Dirichlet character χ1700(1391,⋅)\chi_{1700}(1391,\cdot)

• Label: 1700.1391
• Modulus: $1700$
• Conductor: $1700$
• Order: $80$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1700$
Conductor:	$1700$
Order:	$80$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1700.cq

$\chi_{1700}(11,\cdot)$ $\chi_{1700}(31,\cdot)$ $\chi_{1700}(71,\cdot)$ $\chi_{1700}(91,\cdot)$ $\chi_{1700}(131,\cdot)$ $\chi_{1700}(211,\cdot)$ $\chi_{1700}(231,\cdot)$ $\chi_{1700}(311,\cdot)$ $\chi_{1700}(371,\cdot)$ $\chi_{1700}(411,\cdot)$ $\chi_{1700}(431,\cdot)$ $\chi_{1700}(471,\cdot)$ $\chi_{1700}(571,\cdot)$ $\chi_{1700}(691,\cdot)$ $\chi_{1700}(711,\cdot)$ $\chi_{1700}(771,\cdot)$ $\chi_{1700}(811,\cdot)$ $\chi_{1700}(891,\cdot)$ $\chi_{1700}(911,\cdot)$ $\chi_{1700}(991,\cdot)$ $\chi_{1700}(1031,\cdot)$ $\chi_{1700}(1091,\cdot)$ $\chi_{1700}(1111,\cdot)$ $\chi_{1700}(1231,\cdot)$ $\chi_{1700}(1331,\cdot)$ $\chi_{1700}(1371,\cdot)$ $\chi_{1700}(1391,\cdot)$ $\chi_{1700}(1431,\cdot)$ $\chi_{1700}(1491,\cdot)$ $\chi_{1700}(1571,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{80})$
Fixed field:	Number field defined by a degree 80 polynomial

Values on generators

$(851,477,1601)$ → $(-1,e\left(\frac{1}{5}\right),e\left(\frac{9}{16}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 1700 }(1391, a)$	$1$	$1$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{57}{80}\right)$