Dirichlet character χ900(103,⋅)\chi_{900}(103,\cdot)

• Label: 900.103
• Modulus: $900$
• Conductor: $900$
• Order: $60$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$900$
Conductor:	$900$
Order:	$60$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 900.bs

$\chi_{900}(67,\cdot)$ $\chi_{900}(103,\cdot)$ $\chi_{900}(187,\cdot)$ $\chi_{900}(223,\cdot)$ $\chi_{900}(247,\cdot)$ $\chi_{900}(283,\cdot)$ $\chi_{900}(367,\cdot)$ $\chi_{900}(403,\cdot)$ $\chi_{900}(427,\cdot)$ $\chi_{900}(463,\cdot)$ $\chi_{900}(547,\cdot)$ $\chi_{900}(583,\cdot)$ $\chi_{900}(727,\cdot)$ $\chi_{900}(763,\cdot)$ $\chi_{900}(787,\cdot)$ $\chi_{900}(823,\cdot)$

Related number fields

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

Values on generators

$(451,101,577)$ → $(-1,e\left(\frac{1}{3}\right),e\left(\frac{7}{20}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 900 }(103, a)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{15}\right)$

Gauss sum

Jacobi sum

Kloosterman sum