Dirichlet character \(\chi_{3168}(1157,\cdot)\)

• Label: 3168.1157
• 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.ex

\(\chi_{3168}(29,\cdot)\) \(\chi_{3168}(101,\cdot)\) \(\chi_{3168}(149,\cdot)\) \(\chi_{3168}(173,\cdot)\) \(\chi_{3168}(293,\cdot)\) \(\chi_{3168}(365,\cdot)\) \(\chi_{3168}(437,\cdot)\) \(\chi_{3168}(677,\cdot)\) \(\chi_{3168}(821,\cdot)\) \(\chi_{3168}(893,\cdot)\) \(\chi_{3168}(941,\cdot)\) \(\chi_{3168}(965,\cdot)\) \(\chi_{3168}(1085,\cdot)\) \(\chi_{3168}(1157,\cdot)\) \(\chi_{3168}(1229,\cdot)\) \(\chi_{3168}(1469,\cdot)\) \(\chi_{3168}(1613,\cdot)\) \(\chi_{3168}(1685,\cdot)\) \(\chi_{3168}(1733,\cdot)\) \(\chi_{3168}(1757,\cdot)\) \(\chi_{3168}(1877,\cdot)\) \(\chi_{3168}(1949,\cdot)\) \(\chi_{3168}(2021,\cdot)\) \(\chi_{3168}(2261,\cdot)\) \(\chi_{3168}(2405,\cdot)\) \(\chi_{3168}(2477,\cdot)\) \(\chi_{3168}(2525,\cdot)\) \(\chi_{3168}(2549,\cdot)\) \(\chi_{3168}(2669,\cdot)\) \(\chi_{3168}(2741,\cdot)\) ...

Related number fields

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

Values on generators

\((991,1189,353,1729)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{5}{6}\right),e\left(\frac{1}{10}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\( \chi_{ 3168 }(1157, a) \)	\(1\)	\(1\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{39}{40}\right)\)