Dirichlet character χ2793(1223,⋅)\chi_{2793}(1223,\cdot)

• Label: 2793.1223
• Modulus: $2793$
• Conductor: $2793$
• Order: $42$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2793$
Conductor:	$2793$
Order:	$42$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2793.dw

$\chi_{2793}(26,\cdot)$ $\chi_{2793}(353,\cdot)$ $\chi_{2793}(425,\cdot)$ $\chi_{2793}(752,\cdot)$ $\chi_{2793}(824,\cdot)$ $\chi_{2793}(1151,\cdot)$ $\chi_{2793}(1223,\cdot)$ $\chi_{2793}(1622,\cdot)$ $\chi_{2793}(1949,\cdot)$ $\chi_{2793}(2021,\cdot)$ $\chi_{2793}(2348,\cdot)$ $\chi_{2793}(2747,\cdot)$

Related number fields

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

Values on generators

$(932,2110,2206)$ → $(-1,e\left(\frac{5}{42}\right),e\left(\frac{1}{3}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$20$
$\chi_{ 2793 }(1223, a)$	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{7}\right)$