Dirichlet character χ2600(121,⋅)\chi_{2600}(121,\cdot)

• Label: 2600.121
• Modulus: $2600$
• Conductor: $325$
• Order: $30$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2600$
Conductor:	$325$
Order:	$30$
Real:	no
Primitive:	no, induced from $\chi_{325}(121,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 2600.fd

$\chi_{2600}(121,\cdot)$ $\chi_{2600}(361,\cdot)$ $\chi_{2600}(641,\cdot)$ $\chi_{2600}(881,\cdot)$ $\chi_{2600}(1161,\cdot)$ $\chi_{2600}(1681,\cdot)$ $\chi_{2600}(1921,\cdot)$ $\chi_{2600}(2441,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{15})$
Fixed field:	Number field defined by a degree 30 polynomial

Values on generators

$(1951,1301,1977,1601)$ → $(1,1,e\left(\frac{3}{5}\right),e\left(\frac{1}{6}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 2600 }(121, a)$	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{15}\right)$