Dirichlet character χ8800(611,⋅)\chi_{8800}(611,\cdot)

• Label: 8800.611
• Modulus: $8800$
• Conductor: $8800$
• Order: $40$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$8800$
Conductor:	$8800$
Order:	$40$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 8800.oc

$\chi_{8800}(371,\cdot)$ $\chi_{8800}(611,\cdot)$ $\chi_{8800}(931,\cdot)$ $\chi_{8800}(1091,\cdot)$ $\chi_{8800}(2571,\cdot)$ $\chi_{8800}(2811,\cdot)$ $\chi_{8800}(3131,\cdot)$ $\chi_{8800}(3291,\cdot)$ $\chi_{8800}(4771,\cdot)$ $\chi_{8800}(5011,\cdot)$ $\chi_{8800}(5331,\cdot)$ $\chi_{8800}(5491,\cdot)$ $\chi_{8800}(6971,\cdot)$ $\chi_{8800}(7211,\cdot)$ $\chi_{8800}(7531,\cdot)$ $\chi_{8800}(7691,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{40})$
Fixed field:	Number field defined by a degree 40 polynomial

Values on generators

$(2751,3301,4577,5601)$ → $(-1,e\left(\frac{3}{8}\right),e\left(\frac{4}{5}\right),e\left(\frac{9}{10}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 8800 }(611, a)$	$1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{29}{40}\right)$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{1}{40}\right)$