LMFDB - Dirichlet character orbit 7581.cx

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7581, base_ring=CyclotomicField(114)) M = H._module chi = DirichletCharacter(H, M([0,38,70])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(163,7581)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$7581$
Conductor:	$2527$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$57$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2527.bl	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:	$\Q(\zeta_{57})$
Fixed field:	Number field defined by a degree 57 polynomial

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$20$
$\chi_{7581}(163,\cdot)$	$1$	$1$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{13}{19}\right)$
$\chi_{7581}(235,\cdot)$	$1$	$1$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{10}{19}\right)$
$\chi_{7581}(562,\cdot)$	$1$	$1$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{3}{19}\right)$
$\chi_{7581}(634,\cdot)$	$1$	$1$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{16}{19}\right)$
$\chi_{7581}(961,\cdot)$	$1$	$1$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{12}{19}\right)$
$\chi_{7581}(1033,\cdot)$	$1$	$1$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{3}{19}\right)$
$\chi_{7581}(1360,\cdot)$	$1$	$1$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{2}{19}\right)$
$\chi_{7581}(1432,\cdot)$	$1$	$1$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{9}{19}\right)$
$\chi_{7581}(1759,\cdot)$	$1$	$1$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{11}{19}\right)$
$\chi_{7581}(1831,\cdot)$	$1$	$1$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{15}{19}\right)$
$\chi_{7581}(2158,\cdot)$	$1$	$1$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{1}{19}\right)$
$\chi_{7581}(2230,\cdot)$	$1$	$1$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{2}{19}\right)$
$\chi_{7581}(2557,\cdot)$	$1$	$1$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{10}{19}\right)$
$\chi_{7581}(2629,\cdot)$	$1$	$1$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{8}{19}\right)$
$\chi_{7581}(3028,\cdot)$	$1$	$1$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{14}{19}\right)$
$\chi_{7581}(3355,\cdot)$	$1$	$1$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{9}{19}\right)$
$\chi_{7581}(3427,\cdot)$	$1$	$1$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{1}{19}\right)$
$\chi_{7581}(3754,\cdot)$	$1$	$1$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{18}{19}\right)$
$\chi_{7581}(3826,\cdot)$	$1$	$1$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{7}{19}\right)$
$\chi_{7581}(4153,\cdot)$	$1$	$1$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{8}{19}\right)$
$\chi_{7581}(4225,\cdot)$	$1$	$1$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{13}{19}\right)$
$\chi_{7581}(4552,\cdot)$	$1$	$1$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{17}{19}\right)$
$\chi_{7581}(4951,\cdot)$	$1$	$1$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{7}{19}\right)$
$\chi_{7581}(5023,\cdot)$	$1$	$1$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{6}{19}\right)$
$\chi_{7581}(5350,\cdot)$	$1$	$1$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{16}{19}\right)$
$\chi_{7581}(5422,\cdot)$	$1$	$1$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{12}{19}\right)$
$\chi_{7581}(5749,\cdot)$	$1$	$1$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{6}{19}\right)$
$\chi_{7581}(5821,\cdot)$	$1$	$1$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{18}{19}\right)$
$\chi_{7581}(6148,\cdot)$	$1$	$1$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{15}{19}\right)$
$\chi_{7581}(6220,\cdot)$	$1$	$1$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{5}{19}\right)$
$\chi_{7581}(6547,\cdot)$	$1$	$1$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{5}{19}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Character	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(20\)
\(\chi_{7581}(163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)
\(\chi_{7581}(235,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)
\(\chi_{7581}(562,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)
\(\chi_{7581}(634,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)
\(\chi_{7581}(961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)
\(\chi_{7581}(1033,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)
\(\chi_{7581}(1360,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)
\(\chi_{7581}(1432,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)
\(\chi_{7581}(1759,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)
\(\chi_{7581}(1831,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)
\(\chi_{7581}(2158,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)
\(\chi_{7581}(2230,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)
\(\chi_{7581}(2557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)
\(\chi_{7581}(2629,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)
\(\chi_{7581}(3028,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)
\(\chi_{7581}(3355,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)
\(\chi_{7581}(3427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)
\(\chi_{7581}(3754,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)
\(\chi_{7581}(3826,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)
\(\chi_{7581}(4153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)
\(\chi_{7581}(4225,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)
\(\chi_{7581}(4552,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)
\(\chi_{7581}(4951,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)
\(\chi_{7581}(5023,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)
\(\chi_{7581}(5350,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)
\(\chi_{7581}(5422,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)
\(\chi_{7581}(5749,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)
\(\chi_{7581}(5821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)
\(\chi_{7581}(6148,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)
\(\chi_{7581}(6220,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)
\(\chi_{7581}(6547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)

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First 31 of 36 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	7581.cx
Modulus	$7581$
Conductor	$2527$
Order	$57$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(7581\)
Conductor:	\(2527\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(57\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2527.bl	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)