Dirichlet character \(\chi_{2205}(1418,\cdot)\)

• Label: 2205.1418
• 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.el

\(\chi_{2205}(2,\cdot)\) \(\chi_{2205}(32,\cdot)\) \(\chi_{2205}(158,\cdot)\) \(\chi_{2205}(317,\cdot)\) \(\chi_{2205}(347,\cdot)\) \(\chi_{2205}(443,\cdot)\) \(\chi_{2205}(473,\cdot)\) \(\chi_{2205}(632,\cdot)\) \(\chi_{2205}(662,\cdot)\) \(\chi_{2205}(758,\cdot)\) \(\chi_{2205}(788,\cdot)\) \(\chi_{2205}(947,\cdot)\) \(\chi_{2205}(977,\cdot)\) \(\chi_{2205}(1073,\cdot)\) \(\chi_{2205}(1103,\cdot)\) \(\chi_{2205}(1262,\cdot)\) \(\chi_{2205}(1388,\cdot)\) \(\chi_{2205}(1418,\cdot)\) \(\chi_{2205}(1577,\cdot)\) \(\chi_{2205}(1607,\cdot)\) \(\chi_{2205}(1703,\cdot)\) \(\chi_{2205}(1922,\cdot)\) \(\chi_{2205}(2018,\cdot)\) \(\chi_{2205}(2048,\cdot)\)

Related number fields

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

Values on generators

\((1226,442,1081)\) → \((e\left(\frac{5}{6}\right),-i,e\left(\frac{11}{21}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)	\(22\)	\(23\)
\( \chi_{ 2205 }(1418, a) \)	\(1\)	\(1\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)