Dirichlet character \(\chi_{18225}(686,\cdot)\)

• Label: 18225.686
• Modulus: $18225$
• Conductor: $18225$
• Order: $2430$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(18225\)
Conductor:	\(18225\)
Order:	\(2430\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 18225.cq

\(\chi_{18225}(11,\cdot)\) \(\chi_{18225}(41,\cdot)\) \(\chi_{18225}(56,\cdot)\) \(\chi_{18225}(86,\cdot)\) \(\chi_{18225}(131,\cdot)\) \(\chi_{18225}(146,\cdot)\) \(\chi_{18225}(191,\cdot)\) \(\chi_{18225}(221,\cdot)\) \(\chi_{18225}(236,\cdot)\) \(\chi_{18225}(266,\cdot)\) \(\chi_{18225}(281,\cdot)\) \(\chi_{18225}(311,\cdot)\) \(\chi_{18225}(356,\cdot)\) \(\chi_{18225}(371,\cdot)\) \(\chi_{18225}(416,\cdot)\) \(\chi_{18225}(446,\cdot)\) \(\chi_{18225}(461,\cdot)\) \(\chi_{18225}(491,\cdot)\) \(\chi_{18225}(506,\cdot)\) \(\chi_{18225}(536,\cdot)\) \(\chi_{18225}(581,\cdot)\) \(\chi_{18225}(596,\cdot)\) \(\chi_{18225}(641,\cdot)\) \(\chi_{18225}(671,\cdot)\) \(\chi_{18225}(686,\cdot)\) \(\chi_{18225}(716,\cdot)\) \(\chi_{18225}(731,\cdot)\) \(\chi_{18225}(761,\cdot)\) \(\chi_{18225}(806,\cdot)\) \(\chi_{18225}(821,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{1215})$
Fixed field:	Number field defined by a degree 2430 polynomial (not computed)

Values on generators

\((4376,13852)\) → \((e\left(\frac{211}{486}\right),e\left(\frac{4}{5}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\( \chi_{ 18225 }(686, a) \)	\(-1\)	\(1\)	\(e\left(\frac{569}{2430}\right)\)	\(e\left(\frac{569}{1215}\right)\)	\(e\left(\frac{14}{243}\right)\)	\(e\left(\frac{569}{810}\right)\)	\(e\left(\frac{1619}{2430}\right)\)	\(e\left(\frac{413}{1215}\right)\)	\(e\left(\frac{709}{2430}\right)\)	\(e\left(\frac{1138}{1215}\right)\)	\(e\left(\frac{589}{810}\right)\)	\(e\left(\frac{187}{405}\right)\)