Dirichlet character χ4000(51,⋅)\chi_{4000}(51,\cdot)

• Label: 4000.51
• Modulus: $4000$
• Conductor: $800$
• Order: $40$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$4000$
Conductor:	$800$
Order:	$40$
Real:	no
Primitive:	no, induced from $\chi_{800}(211,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 4000.cc

$\chi_{4000}(51,\cdot)$ $\chi_{4000}(451,\cdot)$ $\chi_{4000}(651,\cdot)$ $\chi_{4000}(851,\cdot)$ $\chi_{4000}(1051,\cdot)$ $\chi_{4000}(1451,\cdot)$ $\chi_{4000}(1651,\cdot)$ $\chi_{4000}(1851,\cdot)$ $\chi_{4000}(2051,\cdot)$ $\chi_{4000}(2451,\cdot)$ $\chi_{4000}(2651,\cdot)$ $\chi_{4000}(2851,\cdot)$ $\chi_{4000}(3051,\cdot)$ $\chi_{4000}(3451,\cdot)$ $\chi_{4000}(3651,\cdot)$ $\chi_{4000}(3851,\cdot)$

Related number fields

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

Values on generators

$(2751,2501,1377)$ → $(-1,e\left(\frac{7}{8}\right),e\left(\frac{4}{5}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 4000 }(51, a)$	$-1$	$1$	$e\left(\frac{29}{40}\right)$	$i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{40}\right)$