Dirichlet character \(\chi_{3645}(229,\cdot)\)

• Label: 3645.229
• Modulus: $3645$
• Conductor: $3645$
• Order: $486$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(3645\)
Conductor:	\(3645\)
Order:	\(486\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3645.bh

\(\chi_{3645}(4,\cdot)\) \(\chi_{3645}(34,\cdot)\) \(\chi_{3645}(49,\cdot)\) \(\chi_{3645}(79,\cdot)\) \(\chi_{3645}(94,\cdot)\) \(\chi_{3645}(124,\cdot)\) \(\chi_{3645}(139,\cdot)\) \(\chi_{3645}(169,\cdot)\) \(\chi_{3645}(184,\cdot)\) \(\chi_{3645}(214,\cdot)\) \(\chi_{3645}(229,\cdot)\) \(\chi_{3645}(259,\cdot)\) \(\chi_{3645}(274,\cdot)\) \(\chi_{3645}(304,\cdot)\) \(\chi_{3645}(319,\cdot)\) \(\chi_{3645}(349,\cdot)\) \(\chi_{3645}(364,\cdot)\) \(\chi_{3645}(394,\cdot)\) \(\chi_{3645}(409,\cdot)\) \(\chi_{3645}(439,\cdot)\) \(\chi_{3645}(454,\cdot)\) \(\chi_{3645}(484,\cdot)\) \(\chi_{3645}(499,\cdot)\) \(\chi_{3645}(529,\cdot)\) \(\chi_{3645}(544,\cdot)\) \(\chi_{3645}(574,\cdot)\) \(\chi_{3645}(589,\cdot)\) \(\chi_{3645}(619,\cdot)\) \(\chi_{3645}(634,\cdot)\) \(\chi_{3645}(664,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{243})$
Fixed field:	Number field defined by a degree 486 polynomial (not computed)

Values on generators

\((731,2917)\) → \((e\left(\frac{157}{243}\right),-1)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\( \chi_{ 3645 }(229, a) \)	\(1\)	\(1\)	\(e\left(\frac{71}{486}\right)\)	\(e\left(\frac{71}{243}\right)\)	\(e\left(\frac{29}{486}\right)\)	\(e\left(\frac{71}{162}\right)\)	\(e\left(\frac{205}{243}\right)\)	\(e\left(\frac{1}{486}\right)\)	\(e\left(\frac{50}{243}\right)\)	\(e\left(\frac{142}{243}\right)\)	\(e\left(\frac{133}{162}\right)\)	\(e\left(\frac{37}{81}\right)\)