Dirichlet character \(\chi_{3645}(263,\cdot)\)

• Label: 3645.263
• Modulus: $3645$
• Conductor: $3645$
• Order: $972$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(3645\)
Conductor:	\(3645\)
Order:	\(972\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3645.bj

\(\chi_{3645}(2,\cdot)\) \(\chi_{3645}(23,\cdot)\) \(\chi_{3645}(32,\cdot)\) \(\chi_{3645}(38,\cdot)\) \(\chi_{3645}(47,\cdot)\) \(\chi_{3645}(68,\cdot)\) \(\chi_{3645}(77,\cdot)\) \(\chi_{3645}(83,\cdot)\) \(\chi_{3645}(92,\cdot)\) \(\chi_{3645}(113,\cdot)\) \(\chi_{3645}(122,\cdot)\) \(\chi_{3645}(128,\cdot)\) \(\chi_{3645}(137,\cdot)\) \(\chi_{3645}(158,\cdot)\) \(\chi_{3645}(167,\cdot)\) \(\chi_{3645}(173,\cdot)\) \(\chi_{3645}(182,\cdot)\) \(\chi_{3645}(203,\cdot)\) \(\chi_{3645}(212,\cdot)\) \(\chi_{3645}(218,\cdot)\) \(\chi_{3645}(227,\cdot)\) \(\chi_{3645}(248,\cdot)\) \(\chi_{3645}(257,\cdot)\) \(\chi_{3645}(263,\cdot)\) \(\chi_{3645}(272,\cdot)\) \(\chi_{3645}(293,\cdot)\) \(\chi_{3645}(302,\cdot)\) \(\chi_{3645}(308,\cdot)\) \(\chi_{3645}(317,\cdot)\) \(\chi_{3645}(338,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{972})$
Fixed field:	Number field defined by a degree 972 polynomial (not computed)

Values on generators

\((731,2917)\) → \((e\left(\frac{349}{486}\right),-i)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\( \chi_{ 3645 }(263, a) \)	\(1\)	\(1\)	\(e\left(\frac{455}{972}\right)\)	\(e\left(\frac{455}{486}\right)\)	\(e\left(\frac{665}{972}\right)\)	\(e\left(\frac{131}{324}\right)\)	\(e\left(\frac{109}{486}\right)\)	\(e\left(\frac{643}{972}\right)\)	\(e\left(\frac{37}{243}\right)\)	\(e\left(\frac{212}{243}\right)\)	\(e\left(\frac{145}{324}\right)\)	\(e\left(\frac{139}{162}\right)\)