Dirichlet character \(\chi_{6900}(89,\cdot)\)

• Label: 6900.89
• Modulus: $6900$
• Conductor: $1725$
• Order: $110$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(6900\)
Conductor:	\(1725\)
Order:	\(110\)
Real:	no
Primitive:	no, induced from \(\chi_{1725}(89,\cdot)\)
Minimal:	yes
Parity:	even

Galois orbit 6900.cz

\(\chi_{6900}(89,\cdot)\) \(\chi_{6900}(329,\cdot)\) \(\chi_{6900}(389,\cdot)\) \(\chi_{6900}(569,\cdot)\) \(\chi_{6900}(1109,\cdot)\) \(\chi_{6900}(1169,\cdot)\) \(\chi_{6900}(1229,\cdot)\) \(\chi_{6900}(1469,\cdot)\) \(\chi_{6900}(1529,\cdot)\) \(\chi_{6900}(1709,\cdot)\) \(\chi_{6900}(1769,\cdot)\) \(\chi_{6900}(2429,\cdot)\) \(\chi_{6900}(2489,\cdot)\) \(\chi_{6900}(2609,\cdot)\) \(\chi_{6900}(2729,\cdot)\) \(\chi_{6900}(2909,\cdot)\) \(\chi_{6900}(3089,\cdot)\) \(\chi_{6900}(3329,\cdot)\) \(\chi_{6900}(3809,\cdot)\) \(\chi_{6900}(3869,\cdot)\) \(\chi_{6900}(3929,\cdot)\) \(\chi_{6900}(3989,\cdot)\) \(\chi_{6900}(4109,\cdot)\) \(\chi_{6900}(4229,\cdot)\) \(\chi_{6900}(4289,\cdot)\) \(\chi_{6900}(4469,\cdot)\) \(\chi_{6900}(4529,\cdot)\) \(\chi_{6900}(4709,\cdot)\) \(\chi_{6900}(5189,\cdot)\) \(\chi_{6900}(5309,\cdot)\) ...

Related number fields

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

Values on generators

\((3451,4601,277,1201)\) → \((1,-1,e\left(\frac{3}{10}\right),e\left(\frac{5}{22}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 6900 }(89, a) \)	\(1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{7}{11}\right)\)