Dirichlet character \(\chi_{1352}(323,\cdot)\)

• Label: 1352.323
• Modulus: $1352$
• Conductor: $1352$
• Order: $156$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1352\)
Conductor:	\(1352\)
Order:	\(156\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1352.bu

\(\chi_{1352}(11,\cdot)\) \(\chi_{1352}(59,\cdot)\) \(\chi_{1352}(67,\cdot)\) \(\chi_{1352}(115,\cdot)\) \(\chi_{1352}(123,\cdot)\) \(\chi_{1352}(163,\cdot)\) \(\chi_{1352}(171,\cdot)\) \(\chi_{1352}(219,\cdot)\) \(\chi_{1352}(227,\cdot)\) \(\chi_{1352}(267,\cdot)\) \(\chi_{1352}(275,\cdot)\) \(\chi_{1352}(323,\cdot)\) \(\chi_{1352}(331,\cdot)\) \(\chi_{1352}(371,\cdot)\) \(\chi_{1352}(379,\cdot)\) \(\chi_{1352}(435,\cdot)\) \(\chi_{1352}(475,\cdot)\) \(\chi_{1352}(483,\cdot)\) \(\chi_{1352}(531,\cdot)\) \(\chi_{1352}(539,\cdot)\) \(\chi_{1352}(579,\cdot)\) \(\chi_{1352}(635,\cdot)\) \(\chi_{1352}(643,\cdot)\) \(\chi_{1352}(683,\cdot)\) \(\chi_{1352}(691,\cdot)\) \(\chi_{1352}(739,\cdot)\) \(\chi_{1352}(747,\cdot)\) \(\chi_{1352}(787,\cdot)\) \(\chi_{1352}(795,\cdot)\) \(\chi_{1352}(843,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{156})$
Fixed field:	Number field defined by a degree 156 polynomial (not computed)

Values on generators

\((1015,677,1185)\) → \((-1,-1,e\left(\frac{55}{156}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\( \chi_{ 1352 }(323, a) \)	\(1\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{1}{3}\right)\)