Dirichlet character χ2600(1237,⋅)\chi_{2600}(1237,\cdot)

• Label: 2600.1237
• Modulus: $2600$
• Conductor: $2600$
• Order: $60$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2600$
Conductor:	$2600$
Order:	$60$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2600.fz

$\chi_{2600}(197,\cdot)$ $\chi_{2600}(453,\cdot)$ $\chi_{2600}(717,\cdot)$ $\chi_{2600}(813,\cdot)$ $\chi_{2600}(877,\cdot)$ $\chi_{2600}(973,\cdot)$ $\chi_{2600}(1237,\cdot)$ $\chi_{2600}(1333,\cdot)$ $\chi_{2600}(1397,\cdot)$ $\chi_{2600}(1853,\cdot)$ $\chi_{2600}(1917,\cdot)$ $\chi_{2600}(2013,\cdot)$ $\chi_{2600}(2277,\cdot)$ $\chi_{2600}(2373,\cdot)$ $\chi_{2600}(2437,\cdot)$ $\chi_{2600}(2533,\cdot)$

Related number fields

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

Values on generators

$(1951,1301,1977,1601)$ → $(1,-1,e\left(\frac{9}{20}\right),e\left(\frac{1}{12}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 2600 }(1237, a)$	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{15}\right)$