Dirichlet character \(\chi_{1725}(404,\cdot)\)

• Label: 1725.404
• Modulus: $1725$
• Conductor: $1725$
• Order: $110$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(1725\)
Conductor:	\(1725\)
Order:	\(110\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1725.bq

\(\chi_{1725}(29,\cdot)\) \(\chi_{1725}(59,\cdot)\) \(\chi_{1725}(104,\cdot)\) \(\chi_{1725}(119,\cdot)\) \(\chi_{1725}(164,\cdot)\) \(\chi_{1725}(179,\cdot)\) \(\chi_{1725}(209,\cdot)\) \(\chi_{1725}(239,\cdot)\) \(\chi_{1725}(269,\cdot)\) \(\chi_{1725}(284,\cdot)\) \(\chi_{1725}(404,\cdot)\) \(\chi_{1725}(464,\cdot)\) \(\chi_{1725}(509,\cdot)\) \(\chi_{1725}(554,\cdot)\) \(\chi_{1725}(584,\cdot)\) \(\chi_{1725}(614,\cdot)\) \(\chi_{1725}(629,\cdot)\) \(\chi_{1725}(719,\cdot)\) \(\chi_{1725}(794,\cdot)\) \(\chi_{1725}(809,\cdot)\) \(\chi_{1725}(854,\cdot)\) \(\chi_{1725}(869,\cdot)\) \(\chi_{1725}(929,\cdot)\) \(\chi_{1725}(959,\cdot)\) \(\chi_{1725}(1064,\cdot)\) \(\chi_{1725}(1094,\cdot)\) \(\chi_{1725}(1139,\cdot)\) \(\chi_{1725}(1154,\cdot)\) \(\chi_{1725}(1214,\cdot)\) \(\chi_{1725}(1244,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{55})$
Fixed field:	Number field defined by a degree 110 polynomial (not computed)

Values on generators

\((1151,277,1201)\) → \((-1,e\left(\frac{1}{10}\right),e\left(\frac{7}{11}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\( \chi_{ 1725 }(404, a) \)	\(-1\)	\(1\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)