Dirichlet character χ2400(821,⋅)\chi_{2400}(821,\cdot)

• Label: 2400.821
• Modulus: $2400$
• Conductor: $2400$
• Order: $40$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$2400$
Conductor:	$2400$
Order:	$40$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 2400.dw

$\chi_{2400}(221,\cdot)$ $\chi_{2400}(341,\cdot)$ $\chi_{2400}(461,\cdot)$ $\chi_{2400}(581,\cdot)$ $\chi_{2400}(821,\cdot)$ $\chi_{2400}(941,\cdot)$ $\chi_{2400}(1061,\cdot)$ $\chi_{2400}(1181,\cdot)$ $\chi_{2400}(1421,\cdot)$ $\chi_{2400}(1541,\cdot)$ $\chi_{2400}(1661,\cdot)$ $\chi_{2400}(1781,\cdot)$ $\chi_{2400}(2021,\cdot)$ $\chi_{2400}(2141,\cdot)$ $\chi_{2400}(2261,\cdot)$ $\chi_{2400}(2381,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{40})$
Fixed field:	Number field defined by a degree 40 polynomial

Values on generators

$(1951,901,1601,577)$ → $(1,e\left(\frac{5}{8}\right),-1,e\left(\frac{3}{5}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 2400 }(821, a)$	$-1$	$1$	$i$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{13}{20}\right)$