Dirichlet character \(\chi_{2700}(1559,\cdot)\)

• Label: 2700.1559
• Modulus: $2700$
• Conductor: $2700$
• Order: $90$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2700\)
Conductor:	\(2700\)
Order:	\(90\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2700.cn

\(\chi_{2700}(59,\cdot)\) \(\chi_{2700}(119,\cdot)\) \(\chi_{2700}(239,\cdot)\) \(\chi_{2700}(419,\cdot)\) \(\chi_{2700}(479,\cdot)\) \(\chi_{2700}(659,\cdot)\) \(\chi_{2700}(779,\cdot)\) \(\chi_{2700}(839,\cdot)\) \(\chi_{2700}(959,\cdot)\) \(\chi_{2700}(1019,\cdot)\) \(\chi_{2700}(1139,\cdot)\) \(\chi_{2700}(1319,\cdot)\) \(\chi_{2700}(1379,\cdot)\) \(\chi_{2700}(1559,\cdot)\) \(\chi_{2700}(1679,\cdot)\) \(\chi_{2700}(1739,\cdot)\) \(\chi_{2700}(1859,\cdot)\) \(\chi_{2700}(1919,\cdot)\) \(\chi_{2700}(2039,\cdot)\) \(\chi_{2700}(2219,\cdot)\) \(\chi_{2700}(2279,\cdot)\) \(\chi_{2700}(2459,\cdot)\) \(\chi_{2700}(2579,\cdot)\) \(\chi_{2700}(2639,\cdot)\)

Related number fields

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

Values on generators

\((1351,1001,2377)\) → \((-1,e\left(\frac{7}{18}\right),e\left(\frac{7}{10}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\( \chi_{ 2700 }(1559, a) \)	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{37}{90}\right)\)