309}(155, \cdot)\)$, \cdots ,$\(\chi_{1309}(1233, \cdot)\)
|
$1309$ |
$17$ |
$8$ |
\(\Q(\zeta_{17})^+\) |
\(\Q(\zeta_{8})\) |
even |
|
|
✓ |
| 1309.x |
\(\chi_{1309}(43, \cdot)\)$, \cdots ,$\(\chi_{1309}(1198, \cdot)\)
|
$1309$ |
$187$ |
$8$ |
8.0.6007768511393.1 |
\(\Q(\zeta_{8})\) |
odd |
|
|
✓ |
| 1309.y |
\(\chi_{1309}(111, \cdot)\)$, \cdots ,$\(\chi_{1309}(1266, \cdot)\)
|
$1309$ |
$119$ |
$8$ |
8.0.985223153873.1 |
\(\Q(\zeta_{8})\) |
odd |
|
|
✓ |
| 1309.z |
\(\chi_{1309}(356, \cdot)\)$, \cdots ,$\(\chi_{1309}(1070, \cdot)\)
|
$1309$ |
$1309$ |
$10$ |
10.0.5115361002064185719.3 |
\(\Q(\zeta_{5})\) |
odd |
|
✓ |
✓ |
| 1309.ba |
\(\chi_{1309}(169, \cdot)\)$, \cdots ,$\(\chi_{1309}(883, \cdot)\)
|
$1309$ |
$187$ |
$10$ |
10.10.304358957700017.1 |
\(\Q(\zeta_{5})\) |
even |
|
|
✓ |
| 1309.bb |
\(\chi_{1309}(69, \cdot)\)$, \cdots ,$\(\chi_{1309}(1259, \cdot)\)
|
$1309$ |
$77$ |
$10$ |
10.0.3602729712967.1 |
\(\Q(\zeta_{5})\) |
odd |
|
|
✓ |
| 1309.bc |
\(\chi_{1309}(118, \cdot)\)$, \cdots ,$\(\chi_{1309}(832, \cdot)\)
|
$1309$ |
$1309$ |
$10$ |
10.10.56268971022706042909.1 |
\(\Q(\zeta_{5})\) |
even |
|
✓ |
✓ |
| 1309.bd |
\(\chi_{1309}(239, \cdot)\)$, \cdots ,$\(\chi_{1309}(953, \cdot)\)
|
$1309$ |
$11$ |
$10$ |
\(\Q(\zeta_{11})\) |
\(\Q(\zeta_{5})\) |
odd |
|
|
✓ |
| 1309.be |
\(\chi_{1309}(426, \cdot)\)$, \cdots ,$\(\chi_{1309}(1140, \cdot)\)
|
$1309$ |
$77$ |
$10$ |
10.10.39630026842637.1 |
\(\Q(\zeta_{5})\) |
even |
|
|
✓ |
| 1309.bf |
\(\chi_{1309}(50, \cdot)\)$, \cdots ,$\(\chi_{1309}(1240, \cdot)\)
|
$1309$ |
$187$ |
$10$ |
10.0.3347948534700187.1 |
\(\Q(\zeta_{5})\) |
odd |
|
|
✓ |
| 1309.bg |
\(\chi_{1309}(956, \cdot)\)$, \cdots ,$\(\chi_{1309}(1220, \cdot)\)
|
$1309$ |
$1309$ |
$12$ |
12.0.1211102005991051069543417.1 |
\(\Q(\zeta_{12})\) |
odd |
|
✓ |
✓ |
| 1309.bh |
\(\chi_{1309}(208, \cdot)\)$, \cdots ,$\(\chi_{1309}(472, \cdot)\)
|
$1309$ |
$1309$ |
$12$ |
12.12.59343998293561502407627433.1 |
\(\Q(\zeta_{12})\) |
even |
|
✓ |
✓ |
| 1309.bi |
\(\chi_{1309}(89, \cdot)\)$, \cdots ,$\(\chi_{1309}(353, \cdot)\)
|
$1309$ |
$119$ |
$12$ |
12.0.33498139941871322753.1 |
\(\Q(\zeta_{12})\) |
odd |
|
|
✓ |
| 1309.bj |
\(\chi_{1309}(837, \cdot)\)$, \cdots ,$\(\chi_{1309}(1101, \cdot)\)
|
$1309$ |
$119$ |
$12$ |
12.12.683635509017782097.1 |
\(\Q(\zeta_{12})\) |
even |
|
|
✓ |
| 1309.bk |
\(\chi_{1309}(86, \cdot)\)$, \cdots ,$\(\chi_{1309}(1208, \cdot)\)
|
$1309$ |
$77$ |
$15$ |
not computed |
\(\Q(\zeta_{15})\) |
even |
|
|
✓ |
| 1309.bl |
\(\chi_{1309}(197, \cdot)\)$, \cdots ,$\(\chi_{1309}(1044, \cdot)\)
|
$1309$ |
$187$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
even |
|
|
✓ |
| 1309.bm |
\(\chi_{1309}(384, \cdot)\)$, \cdots ,$\(\chi_{1309}(1231, \cdot)\)
|
$1309$ |
$1309$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
odd |
|
✓ |
✓ |
| 1309.bn |
\(\chi_{1309}(265, \cdot)\)$, \cdots ,$\(\chi_{1309}(1112, \cdot)\)
|
$1309$ |
$119$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
even |
|
|
✓ |
| 1309.bo |
\(\chi_{1309}(78, \cdot)\)$, \cdots ,$\(\chi_{1309}(925, \cdot)\)
|
$1309$ |
$17$ |
$16$ |
not computed |
\(\Q(\zeta_{16})\) |
odd |
|
|
✓ |
| 1309.bp |
\(\chi_{1309}(13, \cdot)\)$, \cdots ,$\(\chi_{1309}(1245, \cdot)\)
|
$1309$ |
$1309$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
even |
|
✓ |
✓ |
| 1309.bq |
\(\chi_{1309}(106, \cdot)\)$, \cdots ,$\(\chi_{1309}(1135, \cdot)\)
|
$1309$ |
$187$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
odd |
|
|
✓ |
| 1309.br |
\(\chi_{1309}(64, \cdot)\)$, \cdots ,$\(\chi_{1309}(1296, \cdot)\)
|
$1309$ |
$187$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
even |
|
|
✓ |
| 1309.bs |
\(\chi_{1309}(174, \cdot)\)$, \cdots ,$\(\chi_{1309}(1203, \cdot)\)
|
$1309$ |
$1309$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
odd |
|
✓ |
✓ |
| 1309.bt |
\(\chi_{1309}(100, \cdot)\)$, \cdots ,$\(\chi_{1309}(1222, \cdot)\)
|
$1309$ |
$119$ |
$24$ |
not computed |
\(\Q(\zeta_{24})\) |
even |
|
|
✓ |
| 1309.bu |
\(\chi_{1309}(87, \cdot)\)$, \cdots ,$\(\chi_{1309}(1209, \cdot)\)
|
$1309$ |
$1309$ |
$24$ |
not computed |
\(\Q(\zeta_{24})\) |
even |
|
✓ |
✓ |
| 1309.bv |
\(\chi_{1309}(474, \cdot)\)$, \cdots ,$\(\chi_{1309}(1277, \cdot)\)
|
$1309$ |
$119$ |
$24$ |
not computed |
\(\Q(\zeta_{24})\) |
odd |
|
|
✓ |
| 1309.bw |
\(\chi_{1309}(32, \cdot)\)$, \cdots ,$\(\chi_{1309}(835, \cdot)\)
|
$1309$ |
$1309$ |
$24$ |
not computed |
\(\Q(\zeta_{24})\) |
odd |
|
✓ |
✓ |
| 1309.bx |
\(\chi_{1309}(52, \cdot)\)$, \cdots ,$\(\chi_{1309}(1293, \cdot)\)
|
$1309$ |
$77$ |
$30$ |
not computed |
\(\Q(\zeta_{15})\) |
even |
|
|
✓ |
