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Modulus Conductor Order Induced by
Parity Primitive Minimal Real
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Orbit label Conrey labels Modulus Conductor Order Value field Parity Real Primitive Minimal
1.a

\(\chi_{1}(1, \cdot)\)

$1$ $1$ $1$ \(\Q\) even ✓ ✓ ✓
2.a

\(\chi_{2}(1, \cdot)\)

$2$ $1$ $1$ \(\Q\) even ✓ ✓
3.a

\(\chi_{3}(1, \cdot)\)

$3$ $1$ $1$ \(\Q\) even ✓ ✓
3.b

\(\chi_{3}(2, \cdot)\)

$3$ $3$ $2$ \(\Q\) odd ✓ ✓ ✓
4.a

\(\chi_{4}(1, \cdot)\)

$4$ $1$ $1$ \(\Q\) even ✓ ✓
4.b

\(\chi_{4}(3, \cdot)\)

$4$ $4$ $2$ \(\Q\) odd ✓ ✓ ✓
5.a

\(\chi_{5}(1, \cdot)\)

$5$ $1$ $1$ \(\Q\) even ✓ ✓
5.b

\(\chi_{5}(4, \cdot)\)

$5$ $5$ $2$ \(\Q\) even ✓ ✓ ✓
5.c

\(\chi_{5}(2, \cdot)\)$,$ \(\chi_{5}(3, \cdot)\)

$5$ $5$ $4$ \(\mathbb{Q}(i)\) odd ✓ ✓
6.a

\(\chi_{6}(1, \cdot)\)

$6$ $1$ $1$ \(\Q\) even ✓ ✓
6.b

\(\chi_{6}(5, \cdot)\)

$6$ $3$ $2$ \(\Q\) odd ✓ ✓
7.a

\(\chi_{7}(1, \cdot)\)

$7$ $1$ $1$ \(\Q\) even ✓ ✓
7.b

\(\chi_{7}(6, \cdot)\)

$7$ $7$ $2$ \(\Q\) odd ✓ ✓ ✓
7.c

\(\chi_{7}(2, \cdot)\)$,$ \(\chi_{7}(4, \cdot)\)

$7$ $7$ $3$ \(\mathbb{Q}(\zeta_3)\) even ✓ ✓
7.d

\(\chi_{7}(3, \cdot)\)$,$ \(\chi_{7}(5, \cdot)\)

$7$ $7$ $6$ \(\mathbb{Q}(\zeta_3)\) odd ✓ ✓
8.a

\(\chi_{8}(1, \cdot)\)

$8$ $1$ $1$ \(\Q\) even ✓ ✓
8.b

\(\chi_{8}(5, \cdot)\)

$8$ $8$ $2$ \(\Q\) even ✓ ✓ ✓
8.d

\(\chi_{8}(3, \cdot)\)

$8$ $8$ $2$ \(\Q\) odd ✓ ✓ ✓
9.a

\(\chi_{9}(1, \cdot)\)

$9$ $1$ $1$ \(\Q\) even ✓ ✓
9.b

\(\chi_{9}(8, \cdot)\)

$9$ $3$ $2$ \(\Q\) odd ✓ ✓
9.c

\(\chi_{9}(4, \cdot)\)$,$ \(\chi_{9}(7, \cdot)\)

$9$ $9$ $3$ \(\mathbb{Q}(\zeta_3)\) even ✓ ✓
9.d

\(\chi_{9}(2, \cdot)\)$,$ \(\chi_{9}(5, \cdot)\)

$9$ $9$ $6$ \(\mathbb{Q}(\zeta_3)\) odd ✓ ✓
10.a

\(\chi_{10}(1, \cdot)\)

$10$ $1$ $1$ \(\Q\) even ✓ ✓
10.b

\(\chi_{10}(9, \cdot)\)

$10$ $5$ $2$ \(\Q\) even ✓ ✓
10.c

\(\chi_{10}(3, \cdot)\)$,$ \(\chi_{10}(7, \cdot)\)

$10$ $5$ $4$ \(\mathbb{Q}(i)\) odd ✓
11.a

\(\chi_{11}(1, \cdot)\)

$11$ $1$ $1$ \(\Q\) even ✓ ✓
11.b

\(\chi_{11}(10, \cdot)\)

$11$ $11$ $2$ \(\Q\) odd ✓ ✓ ✓
11.c

\(\chi_{11}(3, \cdot)\)$, \cdots ,$\(\chi_{11}(9, \cdot)\)

$11$ $11$ $5$ \(\Q(\zeta_{5})\) even ✓ ✓
11.d

\(\chi_{11}(2, \cdot)\)$, \cdots ,$\(\chi_{11}(8, \cdot)\)

$11$ $11$ $10$ \(\Q(\zeta_{5})\) odd ✓ ✓
12.a

\(\chi_{12}(1, \cdot)\)

$12$ $1$ $1$ \(\Q\) even ✓ ✓
12.b

\(\chi_{12}(11, \cdot)\)

$12$ $12$ $2$ \(\Q\) even ✓ ✓ ✓
12.c

\(\chi_{12}(5, \cdot)\)

$12$ $3$ $2$ \(\Q\) odd ✓ ✓
12.d

\(\chi_{12}(7, \cdot)\)

$12$ $4$ $2$ \(\Q\) odd ✓ ✓
13.a

\(\chi_{13}(1, \cdot)\)

$13$ $1$ $1$ \(\Q\) even ✓ ✓
13.b

\(\chi_{13}(12, \cdot)\)

$13$ $13$ $2$ \(\Q\) even ✓ ✓ ✓
13.c

\(\chi_{13}(3, \cdot)\)$,$ \(\chi_{13}(9, \cdot)\)

$13$ $13$ $3$ \(\mathbb{Q}(\zeta_3)\) even ✓ ✓
13.d

\(\chi_{13}(5, \cdot)\)$,$ \(\chi_{13}(8, \cdot)\)

$13$ $13$ $4$ \(\mathbb{Q}(i)\) odd ✓ ✓
13.e

\(\chi_{13}(4, \cdot)\)$,$ \(\chi_{13}(10, \cdot)\)

$13$ $13$ $6$ \(\mathbb{Q}(\zeta_3)\) even ✓ ✓
13.f

\(\chi_{13}(2, \cdot)\)$, \cdots ,$\(\chi_{13}(11, \cdot)\)

$13$ $13$ $12$ \(\Q(\zeta_{12})\) odd ✓ ✓
14.a

\(\chi_{14}(1, \cdot)\)

$14$ $1$ $1$ \(\Q\) even ✓ ✓
14.b

\(\chi_{14}(13, \cdot)\)

$14$ $7$ $2$ \(\Q\) odd ✓ ✓
14.c

\(\chi_{14}(9, \cdot)\)$,$ \(\chi_{14}(11, \cdot)\)

$14$ $7$ $3$ \(\mathbb{Q}(\zeta_3)\) even ✓
14.d

\(\chi_{14}(3, \cdot)\)$,$ \(\chi_{14}(5, \cdot)\)

$14$ $7$ $6$ \(\mathbb{Q}(\zeta_3)\) odd ✓
15.a

\(\chi_{15}(1, \cdot)\)

$15$ $1$ $1$ \(\Q\) even ✓ ✓
15.b

\(\chi_{15}(4, \cdot)\)

$15$ $5$ $2$ \(\Q\) even ✓ ✓
15.c

\(\chi_{15}(11, \cdot)\)

$15$ $3$ $2$ \(\Q\) odd ✓ ✓
15.d

\(\chi_{15}(14, \cdot)\)

$15$ $15$ $2$ \(\Q\) odd ✓ ✓ ✓
15.e

\(\chi_{15}(2, \cdot)\)$,$ \(\chi_{15}(8, \cdot)\)

$15$ $15$ $4$ \(\mathbb{Q}(i)\) even ✓ ✓
15.f

\(\chi_{15}(7, \cdot)\)$,$ \(\chi_{15}(13, \cdot)\)

$15$ $5$ $4$ \(\mathbb{Q}(i)\) odd ✓
16.c

\(\chi_{16}(15, \cdot)\)

$16$ $4$ $2$ \(\Q\) odd ✓ ✓
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