Dirichlet character χ7800(1237,⋅)\chi_{7800}(1237,\cdot)

• Label: 7800.1237
• Modulus: $7800$
• Conductor: $2600$
• Order: $60$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$7800$
Conductor:	$2600$
Order:	$60$
Real:	no
Primitive:	no, induced from $\chi_{2600}(1237,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 7800.mh

$\chi_{7800}(877,\cdot)$ $\chi_{7800}(973,\cdot)$ $\chi_{7800}(1237,\cdot)$ $\chi_{7800}(1333,\cdot)$ $\chi_{7800}(2437,\cdot)$ $\chi_{7800}(2533,\cdot)$ $\chi_{7800}(2797,\cdot)$ $\chi_{7800}(3997,\cdot)$ $\chi_{7800}(4453,\cdot)$ $\chi_{7800}(5653,\cdot)$ $\chi_{7800}(5917,\cdot)$ $\chi_{7800}(6013,\cdot)$ $\chi_{7800}(7117,\cdot)$ $\chi_{7800}(7213,\cdot)$ $\chi_{7800}(7477,\cdot)$ $\chi_{7800}(7573,\cdot)$

Related number fields

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

Values on generators

$(1951,3901,5201,7177,4201)$ → $(1,-1,1,e\left(\frac{9}{20}\right),e\left(\frac{1}{12}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 7800 }(1237, a)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{5}{12}\right)$