Dirichlet character \(\chi_{3751}(1010,\cdot)\)

• Label: 3751.1010
• 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.dl

\(\chi_{3751}(69,\cdot)\) \(\chi_{3751}(113,\cdot)\) \(\chi_{3751}(152,\cdot)\) \(\chi_{3751}(169,\cdot)\) \(\chi_{3751}(236,\cdot)\) \(\chi_{3751}(257,\cdot)\) \(\chi_{3751}(258,\cdot)\) \(\chi_{3751}(328,\cdot)\) \(\chi_{3751}(410,\cdot)\) \(\chi_{3751}(454,\cdot)\) \(\chi_{3751}(510,\cdot)\) \(\chi_{3751}(577,\cdot)\) \(\chi_{3751}(598,\cdot)\) \(\chi_{3751}(599,\cdot)\) \(\chi_{3751}(669,\cdot)\) \(\chi_{3751}(751,\cdot)\) \(\chi_{3751}(795,\cdot)\) \(\chi_{3751}(834,\cdot)\) \(\chi_{3751}(851,\cdot)\) \(\chi_{3751}(918,\cdot)\) \(\chi_{3751}(939,\cdot)\) \(\chi_{3751}(940,\cdot)\) \(\chi_{3751}(1010,\cdot)\) \(\chi_{3751}(1136,\cdot)\) \(\chi_{3751}(1175,\cdot)\) \(\chi_{3751}(1192,\cdot)\) \(\chi_{3751}(1259,\cdot)\) \(\chi_{3751}(1280,\cdot)\) \(\chi_{3751}(1281,\cdot)\) \(\chi_{3751}(1351,\cdot)\) ...

Related number fields

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

Values on generators

\((2543,2421)\) → \((e\left(\frac{48}{55}\right),e\left(\frac{13}{15}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\( \chi_{ 3751 }(1010, a) \)	\(1\)	\(1\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{56}{165}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{2}{165}\right)\)