Dirichlet character \(\chi_{6897}(89,\cdot)\)

• Label: 6897.89
• Modulus: $6897$
• Conductor: $6897$
• Order: $198$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(6897\)
Conductor:	\(6897\)
Order:	\(198\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 6897.dc

\(\chi_{6897}(89,\cdot)\) \(\chi_{6897}(155,\cdot)\) \(\chi_{6897}(287,\cdot)\) \(\chi_{6897}(452,\cdot)\) \(\chi_{6897}(584,\cdot)\) \(\chi_{6897}(716,\cdot)\) \(\chi_{6897}(782,\cdot)\) \(\chi_{6897}(914,\cdot)\) \(\chi_{6897}(1079,\cdot)\) \(\chi_{6897}(1112,\cdot)\) \(\chi_{6897}(1343,\cdot)\) \(\chi_{6897}(1409,\cdot)\) \(\chi_{6897}(1541,\cdot)\) \(\chi_{6897}(1706,\cdot)\) \(\chi_{6897}(1739,\cdot)\) \(\chi_{6897}(1838,\cdot)\) \(\chi_{6897}(1970,\cdot)\) \(\chi_{6897}(2036,\cdot)\) \(\chi_{6897}(2168,\cdot)\) \(\chi_{6897}(2333,\cdot)\) \(\chi_{6897}(2366,\cdot)\) \(\chi_{6897}(2465,\cdot)\) \(\chi_{6897}(2597,\cdot)\) \(\chi_{6897}(2795,\cdot)\) \(\chi_{6897}(2960,\cdot)\) \(\chi_{6897}(2993,\cdot)\) \(\chi_{6897}(3092,\cdot)\) \(\chi_{6897}(3224,\cdot)\) \(\chi_{6897}(3290,\cdot)\) \(\chi_{6897}(3422,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{99})$
Fixed field:	Number field defined by a degree 198 polynomial (not computed)

Values on generators

\((2300,970,3631)\) → \((-1,e\left(\frac{6}{11}\right),e\left(\frac{5}{18}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(13\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 6897 }(89, a) \)	\(1\)	\(1\)	\(e\left(\frac{32}{99}\right)\)	\(e\left(\frac{64}{99}\right)\)	\(e\left(\frac{61}{198}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{125}{198}\right)\)	\(e\left(\frac{95}{198}\right)\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{1}{198}\right)\)