Dirichlet character χ1700(1403,⋅)\chi_{1700}(1403,\cdot)

• Label: 1700.1403
• Modulus: $1700$
• Conductor: $1700$
• Order: $40$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1700$
Conductor:	$1700$
Order:	$40$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1700.ci

$\chi_{1700}(87,\cdot)$ $\chi_{1700}(263,\cdot)$ $\chi_{1700}(287,\cdot)$ $\chi_{1700}(383,\cdot)$ $\chi_{1700}(427,\cdot)$ $\chi_{1700}(603,\cdot)$ $\chi_{1700}(627,\cdot)$ $\chi_{1700}(723,\cdot)$ $\chi_{1700}(767,\cdot)$ $\chi_{1700}(967,\cdot)$ $\chi_{1700}(1063,\cdot)$ $\chi_{1700}(1283,\cdot)$ $\chi_{1700}(1403,\cdot)$ $\chi_{1700}(1447,\cdot)$ $\chi_{1700}(1623,\cdot)$ $\chi_{1700}(1647,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{40})$
Fixed field:	40.40.108345874259790178191215677547620921193478563800454139709472656250000000000000000000000000000000000000000.1

Values on generators

$(851,477,1601)$ → $(-1,e\left(\frac{7}{20}\right),e\left(\frac{1}{8}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 1700 }(1403, a)$	$1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{40}\right)$