Dirichlet character \(\chi_{2580}(1187,\cdot)\)

• Label: 2580.1187
• Modulus: $2580$
• Conductor: $2580$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2580\)
Conductor:	\(2580\)
Order:	\(84\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2580.dk

\(\chi_{2580}(227,\cdot)\) \(\chi_{2580}(263,\cdot)\) \(\chi_{2580}(287,\cdot)\) \(\chi_{2580}(347,\cdot)\) \(\chi_{2580}(407,\cdot)\) \(\chi_{2580}(503,\cdot)\) \(\chi_{2580}(587,\cdot)\) \(\chi_{2580}(707,\cdot)\) \(\chi_{2580}(743,\cdot)\) \(\chi_{2580}(803,\cdot)\) \(\chi_{2580}(863,\cdot)\) \(\chi_{2580}(923,\cdot)\) \(\chi_{2580}(1007,\cdot)\) \(\chi_{2580}(1103,\cdot)\) \(\chi_{2580}(1187,\cdot)\) \(\chi_{2580}(1223,\cdot)\) \(\chi_{2580}(1367,\cdot)\) \(\chi_{2580}(1523,\cdot)\) \(\chi_{2580}(1667,\cdot)\) \(\chi_{2580}(1703,\cdot)\) \(\chi_{2580}(1883,\cdot)\) \(\chi_{2580}(2183,\cdot)\) \(\chi_{2580}(2327,\cdot)\) \(\chi_{2580}(2567,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Values on generators

\((1291,1721,517,1981)\) → \((-1,-1,i,e\left(\frac{17}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\( \chi_{ 2580 }(1187, a) \)	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{14}\right)\)