Dirichlet character \(\chi_{508288}(29,\cdot)\)

• Label: 508288.29
• Modulus: $508288$
• Conductor: $508288$
• Order: $27360$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(508288\)
Conductor:	\(508288\)
Order:	\(27360\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 508288.vw

\(\chi_{508288}(13,\cdot)\) \(\chi_{508288}(29,\cdot)\) \(\chi_{508288}(117,\cdot)\) \(\chi_{508288}(173,\cdot)\) \(\chi_{508288}(205,\cdot)\) \(\chi_{508288}(261,\cdot)\) \(\chi_{508288}(325,\cdot)\) \(\chi_{508288}(413,\cdot)\) \(\chi_{508288}(469,\cdot)\) \(\chi_{508288}(629,\cdot)\) \(\chi_{508288}(717,\cdot)\) \(\chi_{508288}(789,\cdot)\) \(\chi_{508288}(877,\cdot)\) \(\chi_{508288}(941,\cdot)\) \(\chi_{508288}(965,\cdot)\) \(\chi_{508288}(1085,\cdot)\) \(\chi_{508288}(1117,\cdot)\) \(\chi_{508288}(1173,\cdot)\) \(\chi_{508288}(1229,\cdot)\) \(\chi_{508288}(1245,\cdot)\) \(\chi_{508288}(1333,\cdot)\) \(\chi_{508288}(1381,\cdot)\) \(\chi_{508288}(1421,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{27360})$
Fixed field:	Number field defined by a degree 27360 polynomial (not computed)

Values on generators

\((166783,174725,323457,14081)\) → \((1,e\left(\frac{27}{32}\right),e\left(\frac{7}{10}\right),e\left(\frac{17}{342}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\( \chi_{ 508288 }(29, a) \)	\(1\)	\(1\)	\(e\left(\frac{1111}{27360}\right)\)	\(e\left(\frac{4813}{27360}\right)\)	\(e\left(\frac{3619}{4560}\right)\)	\(e\left(\frac{1111}{13680}\right)\)	\(e\left(\frac{19427}{27360}\right)\)	\(e\left(\frac{1481}{6840}\right)\)	\(e\left(\frac{1087}{6840}\right)\)	\(e\left(\frac{4565}{5472}\right)\)	\(e\left(\frac{191}{2736}\right)\)	\(e\left(\frac{4813}{13680}\right)\)