LMFDB - Dirichlet character orbit 1309.ct

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1309, base_ring=CyclotomicField(80)) M = H._module chi = DirichletCharacter(H, M([0,56,65])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(29,1309)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1309$
Conductor:	$187$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$80$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 187.t	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:	$\Q(\zeta_{80})$
Fixed field:	Number field defined by a degree 80 polynomial

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$12$	$13$
$\chi_{1309}(29,\cdot)$	$1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1309}(57,\cdot)$	$1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{1309}(211,\cdot)$	$1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{1309}(260,\cdot)$	$1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1309}(316,\cdot)$	$1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1309}(337,\cdot)$	$1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1309}(414,\cdot)$	$1$	$1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{1309}(435,\cdot)$	$1$	$1$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{1309}(470,\cdot)$	$1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1309}(547,\cdot)$	$1$	$1$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{1309}(568,\cdot)$	$1$	$1$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{1309}(589,\cdot)$	$1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{1309}(624,\cdot)$	$1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{1309}(666,\cdot)$	$1$	$1$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1309}(673,\cdot)$	$1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{1309}(743,\cdot)$	$1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1309}(827,\cdot)$	$1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{1309}(855,\cdot)$	$1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{1309}(904,\cdot)$	$1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{1309}(932,\cdot)$	$1$	$1$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{1309}(974,\cdot)$	$1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1309}(981,\cdot)$	$1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{1309}(1009,\cdot)$	$1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1309}(1030,\cdot)$	$1$	$1$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{1309}(1051,\cdot)$	$1$	$1$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1309}(1128,\cdot)$	$1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{1309}(1163,\cdot)$	$1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1309}(1184,\cdot)$	$1$	$1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{1309}(1212,\cdot)$	$1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{1309}(1261,\cdot)$	$1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1309}(1282,\cdot)$	$1$	$1$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{20}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(12\)	\(13\)
\(\chi_{1309}(29,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{1309}(57,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{1309}(211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{1309}(260,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{1309}(316,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{1309}(337,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{1309}(414,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{1309}(435,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{1309}(470,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{1309}(547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{1309}(568,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{1309}(589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{1309}(624,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{1309}(666,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{1309}(673,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{1309}(743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{1309}(827,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{1309}(855,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{1309}(904,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{1309}(932,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{1309}(974,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{1309}(981,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{1309}(1009,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{1309}(1030,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{1309}(1051,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{1309}(1128,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{1309}(1163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{1309}(1184,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{1309}(1212,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{1309}(1261,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{1309}(1282,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{20}\right)\)

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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.ct
Modulus	$1309$
Conductor	$187$
Order	$80$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(1309\)
Conductor:	\(187\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(80\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 187.t	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)