Dirichlet character \(\chi_{1352}(933,\cdot)\)

• Label: 1352.933
• Modulus: $1352$
• Conductor: $1352$
• Order: $78$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1352\)
Conductor:	\(1352\)
Order:	\(78\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1352.bm

\(\chi_{1352}(69,\cdot)\) \(\chi_{1352}(101,\cdot)\) \(\chi_{1352}(173,\cdot)\) \(\chi_{1352}(205,\cdot)\) \(\chi_{1352}(277,\cdot)\) \(\chi_{1352}(309,\cdot)\) \(\chi_{1352}(381,\cdot)\) \(\chi_{1352}(413,\cdot)\) \(\chi_{1352}(517,\cdot)\) \(\chi_{1352}(589,\cdot)\) \(\chi_{1352}(621,\cdot)\) \(\chi_{1352}(693,\cdot)\) \(\chi_{1352}(725,\cdot)\) \(\chi_{1352}(797,\cdot)\) \(\chi_{1352}(829,\cdot)\) \(\chi_{1352}(901,\cdot)\) \(\chi_{1352}(933,\cdot)\) \(\chi_{1352}(1005,\cdot)\) \(\chi_{1352}(1109,\cdot)\) \(\chi_{1352}(1141,\cdot)\) \(\chi_{1352}(1213,\cdot)\) \(\chi_{1352}(1245,\cdot)\) \(\chi_{1352}(1317,\cdot)\) \(\chi_{1352}(1349,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{39})$
Fixed field:	Number field defined by a degree 78 polynomial

Values on generators

\((1015,677,1185)\) → \((1,-1,e\left(\frac{53}{78}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\( \chi_{ 1352 }(933, a) \)	\(1\)	\(1\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)