LMFDB - Dirichlet character orbit 767.o

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(767, base_ring=CyclotomicField(58)) M = H._module chi = DirichletCharacter(H, M([0,19])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(14, 767)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("767.14"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$767$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$59$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$58$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 59.d	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{29})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 58 polynomial	comment:Fixed field sage:chi.fixed_field()

Characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{767}(14,\cdot)$	$-1$	$1$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{11}{58}\right)$
$\chi_{767}(40,\cdot)$	$-1$	$1$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{51}{58}\right)$
$\chi_{767}(92,\cdot)$	$-1$	$1$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{19}{58}\right)$
$\chi_{767}(131,\cdot)$	$-1$	$1$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{23}{58}\right)$
$\chi_{767}(157,\cdot)$	$-1$	$1$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{55}{58}\right)$
$\chi_{767}(170,\cdot)$	$-1$	$1$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{15}{58}\right)$
$\chi_{767}(183,\cdot)$	$-1$	$1$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{57}{58}\right)$
$\chi_{767}(209,\cdot)$	$-1$	$1$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{9}{58}\right)$
$\chi_{767}(274,\cdot)$	$-1$	$1$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{47}{58}\right)$
$\chi_{767}(313,\cdot)$	$-1$	$1$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{31}{58}\right)$
$\chi_{767}(326,\cdot)$	$-1$	$1$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{7}{58}\right)$
$\chi_{767}(339,\cdot)$	$-1$	$1$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{37}{58}\right)$
$\chi_{767}(365,\cdot)$	$-1$	$1$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{45}{58}\right)$
$\chi_{767}(378,\cdot)$	$-1$	$1$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{49}{58}\right)$
$\chi_{767}(391,\cdot)$	$-1$	$1$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{41}{58}\right)$
$\chi_{767}(404,\cdot)$	$-1$	$1$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{35}{58}\right)$
$\chi_{767}(443,\cdot)$	$-1$	$1$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{33}{58}\right)$
$\chi_{767}(456,\cdot)$	$-1$	$1$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{13}{58}\right)$
$\chi_{767}(469,\cdot)$	$-1$	$1$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{3}{58}\right)$
$\chi_{767}(482,\cdot)$	$-1$	$1$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{1}{58}\right)$
$\chi_{767}(495,\cdot)$	$-1$	$1$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{27}{58}\right)$
$\chi_{767}(573,\cdot)$	$-1$	$1$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{43}{58}\right)$
$\chi_{767}(586,\cdot)$	$-1$	$1$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{21}{58}\right)$
$\chi_{767}(651,\cdot)$	$-1$	$1$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{25}{58}\right)$
$\chi_{767}(703,\cdot)$	$-1$	$1$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{5}{58}\right)$
$\chi_{767}(716,\cdot)$	$-1$	$1$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{17}{58}\right)$
$\chi_{767}(742,\cdot)$	$-1$	$1$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{39}{58}\right)$
$\chi_{767}(755,\cdot)$	$-1$	$1$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{53}{58}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{767}(14,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{11}{58}\right)\)
\(\chi_{767}(40,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{51}{58}\right)\)
\(\chi_{767}(92,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{19}{58}\right)\)
\(\chi_{767}(131,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{23}{58}\right)\)
\(\chi_{767}(157,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{55}{58}\right)\)
\(\chi_{767}(170,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{15}{58}\right)\)
\(\chi_{767}(183,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{57}{58}\right)\)
\(\chi_{767}(209,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{9}{58}\right)\)
\(\chi_{767}(274,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{47}{58}\right)\)
\(\chi_{767}(313,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{31}{58}\right)\)
\(\chi_{767}(326,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{7}{58}\right)\)
\(\chi_{767}(339,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{37}{58}\right)\)
\(\chi_{767}(365,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{45}{58}\right)\)
\(\chi_{767}(378,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{49}{58}\right)\)
\(\chi_{767}(391,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{41}{58}\right)\)
\(\chi_{767}(404,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{35}{58}\right)\)
\(\chi_{767}(443,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{33}{58}\right)\)
\(\chi_{767}(456,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{13}{58}\right)\)
\(\chi_{767}(469,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{3}{58}\right)\)
\(\chi_{767}(482,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{1}{58}\right)\)
\(\chi_{767}(495,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{27}{58}\right)\)
\(\chi_{767}(573,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{43}{58}\right)\)
\(\chi_{767}(586,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{21}{58}\right)\)
\(\chi_{767}(651,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{25}{58}\right)\)
\(\chi_{767}(703,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{5}{58}\right)\)
\(\chi_{767}(716,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{17}{58}\right)\)
\(\chi_{767}(742,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{39}{58}\right)\)
\(\chi_{767}(755,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{53}{58}\right)\)

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Basic properties

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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	767.o
Modulus	$767$
Conductor	$59$
Order	$58$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(767\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(59\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(58\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 59.d	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);