| Orbit label |
Conrey labels |
Modulus |
Conductor |
Order |
Kernel field |
Value field |
Parity |
Real |
Primitive |
Minimal |
| 440.a |
\(\chi_{440}(1, \cdot)\)
|
$440$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
| 440.b |
\(\chi_{440}(89, \cdot)\)
|
$440$ |
$5$ |
$2$ |
\(\Q(\sqrt{5}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 440.c |
\(\chi_{440}(219, \cdot)\)
|
$440$ |
$440$ |
$2$ |
\(\Q(\sqrt{110}) \) |
\(\Q\) |
even |
✓ |
✓ |
✓ |
| 440.d |
\(\chi_{440}(21, \cdot)\)
|
$440$ |
$88$ |
$2$ |
\(\Q(\sqrt{-22}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 440.e |
\(\chi_{440}(111, \cdot)\)
|
$440$ |
$4$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 440.f |
\(\chi_{440}(351, \cdot)\)
|
$440$ |
$44$ |
$2$ |
\(\Q(\sqrt{11}) \) |
\(\Q\) |
even |
✓ |
|
|
| 440.g |
\(\chi_{440}(221, \cdot)\)
|
$440$ |
$8$ |
$2$ |
\(\Q(\sqrt{2}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 440.h |
\(\chi_{440}(419, \cdot)\)
|
$440$ |
$40$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 440.i |
\(\chi_{440}(329, \cdot)\)
|
$440$ |
$55$ |
$2$ |
\(\Q(\sqrt{-55}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 440.j |
\(\chi_{440}(241, \cdot)\)
|
$440$ |
$11$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 440.k |
\(\chi_{440}(331, \cdot)\)
|
$440$ |
$8$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 440.l |
\(\chi_{440}(309, \cdot)\)
|
$440$ |
$40$ |
$2$ |
\(\Q(\sqrt{10}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 440.m |
\(\chi_{440}(439, \cdot)\)
|
$440$ |
$220$ |
$2$ |
\(\Q(\sqrt{55}) \) |
\(\Q\) |
even |
✓ |
|
|
| 440.n |
\(\chi_{440}(199, \cdot)\)
|
$440$ |
$20$ |
$2$ |
\(\Q(\sqrt{-5}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 440.o |
\(\chi_{440}(109, \cdot)\)
|
$440$ |
$440$ |
$2$ |
\(\Q(\sqrt{-110}) \) |
\(\Q\) |
odd |
✓ |
✓ |
✓ |
| 440.p |
\(\chi_{440}(131, \cdot)\)
|
$440$ |
$88$ |
$2$ |
\(\Q(\sqrt{22}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 440.q |
\(\chi_{440}(87, \cdot)\)$,$ \(\chi_{440}(263, \cdot)\)
|
$440$ |
$220$ |
$4$ |
4.0.242000.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 440.r |
\(\chi_{440}(67, \cdot)\)$,$ \(\chi_{440}(243, \cdot)\)
|
$440$ |
$40$ |
$4$ |
4.4.8000.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
✓ |
| 440.s |
\(\chi_{440}(177, \cdot)\)$,$ \(\chi_{440}(353, \cdot)\)
|
$440$ |
$5$ |
$4$ |
\(\Q(\zeta_{5})\) |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
| 440.t |
\(\chi_{440}(197, \cdot)\)$,$ \(\chi_{440}(373, \cdot)\)
|
$440$ |
$440$ |
$4$ |
4.4.968000.2 |
\(\mathbb{Q}(i)\) |
even |
|
✓ |
✓ |
| 440.u |
\(\chi_{440}(133, \cdot)\)$,$ \(\chi_{440}(397, \cdot)\)
|
$440$ |
$40$ |
$4$ |
4.0.8000.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
| 440.v |
\(\chi_{440}(153, \cdot)\)$,$ \(\chi_{440}(417, \cdot)\)
|
$440$ |
$55$ |
$4$ |
4.4.15125.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
✓ |
| 440.w |
\(\chi_{440}(43, \cdot)\)$,$ \(\chi_{440}(307, \cdot)\)
|
$440$ |
$440$ |
$4$ |
4.0.968000.5 |
\(\mathbb{Q}(i)\) |
odd |
|
✓ |
✓ |
| 440.x |
\(\chi_{440}(23, \cdot)\)$,$ \(\chi_{440}(287, \cdot)\)
|
$440$ |
$20$ |
$4$ |
\(\Q(\zeta_{20})^+\) |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 440.y |
\(\chi_{440}(81, \cdot)\)$, \cdots ,$\(\chi_{440}(401, \cdot)\)
|
$440$ |
$11$ |
$5$ |
\(\Q(\zeta_{11})^+\) |
\(\Q(\zeta_{5})\) |
even |
|
|
✓ |
| 440.z |
\(\chi_{440}(51, \cdot)\)$, \cdots ,$\(\chi_{440}(371, \cdot)\)
|
$440$ |
$88$ |
$10$ |
10.10.77265229938688.1 |
\(\Q(\zeta_{5})\) |
even |
|
|
✓ |
| 440.ba |
\(\chi_{440}(29, \cdot)\)$, \cdots ,$\(\chi_{440}(349, \cdot)\)
|
$440$ |
$440$ |
$10$ |
10.0.241453843558400000.1 |
\(\Q(\zeta_{5})\) |
odd |
|
✓ |
✓ |
| 440.bb |
\(\chi_{440}(119, \cdot)\)$, \cdots ,$\(\chi_{440}(399, \cdot)\)
|
$440$ |
$220$ |
$10$ |
10.0.685948419200000.1 |
\(\Q(\zeta_{5})\) |
odd |
|
|
|
| 440.bc |
\(\chi_{440}(39, \cdot)\)$, \cdots ,$\(\chi_{440}(359, \cdot)\)
|
$440$ |
$220$ |
$10$ |
10.10.7545432611200000.1 |
\(\Q(\zeta_{5})\) |
even |
|
|
|
| 440.bd |
\(\chi_{440}(69, \cdot)\)$, \cdots ,$\(\chi_{440}(389, \cdot)\)
|
$440$ |
$440$ |
$10$ |
10.10.21950349414400000.1 |
\(\Q(\zeta_{5})\) |
even |
|
✓ |
✓ |
| 440.be |
\(\chi_{440}(91, \cdot)\)$, \cdots ,$\(\chi_{440}(411, \cdot)\)
|
$440$ |
$88$ |
$10$ |
10.0.7024111812608.1 |
\(\Q(\zeta_{5})\) |
odd |
|
|
✓ |
| 440.bf |
\(\chi_{440}(41, \cdot)\)$, \cdots ,$\(\chi_{440}(321, \cdot)\)
|
$440$ |
$11$ |
$10$ |
\(\Q(\zeta_{11})\) |
\(\Q(\zeta_{5})\) |
odd |
|
|
✓ |
| 440.bg |
\(\chi_{440}(129, \cdot)\)$, \cdots ,$\(\chi_{440}(409, \cdot)\)
|
$440$ |
$55$ |
$10$ |
10.0.7368586534375.1 |
\(\Q(\zeta_{5})\) |
odd |
|
|
✓ |
| 440.bh |
\(\chi_{440}(59, \cdot)\)$, \cdots ,$\(\chi_{440}(379, \cdot)\)
|
$440$ |
$440$ |
$10$ |
10.0.21950349414400000.4 |
\(\Q(\zeta_{5})\) |
odd |
|
✓ |
✓ |
| 440.bi |
\(\chi_{440}(141, \cdot)\)$, \cdots ,$\(\chi_{440}(421, \cdot)\)
|
$440$ |
$88$ |
$10$ |
10.10.7024111812608.1 |
\(\Q(\zeta_{5})\) |
even |
|
|
✓ |
| 440.bj |
\(\chi_{440}(151, \cdot)\)$, \cdots ,$\(\chi_{440}(431, \cdot)\)
|
$440$ |
$44$ |
$10$ |
\(\Q(\zeta_{44})^+\) |
\(\Q(\zeta_{5})\) |
even |
|
|
|
| 440.bk |
\(\chi_{440}(31, \cdot)\)$, \cdots ,$\(\chi_{440}(311, \cdot)\)
|
$440$ |
$44$ |
$10$ |
10.0.219503494144.1 |
\(\Q(\zeta_{5})\) |
odd |
|
|
|
| 440.bl |
\(\chi_{440}(61, \cdot)\)$, \cdots ,$\(\chi_{440}(381, \cdot)\)
|
$440$ |
$88$ |
$10$ |
10.0.77265229938688.1 |
\(\Q(\zeta_{5})\) |
odd |
|
|
✓ |
| 440.bm |
\(\chi_{440}(19, \cdot)\)$, \cdots ,$\(\chi_{440}(299, \cdot)\)
|
$440$ |
$440$ |
$10$ |
10.10.241453843558400000.1 |
\(\Q(\zeta_{5})\) |
even |
|
✓ |
✓ |
| 440.bn |
\(\chi_{440}(9, \cdot)\)$, \cdots ,$\(\chi_{440}(289, \cdot)\)
|
$440$ |
$55$ |
$10$ |
10.10.669871503125.1 |
\(\Q(\zeta_{5})\) |
even |
|
|
✓ |
| 440.bo |
\(\chi_{440}(17, \cdot)\)$, \cdots ,$\(\chi_{440}(393, \cdot)\)
|
$440$ |
$55$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
even |
|
|
✓ |
| 440.bp |
\(\chi_{440}(37, \cdot)\)$, \cdots ,$\(\chi_{440}(357, \cdot)\)
|
$440$ |
$440$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
odd |
|
✓ |
✓ |
| 440.bq |
\(\chi_{440}(47, \cdot)\)$, \cdots ,$\(\chi_{440}(423, \cdot)\)
|
$440$ |
$220$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
even |
|
|
|
| 440.br |
\(\chi_{440}(83, \cdot)\)$, \cdots ,$\(\chi_{440}(403, \cdot)\)
|
$440$ |
$440$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
odd |
|
✓ |
✓ |
| 440.bs |
\(\chi_{440}(3, \cdot)\)$, \cdots ,$\(\chi_{440}(427, \cdot)\)
|
$440$ |
$440$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
even |
|
✓ |
✓ |
| 440.bt |
\(\chi_{440}(7, \cdot)\)$, \cdots ,$\(\chi_{440}(343, \cdot)\)
|
$440$ |
$220$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
odd |
|
|
|
| 440.bu |
\(\chi_{440}(13, \cdot)\)$, \cdots ,$\(\chi_{440}(437, \cdot)\)
|
$440$ |
$440$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
even |
|
✓ |
✓ |
| 440.bv |
\(\chi_{440}(97, \cdot)\)$, \cdots ,$\(\chi_{440}(433, \cdot)\)
|
$440$ |
$55$ |
$20$ |
not computed |
\(\Q(\zeta_{20})\) |
odd |
|
|
✓ |
