Dirichlet character \(\chi_{1352}(61,\cdot)\)

• Label: 1352.61
• 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.bn

\(\chi_{1352}(29,\cdot)\) \(\chi_{1352}(61,\cdot)\) \(\chi_{1352}(133,\cdot)\) \(\chi_{1352}(165,\cdot)\) \(\chi_{1352}(237,\cdot)\) \(\chi_{1352}(269,\cdot)\) \(\chi_{1352}(341,\cdot)\) \(\chi_{1352}(373,\cdot)\) \(\chi_{1352}(445,\cdot)\) \(\chi_{1352}(477,\cdot)\) \(\chi_{1352}(549,\cdot)\) \(\chi_{1352}(581,\cdot)\) \(\chi_{1352}(685,\cdot)\) \(\chi_{1352}(757,\cdot)\) \(\chi_{1352}(789,\cdot)\) \(\chi_{1352}(861,\cdot)\) \(\chi_{1352}(893,\cdot)\) \(\chi_{1352}(965,\cdot)\) \(\chi_{1352}(997,\cdot)\) \(\chi_{1352}(1069,\cdot)\) \(\chi_{1352}(1101,\cdot)\) \(\chi_{1352}(1173,\cdot)\) \(\chi_{1352}(1277,\cdot)\) \(\chi_{1352}(1309,\cdot)\)

Related number fields

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

Values on generators

\((1015,677,1185)\) → \((1,-1,e\left(\frac{35}{39}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\( \chi_{ 1352 }(61, a) \)	\(1\)	\(1\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)