LMFDB - Dirichlet character orbit 8007.dt

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8007, base_ring=CyclotomicField(78)) M = H._module chi = DirichletCharacter(H, M([0,0,11])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(205,8007)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8007$
Conductor:	$157$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$78$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 157.k	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{39})$
Fixed field:	Number field defined by a degree 78 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{8007}(205,\cdot)$	$1$	$1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{8007}(358,\cdot)$	$1$	$1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{8007}(460,\cdot)$	$1$	$1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{8007}(664,\cdot)$	$1$	$1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{8007}(766,\cdot)$	$1$	$1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{8007}(1378,\cdot)$	$1$	$1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{8007}(1837,\cdot)$	$1$	$1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{8007}(2092,\cdot)$	$1$	$1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{8007}(2755,\cdot)$	$1$	$1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{8007}(2857,\cdot)$	$1$	$1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{8007}(3571,\cdot)$	$1$	$1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{8007}(3928,\cdot)$	$1$	$1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{8007}(4030,\cdot)$	$1$	$1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{8007}(4387,\cdot)$	$1$	$1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{8007}(4438,\cdot)$	$1$	$1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{8007}(4693,\cdot)$	$1$	$1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{8007}(5458,\cdot)$	$1$	$1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{8007}(5662,\cdot)$	$1$	$1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{8007}(5866,\cdot)$	$1$	$1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{8007}(6784,\cdot)$	$1$	$1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{8007}(7090,\cdot)$	$1$	$1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{8007}(7141,\cdot)$	$1$	$1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{8007}(7192,\cdot)$	$1$	$1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{8007}(7447,\cdot)$	$1$	$1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{2}{13}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{8007}(205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{8007}(358,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{8007}(460,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{8007}(664,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{8007}(766,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{8007}(1378,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{8007}(1837,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{8007}(2092,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{8007}(2755,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{8007}(2857,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{8007}(3571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{8007}(3928,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{8007}(4030,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{8007}(4387,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{8007}(4438,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{8007}(4693,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{8007}(5458,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{8007}(5662,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{8007}(5866,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{8007}(6784,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{8007}(7090,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{8007}(7141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{8007}(7192,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{8007}(7447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)

Introduction

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Groups

Database

Properties

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Basic properties

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Characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	8007.dt
Modulus	$8007$
Conductor	$157$
Order	$78$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8007\)
Conductor:	\(157\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(78\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 157.k	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)