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Orbit label Conrey labels Modulus Conductor Order Value field Parity Real Primitive Minimal
13.f

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

$13$ $13$ $12$ \(\Q(\zeta_{12})\) odd
17.e

\(\chi_{17}(3, \cdot)\)$, \cdots ,$\(\chi_{17}(14, \cdot)\)

$17$ $17$ $16$ \(\Q(\zeta_{16})\) odd
19.f

\(\chi_{19}(2, \cdot)\)$, \cdots ,$\(\chi_{19}(15, \cdot)\)

$19$ $19$ $18$ \(\Q(\zeta_{9})\) odd
23.c

\(\chi_{23}(2, \cdot)\)$, \cdots ,$\(\chi_{23}(18, \cdot)\)

$23$ $23$ $11$ \(\Q(\zeta_{11})\) even
23.d

\(\chi_{23}(5, \cdot)\)$, \cdots ,$\(\chi_{23}(21, \cdot)\)

$23$ $23$ $22$ \(\Q(\zeta_{11})\) odd
25.f

\(\chi_{25}(2, \cdot)\)$, \cdots ,$\(\chi_{25}(23, \cdot)\)

$25$ $25$ $20$ \(\Q(\zeta_{20})\) odd
26.f

\(\chi_{26}(7, \cdot)\)$, \cdots ,$\(\chi_{26}(19, \cdot)\)

$26$ $13$ $12$ \(\Q(\zeta_{12})\) odd
27.f

\(\chi_{27}(2, \cdot)\)$, \cdots ,$\(\chi_{27}(23, \cdot)\)

$27$ $27$ $18$ \(\Q(\zeta_{9})\) odd
29.e

\(\chi_{29}(4, \cdot)\)$, \cdots ,$\(\chi_{29}(22, \cdot)\)

$29$ $29$ $14$ \(\Q(\zeta_{7})\) even
29.f

\(\chi_{29}(2, \cdot)\)$, \cdots ,$\(\chi_{29}(27, \cdot)\)

$29$ $29$ $28$ \(\Q(\zeta_{28})\) odd
31.g

\(\chi_{31}(7, \cdot)\)$, \cdots ,$\(\chi_{31}(28, \cdot)\)

$31$ $31$ $15$ \(\Q(\zeta_{15})\) even
31.h

\(\chi_{31}(3, \cdot)\)$, \cdots ,$\(\chi_{31}(24, \cdot)\)

$31$ $31$ $30$ \(\Q(\zeta_{15})\) odd
34.e

\(\chi_{34}(3, \cdot)\)$, \cdots ,$\(\chi_{34}(31, \cdot)\)

$34$ $17$ $16$ \(\Q(\zeta_{16})\) odd
35.k

\(\chi_{35}(3, \cdot)\)$, \cdots ,$\(\chi_{35}(33, \cdot)\)

$35$ $35$ $12$ \(\Q(\zeta_{12})\) even
35.l

\(\chi_{35}(2, \cdot)\)$, \cdots ,$\(\chi_{35}(32, \cdot)\)

$35$ $35$ $12$ \(\Q(\zeta_{12})\) odd
37.g

\(\chi_{37}(8, \cdot)\)$, \cdots ,$\(\chi_{37}(29, \cdot)\)

$37$ $37$ $12$ \(\Q(\zeta_{12})\) odd
37.h

\(\chi_{37}(3, \cdot)\)$, \cdots ,$\(\chi_{37}(30, \cdot)\)

$37$ $37$ $18$ \(\Q(\zeta_{9})\) even
37.i

\(\chi_{37}(2, \cdot)\)$, \cdots ,$\(\chi_{37}(35, \cdot)\)

$37$ $37$ $36$ \(\Q(\zeta_{36})\) odd
38.f

\(\chi_{38}(3, \cdot)\)$, \cdots ,$\(\chi_{38}(33, \cdot)\)

$38$ $19$ $18$ \(\Q(\zeta_{9})\) odd
39.k

\(\chi_{39}(2, \cdot)\)$, \cdots ,$\(\chi_{39}(32, \cdot)\)

$39$ $39$ $12$ \(\Q(\zeta_{12})\) even
39.l

\(\chi_{39}(7, \cdot)\)$, \cdots ,$\(\chi_{39}(37, \cdot)\)

$39$ $13$ $12$ \(\Q(\zeta_{12})\) odd
41.g

\(\chi_{41}(2, \cdot)\)$, \cdots ,$\(\chi_{41}(39, \cdot)\)

$41$ $41$ $20$ \(\Q(\zeta_{20})\) even
41.h

\(\chi_{41}(6, \cdot)\)$, \cdots ,$\(\chi_{41}(35, \cdot)\)

$41$ $41$ $40$ \(\Q(\zeta_{40})\) odd
43.f

\(\chi_{43}(2, \cdot)\)$, \cdots ,$\(\chi_{43}(39, \cdot)\)

$43$ $43$ $14$ \(\Q(\zeta_{7})\) odd
43.g

\(\chi_{43}(9, \cdot)\)$, \cdots ,$\(\chi_{43}(40, \cdot)\)

$43$ $43$ $21$ \(\Q(\zeta_{21})\) even
43.h

\(\chi_{43}(3, \cdot)\)$, \cdots ,$\(\chi_{43}(34, \cdot)\)

$43$ $43$ $42$ \(\Q(\zeta_{21})\) odd
45.k

\(\chi_{45}(7, \cdot)\)$, \cdots ,$\(\chi_{45}(43, \cdot)\)

$45$ $45$ $12$ \(\Q(\zeta_{12})\) odd
45.l

\(\chi_{45}(2, \cdot)\)$, \cdots ,$\(\chi_{45}(38, \cdot)\)

$45$ $45$ $12$ \(\Q(\zeta_{12})\) even
46.c

\(\chi_{46}(3, \cdot)\)$, \cdots ,$\(\chi_{46}(41, \cdot)\)

$46$ $23$ $11$ \(\Q(\zeta_{11})\) even
46.d

\(\chi_{46}(5, \cdot)\)$, \cdots ,$\(\chi_{46}(43, \cdot)\)

$46$ $23$ $22$ \(\Q(\zeta_{11})\) odd
47.c

\(\chi_{47}(2, \cdot)\)$, \cdots ,$\(\chi_{47}(42, \cdot)\)

$47$ $47$ $23$ \(\Q(\zeta_{23})\) even
47.d

\(\chi_{47}(5, \cdot)\)$, \cdots ,$\(\chi_{47}(45, \cdot)\)

$47$ $47$ $46$ \(\Q(\zeta_{23})\) odd
49.f

\(\chi_{49}(6, \cdot)\)$, \cdots ,$\(\chi_{49}(41, \cdot)\)

$49$ $49$ $14$ \(\Q(\zeta_{7})\) odd
49.g

\(\chi_{49}(2, \cdot)\)$, \cdots ,$\(\chi_{49}(46, \cdot)\)

$49$ $49$ $21$ \(\Q(\zeta_{21})\) even
49.h

\(\chi_{49}(3, \cdot)\)$, \cdots ,$\(\chi_{49}(47, \cdot)\)

$49$ $49$ $42$ \(\Q(\zeta_{21})\) odd
50.f

\(\chi_{50}(3, \cdot)\)$, \cdots ,$\(\chi_{50}(47, \cdot)\)

$50$ $25$ $20$ \(\Q(\zeta_{20})\) odd
51.i

\(\chi_{51}(5, \cdot)\)$, \cdots ,$\(\chi_{51}(44, \cdot)\)

$51$ $51$ $16$ \(\Q(\zeta_{16})\) even
51.j

\(\chi_{51}(7, \cdot)\)$, \cdots ,$\(\chi_{51}(46, \cdot)\)

$51$ $17$ $16$ \(\Q(\zeta_{16})\) odd
52.k

\(\chi_{52}(33, \cdot)\)$, \cdots ,$\(\chi_{52}(45, \cdot)\)

$52$ $13$ $12$ \(\Q(\zeta_{12})\) odd
52.l

\(\chi_{52}(7, \cdot)\)$, \cdots ,$\(\chi_{52}(19, \cdot)\)

$52$ $52$ $12$ \(\Q(\zeta_{12})\) even
53.d

\(\chi_{53}(10, \cdot)\)$, \cdots ,$\(\chi_{53}(49, \cdot)\)

$53$ $53$ $13$ \(\Q(\zeta_{13})\) even
53.e

\(\chi_{53}(4, \cdot)\)$, \cdots ,$\(\chi_{53}(43, \cdot)\)

$53$ $53$ $26$ \(\Q(\zeta_{13})\) even
53.f

\(\chi_{53}(2, \cdot)\)$, \cdots ,$\(\chi_{53}(51, \cdot)\)

$53$ $53$ $52$ $\Q(\zeta_{52})$ odd
54.f

\(\chi_{54}(5, \cdot)\)$, \cdots ,$\(\chi_{54}(47, \cdot)\)

$54$ $27$ $18$ \(\Q(\zeta_{9})\) odd
55.k

\(\chi_{55}(3, \cdot)\)$, \cdots ,$\(\chi_{55}(53, \cdot)\)

$55$ $55$ $20$ \(\Q(\zeta_{20})\) odd
55.l

\(\chi_{55}(2, \cdot)\)$, \cdots ,$\(\chi_{55}(52, \cdot)\)

$55$ $55$ $20$ \(\Q(\zeta_{20})\) even
57.j

\(\chi_{57}(2, \cdot)\)$, \cdots ,$\(\chi_{57}(53, \cdot)\)

$57$ $57$ $18$ \(\Q(\zeta_{9})\) even
57.k

\(\chi_{57}(10, \cdot)\)$, \cdots ,$\(\chi_{57}(52, \cdot)\)

$57$ $19$ $18$ \(\Q(\zeta_{9})\) odd
57.l

\(\chi_{57}(5, \cdot)\)$, \cdots ,$\(\chi_{57}(47, \cdot)\)

$57$ $57$ $18$ \(\Q(\zeta_{9})\) odd
58.e

\(\chi_{58}(5, \cdot)\)$, \cdots ,$\(\chi_{58}(51, \cdot)\)

$58$ $29$ $14$ \(\Q(\zeta_{7})\) even
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