Dirichlet character \(\chi_{3751}(1009,\cdot)\)

• Label: 3751.1009
• Modulus: $3751$
• Conductor: $3751$
• Order: $330$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(3751\)
Conductor:	\(3751\)
Order:	\(330\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3751.dt

\(\chi_{3751}(73,\cdot)\) \(\chi_{3751}(117,\cdot)\) \(\chi_{3751}(127,\cdot)\) \(\chi_{3751}(145,\cdot)\) \(\chi_{3751}(167,\cdot)\) \(\chi_{3751}(292,\cdot)\) \(\chi_{3751}(327,\cdot)\) \(\chi_{3751}(414,\cdot)\) \(\chi_{3751}(458,\cdot)\) \(\chi_{3751}(468,\cdot)\) \(\chi_{3751}(486,\cdot)\) \(\chi_{3751}(508,\cdot)\) \(\chi_{3751}(580,\cdot)\) \(\chi_{3751}(633,\cdot)\) \(\chi_{3751}(668,\cdot)\) \(\chi_{3751}(755,\cdot)\) \(\chi_{3751}(799,\cdot)\) \(\chi_{3751}(809,\cdot)\) \(\chi_{3751}(827,\cdot)\) \(\chi_{3751}(849,\cdot)\) \(\chi_{3751}(921,\cdot)\) \(\chi_{3751}(974,\cdot)\) \(\chi_{3751}(1009,\cdot)\) \(\chi_{3751}(1096,\cdot)\) \(\chi_{3751}(1140,\cdot)\) \(\chi_{3751}(1150,\cdot)\) \(\chi_{3751}(1168,\cdot)\) \(\chi_{3751}(1190,\cdot)\) \(\chi_{3751}(1262,\cdot)\) \(\chi_{3751}(1315,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{165})$
Fixed field:	Number field defined by a degree 330 polynomial (not computed)

Values on generators

\((2543,2421)\) → \((e\left(\frac{23}{110}\right),e\left(\frac{7}{30}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\( \chi_{ 3751 }(1009, a) \)	\(1\)	\(1\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{23}{165}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{329}{330}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{83}{330}\right)\)