LMFDB - Dirichlet character orbit 1309.cs

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1309, base_ring=CyclotomicField(80)) M = H._module chi = DirichletCharacter(H, M([40,72,75])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(6,1309)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1309$
Conductor:	$1309$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$80$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$12$	$13$
$\chi_{1309}(6,\cdot)$	$-1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1309}(41,\cdot)$	$-1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{1309}(62,\cdot)$	$-1$	$1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1309}(90,\cdot)$	$-1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{1309}(139,\cdot)$	$-1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{1309}(160,\cdot)$	$-1$	$1$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1309}(167,\cdot)$	$-1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{1309}(216,\cdot)$	$-1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{1309}(244,\cdot)$	$-1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{1309}(398,\cdot)$	$-1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{1309}(447,\cdot)$	$-1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{1309}(503,\cdot)$	$-1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{1309}(524,\cdot)$	$-1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{1309}(601,\cdot)$	$-1$	$1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1309}(622,\cdot)$	$-1$	$1$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1309}(657,\cdot)$	$-1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{1309}(734,\cdot)$	$-1$	$1$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1309}(755,\cdot)$	$-1$	$1$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1309}(776,\cdot)$	$-1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1309}(811,\cdot)$	$-1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1309}(853,\cdot)$	$-1$	$1$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{1309}(860,\cdot)$	$-1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{1309}(930,\cdot)$	$-1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{1309}(1014,\cdot)$	$-1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{1309}(1042,\cdot)$	$-1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1309}(1091,\cdot)$	$-1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{1309}(1119,\cdot)$	$-1$	$1$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1309}(1161,\cdot)$	$-1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{1309}(1168,\cdot)$	$-1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{1309}(1196,\cdot)$	$-1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{1309}(1217,\cdot)$	$-1$	$1$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{19}{20}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(12\)	\(13\)
\(\chi_{1309}(6,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{1309}(41,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{1309}(62,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{1309}(90,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{1309}(139,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{1309}(160,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{1309}(167,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{1309}(216,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{1309}(244,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{1309}(398,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{1309}(447,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{1309}(503,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{1309}(524,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{1309}(601,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{1309}(622,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{1309}(657,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{1309}(734,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{1309}(755,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{1309}(776,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{1309}(811,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{1309}(853,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{1309}(860,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{1309}(930,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{1309}(1014,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{1309}(1042,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{1309}(1091,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{1309}(1119,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{1309}(1161,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{1309}(1168,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{1309}(1196,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{1309}(1217,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{19}{20}\right)\)

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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	1309.cs
Modulus	$1309$
Conductor	$1309$
Order	$80$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(1309\)
Conductor:	\(1309\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(80\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)