Dirichlet character \(\chi_{2898}(193,\cdot)\)

• Label: 2898.193
• Modulus: $2898$
• Conductor: $1449$
• Order: $33$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2898\)
Conductor:	\(1449\)
Order:	\(33\)
Real:	no
Primitive:	no, induced from \(\chi_{1449}(193,\cdot)\)
Minimal:	yes
Parity:	even

Galois orbit 2898.bw

\(\chi_{2898}(193,\cdot)\) \(\chi_{2898}(331,\cdot)\) \(\chi_{2898}(445,\cdot)\) \(\chi_{2898}(583,\cdot)\) \(\chi_{2898}(823,\cdot)\) \(\chi_{2898}(949,\cdot)\) \(\chi_{2898}(961,\cdot)\) \(\chi_{2898}(1087,\cdot)\) \(\chi_{2898}(1327,\cdot)\) \(\chi_{2898}(1453,\cdot)\) \(\chi_{2898}(1465,\cdot)\) \(\chi_{2898}(1591,\cdot)\) \(\chi_{2898}(1705,\cdot)\) \(\chi_{2898}(1843,\cdot)\) \(\chi_{2898}(1957,\cdot)\) \(\chi_{2898}(2083,\cdot)\) \(\chi_{2898}(2095,\cdot)\) \(\chi_{2898}(2221,\cdot)\) \(\chi_{2898}(2335,\cdot)\) \(\chi_{2898}(2473,\cdot)\)

Related number fields

Field of values:	\(\Q(\zeta_{33})\)
Fixed field:	Number field defined by a degree 33 polynomial

Values on generators

\((1289,829,1891)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{2}{3}\right),e\left(\frac{5}{11}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\( \chi_{ 2898 }(193, a) \)	\(1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)