Dirichlet character \(\chi_{2415}(1292,\cdot)\)

• Label: 2415.1292
• Modulus: $2415$
• Conductor: $2415$
• Order: $132$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2415\)
Conductor:	\(2415\)
Order:	\(132\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2415.dk

\(\chi_{2415}(2,\cdot)\) \(\chi_{2415}(32,\cdot)\) \(\chi_{2415}(128,\cdot)\) \(\chi_{2415}(233,\cdot)\) \(\chi_{2415}(242,\cdot)\) \(\chi_{2415}(317,\cdot)\) \(\chi_{2415}(338,\cdot)\) \(\chi_{2415}(347,\cdot)\) \(\chi_{2415}(422,\cdot)\) \(\chi_{2415}(443,\cdot)\) \(\chi_{2415}(473,\cdot)\) \(\chi_{2415}(578,\cdot)\) \(\chi_{2415}(653,\cdot)\) \(\chi_{2415}(662,\cdot)\) \(\chi_{2415}(683,\cdot)\) \(\chi_{2415}(767,\cdot)\) \(\chi_{2415}(788,\cdot)\) \(\chi_{2415}(863,\cdot)\) \(\chi_{2415}(947,\cdot)\) \(\chi_{2415}(968,\cdot)\) \(\chi_{2415}(998,\cdot)\) \(\chi_{2415}(1208,\cdot)\) \(\chi_{2415}(1283,\cdot)\) \(\chi_{2415}(1292,\cdot)\) \(\chi_{2415}(1313,\cdot)\) \(\chi_{2415}(1388,\cdot)\) \(\chi_{2415}(1577,\cdot)\) \(\chi_{2415}(1628,\cdot)\) \(\chi_{2415}(1682,\cdot)\) \(\chi_{2415}(1733,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{132})$
Fixed field:	Number field defined by a degree 132 polynomial (not computed)

Values on generators

\((806,967,346,1891)\) → \((-1,i,e\left(\frac{2}{3}\right),e\left(\frac{2}{11}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)	\(22\)	\(26\)
\( \chi_{ 2415 }(1292, a) \)	\(1\)	\(1\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(i\)	\(e\left(\frac{49}{66}\right)\)