Dirichlet character \(\chi_{1045}(212,\cdot)\)

• Label: 1045.212
• Modulus: $1045$
• Conductor: $1045$
• Order: $180$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1045\)
Conductor:	\(1045\)
Order:	\(180\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1045.cr

\(\chi_{1045}(3,\cdot)\) \(\chi_{1045}(48,\cdot)\) \(\chi_{1045}(53,\cdot)\) \(\chi_{1045}(97,\cdot)\) \(\chi_{1045}(108,\cdot)\) \(\chi_{1045}(147,\cdot)\) \(\chi_{1045}(148,\cdot)\) \(\chi_{1045}(192,\cdot)\) \(\chi_{1045}(203,\cdot)\) \(\chi_{1045}(212,\cdot)\) \(\chi_{1045}(223,\cdot)\) \(\chi_{1045}(257,\cdot)\) \(\chi_{1045}(262,\cdot)\) \(\chi_{1045}(268,\cdot)\) \(\chi_{1045}(317,\cdot)\) \(\chi_{1045}(333,\cdot)\) \(\chi_{1045}(357,\cdot)\) \(\chi_{1045}(383,\cdot)\) \(\chi_{1045}(412,\cdot)\) \(\chi_{1045}(432,\cdot)\) \(\chi_{1045}(433,\cdot)\) \(\chi_{1045}(477,\cdot)\) \(\chi_{1045}(478,\cdot)\) \(\chi_{1045}(488,\cdot)\) \(\chi_{1045}(542,\cdot)\) \(\chi_{1045}(553,\cdot)\) \(\chi_{1045}(592,\cdot)\) \(\chi_{1045}(603,\cdot)\) \(\chi_{1045}(642,\cdot)\) \(\chi_{1045}(687,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{180})$
Fixed field:	Number field defined by a degree 180 polynomial (not computed)

Values on generators

\((837,761,496)\) → \((i,e\left(\frac{4}{5}\right),e\left(\frac{13}{18}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\( \chi_{ 1045 }(212, a) \)	\(1\)	\(1\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{43}{45}\right)\)