LMFDB - Dirichlet character orbit 5610.fl

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5610, base_ring=CyclotomicField(80)) M = H._module chi = DirichletCharacter(H, M([0,20,16,15])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(367,5610)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$5610$
Conductor:	$935$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$80$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 935.cs	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	$-1$	$1$	$7$	$13$	$19$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{5610}(367,\cdot)$	$1$	$1$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{5610}(487,\cdot)$	$1$	$1$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{5610}(643,\cdot)$	$1$	$1$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{5610}(907,\cdot)$	$1$	$1$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{5610}(1027,\cdot)$	$1$	$1$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{5610}(1093,\cdot)$	$1$	$1$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{5610}(1153,\cdot)$	$1$	$1$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{5610}(1417,\cdot)$	$1$	$1$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{5610}(1423,\cdot)$	$1$	$1$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{5610}(1873,\cdot)$	$1$	$1$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{5610}(1897,\cdot)$	$1$	$1$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{5610}(2017,\cdot)$	$1$	$1$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{5610}(2407,\cdot)$	$1$	$1$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{5610}(2557,\cdot)$	$1$	$1$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{5610}(2623,\cdot)$	$1$	$1$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{5610}(2953,\cdot)$	$1$	$1$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{5610}(3067,\cdot)$	$1$	$1$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{5610}(3133,\cdot)$	$1$	$1$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{5610}(3193,\cdot)$	$1$	$1$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{5610}(3403,\cdot)$	$1$	$1$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{5610}(3457,\cdot)$	$1$	$1$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{5610}(3463,\cdot)$	$1$	$1$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{5610}(3547,\cdot)$	$1$	$1$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{5610}(4057,\cdot)$	$1$	$1$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{5610}(4447,\cdot)$	$1$	$1$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{5610}(4723,\cdot)$	$1$	$1$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{5610}(4933,\cdot)$	$1$	$1$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{5610}(4987,\cdot)$	$1$	$1$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{5610}(5107,\cdot)$	$1$	$1$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{5610}(5173,\cdot)$	$1$	$1$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{5610}(5443,\cdot)$	$1$	$1$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{4}{5}\right)$

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	\(-1\)	\(1\)	\(7\)	\(13\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{5610}(367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{5610}(487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{5610}(643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{5610}(907,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{5610}(1027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{5610}(1093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{5610}(1153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{5610}(1417,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{5610}(1423,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{5610}(1873,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{5610}(1897,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{5610}(2017,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{5610}(2407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{5610}(2557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{5610}(2623,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{5610}(2953,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{5610}(3067,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{5610}(3133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{5610}(3193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{5610}(3403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{5610}(3457,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{5610}(3463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{5610}(3547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{5610}(4057,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{5610}(4447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{5610}(4723,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{5610}(4933,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{5610}(4987,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{5610}(5107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{5610}(5173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{5610}(5443,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)

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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	5610.fl
Modulus	$5610$
Conductor	$935$
Order	$80$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(5610\)
Conductor:	\(935\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(80\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 935.cs	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)