Dirichlet character \(\chi_{9200}(111,\cdot)\)

• Label: 9200.111
• Modulus: $9200$
• Conductor: $2300$
• Order: $110$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(9200\)
Conductor:	\(2300\)
Order:	\(110\)
Real:	no
Primitive:	no, induced from \(\chi_{2300}(111,\cdot)\)
Minimal:	yes
Parity:	even

Galois orbit 9200.eu

\(\chi_{9200}(111,\cdot)\) \(\chi_{9200}(191,\cdot)\) \(\chi_{9200}(431,\cdot)\) \(\chi_{9200}(511,\cdot)\) \(\chi_{9200}(911,\cdot)\) \(\chi_{9200}(1391,\cdot)\) \(\chi_{9200}(1631,\cdot)\) \(\chi_{9200}(1791,\cdot)\) \(\chi_{9200}(2031,\cdot)\) \(\chi_{9200}(2271,\cdot)\) \(\chi_{9200}(2591,\cdot)\) \(\chi_{9200}(3231,\cdot)\) \(\chi_{9200}(3391,\cdot)\) \(\chi_{9200}(3471,\cdot)\) \(\chi_{9200}(3631,\cdot)\) \(\chi_{9200}(3791,\cdot)\) \(\chi_{9200}(3871,\cdot)\) \(\chi_{9200}(4111,\cdot)\) \(\chi_{9200}(4191,\cdot)\) \(\chi_{9200}(4431,\cdot)\) \(\chi_{9200}(4591,\cdot)\) \(\chi_{9200}(5071,\cdot)\) \(\chi_{9200}(5231,\cdot)\) \(\chi_{9200}(5311,\cdot)\) \(\chi_{9200}(5471,\cdot)\) \(\chi_{9200}(5631,\cdot)\) \(\chi_{9200}(5711,\cdot)\) \(\chi_{9200}(6031,\cdot)\) \(\chi_{9200}(6271,\cdot)\) \(\chi_{9200}(6431,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{55})$
Fixed field:	Number field defined by a degree 110 polynomial (not computed)

Values on generators

\((1151,6901,2577,1201)\) → \((-1,1,e\left(\frac{4}{5}\right),e\left(\frac{15}{22}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(27\)	\(29\)
\( \chi_{ 9200 }(111, a) \)	\(1\)	\(1\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)