Dirichlet character \(\chi_{3168}(515,\cdot)\)

• Label: 3168.515
• Modulus: $3168$
• Conductor: $3168$
• Order: $120$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(3168\)
Conductor:	\(3168\)
Order:	\(120\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3168.eq

\(\chi_{3168}(59,\cdot)\) \(\chi_{3168}(203,\cdot)\) \(\chi_{3168}(443,\cdot)\) \(\chi_{3168}(515,\cdot)\) \(\chi_{3168}(587,\cdot)\) \(\chi_{3168}(707,\cdot)\) \(\chi_{3168}(731,\cdot)\) \(\chi_{3168}(779,\cdot)\) \(\chi_{3168}(851,\cdot)\) \(\chi_{3168}(995,\cdot)\) \(\chi_{3168}(1235,\cdot)\) \(\chi_{3168}(1307,\cdot)\) \(\chi_{3168}(1379,\cdot)\) \(\chi_{3168}(1499,\cdot)\) \(\chi_{3168}(1523,\cdot)\) \(\chi_{3168}(1571,\cdot)\) \(\chi_{3168}(1643,\cdot)\) \(\chi_{3168}(1787,\cdot)\) \(\chi_{3168}(2027,\cdot)\) \(\chi_{3168}(2099,\cdot)\) \(\chi_{3168}(2171,\cdot)\) \(\chi_{3168}(2291,\cdot)\) \(\chi_{3168}(2315,\cdot)\) \(\chi_{3168}(2363,\cdot)\) \(\chi_{3168}(2435,\cdot)\) \(\chi_{3168}(2579,\cdot)\) \(\chi_{3168}(2819,\cdot)\) \(\chi_{3168}(2891,\cdot)\) \(\chi_{3168}(2963,\cdot)\) \(\chi_{3168}(3083,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{120})$
Fixed field:	Number field defined by a degree 120 polynomial (not computed)

Values on generators

\((991,1189,353,1729)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{1}{6}\right),e\left(\frac{3}{5}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\( \chi_{ 3168 }(515, a) \)	\(1\)	\(1\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{29}{40}\right)\)