Dirichlet character \(\chi_{3160}(1749,\cdot)\)

• Label: 3160.1749
• Modulus: $3160$
• Conductor: $3160$
• Order: $78$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(3160\)
Conductor:	\(3160\)
Order:	\(78\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3160.de

\(\chi_{3160}(189,\cdot)\) \(\chi_{3160}(269,\cdot)\) \(\chi_{3160}(309,\cdot)\) \(\chi_{3160}(389,\cdot)\) \(\chi_{3160}(589,\cdot)\) \(\chi_{3160}(629,\cdot)\) \(\chi_{3160}(909,\cdot)\) \(\chi_{3160}(1029,\cdot)\) \(\chi_{3160}(1069,\cdot)\) \(\chi_{3160}(1189,\cdot)\) \(\chi_{3160}(1229,\cdot)\) \(\chi_{3160}(1269,\cdot)\) \(\chi_{3160}(1309,\cdot)\) \(\chi_{3160}(1589,\cdot)\) \(\chi_{3160}(1629,\cdot)\) \(\chi_{3160}(1709,\cdot)\) \(\chi_{3160}(1749,\cdot)\) \(\chi_{3160}(1789,\cdot)\) \(\chi_{3160}(1909,\cdot)\) \(\chi_{3160}(2149,\cdot)\) \(\chi_{3160}(2389,\cdot)\) \(\chi_{3160}(2469,\cdot)\) \(\chi_{3160}(2869,\cdot)\) \(\chi_{3160}(2949,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{39})$
Fixed field:	Number field defined by a degree 78 polynomial

Values on generators

\((791,1581,1897,161)\) → \((1,-1,-1,e\left(\frac{34}{39}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\( \chi_{ 3160 }(1749, a) \)	\(1\)	\(1\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{13}\right)\)