Dirichlet character \(\chi_{4205}(1172,\cdot)\)

• Label: 4205.1172
• Modulus: $4205$
• Conductor: $4205$
• Order: $116$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(4205\)
Conductor:	\(4205\)
Order:	\(116\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4205.bd

\(\chi_{4205}(12,\cdot)\) \(\chi_{4205}(133,\cdot)\) \(\chi_{4205}(157,\cdot)\) \(\chi_{4205}(278,\cdot)\) \(\chi_{4205}(302,\cdot)\) \(\chi_{4205}(423,\cdot)\) \(\chi_{4205}(447,\cdot)\) \(\chi_{4205}(568,\cdot)\) \(\chi_{4205}(592,\cdot)\) \(\chi_{4205}(713,\cdot)\) \(\chi_{4205}(737,\cdot)\) \(\chi_{4205}(858,\cdot)\) \(\chi_{4205}(1003,\cdot)\) \(\chi_{4205}(1027,\cdot)\) \(\chi_{4205}(1148,\cdot)\) \(\chi_{4205}(1172,\cdot)\) \(\chi_{4205}(1293,\cdot)\) \(\chi_{4205}(1317,\cdot)\) \(\chi_{4205}(1438,\cdot)\) \(\chi_{4205}(1462,\cdot)\) \(\chi_{4205}(1583,\cdot)\) \(\chi_{4205}(1607,\cdot)\) \(\chi_{4205}(1728,\cdot)\) \(\chi_{4205}(1752,\cdot)\) \(\chi_{4205}(1873,\cdot)\) \(\chi_{4205}(1897,\cdot)\) \(\chi_{4205}(2018,\cdot)\) \(\chi_{4205}(2042,\cdot)\) \(\chi_{4205}(2163,\cdot)\) \(\chi_{4205}(2187,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{116})$
Fixed field:	Number field defined by a degree 116 polynomial (not computed)

Values on generators

\((842,3366)\) → \((i,e\left(\frac{13}{116}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\( \chi_{ 4205 }(1172, a) \)	\(1\)	\(1\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{45}{116}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{9}{116}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{109}{116}\right)\)