LMFDB - Dirichlet character orbit 7744.bx

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7744, base_ring=CyclotomicField(80)) M = H._module chi = DirichletCharacter(H, M([40,35,56])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(403,7744)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$7744$
Conductor:	$704$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$80$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 704.bk	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{80})$
Fixed field:	Number field defined by a degree 80 polynomial

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{7744}(403,\cdot)$	$1$	$1$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{7744}(475,\cdot)$	$1$	$1$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{7744}(699,\cdot)$	$1$	$1$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{7744}(723,\cdot)$	$1$	$1$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{7744}(1371,\cdot)$	$1$	$1$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{7744}(1443,\cdot)$	$1$	$1$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{7744}(1667,\cdot)$	$1$	$1$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{7744}(1691,\cdot)$	$1$	$1$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{7744}(2339,\cdot)$	$1$	$1$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{7744}(2411,\cdot)$	$1$	$1$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{7744}(2635,\cdot)$	$1$	$1$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{7744}(2659,\cdot)$	$1$	$1$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{7744}(3307,\cdot)$	$1$	$1$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{7744}(3379,\cdot)$	$1$	$1$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{7744}(3603,\cdot)$	$1$	$1$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{7744}(3627,\cdot)$	$1$	$1$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{7744}(4275,\cdot)$	$1$	$1$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{7744}(4347,\cdot)$	$1$	$1$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{7744}(4571,\cdot)$	$1$	$1$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{7744}(4595,\cdot)$	$1$	$1$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{7744}(5243,\cdot)$	$1$	$1$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{7744}(5315,\cdot)$	$1$	$1$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{7744}(5539,\cdot)$	$1$	$1$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{7744}(5563,\cdot)$	$1$	$1$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{7744}(6211,\cdot)$	$1$	$1$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{7744}(6283,\cdot)$	$1$	$1$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{7744}(6507,\cdot)$	$1$	$1$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{7744}(6531,\cdot)$	$1$	$1$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{7744}(7179,\cdot)$	$1$	$1$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{7744}(7251,\cdot)$	$1$	$1$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{7744}(7475,\cdot)$	$1$	$1$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{7744}(403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{7744}(475,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{7744}(699,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{7744}(723,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{7744}(1371,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{7744}(1443,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{7744}(1667,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{7744}(1691,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{7744}(2339,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{7744}(2411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{7744}(2635,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{7744}(2659,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{7744}(3307,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{7744}(3379,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{7744}(3603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{7744}(3627,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{7744}(4275,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{7744}(4347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{7744}(4571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{7744}(4595,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{7744}(5243,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{7744}(5315,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{7744}(5539,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{7744}(5563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{7744}(6211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{7744}(6283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{7744}(6507,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{7744}(6531,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{7744}(7179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{7744}(7251,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{7744}(7475,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)

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First 31 of 32 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	7744.bx
Modulus	$7744$
Conductor	$704$
Order	$80$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(7744\)
Conductor:	\(704\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(80\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 704.bk	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)