| Orbit label |
Conrey labels |
Modulus |
Conductor |
Order |
Kernel field |
Value field |
Parity |
Real |
Primitive |
Minimal |
| 240.a |
\(\chi_{240}(1, \cdot)\)
|
$240$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
|
| 240.b |
\(\chi_{240}(71, \cdot)\)
|
$240$ |
$24$ |
$2$ |
\(\Q(\sqrt{6}) \) |
\(\Q\) |
even |
✓ |
|
|
| 240.c |
\(\chi_{240}(209, \cdot)\)
|
$240$ |
$15$ |
$2$ |
\(\Q(\sqrt{-15}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 240.d |
\(\chi_{240}(169, \cdot)\)
|
$240$ |
$40$ |
$2$ |
\(\Q(\sqrt{10}) \) |
\(\Q\) |
even |
✓ |
|
|
| 240.e |
\(\chi_{240}(31, \cdot)\)
|
$240$ |
$4$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 240.f |
\(\chi_{240}(49, \cdot)\)
|
$240$ |
$5$ |
$2$ |
\(\Q(\sqrt{5}) \) |
\(\Q\) |
even |
✓ |
|
|
| 240.g |
\(\chi_{240}(151, \cdot)\)
|
$240$ |
$8$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 240.h |
\(\chi_{240}(191, \cdot)\)
|
$240$ |
$12$ |
$2$ |
\(\Q(\sqrt{3}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 240.i |
\(\chi_{240}(89, \cdot)\)
|
$240$ |
$120$ |
$2$ |
\(\Q(\sqrt{-30}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 240.j |
\(\chi_{240}(79, \cdot)\)
|
$240$ |
$20$ |
$2$ |
\(\Q(\sqrt{-5}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
| 240.k |
\(\chi_{240}(121, \cdot)\)
|
$240$ |
$8$ |
$2$ |
\(\Q(\sqrt{2}) \) |
\(\Q\) |
even |
✓ |
|
|
| 240.l |
\(\chi_{240}(161, \cdot)\)
|
$240$ |
$3$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 240.m |
\(\chi_{240}(119, \cdot)\)
|
$240$ |
$120$ |
$2$ |
\(\Q(\sqrt{30}) \) |
\(\Q\) |
even |
✓ |
|
|
| 240.n |
\(\chi_{240}(41, \cdot)\)
|
$240$ |
$24$ |
$2$ |
\(\Q(\sqrt{-6}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 240.o |
\(\chi_{240}(239, \cdot)\)
|
$240$ |
$60$ |
$2$ |
\(\Q(\sqrt{15}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
| 240.p |
\(\chi_{240}(199, \cdot)\)
|
$240$ |
$40$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
\(\Q\) |
odd |
✓ |
|
|
| 240.q |
\(\chi_{240}(19, \cdot)\)$,$ \(\chi_{240}(139, \cdot)\)
|
$240$ |
$80$ |
$4$ |
4.0.51200.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
| 240.r |
\(\chi_{240}(101, \cdot)\)$,$ \(\chi_{240}(221, \cdot)\)
|
$240$ |
$48$ |
$4$ |
4.0.18432.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
| 240.s |
\(\chi_{240}(61, \cdot)\)$,$ \(\chi_{240}(181, \cdot)\)
|
$240$ |
$16$ |
$4$ |
\(\Q(\zeta_{16})^+\) |
\(\mathbb{Q}(i)\) |
even |
|
|
✓ |
| 240.t |
\(\chi_{240}(59, \cdot)\)$,$ \(\chi_{240}(179, \cdot)\)
|
$240$ |
$240$ |
$4$ |
4.4.460800.1 |
\(\mathbb{Q}(i)\) |
even |
|
✓ |
✓ |
| 240.u |
\(\chi_{240}(23, \cdot)\)$,$ \(\chi_{240}(167, \cdot)\)
|
$240$ |
$120$ |
$4$ |
4.0.72000.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 240.v |
\(\chi_{240}(17, \cdot)\)$,$ \(\chi_{240}(113, \cdot)\)
|
$240$ |
$15$ |
$4$ |
\(\Q(\zeta_{15})^+\) |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 240.w |
\(\chi_{240}(127, \cdot)\)$,$ \(\chi_{240}(223, \cdot)\)
|
$240$ |
$20$ |
$4$ |
\(\Q(\zeta_{20})^+\) |
\(\mathbb{Q}(i)\) |
even |
|
|
✓ |
| 240.x |
\(\chi_{240}(73, \cdot)\)$,$ \(\chi_{240}(217, \cdot)\)
|
$240$ |
$40$ |
$4$ |
4.0.8000.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 240.y |
\(\chi_{240}(163, \cdot)\)$,$ \(\chi_{240}(187, \cdot)\)
|
$240$ |
$80$ |
$4$ |
4.4.256000.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
✓ |
| 240.z |
\(\chi_{240}(83, \cdot)\)$,$ \(\chi_{240}(107, \cdot)\)
|
$240$ |
$240$ |
$4$ |
4.0.2304000.1 |
\(\mathbb{Q}(i)\) |
odd |
|
✓ |
✓ |
| 240.ba |
\(\chi_{240}(13, \cdot)\)$,$ \(\chi_{240}(37, \cdot)\)
|
$240$ |
$80$ |
$4$ |
4.0.256000.4 |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
| 240.bb |
\(\chi_{240}(173, \cdot)\)$,$ \(\chi_{240}(197, \cdot)\)
|
$240$ |
$240$ |
$4$ |
4.4.2304000.1 |
\(\mathbb{Q}(i)\) |
even |
|
✓ |
✓ |
| 240.bc |
\(\chi_{240}(43, \cdot)\)$,$ \(\chi_{240}(67, \cdot)\)
|
$240$ |
$80$ |
$4$ |
4.4.256000.2 |
\(\mathbb{Q}(i)\) |
even |
|
|
✓ |
| 240.bd |
\(\chi_{240}(203, \cdot)\)$,$ \(\chi_{240}(227, \cdot)\)
|
$240$ |
$240$ |
$4$ |
4.0.2304000.2 |
\(\mathbb{Q}(i)\) |
odd |
|
✓ |
✓ |
| 240.be |
\(\chi_{240}(133, \cdot)\)$,$ \(\chi_{240}(157, \cdot)\)
|
$240$ |
$80$ |
$4$ |
4.0.256000.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
| 240.bf |
\(\chi_{240}(53, \cdot)\)$,$ \(\chi_{240}(77, \cdot)\)
|
$240$ |
$240$ |
$4$ |
4.4.2304000.2 |
\(\mathbb{Q}(i)\) |
even |
|
✓ |
✓ |
| 240.bg |
\(\chi_{240}(97, \cdot)\)$,$ \(\chi_{240}(193, \cdot)\)
|
$240$ |
$5$ |
$4$ |
\(\Q(\zeta_{5})\) |
\(\mathbb{Q}(i)\) |
odd |
|
|
|
| 240.bh |
\(\chi_{240}(7, \cdot)\)$,$ \(\chi_{240}(103, \cdot)\)
|
$240$ |
$40$ |
$4$ |
4.4.8000.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 240.bi |
\(\chi_{240}(137, \cdot)\)$,$ \(\chi_{240}(233, \cdot)\)
|
$240$ |
$120$ |
$4$ |
4.4.72000.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
|
| 240.bj |
\(\chi_{240}(47, \cdot)\)$,$ \(\chi_{240}(143, \cdot)\)
|
$240$ |
$60$ |
$4$ |
4.0.18000.1 |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
| 240.bk |
\(\chi_{240}(11, \cdot)\)$,$ \(\chi_{240}(131, \cdot)\)
|
$240$ |
$48$ |
$4$ |
4.4.18432.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
✓ |
| 240.bl |
\(\chi_{240}(109, \cdot)\)$,$ \(\chi_{240}(229, \cdot)\)
|
$240$ |
$80$ |
$4$ |
4.4.51200.1 |
\(\mathbb{Q}(i)\) |
even |
|
|
✓ |
| 240.bm |
\(\chi_{240}(29, \cdot)\)$,$ \(\chi_{240}(149, \cdot)\)
|
$240$ |
$240$ |
$4$ |
4.0.460800.2 |
\(\mathbb{Q}(i)\) |
odd |
|
✓ |
✓ |
| 240.bn |
\(\chi_{240}(91, \cdot)\)$,$ \(\chi_{240}(211, \cdot)\)
|
$240$ |
$16$ |
$4$ |
4.0.2048.2 |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
