Dirichlet character \(\chi_{3240}(1003,\cdot)\)

• Label: 3240.1003
• Modulus: $3240$
• Conductor: $3240$
• Order: $108$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(3240\)
Conductor:	\(3240\)
Order:	\(108\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3240.dn

\(\chi_{3240}(43,\cdot)\) \(\chi_{3240}(67,\cdot)\) \(\chi_{3240}(187,\cdot)\) \(\chi_{3240}(283,\cdot)\) \(\chi_{3240}(403,\cdot)\) \(\chi_{3240}(427,\cdot)\) \(\chi_{3240}(547,\cdot)\) \(\chi_{3240}(643,\cdot)\) \(\chi_{3240}(763,\cdot)\) \(\chi_{3240}(787,\cdot)\) \(\chi_{3240}(907,\cdot)\) \(\chi_{3240}(1003,\cdot)\) \(\chi_{3240}(1123,\cdot)\) \(\chi_{3240}(1147,\cdot)\) \(\chi_{3240}(1267,\cdot)\) \(\chi_{3240}(1363,\cdot)\) \(\chi_{3240}(1483,\cdot)\) \(\chi_{3240}(1507,\cdot)\) \(\chi_{3240}(1627,\cdot)\) \(\chi_{3240}(1723,\cdot)\) \(\chi_{3240}(1843,\cdot)\) \(\chi_{3240}(1867,\cdot)\) \(\chi_{3240}(1987,\cdot)\) \(\chi_{3240}(2083,\cdot)\) \(\chi_{3240}(2203,\cdot)\) \(\chi_{3240}(2227,\cdot)\) \(\chi_{3240}(2347,\cdot)\) \(\chi_{3240}(2443,\cdot)\) \(\chi_{3240}(2563,\cdot)\) \(\chi_{3240}(2587,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{108})$
Fixed field:	Number field defined by a degree 108 polynomial (not computed)

Values on generators

\((2431,1621,3161,1297)\) → \((-1,-1,e\left(\frac{10}{27}\right),-i)\)

First values

\(a\)	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\( \chi_{ 3240 }(1003, a) \)	\(1\)	\(1\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{27}\right)\)