Dirichlet character χ2793(37,⋅)\chi_{2793}(37,\cdot)

• Label: 2793.37
• Modulus: $2793$
• Conductor: $931$
• Order: $42$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$2793$
Conductor:	$931$
Order:	$42$
Real:	no
Primitive:	no, induced from $\chi_{931}(37,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 2793.dl

$\chi_{2793}(37,\cdot)$ $\chi_{2793}(151,\cdot)$ $\chi_{2793}(436,\cdot)$ $\chi_{2793}(550,\cdot)$ $\chi_{2793}(835,\cdot)$ $\chi_{2793}(1234,\cdot)$ $\chi_{2793}(1348,\cdot)$ $\chi_{2793}(1633,\cdot)$ $\chi_{2793}(1747,\cdot)$ $\chi_{2793}(2032,\cdot)$ $\chi_{2793}(2146,\cdot)$ $\chi_{2793}(2545,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{21})$
Fixed field:	Number field defined by a degree 42 polynomial

Values on generators

$(932,2110,2206)$ → $(1,e\left(\frac{16}{21}\right),-1)$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$20$
$\chi_{ 2793 }(37, a)$	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{7}\right)$