Dirichlet character χ28900(2089,⋅)\chi_{28900}(2089,\cdot)

• Label: 28900.2089
• Modulus: $28900$
• Conductor: $7225$
• Order: $680$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$28900$
Conductor:	$7225$
Order:	$680$
Real:	no
Primitive:	no, induced from $\chi_{7225}(2089,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 28900.ff

$\chi_{28900}(9,\cdot)$ $\chi_{28900}(189,\cdot)$ $\chi_{28900}(229,\cdot)$ $\chi_{28900}(389,\cdot)$ $\chi_{28900}(529,\cdot)$ $\chi_{28900}(569,\cdot)$ $\chi_{28900}(689,\cdot)$ $\chi_{28900}(729,\cdot)$ $\chi_{28900}(869,\cdot)$ $\chi_{28900}(909,\cdot)$ $\chi_{28900}(1029,\cdot)$ $\chi_{28900}(1069,\cdot)$ $\chi_{28900}(1209,\cdot)$ $\chi_{28900}(1369,\cdot)$ $\chi_{28900}(1409,\cdot)$ $\chi_{28900}(1589,\cdot)$ $\chi_{28900}(1709,\cdot)$ $\chi_{28900}(1929,\cdot)$ $\chi_{28900}(2089,\cdot)$ $\chi_{28900}(2229,\cdot)$ $\chi_{28900}(2269,\cdot)$ $\chi_{28900}(2389,\cdot)$ $\chi_{28900}(2429,\cdot)$ $\chi_{28900}(2569,\cdot)$ $\chi_{28900}(2609,\cdot)$ $\chi_{28900}(2729,\cdot)$ $\chi_{28900}(2769,\cdot)$ $\chi_{28900}(2909,\cdot)$ $\chi_{28900}(3109,\cdot)$ $\chi_{28900}(3409,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{680})$
Fixed field:	Number field defined by a degree 680 polynomial (not computed)

Values on generators

$(14451,24277,23701)$ → $(1,e\left(\frac{3}{10}\right),e\left(\frac{107}{136}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 28900 }(2089, a)$	$1$	$1$	$e\left(\frac{603}{680}\right)$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{263}{340}\right)$	$e\left(\frac{609}{680}\right)$	$e\left(\frac{77}{85}\right)$	$e\left(\frac{141}{340}\right)$	$e\left(\frac{57}{170}\right)$	$e\left(\frac{509}{680}\right)$	$e\left(\frac{449}{680}\right)$	$e\left(\frac{643}{680}\right)$