Dirichlet character χ1760(1709,⋅)\chi_{1760}(1709,\cdot)

• Label: 1760.1709
• Modulus: $1760$
• Conductor: $1760$
• Order: $40$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1760$
Conductor:	$1760$
Order:	$40$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1760.dw

$\chi_{1760}(69,\cdot)$ $\chi_{1760}(229,\cdot)$ $\chi_{1760}(269,\cdot)$ $\chi_{1760}(389,\cdot)$ $\chi_{1760}(509,\cdot)$ $\chi_{1760}(669,\cdot)$ $\chi_{1760}(709,\cdot)$ $\chi_{1760}(829,\cdot)$ $\chi_{1760}(949,\cdot)$ $\chi_{1760}(1109,\cdot)$ $\chi_{1760}(1149,\cdot)$ $\chi_{1760}(1269,\cdot)$ $\chi_{1760}(1389,\cdot)$ $\chi_{1760}(1549,\cdot)$ $\chi_{1760}(1589,\cdot)$ $\chi_{1760}(1709,\cdot)$

Related number fields

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

Values on generators

$(991,1541,1057,321)$ → $(1,e\left(\frac{7}{8}\right),-1,e\left(\frac{1}{5}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 1760 }(1709, a)$	$1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{40}\right)$