Dirichlet character \(\chi_{1824}(269,\cdot)\)

• Label: 1824.269
• Modulus: $1824$
• Conductor: $1824$
• Order: $72$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

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

Galois orbit 1824.do

\(\chi_{1824}(29,\cdot)\) \(\chi_{1824}(53,\cdot)\) \(\chi_{1824}(173,\cdot)\) \(\chi_{1824}(269,\cdot)\) \(\chi_{1824}(317,\cdot)\) \(\chi_{1824}(413,\cdot)\) \(\chi_{1824}(485,\cdot)\) \(\chi_{1824}(509,\cdot)\) \(\chi_{1824}(629,\cdot)\) \(\chi_{1824}(725,\cdot)\) \(\chi_{1824}(773,\cdot)\) \(\chi_{1824}(869,\cdot)\) \(\chi_{1824}(941,\cdot)\) \(\chi_{1824}(965,\cdot)\) \(\chi_{1824}(1085,\cdot)\) \(\chi_{1824}(1181,\cdot)\) \(\chi_{1824}(1229,\cdot)\) \(\chi_{1824}(1325,\cdot)\) \(\chi_{1824}(1397,\cdot)\) \(\chi_{1824}(1421,\cdot)\) \(\chi_{1824}(1541,\cdot)\) \(\chi_{1824}(1637,\cdot)\) \(\chi_{1824}(1685,\cdot)\) \(\chi_{1824}(1781,\cdot)\)

Related number fields

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

Values on generators

\((799,229,1217,97)\) → \((1,e\left(\frac{7}{8}\right),-1,e\left(\frac{13}{18}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\( \chi_{ 1824 }(269, a) \)	\(1\)	\(1\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{72}\right)\)