Dirichlet character \(\chi_{2205}(1357,\cdot)\)

• Label: 2205.1357
• 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.ej

\(\chi_{2205}(13,\cdot)\) \(\chi_{2205}(202,\cdot)\) \(\chi_{2205}(223,\cdot)\) \(\chi_{2205}(328,\cdot)\) \(\chi_{2205}(412,\cdot)\) \(\chi_{2205}(517,\cdot)\) \(\chi_{2205}(643,\cdot)\) \(\chi_{2205}(727,\cdot)\) \(\chi_{2205}(853,\cdot)\) \(\chi_{2205}(958,\cdot)\) \(\chi_{2205}(1042,\cdot)\) \(\chi_{2205}(1147,\cdot)\) \(\chi_{2205}(1168,\cdot)\) \(\chi_{2205}(1357,\cdot)\) \(\chi_{2205}(1462,\cdot)\) \(\chi_{2205}(1483,\cdot)\) \(\chi_{2205}(1588,\cdot)\) \(\chi_{2205}(1672,\cdot)\) \(\chi_{2205}(1777,\cdot)\) \(\chi_{2205}(1798,\cdot)\) \(\chi_{2205}(1903,\cdot)\) \(\chi_{2205}(1987,\cdot)\) \(\chi_{2205}(2092,\cdot)\) \(\chi_{2205}(2113,\cdot)\)

Related number fields

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

Values on generators

\((1226,442,1081)\) → \((e\left(\frac{2}{3}\right),i,e\left(\frac{3}{14}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)	\(22\)	\(23\)
\( \chi_{ 2205 }(1357, a) \)	\(1\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{19}{84}\right)\)