Dirichlet character \(\chi_{1407}(1145,\cdot)\)

• Label: 1407.1145
• Modulus: $1407$
• Conductor: $1407$
• Order: $66$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(1407\)
Conductor:	\(1407\)
Order:	\(66\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1407.cg

\(\chi_{1407}(116,\cdot)\) \(\chi_{1407}(170,\cdot)\) \(\chi_{1407}(284,\cdot)\) \(\chi_{1407}(389,\cdot)\) \(\chi_{1407}(569,\cdot)\) \(\chi_{1407}(620,\cdot)\) \(\chi_{1407}(674,\cdot)\) \(\chi_{1407}(758,\cdot)\) \(\chi_{1407}(926,\cdot)\) \(\chi_{1407}(977,\cdot)\) \(\chi_{1407}(1031,\cdot)\) \(\chi_{1407}(1052,\cdot)\) \(\chi_{1407}(1082,\cdot)\) \(\chi_{1407}(1145,\cdot)\) \(\chi_{1407}(1199,\cdot)\) \(\chi_{1407}(1229,\cdot)\) \(\chi_{1407}(1241,\cdot)\) \(\chi_{1407}(1262,\cdot)\) \(\chi_{1407}(1271,\cdot)\) \(\chi_{1407}(1292,\cdot)\)

Related number fields

Field of values:	\(\Q(\zeta_{33})\)
Fixed field:	Number field defined by a degree 66 polynomial

Values on generators

\((470,1207,337)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{20}{33}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\( \chi_{ 1407 }(1145, a) \)	\(-1\)	\(1\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{13}{33}\right)\)