Dirichlet character \(\chi_{1225}(61,\cdot)\)

• Label: 1225.61
• Modulus: $1225$
• Conductor: $1225$
• Order: $210$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(1225\)
Conductor:	\(1225\)
Order:	\(210\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1225.br

\(\chi_{1225}(61,\cdot)\) \(\chi_{1225}(66,\cdot)\) \(\chi_{1225}(96,\cdot)\) \(\chi_{1225}(131,\cdot)\) \(\chi_{1225}(136,\cdot)\) \(\chi_{1225}(171,\cdot)\) \(\chi_{1225}(206,\cdot)\) \(\chi_{1225}(236,\cdot)\) \(\chi_{1225}(241,\cdot)\) \(\chi_{1225}(271,\cdot)\) \(\chi_{1225}(306,\cdot)\) \(\chi_{1225}(311,\cdot)\) \(\chi_{1225}(341,\cdot)\) \(\chi_{1225}(346,\cdot)\) \(\chi_{1225}(381,\cdot)\) \(\chi_{1225}(416,\cdot)\) \(\chi_{1225}(446,\cdot)\) \(\chi_{1225}(481,\cdot)\) \(\chi_{1225}(486,\cdot)\) \(\chi_{1225}(516,\cdot)\) \(\chi_{1225}(556,\cdot)\) \(\chi_{1225}(586,\cdot)\) \(\chi_{1225}(591,\cdot)\) \(\chi_{1225}(621,\cdot)\) \(\chi_{1225}(661,\cdot)\) \(\chi_{1225}(691,\cdot)\) \(\chi_{1225}(696,\cdot)\) \(\chi_{1225}(731,\cdot)\) \(\chi_{1225}(761,\cdot)\) \(\chi_{1225}(796,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{105})$
Fixed field:	Number field defined by a degree 210 polynomial (not computed)

Values on generators

\((1177,101)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{11}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\( \chi_{ 1225 }(61, a) \)	\(-1\)	\(1\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{46}{105}\right)\)