Dirichlet character \(\chi_{9200}(9,\cdot)\)

• Label: 9200.9
• Modulus: $9200$
• Conductor: $4600$
• Order: $110$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	\(9200\)
Conductor:	\(4600\)
Order:	\(110\)
Real:	no
Primitive:	no, induced from \(\chi_{4600}(2309,\cdot)\)
Minimal:	no
Parity:	even

Galois orbit 9200.fc

\(\chi_{9200}(9,\cdot)\) \(\chi_{9200}(169,\cdot)\) \(\chi_{9200}(409,\cdot)\) \(\chi_{9200}(489,\cdot)\) \(\chi_{9200}(729,\cdot)\) \(\chi_{9200}(809,\cdot)\) \(\chi_{9200}(969,\cdot)\) \(\chi_{9200}(1129,\cdot)\) \(\chi_{9200}(1209,\cdot)\) \(\chi_{9200}(1369,\cdot)\) \(\chi_{9200}(2009,\cdot)\) \(\chi_{9200}(2329,\cdot)\) \(\chi_{9200}(2569,\cdot)\) \(\chi_{9200}(2809,\cdot)\) \(\chi_{9200}(2969,\cdot)\) \(\chi_{9200}(3209,\cdot)\) \(\chi_{9200}(3689,\cdot)\) \(\chi_{9200}(4089,\cdot)\) \(\chi_{9200}(4169,\cdot)\) \(\chi_{9200}(4409,\cdot)\) \(\chi_{9200}(4489,\cdot)\) \(\chi_{9200}(4809,\cdot)\) \(\chi_{9200}(4889,\cdot)\) \(\chi_{9200}(5529,\cdot)\) \(\chi_{9200}(5689,\cdot)\) \(\chi_{9200}(5929,\cdot)\) \(\chi_{9200}(6009,\cdot)\) \(\chi_{9200}(6329,\cdot)\) \(\chi_{9200}(6489,\cdot)\) \(\chi_{9200}(6729,\cdot)\) ...

Related number fields

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

Values on generators

\((1151,6901,2577,1201)\) → \((1,-1,e\left(\frac{7}{10}\right),e\left(\frac{5}{11}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(27\)	\(29\)
\( \chi_{ 9200 }(9, a) \)	\(1\)	\(1\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)