Dirichlet character \(\chi_{2205}(578,\cdot)\)

• Label: 2205.578
• 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.en

\(\chi_{2205}(23,\cdot)\) \(\chi_{2205}(137,\cdot)\) \(\chi_{2205}(212,\cdot)\) \(\chi_{2205}(338,\cdot)\) \(\chi_{2205}(452,\cdot)\) \(\chi_{2205}(527,\cdot)\) \(\chi_{2205}(578,\cdot)\) \(\chi_{2205}(653,\cdot)\) \(\chi_{2205}(767,\cdot)\) \(\chi_{2205}(842,\cdot)\) \(\chi_{2205}(893,\cdot)\) \(\chi_{2205}(968,\cdot)\) \(\chi_{2205}(1082,\cdot)\) \(\chi_{2205}(1208,\cdot)\) \(\chi_{2205}(1283,\cdot)\) \(\chi_{2205}(1397,\cdot)\) \(\chi_{2205}(1472,\cdot)\) \(\chi_{2205}(1523,\cdot)\) \(\chi_{2205}(1712,\cdot)\) \(\chi_{2205}(1787,\cdot)\) \(\chi_{2205}(1838,\cdot)\) \(\chi_{2205}(1913,\cdot)\) \(\chi_{2205}(2102,\cdot)\) \(\chi_{2205}(2153,\cdot)\)

Related number fields

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

Values on generators

\((1226,442,1081)\) → \((e\left(\frac{1}{6}\right),-i,e\left(\frac{17}{21}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)	\(22\)	\(23\)
\( \chi_{ 2205 }(578, a) \)	\(1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)