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Orbit label Conrey labels Modulus Conductor Order Value field Parity Real Primitive Minimal
5.c

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

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

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

$10$ $5$ $4$ \(\mathbb{Q}(i)\) odd ✓
13.d

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

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

\(\chi_{16}(5, \cdot)\)$,$ \(\chi_{16}(13, \cdot)\)

$16$ $16$ $4$ \(\mathbb{Q}(i)\) even ✓ ✓
16.f

\(\chi_{16}(3, \cdot)\)$,$ \(\chi_{16}(11, \cdot)\)

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

\(\chi_{17}(4, \cdot)\)$,$ \(\chi_{17}(13, \cdot)\)

$17$ $17$ $4$ \(\mathbb{Q}(i)\) even ✓ ✓
20.e

\(\chi_{20}(3, \cdot)\)$,$ \(\chi_{20}(7, \cdot)\)

$20$ $20$ $4$ \(\mathbb{Q}(i)\) even ✓ ✓
20.f

\(\chi_{20}(13, \cdot)\)$,$ \(\chi_{20}(17, \cdot)\)

$20$ $5$ $4$ \(\mathbb{Q}(i)\) odd ✓
25.c

\(\chi_{25}(7, \cdot)\)$,$ \(\chi_{25}(18, \cdot)\)

$25$ $5$ $4$ \(\mathbb{Q}(i)\) odd ✓
26.d

\(\chi_{26}(5, \cdot)\)$,$ \(\chi_{26}(21, \cdot)\)

$26$ $13$ $4$ \(\mathbb{Q}(i)\) odd ✓
29.c

\(\chi_{29}(12, \cdot)\)$,$ \(\chi_{29}(17, \cdot)\)

$29$ $29$ $4$ \(\mathbb{Q}(i)\) odd ✓ ✓
30.e

\(\chi_{30}(17, \cdot)\)$,$ \(\chi_{30}(23, \cdot)\)

$30$ $15$ $4$ \(\mathbb{Q}(i)\) even ✓
30.f

\(\chi_{30}(7, \cdot)\)$,$ \(\chi_{30}(13, \cdot)\)

$30$ $5$ $4$ \(\mathbb{Q}(i)\) odd ✓
32.e

\(\chi_{32}(9, \cdot)\)$,$ \(\chi_{32}(25, \cdot)\)

$32$ $16$ $4$ \(\mathbb{Q}(i)\) even
32.f

\(\chi_{32}(7, \cdot)\)$,$ \(\chi_{32}(23, \cdot)\)

$32$ $16$ $4$ \(\mathbb{Q}(i)\) odd
34.c

\(\chi_{34}(13, \cdot)\)$,$ \(\chi_{34}(21, \cdot)\)

$34$ $17$ $4$ \(\mathbb{Q}(i)\) even ✓
35.f

\(\chi_{35}(13, \cdot)\)$,$ \(\chi_{35}(27, \cdot)\)

$35$ $35$ $4$ \(\mathbb{Q}(i)\) even ✓ ✓
35.g

\(\chi_{35}(8, \cdot)\)$,$ \(\chi_{35}(22, \cdot)\)

$35$ $5$ $4$ \(\mathbb{Q}(i)\) odd ✓
37.d

\(\chi_{37}(6, \cdot)\)$,$ \(\chi_{37}(31, \cdot)\)

$37$ $37$ $4$ \(\mathbb{Q}(i)\) odd ✓ ✓
39.f

\(\chi_{39}(5, \cdot)\)$,$ \(\chi_{39}(8, \cdot)\)

$39$ $39$ $4$ \(\mathbb{Q}(i)\) even ✓ ✓
39.g

\(\chi_{39}(31, \cdot)\)$,$ \(\chi_{39}(34, \cdot)\)

$39$ $13$ $4$ \(\mathbb{Q}(i)\) odd ✓
40.i

\(\chi_{40}(13, \cdot)\)$,$ \(\chi_{40}(37, \cdot)\)

$40$ $40$ $4$ \(\mathbb{Q}(i)\) odd ✓ ✓
40.j

\(\chi_{40}(7, \cdot)\)$,$ \(\chi_{40}(23, \cdot)\)

$40$ $20$ $4$ \(\mathbb{Q}(i)\) even
40.k

\(\chi_{40}(3, \cdot)\)$,$ \(\chi_{40}(27, \cdot)\)

$40$ $40$ $4$ \(\mathbb{Q}(i)\) even ✓ ✓
40.l

\(\chi_{40}(17, \cdot)\)$,$ \(\chi_{40}(33, \cdot)\)

$40$ $5$ $4$ \(\mathbb{Q}(i)\) odd ✓
41.c

\(\chi_{41}(9, \cdot)\)$,$ \(\chi_{41}(32, \cdot)\)

$41$ $41$ $4$ \(\mathbb{Q}(i)\) even ✓ ✓
45.f

\(\chi_{45}(8, \cdot)\)$,$ \(\chi_{45}(17, \cdot)\)

$45$ $15$ $4$ \(\mathbb{Q}(i)\) even ✓
45.g

\(\chi_{45}(28, \cdot)\)$,$ \(\chi_{45}(37, \cdot)\)

$45$ $5$ $4$ \(\mathbb{Q}(i)\) odd ✓
48.i

\(\chi_{48}(5, \cdot)\)$,$ \(\chi_{48}(29, \cdot)\)

$48$ $48$ $4$ \(\mathbb{Q}(i)\) odd ✓ ✓
48.j

\(\chi_{48}(13, \cdot)\)$,$ \(\chi_{48}(37, \cdot)\)

$48$ $16$ $4$ \(\mathbb{Q}(i)\) even ✓
48.k

\(\chi_{48}(11, \cdot)\)$,$ \(\chi_{48}(35, \cdot)\)

$48$ $48$ $4$ \(\mathbb{Q}(i)\) even ✓ ✓
48.l

\(\chi_{48}(19, \cdot)\)$,$ \(\chi_{48}(43, \cdot)\)

$48$ $16$ $4$ \(\mathbb{Q}(i)\) odd ✓
50.c

\(\chi_{50}(7, \cdot)\)$,$ \(\chi_{50}(43, \cdot)\)

$50$ $5$ $4$ \(\mathbb{Q}(i)\) odd ✓
51.e

\(\chi_{51}(4, \cdot)\)$,$ \(\chi_{51}(13, \cdot)\)

$51$ $17$ $4$ \(\mathbb{Q}(i)\) even ✓
51.f

\(\chi_{51}(38, \cdot)\)$,$ \(\chi_{51}(47, \cdot)\)

$51$ $51$ $4$ \(\mathbb{Q}(i)\) odd ✓ ✓
52.f

\(\chi_{52}(31, \cdot)\)$,$ \(\chi_{52}(47, \cdot)\)

$52$ $52$ $4$ \(\mathbb{Q}(i)\) even ✓ ✓
52.g

\(\chi_{52}(5, \cdot)\)$,$ \(\chi_{52}(21, \cdot)\)

$52$ $13$ $4$ \(\mathbb{Q}(i)\) odd ✓
53.c

\(\chi_{53}(23, \cdot)\)$,$ \(\chi_{53}(30, \cdot)\)

$53$ $53$ $4$ \(\mathbb{Q}(i)\) odd ✓ ✓
55.e

\(\chi_{55}(32, \cdot)\)$,$ \(\chi_{55}(43, \cdot)\)

$55$ $55$ $4$ \(\mathbb{Q}(i)\) even ✓ ✓
55.f

\(\chi_{55}(12, \cdot)\)$,$ \(\chi_{55}(23, \cdot)\)

$55$ $5$ $4$ \(\mathbb{Q}(i)\) odd ✓
58.c

\(\chi_{58}(17, \cdot)\)$,$ \(\chi_{58}(41, \cdot)\)

$58$ $29$ $4$ \(\mathbb{Q}(i)\) odd ✓
60.i

\(\chi_{60}(17, \cdot)\)$,$ \(\chi_{60}(53, \cdot)\)

$60$ $15$ $4$ \(\mathbb{Q}(i)\) even ✓
60.j

\(\chi_{60}(7, \cdot)\)$,$ \(\chi_{60}(43, \cdot)\)

$60$ $20$ $4$ \(\mathbb{Q}(i)\) even ✓
60.k

\(\chi_{60}(13, \cdot)\)$,$ \(\chi_{60}(37, \cdot)\)

$60$ $5$ $4$ \(\mathbb{Q}(i)\) odd ✓
60.l

\(\chi_{60}(23, \cdot)\)$,$ \(\chi_{60}(47, \cdot)\)

$60$ $60$ $4$ \(\mathbb{Q}(i)\) odd ✓ ✓
61.d

\(\chi_{61}(11, \cdot)\)$,$ \(\chi_{61}(50, \cdot)\)

$61$ $61$ $4$ \(\mathbb{Q}(i)\) odd ✓ ✓
64.e

\(\chi_{64}(17, \cdot)\)$,$ \(\chi_{64}(49, \cdot)\)

$64$ $16$ $4$ \(\mathbb{Q}(i)\) even
64.f

\(\chi_{64}(15, \cdot)\)$,$ \(\chi_{64}(47, \cdot)\)

$64$ $16$ $4$ \(\mathbb{Q}(i)\) odd
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