Dirichlet character \(\chi_{2205}(1678,\cdot)\)

• Label: 2205.1678
• 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.eo

\(\chi_{2205}(52,\cdot)\) \(\chi_{2205}(103,\cdot)\) \(\chi_{2205}(292,\cdot)\) \(\chi_{2205}(367,\cdot)\) \(\chi_{2205}(418,\cdot)\) \(\chi_{2205}(493,\cdot)\) \(\chi_{2205}(682,\cdot)\) \(\chi_{2205}(733,\cdot)\) \(\chi_{2205}(808,\cdot)\) \(\chi_{2205}(922,\cdot)\) \(\chi_{2205}(997,\cdot)\) \(\chi_{2205}(1123,\cdot)\) \(\chi_{2205}(1237,\cdot)\) \(\chi_{2205}(1312,\cdot)\) \(\chi_{2205}(1363,\cdot)\) \(\chi_{2205}(1438,\cdot)\) \(\chi_{2205}(1552,\cdot)\) \(\chi_{2205}(1627,\cdot)\) \(\chi_{2205}(1678,\cdot)\) \(\chi_{2205}(1753,\cdot)\) \(\chi_{2205}(1867,\cdot)\) \(\chi_{2205}(1993,\cdot)\) \(\chi_{2205}(2068,\cdot)\) \(\chi_{2205}(2182,\cdot)\)

Related number fields

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

Values on generators

\((1226,442,1081)\) → \((e\left(\frac{1}{3}\right),-i,e\left(\frac{11}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)	\(22\)	\(23\)
\( \chi_{ 2205 }(1678, a) \)	\(1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)