Dirichlet character χ4000(391,⋅)\chi_{4000}(391,\cdot)

• Label: 4000.391
• Modulus: $4000$
• Conductor: $2000$
• Order: $100$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$4000$
Conductor:	$2000$
Order:	$100$
Real:	no
Primitive:	no, induced from $\chi_{2000}(891,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 4000.cm

$\chi_{4000}(71,\cdot)$ $\chi_{4000}(231,\cdot)$ $\chi_{4000}(311,\cdot)$ $\chi_{4000}(391,\cdot)$ $\chi_{4000}(471,\cdot)$ $\chi_{4000}(631,\cdot)$ $\chi_{4000}(711,\cdot)$ $\chi_{4000}(791,\cdot)$ $\chi_{4000}(871,\cdot)$ $\chi_{4000}(1031,\cdot)$ $\chi_{4000}(1111,\cdot)$ $\chi_{4000}(1191,\cdot)$ $\chi_{4000}(1271,\cdot)$ $\chi_{4000}(1431,\cdot)$ $\chi_{4000}(1511,\cdot)$ $\chi_{4000}(1591,\cdot)$ $\chi_{4000}(1671,\cdot)$ $\chi_{4000}(1831,\cdot)$ $\chi_{4000}(1911,\cdot)$ $\chi_{4000}(1991,\cdot)$ $\chi_{4000}(2071,\cdot)$ $\chi_{4000}(2231,\cdot)$ $\chi_{4000}(2311,\cdot)$ $\chi_{4000}(2391,\cdot)$ $\chi_{4000}(2471,\cdot)$ $\chi_{4000}(2631,\cdot)$ $\chi_{4000}(2711,\cdot)$ $\chi_{4000}(2791,\cdot)$ $\chi_{4000}(2871,\cdot)$ $\chi_{4000}(3031,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{100})$
Fixed field:	Number field defined by a degree 100 polynomial

Values on generators

$(2751,2501,1377)$ → $(-1,i,e\left(\frac{1}{25}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 4000 }(391, a)$	$-1$	$1$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{59}{100}\right)$