Dirichlet character \(\chi_{1588}(1371,\cdot)\)

• Label: 1588.1371
• Modulus: $1588$
• Conductor: $1588$
• Order: $396$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1588\)
Conductor:	\(1588\)
Order:	\(396\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1588.bj

\(\chi_{1588}(7,\cdot)\) \(\chi_{1588}(39,\cdot)\) \(\chi_{1588}(51,\cdot)\) \(\chi_{1588}(59,\cdot)\) \(\chi_{1588}(135,\cdot)\) \(\chi_{1588}(139,\cdot)\) \(\chi_{1588}(143,\cdot)\) \(\chi_{1588}(155,\cdot)\) \(\chi_{1588}(159,\cdot)\) \(\chi_{1588}(175,\cdot)\) \(\chi_{1588}(187,\cdot)\) \(\chi_{1588}(211,\cdot)\) \(\chi_{1588}(215,\cdot)\) \(\chi_{1588}(223,\cdot)\) \(\chi_{1588}(227,\cdot)\) \(\chi_{1588}(235,\cdot)\) \(\chi_{1588}(239,\cdot)\) \(\chi_{1588}(247,\cdot)\) \(\chi_{1588}(251,\cdot)\) \(\chi_{1588}(259,\cdot)\) \(\chi_{1588}(263,\cdot)\) \(\chi_{1588}(283,\cdot)\) \(\chi_{1588}(299,\cdot)\) \(\chi_{1588}(303,\cdot)\) \(\chi_{1588}(323,\cdot)\) \(\chi_{1588}(331,\cdot)\) \(\chi_{1588}(339,\cdot)\) \(\chi_{1588}(347,\cdot)\) \(\chi_{1588}(351,\cdot)\) \(\chi_{1588}(359,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{396})$
Fixed field:	Number field defined by a degree 396 polynomial (not computed)

Values on generators

\((795,5)\) → \((-1,e\left(\frac{59}{396}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 1588 }(1371, a) \)	\(1\)	\(1\)	\(e\left(\frac{61}{99}\right)\)	\(e\left(\frac{59}{396}\right)\)	\(e\left(\frac{205}{396}\right)\)	\(e\left(\frac{23}{99}\right)\)	\(e\left(\frac{71}{198}\right)\)	\(e\left(\frac{19}{396}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{113}{198}\right)\)	\(e\left(\frac{53}{396}\right)\)