Dirichlet character \(\chi_{31360}(643,\cdot)\)

• Label: 31360.643
• Modulus: $31360$
• Conductor: $31360$
• Order: $224$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(31360\)
Conductor:	\(31360\)
Order:	\(224\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 31360.lu

\(\chi_{31360}(27,\cdot)\) \(\chi_{31360}(83,\cdot)\) \(\chi_{31360}(643,\cdot)\) \(\chi_{31360}(1147,\cdot)\) \(\chi_{31360}(1203,\cdot)\) \(\chi_{31360}(1707,\cdot)\) \(\chi_{31360}(2267,\cdot)\) \(\chi_{31360}(2323,\cdot)\) \(\chi_{31360}(2827,\cdot)\) \(\chi_{31360}(2883,\cdot)\) \(\chi_{31360}(3387,\cdot)\) \(\chi_{31360}(3443,\cdot)\) \(\chi_{31360}(3947,\cdot)\) \(\chi_{31360}(4003,\cdot)\) \(\chi_{31360}(4563,\cdot)\) \(\chi_{31360}(5067,\cdot)\) \(\chi_{31360}(5123,\cdot)\) \(\chi_{31360}(5627,\cdot)\) \(\chi_{31360}(6187,\cdot)\) \(\chi_{31360}(6243,\cdot)\) \(\chi_{31360}(6747,\cdot)\) \(\chi_{31360}(6803,\cdot)\) \(\chi_{31360}(7307,\cdot)\) \(\chi_{31360}(7363,\cdot)\) \(\chi_{31360}(7867,\cdot)\) \(\chi_{31360}(7923,\cdot)\) \(\chi_{31360}(8483,\cdot)\) \(\chi_{31360}(8987,\cdot)\) \(\chi_{31360}(9043,\cdot)\) \(\chi_{31360}(9547,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{224})$
Fixed field:	Number field defined by a degree 224 polynomial (not computed)

Values on generators

\((17151,28421,18817,10881)\) → \((-1,e\left(\frac{3}{32}\right),-i,e\left(\frac{9}{14}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\( \chi_{ 31360 }(643, a) \)	\(-1\)	\(1\)	\(e\left(\frac{151}{224}\right)\)	\(e\left(\frac{39}{112}\right)\)	\(e\left(\frac{41}{224}\right)\)	\(e\left(\frac{195}{224}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{5}{224}\right)\)	\(e\left(\frac{135}{224}\right)\)	\(-i\)