Dirichlet character \(\chi_{3751}(999,\cdot)\)

• Label: 3751.999
• Modulus: $3751$
• Conductor: $3751$
• Order: $165$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(3751\)
Conductor:	\(3751\)
Order:	\(165\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3751.dk

\(\chi_{3751}(20,\cdot)\) \(\chi_{3751}(59,\cdot)\) \(\chi_{3751}(71,\cdot)\) \(\chi_{3751}(235,\cdot)\) \(\chi_{3751}(267,\cdot)\) \(\chi_{3751}(289,\cdot)\) \(\chi_{3751}(317,\cdot)\) \(\chi_{3751}(324,\cdot)\) \(\chi_{3751}(361,\cdot)\) \(\chi_{3751}(400,\cdot)\) \(\chi_{3751}(412,\cdot)\) \(\chi_{3751}(576,\cdot)\) \(\chi_{3751}(630,\cdot)\) \(\chi_{3751}(658,\cdot)\) \(\chi_{3751}(665,\cdot)\) \(\chi_{3751}(702,\cdot)\) \(\chi_{3751}(741,\cdot)\) \(\chi_{3751}(917,\cdot)\) \(\chi_{3751}(949,\cdot)\) \(\chi_{3751}(999,\cdot)\) \(\chi_{3751}(1006,\cdot)\) \(\chi_{3751}(1043,\cdot)\) \(\chi_{3751}(1082,\cdot)\) \(\chi_{3751}(1094,\cdot)\) \(\chi_{3751}(1258,\cdot)\) \(\chi_{3751}(1290,\cdot)\) \(\chi_{3751}(1312,\cdot)\) \(\chi_{3751}(1347,\cdot)\) \(\chi_{3751}(1384,\cdot)\) \(\chi_{3751}(1423,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{165})$
Fixed field:	Number field defined by a degree 165 polynomial (not computed)

Values on generators

\((2543,2421)\) → \((e\left(\frac{43}{55}\right),e\left(\frac{14}{15}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\( \chi_{ 3751 }(999, a) \)	\(1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{16}{165}\right)\)