Orbit label |
Conrey labels |
Modulus |
Conductor |
Order |
Kernel field |
Value field |
Parity |
Real |
Primitive |
Minimal |
1.a |
\(\chi_{1}(1, \cdot)\)
|
$1$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
✓ |
✓ |
2.a |
\(\chi_{2}(1, \cdot)\)
|
$2$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
3.a |
\(\chi_{3}(1, \cdot)\)
|
$3$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
3.b |
\(\chi_{3}(2, \cdot)\)
|
$3$ |
$3$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
\(\Q\) |
odd |
✓ |
✓ |
✓ |
4.a |
\(\chi_{4}(1, \cdot)\)
|
$4$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
4.b |
\(\chi_{4}(3, \cdot)\)
|
$4$ |
$4$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
\(\Q\) |
odd |
✓ |
✓ |
✓ |
5.a |
\(\chi_{5}(1, \cdot)\)
|
$5$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
5.b |
\(\chi_{5}(4, \cdot)\)
|
$5$ |
$5$ |
$2$ |
\(\Q(\sqrt{5}) \) |
\(\Q\) |
even |
✓ |
✓ |
✓ |
5.c |
\(\chi_{5}(2, \cdot)\)$,$ \(\chi_{5}(3, \cdot)\)
|
$5$ |
$5$ |
$4$ |
\(\Q(\zeta_{5})\) |
\(\mathbb{Q}(i)\) |
odd |
|
✓ |
✓ |
6.a |
\(\chi_{6}(1, \cdot)\)
|
$6$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
6.b |
\(\chi_{6}(5, \cdot)\)
|
$6$ |
$3$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
7.a |
\(\chi_{7}(1, \cdot)\)
|
$7$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
7.b |
\(\chi_{7}(6, \cdot)\)
|
$7$ |
$7$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
\(\Q\) |
odd |
✓ |
✓ |
✓ |
7.c |
\(\chi_{7}(2, \cdot)\)$,$ \(\chi_{7}(4, \cdot)\)
|
$7$ |
$7$ |
$3$ |
\(\Q(\zeta_{7})^+\) |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
✓ |
✓ |
7.d |
\(\chi_{7}(3, \cdot)\)$,$ \(\chi_{7}(5, \cdot)\)
|
$7$ |
$7$ |
$6$ |
\(\Q(\zeta_{7})\) |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
✓ |
✓ |
8.a |
\(\chi_{8}(1, \cdot)\)
|
$8$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
8.b |
\(\chi_{8}(5, \cdot)\)
|
$8$ |
$8$ |
$2$ |
\(\Q(\sqrt{2}) \) |
\(\Q\) |
even |
✓ |
✓ |
✓ |
8.c |
\(\chi_{8}(7, \cdot)\)
|
$8$ |
$4$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
\(\Q\) |
odd |
✓ |
|
|
8.d |
\(\chi_{8}(3, \cdot)\)
|
$8$ |
$8$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
\(\Q\) |
odd |
✓ |
✓ |
✓ |
9.a |
\(\chi_{9}(1, \cdot)\)
|
$9$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
9.b |
\(\chi_{9}(8, \cdot)\)
|
$9$ |
$3$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
9.c |
\(\chi_{9}(4, \cdot)\)$,$ \(\chi_{9}(7, \cdot)\)
|
$9$ |
$9$ |
$3$ |
\(\Q(\zeta_{9})^+\) |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
✓ |
✓ |
9.d |
\(\chi_{9}(2, \cdot)\)$,$ \(\chi_{9}(5, \cdot)\)
|
$9$ |
$9$ |
$6$ |
\(\Q(\zeta_{9})\) |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
✓ |
✓ |
10.a |
\(\chi_{10}(1, \cdot)\)
|
$10$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
10.b |
\(\chi_{10}(9, \cdot)\)
|
$10$ |
$5$ |
$2$ |
\(\Q(\sqrt{5}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
10.c |
\(\chi_{10}(3, \cdot)\)$,$ \(\chi_{10}(7, \cdot)\)
|
$10$ |
$5$ |
$4$ |
\(\Q(\zeta_{5})\) |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
11.a |
\(\chi_{11}(1, \cdot)\)
|
$11$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
12.a |
\(\chi_{12}(1, \cdot)\)
|
$12$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
12.c |
\(\chi_{12}(5, \cdot)\)
|
$12$ |
$3$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
12.d |
\(\chi_{12}(7, \cdot)\)
|
$12$ |
$4$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
13.a |
\(\chi_{13}(1, \cdot)\)
|
$13$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
14.a |
\(\chi_{14}(1, \cdot)\)
|
$14$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
14.b |
\(\chi_{14}(13, \cdot)\)
|
$14$ |
$7$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
14.c |
\(\chi_{14}(9, \cdot)\)$,$ \(\chi_{14}(11, \cdot)\)
|
$14$ |
$7$ |
$3$ |
\(\Q(\zeta_{7})^+\) |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
✓ |
14.d |
\(\chi_{14}(3, \cdot)\)$,$ \(\chi_{14}(5, \cdot)\)
|
$14$ |
$7$ |
$6$ |
\(\Q(\zeta_{7})\) |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
✓ |
15.a |
\(\chi_{15}(1, \cdot)\)
|
$15$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
15.b |
\(\chi_{15}(4, \cdot)\)
|
$15$ |
$5$ |
$2$ |
\(\Q(\sqrt{5}) \) |
\(\Q\) |
even |
✓ |
|
✓ |
15.c |
\(\chi_{15}(11, \cdot)\)
|
$15$ |
$3$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
15.f |
\(\chi_{15}(7, \cdot)\)$,$ \(\chi_{15}(13, \cdot)\)
|
$15$ |
$5$ |
$4$ |
\(\Q(\zeta_{5})\) |
\(\mathbb{Q}(i)\) |
odd |
|
|
✓ |
16.a |
\(\chi_{16}(1, \cdot)\)
|
$16$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
|
16.b |
\(\chi_{16}(9, \cdot)\)
|
$16$ |
$8$ |
$2$ |
\(\Q(\sqrt{2}) \) |
\(\Q\) |
even |
✓ |
|
|
16.c |
\(\chi_{16}(15, \cdot)\)
|
$16$ |
$4$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
16.d |
\(\chi_{16}(7, \cdot)\)
|
$16$ |
$8$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
\(\Q\) |
odd |
✓ |
|
|
17.a |
\(\chi_{17}(1, \cdot)\)
|
$17$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
18.a |
\(\chi_{18}(1, \cdot)\)
|
$18$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
18.b |
\(\chi_{18}(17, \cdot)\)
|
$18$ |
$3$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
\(\Q\) |
odd |
✓ |
|
✓ |
18.c |
\(\chi_{18}(7, \cdot)\)$,$ \(\chi_{18}(13, \cdot)\)
|
$18$ |
$9$ |
$3$ |
\(\Q(\zeta_{9})^+\) |
\(\mathbb{Q}(\zeta_3)\) |
even |
|
|
✓ |
18.d |
\(\chi_{18}(5, \cdot)\)$,$ \(\chi_{18}(11, \cdot)\)
|
$18$ |
$9$ |
$6$ |
\(\Q(\zeta_{9})\) |
\(\mathbb{Q}(\zeta_3)\) |
odd |
|
|
✓ |
19.a |
\(\chi_{19}(1, \cdot)\)
|
$19$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |
20.a |
\(\chi_{20}(1, \cdot)\)
|
$20$ |
$1$ |
$1$ |
\(\Q\) |
\(\Q\) |
even |
✓ |
|
✓ |