Dirichlet character \(\chi_{2205}(1688,\cdot)\)

• Label: 2205.1688
• Modulus: $2205$
• Conductor: $2205$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2205\)
Conductor:	\(2205\)
Order:	\(84\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2205.ec

\(\chi_{2205}(92,\cdot)\) \(\chi_{2205}(113,\cdot)\) \(\chi_{2205}(218,\cdot)\) \(\chi_{2205}(302,\cdot)\) \(\chi_{2205}(407,\cdot)\) \(\chi_{2205}(428,\cdot)\) \(\chi_{2205}(533,\cdot)\) \(\chi_{2205}(617,\cdot)\) \(\chi_{2205}(722,\cdot)\) \(\chi_{2205}(743,\cdot)\) \(\chi_{2205}(848,\cdot)\) \(\chi_{2205}(1037,\cdot)\) \(\chi_{2205}(1058,\cdot)\) \(\chi_{2205}(1163,\cdot)\) \(\chi_{2205}(1247,\cdot)\) \(\chi_{2205}(1352,\cdot)\) \(\chi_{2205}(1478,\cdot)\) \(\chi_{2205}(1562,\cdot)\) \(\chi_{2205}(1688,\cdot)\) \(\chi_{2205}(1793,\cdot)\) \(\chi_{2205}(1877,\cdot)\) \(\chi_{2205}(1982,\cdot)\) \(\chi_{2205}(2003,\cdot)\) \(\chi_{2205}(2192,\cdot)\)

Related number fields

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

Values on generators

\((1226,442,1081)\) → \((e\left(\frac{5}{6}\right),-i,e\left(\frac{4}{7}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)	\(22\)	\(23\)
\( \chi_{ 2205 }(1688, a) \)	\(1\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(-1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)