Dirichlet character χ28900(77,⋅)\chi_{28900}(77,\cdot)

• Label: 28900.77
• Modulus: $28900$
• Conductor: $7225$
• Order: $680$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$28900$
Conductor:	$7225$
Order:	$680$
Real:	no
Primitive:	no, induced from $\chi_{7225}(77,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 28900.fa

$\chi_{28900}(53,\cdot)$ $\chi_{28900}(77,\cdot)$ $\chi_{28900}(253,\cdot)$ $\chi_{28900}(297,\cdot)$ $\chi_{28900}(417,\cdot)$ $\chi_{28900}(637,\cdot)$ $\chi_{28900}(933,\cdot)$ $\chi_{28900}(1073,\cdot)$ $\chi_{28900}(1097,\cdot)$ $\chi_{28900}(1273,\cdot)$ $\chi_{28900}(1317,\cdot)$ $\chi_{28900}(1413,\cdot)$ $\chi_{28900}(1437,\cdot)$ $\chi_{28900}(1613,\cdot)$ $\chi_{28900}(1753,\cdot)$ $\chi_{28900}(1777,\cdot)$ $\chi_{28900}(1953,\cdot)$ $\chi_{28900}(1997,\cdot)$ $\chi_{28900}(2117,\cdot)$ $\chi_{28900}(2337,\cdot)$ $\chi_{28900}(2433,\cdot)$ $\chi_{28900}(2633,\cdot)$ $\chi_{28900}(2677,\cdot)$ $\chi_{28900}(2773,\cdot)$ $\chi_{28900}(2797,\cdot)$ $\chi_{28900}(2973,\cdot)$ $\chi_{28900}(3017,\cdot)$ $\chi_{28900}(3113,\cdot)$ $\chi_{28900}(3137,\cdot)$ $\chi_{28900}(3453,\cdot)$ ...

Related number fields

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

Values on generators

$(14451,24277,23701)$ → $(1,e\left(\frac{1}{20}\right),e\left(\frac{89}{136}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 28900 }(77, a)$	$-1$	$1$	$e\left(\frac{3}{680}\right)$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{3}{340}\right)$	$e\left(\frac{579}{680}\right)$	$e\left(\frac{73}{340}\right)$	$e\left(\frac{21}{340}\right)$	$e\left(\frac{117}{170}\right)$	$e\left(\frac{329}{680}\right)$	$e\left(\frac{9}{680}\right)$	$e\left(\frac{613}{680}\right)$