Dirichlet character \(\chi_{3724}(1315,\cdot)\)

• Label: 3724.1315
• Modulus: $3724$
• Conductor: $3724$
• Order: $126$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(3724\)
Conductor:	\(3724\)
Order:	\(126\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3724.ek

\(\chi_{3724}(55,\cdot)\) \(\chi_{3724}(111,\cdot)\) \(\chi_{3724}(139,\cdot)\) \(\chi_{3724}(251,\cdot)\) \(\chi_{3724}(503,\cdot)\) \(\chi_{3724}(643,\cdot)\) \(\chi_{3724}(671,\cdot)\) \(\chi_{3724}(727,\cdot)\) \(\chi_{3724}(1035,\cdot)\) \(\chi_{3724}(1119,\cdot)\) \(\chi_{3724}(1203,\cdot)\) \(\chi_{3724}(1259,\cdot)\) \(\chi_{3724}(1315,\cdot)\) \(\chi_{3724}(1651,\cdot)\) \(\chi_{3724}(1707,\cdot)\) \(\chi_{3724}(1735,\cdot)\) \(\chi_{3724}(1791,\cdot)\) \(\chi_{3724}(1847,\cdot)\) \(\chi_{3724}(2099,\cdot)\) \(\chi_{3724}(2183,\cdot)\) \(\chi_{3724}(2239,\cdot)\) \(\chi_{3724}(2267,\cdot)\) \(\chi_{3724}(2323,\cdot)\) \(\chi_{3724}(2379,\cdot)\) \(\chi_{3724}(2631,\cdot)\) \(\chi_{3724}(2715,\cdot)\) \(\chi_{3724}(2771,\cdot)\) \(\chi_{3724}(2799,\cdot)\) \(\chi_{3724}(2855,\cdot)\) \(\chi_{3724}(2911,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{63})$
Fixed field:	Number field defined by a degree 126 polynomial (not computed)

Values on generators

\((1863,3041,3137)\) → \((-1,e\left(\frac{5}{14}\right),e\left(\frac{1}{9}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(23\)	\(25\)	\(27\)
\( \chi_{ 3724 }(1315, a) \)	\(1\)	\(1\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)