Dirichlet character \(\chi_{1407}(1136,\cdot)\)

• Label: 1407.1136
• 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.ch

\(\chi_{1407}(107,\cdot)\) \(\chi_{1407}(149,\cdot)\) \(\chi_{1407}(158,\cdot)\) \(\chi_{1407}(263,\cdot)\) \(\chi_{1407}(359,\cdot)\) \(\chi_{1407}(464,\cdot)\) \(\chi_{1407}(494,\cdot)\) \(\chi_{1407}(662,\cdot)\) \(\chi_{1407}(695,\cdot)\) \(\chi_{1407}(746,\cdot)\) \(\chi_{1407}(863,\cdot)\) \(\chi_{1407}(893,\cdot)\) \(\chi_{1407}(935,\cdot)\) \(\chi_{1407}(947,\cdot)\) \(\chi_{1407}(1019,\cdot)\) \(\chi_{1407}(1094,\cdot)\) \(\chi_{1407}(1136,\cdot)\) \(\chi_{1407}(1220,\cdot)\) \(\chi_{1407}(1313,\cdot)\) \(\chi_{1407}(1355,\cdot)\)

Related number fields

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

Values on generators

\((470,1207,337)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{1}{11}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\( \chi_{ 1407 }(1136, a) \)	\(-1\)	\(1\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)