Dirichlet character \(\chi_{5733}(3287,\cdot)\)

• Label: 5733.3287
• Modulus: $5733$
• Conductor: $5733$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(5733\)
Conductor:	\(5733\)
Order:	\(84\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 5733.mf

\(\chi_{5733}(11,\cdot)\) \(\chi_{5733}(149,\cdot)\) \(\chi_{5733}(527,\cdot)\) \(\chi_{5733}(830,\cdot)\) \(\chi_{5733}(968,\cdot)\) \(\chi_{5733}(1346,\cdot)\) \(\chi_{5733}(1523,\cdot)\) \(\chi_{5733}(1649,\cdot)\) \(\chi_{5733}(1787,\cdot)\) \(\chi_{5733}(2165,\cdot)\) \(\chi_{5733}(2342,\cdot)\) \(\chi_{5733}(2606,\cdot)\) \(\chi_{5733}(2984,\cdot)\) \(\chi_{5733}(3161,\cdot)\) \(\chi_{5733}(3287,\cdot)\) \(\chi_{5733}(3425,\cdot)\) \(\chi_{5733}(3980,\cdot)\) \(\chi_{5733}(4106,\cdot)\) \(\chi_{5733}(4622,\cdot)\) \(\chi_{5733}(4799,\cdot)\) \(\chi_{5733}(4925,\cdot)\) \(\chi_{5733}(5063,\cdot)\) \(\chi_{5733}(5441,\cdot)\) \(\chi_{5733}(5618,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Values on generators

\((2549,1522,5293)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{5}{21}\right),e\left(\frac{7}{12}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(16\)	\(17\)	\(19\)	\(20\)
\( \chi_{ 5733 }(3287, a) \)	\(1\)	\(1\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(i\)	\(e\left(\frac{73}{84}\right)\)