Dirichlet character \(\chi_{2032}(1133,\cdot)\)

• Label: 2032.1133
• Modulus: $2032$
• Conductor: $2032$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2032\)
Conductor:	\(2032\)
Order:	\(84\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2032.cg

\(\chi_{2032}(61,\cdot)\) \(\chi_{2032}(117,\cdot)\) \(\chi_{2032}(165,\cdot)\) \(\chi_{2032}(221,\cdot)\) \(\chi_{2032}(301,\cdot)\) \(\chi_{2032}(341,\cdot)\) \(\chi_{2032}(533,\cdot)\) \(\chi_{2032}(581,\cdot)\) \(\chi_{2032}(685,\cdot)\) \(\chi_{2032}(757,\cdot)\) \(\chi_{2032}(965,\cdot)\) \(\chi_{2032}(989,\cdot)\) \(\chi_{2032}(1077,\cdot)\) \(\chi_{2032}(1133,\cdot)\) \(\chi_{2032}(1181,\cdot)\) \(\chi_{2032}(1237,\cdot)\) \(\chi_{2032}(1317,\cdot)\) \(\chi_{2032}(1357,\cdot)\) \(\chi_{2032}(1549,\cdot)\) \(\chi_{2032}(1597,\cdot)\) \(\chi_{2032}(1701,\cdot)\) \(\chi_{2032}(1773,\cdot)\) \(\chi_{2032}(1981,\cdot)\) \(\chi_{2032}(2005,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Values on generators

\((255,1525,257)\) → \((1,-i,e\left(\frac{16}{21}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 2032 }(1133, a) \)	\(1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(i\)	\(e\left(\frac{11}{84}\right)\)