Dirichlet character χ1700(159,⋅)\chi_{1700}(159,\cdot)

• Label: 1700.159
• 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.cp

$\chi_{1700}(39,\cdot)$ $\chi_{1700}(79,\cdot)$ $\chi_{1700}(139,\cdot)$ $\chi_{1700}(159,\cdot)$ $\chi_{1700}(279,\cdot)$ $\chi_{1700}(379,\cdot)$ $\chi_{1700}(419,\cdot)$ $\chi_{1700}(439,\cdot)$ $\chi_{1700}(479,\cdot)$ $\chi_{1700}(539,\cdot)$ $\chi_{1700}(619,\cdot)$ $\chi_{1700}(639,\cdot)$ $\chi_{1700}(719,\cdot)$ $\chi_{1700}(759,\cdot)$ $\chi_{1700}(779,\cdot)$ $\chi_{1700}(819,\cdot)$ $\chi_{1700}(839,\cdot)$ $\chi_{1700}(879,\cdot)$ $\chi_{1700}(959,\cdot)$ $\chi_{1700}(979,\cdot)$ $\chi_{1700}(1059,\cdot)$ $\chi_{1700}(1119,\cdot)$ $\chi_{1700}(1159,\cdot)$ $\chi_{1700}(1179,\cdot)$ $\chi_{1700}(1219,\cdot)$ $\chi_{1700}(1319,\cdot)$ $\chi_{1700}(1439,\cdot)$ $\chi_{1700}(1459,\cdot)$ $\chi_{1700}(1519,\cdot)$ $\chi_{1700}(1559,\cdot)$ ...

Related number fields

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

Values on generators

$(851,477,1601)$ → $(-1,e\left(\frac{7}{10}\right),e\left(\frac{15}{16}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 1700 }(159, a)$	$1$	$1$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{47}{80}\right)$