Dirichlet character \(\chi_{1824}(203,\cdot)\)

• Label: 1824.203
• Modulus: $1824$
• Conductor: $1824$
• Order: $72$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(1824\)
Conductor:	\(1824\)
Order:	\(72\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1824.dk

\(\chi_{1824}(59,\cdot)\) \(\chi_{1824}(155,\cdot)\) \(\chi_{1824}(203,\cdot)\) \(\chi_{1824}(299,\cdot)\) \(\chi_{1824}(371,\cdot)\) \(\chi_{1824}(395,\cdot)\) \(\chi_{1824}(515,\cdot)\) \(\chi_{1824}(611,\cdot)\) \(\chi_{1824}(659,\cdot)\) \(\chi_{1824}(755,\cdot)\) \(\chi_{1824}(827,\cdot)\) \(\chi_{1824}(851,\cdot)\) \(\chi_{1824}(971,\cdot)\) \(\chi_{1824}(1067,\cdot)\) \(\chi_{1824}(1115,\cdot)\) \(\chi_{1824}(1211,\cdot)\) \(\chi_{1824}(1283,\cdot)\) \(\chi_{1824}(1307,\cdot)\) \(\chi_{1824}(1427,\cdot)\) \(\chi_{1824}(1523,\cdot)\) \(\chi_{1824}(1571,\cdot)\) \(\chi_{1824}(1667,\cdot)\) \(\chi_{1824}(1739,\cdot)\) \(\chi_{1824}(1763,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{72})$
Fixed field:	Number field defined by a degree 72 polynomial

Values on generators

\((799,229,1217,97)\) → \((-1,e\left(\frac{5}{8}\right),-1,e\left(\frac{5}{18}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\( \chi_{ 1824 }(203, a) \)	\(-1\)	\(1\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{71}{72}\right)\)