Dirichlet character χ7800(89,⋅)\chi_{7800}(89,\cdot)

• Label: 7800.89
• Modulus: $7800$
• Conductor: $975$
• Order: $60$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$7800$
Conductor:	$975$
Order:	$60$
Real:	no
Primitive:	no, induced from $\chi_{975}(89,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 7800.lc

$\chi_{7800}(89,\cdot)$ $\chi_{7800}(929,\cdot)$ $\chi_{7800}(1289,\cdot)$ $\chi_{7800}(2009,\cdot)$ $\chi_{7800}(2489,\cdot)$ $\chi_{7800}(3209,\cdot)$ $\chi_{7800}(3569,\cdot)$ $\chi_{7800}(4409,\cdot)$ $\chi_{7800}(4769,\cdot)$ $\chi_{7800}(5129,\cdot)$ $\chi_{7800}(5609,\cdot)$ $\chi_{7800}(5969,\cdot)$ $\chi_{7800}(6329,\cdot)$ $\chi_{7800}(6689,\cdot)$ $\chi_{7800}(7169,\cdot)$ $\chi_{7800}(7529,\cdot)$

Related number fields

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

Values on generators

$(1951,3901,5201,7177,4201)$ → $(1,1,-1,e\left(\frac{3}{10}\right),e\left(\frac{7}{12}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 7800 }(89, a)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{2}{3}\right)$