Dirichlet character χ2600(347,⋅)\chi_{2600}(347,\cdot)

• Label: 2600.347
• 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.fv

$\chi_{2600}(3,\cdot)$ $\chi_{2600}(347,\cdot)$ $\chi_{2600}(523,\cdot)$ $\chi_{2600}(627,\cdot)$ $\chi_{2600}(763,\cdot)$ $\chi_{2600}(867,\cdot)$ $\chi_{2600}(1147,\cdot)$ $\chi_{2600}(1283,\cdot)$ $\chi_{2600}(1387,\cdot)$ $\chi_{2600}(1563,\cdot)$ $\chi_{2600}(1667,\cdot)$ $\chi_{2600}(1803,\cdot)$ $\chi_{2600}(2083,\cdot)$ $\chi_{2600}(2187,\cdot)$ $\chi_{2600}(2323,\cdot)$ $\chi_{2600}(2427,\cdot)$

Related number fields

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

Values on generators

$(1951,1301,1977,1601)$ → $(-1,-1,e\left(\frac{17}{20}\right),e\left(\frac{2}{3}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 2600 }(347, a)$	$1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{15}\right)$