Dirichlet character χ1700(1039,⋅)\chi_{1700}(1039,\cdot)

• Label: 1700.1039
• Modulus: $1700$
• Conductor: $1700$
• Order: $40$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

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

Galois orbit 1700.cf

$\chi_{1700}(19,\cdot)$ $\chi_{1700}(59,\cdot)$ $\chi_{1700}(179,\cdot)$ $\chi_{1700}(219,\cdot)$ $\chi_{1700}(359,\cdot)$ $\chi_{1700}(519,\cdot)$ $\chi_{1700}(559,\cdot)$ $\chi_{1700}(739,\cdot)$ $\chi_{1700}(859,\cdot)$ $\chi_{1700}(1039,\cdot)$ $\chi_{1700}(1079,\cdot)$ $\chi_{1700}(1239,\cdot)$ $\chi_{1700}(1379,\cdot)$ $\chi_{1700}(1419,\cdot)$ $\chi_{1700}(1539,\cdot)$ $\chi_{1700}(1579,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{40})$
Fixed field:	40.0.4333834970391607127648627101904836847739142552018165588378906250000000000000000000000000000000000000000.1

Values on generators

$(851,477,1601)$ → $(-1,e\left(\frac{3}{10}\right),e\left(\frac{7}{8}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 1700 }(1039, a)$	$-1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{39}{40}\right)$