Dirichlet character \(\chi_{3724}(599,\cdot)\)

• Label: 3724.599
• 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.ew

\(\chi_{3724}(135,\cdot)\) \(\chi_{3724}(319,\cdot)\) \(\chi_{3724}(431,\cdot)\) \(\chi_{3724}(527,\cdot)\) \(\chi_{3724}(599,\cdot)\) \(\chi_{3724}(611,\cdot)\) \(\chi_{3724}(963,\cdot)\) \(\chi_{3724}(1131,\cdot)\) \(\chi_{3724}(1143,\cdot)\) \(\chi_{3724}(1199,\cdot)\) \(\chi_{3724}(1383,\cdot)\) \(\chi_{3724}(1495,\cdot)\) \(\chi_{3724}(1591,\cdot)\) \(\chi_{3724}(1663,\cdot)\) \(\chi_{3724}(1675,\cdot)\) \(\chi_{3724}(1731,\cdot)\) \(\chi_{3724}(1915,\cdot)\) \(\chi_{3724}(2123,\cdot)\) \(\chi_{3724}(2195,\cdot)\) \(\chi_{3724}(2207,\cdot)\) \(\chi_{3724}(2263,\cdot)\) \(\chi_{3724}(2447,\cdot)\) \(\chi_{3724}(2559,\cdot)\) \(\chi_{3724}(2655,\cdot)\) \(\chi_{3724}(2727,\cdot)\) \(\chi_{3724}(2739,\cdot)\) \(\chi_{3724}(2795,\cdot)\) \(\chi_{3724}(2979,\cdot)\) \(\chi_{3724}(3091,\cdot)\) \(\chi_{3724}(3187,\cdot)\) ...

Related number fields

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

Values on generators

\((1863,3041,3137)\) → \((-1,e\left(\frac{20}{21}\right),e\left(\frac{17}{18}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(23\)	\(25\)	\(27\)
\( \chi_{ 3724 }(599, a) \)	\(1\)	\(1\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)