Dirichlet character \(\chi_{3645}(1282,\cdot)\)

• Label: 3645.1282
• Modulus: $3645$
• Conductor: $3645$
• Order: $972$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

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

Galois orbit 3645.bi

\(\chi_{3645}(7,\cdot)\) \(\chi_{3645}(13,\cdot)\) \(\chi_{3645}(22,\cdot)\) \(\chi_{3645}(43,\cdot)\) \(\chi_{3645}(52,\cdot)\) \(\chi_{3645}(58,\cdot)\) \(\chi_{3645}(67,\cdot)\) \(\chi_{3645}(88,\cdot)\) \(\chi_{3645}(97,\cdot)\) \(\chi_{3645}(103,\cdot)\) \(\chi_{3645}(112,\cdot)\) \(\chi_{3645}(133,\cdot)\) \(\chi_{3645}(142,\cdot)\) \(\chi_{3645}(148,\cdot)\) \(\chi_{3645}(157,\cdot)\) \(\chi_{3645}(178,\cdot)\) \(\chi_{3645}(187,\cdot)\) \(\chi_{3645}(193,\cdot)\) \(\chi_{3645}(202,\cdot)\) \(\chi_{3645}(223,\cdot)\) \(\chi_{3645}(232,\cdot)\) \(\chi_{3645}(238,\cdot)\) \(\chi_{3645}(247,\cdot)\) \(\chi_{3645}(268,\cdot)\) \(\chi_{3645}(277,\cdot)\) \(\chi_{3645}(283,\cdot)\) \(\chi_{3645}(292,\cdot)\) \(\chi_{3645}(313,\cdot)\) \(\chi_{3645}(322,\cdot)\) \(\chi_{3645}(328,\cdot)\) ...

Related number fields

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

Values on generators

\((731,2917)\) → \((e\left(\frac{22}{243}\right),i)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\( \chi_{ 3645 }(1282, a) \)	\(-1\)	\(1\)	\(e\left(\frac{331}{972}\right)\)	\(e\left(\frac{331}{486}\right)\)	\(e\left(\frac{895}{972}\right)\)	\(e\left(\frac{7}{324}\right)\)	\(e\left(\frac{151}{243}\right)\)	\(e\left(\frac{785}{972}\right)\)	\(e\left(\frac{127}{486}\right)\)	\(e\left(\frac{88}{243}\right)\)	\(e\left(\frac{77}{324}\right)\)	\(e\left(\frac{47}{162}\right)\)