Dirichlet character \(\chi_{8732}(863,\cdot)\)

• Label: 8732.863
• Modulus: $8732$
• Conductor: $8732$
• Order: $522$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(8732\)
Conductor:	\(8732\)
Order:	\(522\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 8732.cp

\(\chi_{8732}(83,\cdot)\) \(\chi_{8732}(155,\cdot)\) \(\chi_{8732}(219,\cdot)\) \(\chi_{8732}(231,\cdot)\) \(\chi_{8732}(275,\cdot)\) \(\chi_{8732}(303,\cdot)\) \(\chi_{8732}(367,\cdot)\) \(\chi_{8732}(419,\cdot)\) \(\chi_{8732}(423,\cdot)\) \(\chi_{8732}(451,\cdot)\) \(\chi_{8732}(515,\cdot)\) \(\chi_{8732}(527,\cdot)\) \(\chi_{8732}(571,\cdot)\) \(\chi_{8732}(663,\cdot)\) \(\chi_{8732}(699,\cdot)\) \(\chi_{8732}(719,\cdot)\) \(\chi_{8732}(747,\cdot)\) \(\chi_{8732}(811,\cdot)\) \(\chi_{8732}(823,\cdot)\) \(\chi_{8732}(863,\cdot)\) \(\chi_{8732}(895,\cdot)\) \(\chi_{8732}(1011,\cdot)\) \(\chi_{8732}(1043,\cdot)\) \(\chi_{8732}(1159,\cdot)\) \(\chi_{8732}(1163,\cdot)\) \(\chi_{8732}(1191,\cdot)\) \(\chi_{8732}(1291,\cdot)\) \(\chi_{8732}(1311,\cdot)\) \(\chi_{8732}(1439,\cdot)\) \(\chi_{8732}(1455,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{261})$
Fixed field:	Number field defined by a degree 522 polynomial (not computed)

Values on generators

\((4367,1889,297)\) → \((-1,e\left(\frac{7}{9}\right),e\left(\frac{55}{58}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 8732 }(863, a) \)	\(1\)	\(1\)	\(e\left(\frac{71}{522}\right)\)	\(e\left(\frac{151}{261}\right)\)	\(e\left(\frac{239}{522}\right)\)	\(e\left(\frac{71}{261}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{119}{522}\right)\)	\(e\left(\frac{373}{522}\right)\)	\(e\left(\frac{98}{261}\right)\)	\(e\left(\frac{395}{522}\right)\)	\(e\left(\frac{155}{261}\right)\)