Dirichlet character \(\chi_{3800}(2019,\cdot)\)

• Label: 3800.2019
• Modulus: $3800$
• Conductor: $3800$
• Order: $90$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(3800\)
Conductor:	\(3800\)
Order:	\(90\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 3800.ev

\(\chi_{3800}(139,\cdot)\) \(\chi_{3800}(339,\cdot)\) \(\chi_{3800}(579,\cdot)\) \(\chi_{3800}(739,\cdot)\) \(\chi_{3800}(859,\cdot)\) \(\chi_{3800}(1259,\cdot)\) \(\chi_{3800}(1339,\cdot)\) \(\chi_{3800}(1619,\cdot)\) \(\chi_{3800}(1659,\cdot)\) \(\chi_{3800}(1859,\cdot)\) \(\chi_{3800}(2019,\cdot)\) \(\chi_{3800}(2259,\cdot)\) \(\chi_{3800}(2379,\cdot)\) \(\chi_{3800}(2419,\cdot)\) \(\chi_{3800}(2619,\cdot)\) \(\chi_{3800}(2779,\cdot)\) \(\chi_{3800}(2859,\cdot)\) \(\chi_{3800}(3019,\cdot)\) \(\chi_{3800}(3139,\cdot)\) \(\chi_{3800}(3179,\cdot)\) \(\chi_{3800}(3379,\cdot)\) \(\chi_{3800}(3539,\cdot)\) \(\chi_{3800}(3619,\cdot)\) \(\chi_{3800}(3779,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{45})$
Fixed field:	Number field defined by a degree 90 polynomial

Values on generators

\((951,1901,1977,401)\) → \((-1,-1,e\left(\frac{9}{10}\right),e\left(\frac{8}{9}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(21\)	\(23\)	\(27\)	\(29\)
\( \chi_{ 3800 }(2019, a) \)	\(-1\)	\(1\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{37}{90}\right)\)