Dirichlet character χ1800(797,⋅)\chi_{1800}(797,\cdot)

• Label: 1800.797
• Modulus: $1800$
• Conductor: $1800$
• Order: $60$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1800$
Conductor:	$1800$
Order:	$60$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1800.do

$\chi_{1800}(77,\cdot)$ $\chi_{1800}(173,\cdot)$ $\chi_{1800}(317,\cdot)$ $\chi_{1800}(437,\cdot)$ $\chi_{1800}(533,\cdot)$ $\chi_{1800}(653,\cdot)$ $\chi_{1800}(677,\cdot)$ $\chi_{1800}(797,\cdot)$ $\chi_{1800}(1013,\cdot)$ $\chi_{1800}(1037,\cdot)$ $\chi_{1800}(1253,\cdot)$ $\chi_{1800}(1373,\cdot)$ $\chi_{1800}(1397,\cdot)$ $\chi_{1800}(1517,\cdot)$ $\chi_{1800}(1613,\cdot)$ $\chi_{1800}(1733,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{60})$
Fixed field:	Number field defined by a degree 60 polynomial

Values on generators

$(1351,901,1001,577)$ → $(1,-1,e\left(\frac{5}{6}\right),e\left(\frac{17}{20}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 1800 }(797, a)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{30}\right)$