Dirichlet character \(\chi_{254144}(238269,\cdot)\)

• Label: 254144.238269
• Modulus: $254144$
• Conductor: $254144$
• Order: $13680$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(254144\)
Conductor:	\(254144\)
Order:	\(13680\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 254144.sl

\(\chi_{254144}(5,\cdot)\) \(\chi_{254144}(93,\cdot)\) \(\chi_{254144}(157,\cdot)\) \(\chi_{254144}(213,\cdot)\) \(\chi_{254144}(301,\cdot)\) \(\chi_{254144}(405,\cdot)\) \(\chi_{254144}(669,\cdot)\) \(\chi_{254144}(709,\cdot)\) \(\chi_{254144}(757,\cdot)\) \(\chi_{254144}(845,\cdot)\) \(\chi_{254144}(861,\cdot)\) \(\chi_{254144}(917,\cdot)\) \(\chi_{254144}(973,\cdot)\) \(\chi_{254144}(1005,\cdot)\) \(\chi_{254144}(1061,\cdot)\) \(\chi_{254144}(1125,\cdot)\) \(\chi_{254144}(1149,\cdot)\) \(\chi_{254144}(1213,\cdot)\) \(\chi_{254144}(1301,\cdot)\) \(\chi_{254144}(1373,\cdot)\) \(\chi_{254144}(1461,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{13680})$
Fixed field:	Number field defined by a degree 13680 polynomial (not computed)

Values on generators

\((166783,174725,69313,14081)\) → \((1,e\left(\frac{3}{16}\right),e\left(\frac{3}{5}\right),e\left(\frac{139}{171}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\( \chi_{ 254144 }(238269, a) \)	\(1\)	\(1\)	\(e\left(\frac{4799}{13680}\right)\)	\(e\left(\frac{2357}{13680}\right)\)	\(e\left(\frac{11}{2280}\right)\)	\(e\left(\frac{4799}{6840}\right)\)	\(e\left(\frac{11563}{13680}\right)\)	\(e\left(\frac{1789}{3420}\right)\)	\(e\left(\frac{1223}{3420}\right)\)	\(e\left(\frac{973}{2736}\right)\)	\(e\left(\frac{415}{1368}\right)\)	\(e\left(\frac{2357}{6840}\right)\)