Dirichlet character χ300(37,⋅)\chi_{300}(37,\cdot)

• Label: 300.37
• Modulus: $300$
• Conductor: $25$
• Order: $20$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$300$
Conductor:	$25$
Order:	$20$
Real:	no
Primitive:	no, induced from $\chi_{25}(12,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 300.v

$\chi_{300}(13,\cdot)$ $\chi_{300}(37,\cdot)$ $\chi_{300}(73,\cdot)$ $\chi_{300}(97,\cdot)$ $\chi_{300}(133,\cdot)$ $\chi_{300}(217,\cdot)$ $\chi_{300}(253,\cdot)$ $\chi_{300}(277,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	Number field defined by a degree 20 polynomial

Values on generators

$(151,101,277)$ → $(1,1,e\left(\frac{9}{20}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 300 }(37, a)$	$-1$	$1$	$i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$

Gauss sum

Jacobi sum

Kloosterman sum