Dirichlet character \(\chi_{2704}(1731,\cdot)\)

• Label: 2704.1731
• Modulus: $2704$
• Conductor: $2704$
• Order: $156$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2704\)
Conductor:	\(2704\)
Order:	\(156\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2704.cy

\(\chi_{2704}(11,\cdot)\) \(\chi_{2704}(59,\cdot)\) \(\chi_{2704}(67,\cdot)\) \(\chi_{2704}(219,\cdot)\) \(\chi_{2704}(227,\cdot)\) \(\chi_{2704}(267,\cdot)\) \(\chi_{2704}(275,\cdot)\) \(\chi_{2704}(435,\cdot)\) \(\chi_{2704}(475,\cdot)\) \(\chi_{2704}(483,\cdot)\) \(\chi_{2704}(635,\cdot)\) \(\chi_{2704}(643,\cdot)\) \(\chi_{2704}(683,\cdot)\) \(\chi_{2704}(691,\cdot)\) \(\chi_{2704}(843,\cdot)\) \(\chi_{2704}(851,\cdot)\) \(\chi_{2704}(891,\cdot)\) \(\chi_{2704}(899,\cdot)\) \(\chi_{2704}(1051,\cdot)\) \(\chi_{2704}(1059,\cdot)\) \(\chi_{2704}(1099,\cdot)\) \(\chi_{2704}(1107,\cdot)\) \(\chi_{2704}(1259,\cdot)\) \(\chi_{2704}(1267,\cdot)\) \(\chi_{2704}(1307,\cdot)\) \(\chi_{2704}(1315,\cdot)\) \(\chi_{2704}(1467,\cdot)\) \(\chi_{2704}(1475,\cdot)\) \(\chi_{2704}(1515,\cdot)\) \(\chi_{2704}(1523,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{156})$
Fixed field:	Number field defined by a degree 156 polynomial (not computed)

Values on generators

\((2367,677,1185)\) → \((-1,-i,e\left(\frac{85}{156}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\( \chi_{ 2704 }(1731, a) \)	\(1\)	\(1\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)