Dirichlet character \(\chi_{2205}(1447,\cdot)\)

• Label: 2205.1447
• 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.ea

\(\chi_{2205}(157,\cdot)\) \(\chi_{2205}(187,\cdot)\) \(\chi_{2205}(283,\cdot)\) \(\chi_{2205}(502,\cdot)\) \(\chi_{2205}(598,\cdot)\) \(\chi_{2205}(628,\cdot)\) \(\chi_{2205}(787,\cdot)\) \(\chi_{2205}(817,\cdot)\) \(\chi_{2205}(943,\cdot)\) \(\chi_{2205}(1102,\cdot)\) \(\chi_{2205}(1132,\cdot)\) \(\chi_{2205}(1228,\cdot)\) \(\chi_{2205}(1258,\cdot)\) \(\chi_{2205}(1417,\cdot)\) \(\chi_{2205}(1447,\cdot)\) \(\chi_{2205}(1543,\cdot)\) \(\chi_{2205}(1573,\cdot)\) \(\chi_{2205}(1732,\cdot)\) \(\chi_{2205}(1762,\cdot)\) \(\chi_{2205}(1858,\cdot)\) \(\chi_{2205}(1888,\cdot)\) \(\chi_{2205}(2047,\cdot)\) \(\chi_{2205}(2173,\cdot)\) \(\chi_{2205}(2203,\cdot)\)

Related number fields

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

Values on generators

\((1226,442,1081)\) → \((e\left(\frac{2}{3}\right),i,e\left(\frac{17}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)	\(22\)	\(23\)
\( \chi_{ 2205 }(1447, a) \)	\(1\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)