LMFDB - Dirichlet character orbit 1832.bj

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1832, base_ring=CyclotomicField(76)) M = H._module chi = DirichletCharacter(H, M([0,38,39])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(13, 1832)) 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("1832.13"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$1832$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1832$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$76$	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:	yes	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:	$\Q(\zeta_{76})$
Fixed field:	Number field defined by a degree 76 polynomial

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{1832}(13,\cdot)$	$-1$	$1$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{69}{76}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{41}{76}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{11}{76}\right)$
$\chi_{1832}(21,\cdot)$	$-1$	$1$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{63}{76}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{11}{76}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{53}{76}\right)$
$\chi_{1832}(93,\cdot)$	$-1$	$1$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{17}{76}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{9}{76}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{71}{76}\right)$
$\chi_{1832}(101,\cdot)$	$-1$	$1$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{37}{76}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{33}{76}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{7}{76}\right)$
$\chi_{1832}(109,\cdot)$	$-1$	$1$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{51}{76}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{27}{76}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{61}{76}\right)$
$\chi_{1832}(141,\cdot)$	$-1$	$1$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{7}{76}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{35}{76}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{65}{76}\right)$
$\chi_{1832}(197,\cdot)$	$-1$	$1$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{59}{76}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{67}{76}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{5}{76}\right)$
$\chi_{1832}(221,\cdot)$	$-1$	$1$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{5}{76}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{25}{76}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{3}{76}\right)$
$\chi_{1832}(237,\cdot)$	$-1$	$1$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{43}{76}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{63}{76}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{41}{76}\right)$
$\chi_{1832}(261,\cdot)$	$-1$	$1$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{21}{76}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{29}{76}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{43}{76}\right)$
$\chi_{1832}(317,\cdot)$	$-1$	$1$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{45}{76}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{73}{76}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{27}{76}\right)$
$\chi_{1832}(349,\cdot)$	$-1$	$1$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{13}{76}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{65}{76}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{23}{76}\right)$
$\chi_{1832}(357,\cdot)$	$-1$	$1$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{75}{76}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{71}{76}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{45}{76}\right)$
$\chi_{1832}(365,\cdot)$	$-1$	$1$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{55}{76}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{47}{76}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{33}{76}\right)$
$\chi_{1832}(437,\cdot)$	$-1$	$1$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{25}{76}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{49}{76}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{15}{76}\right)$
$\chi_{1832}(445,\cdot)$	$-1$	$1$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{31}{76}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{3}{76}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{49}{76}\right)$
$\chi_{1832}(573,\cdot)$	$-1$	$1$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{11}{76}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{55}{76}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{37}{76}\right)$
$\chi_{1832}(581,\cdot)$	$-1$	$1$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{23}{76}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{39}{76}\right)$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{29}{76}\right)$
$\chi_{1832}(653,\cdot)$	$-1$	$1$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{39}{76}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{43}{76}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{69}{76}\right)$
$\chi_{1832}(685,\cdot)$	$-1$	$1$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{27}{76}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{59}{76}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{1}{76}\right)$
$\chi_{1832}(709,\cdot)$	$-1$	$1$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{67}{76}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{31}{76}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{25}{76}\right)$
$\chi_{1832}(717,\cdot)$	$-1$	$1$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{35}{76}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{23}{76}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{21}{76}\right)$
$\chi_{1832}(741,\cdot)$	$-1$	$1$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{53}{76}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{37}{76}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{47}{76}\right)$
$\chi_{1832}(773,\cdot)$	$-1$	$1$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{33}{76}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{13}{76}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{35}{76}\right)$
$\chi_{1832}(1061,\cdot)$	$-1$	$1$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{3}{76}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{15}{76}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{17}{76}\right)$
$\chi_{1832}(1093,\cdot)$	$-1$	$1$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{9}{76}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{45}{76}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{51}{76}\right)$
$\chi_{1832}(1197,\cdot)$	$-1$	$1$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{47}{76}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{7}{76}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{13}{76}\right)$
$\chi_{1832}(1229,\cdot)$	$-1$	$1$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{41}{76}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{53}{76}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{55}{76}\right)$
$\chi_{1832}(1517,\cdot)$	$-1$	$1$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{71}{76}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{51}{76}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{73}{76}\right)$
$\chi_{1832}(1549,\cdot)$	$-1$	$1$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{15}{76}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{75}{76}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{9}{76}\right)$
$\chi_{1832}(1573,\cdot)$	$-1$	$1$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{73}{76}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{61}{76}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{59}{76}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{1832}(13,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{69}{76}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{41}{76}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{11}{76}\right)\)
\(\chi_{1832}(21,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{63}{76}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{11}{76}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{53}{76}\right)\)
\(\chi_{1832}(93,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{17}{76}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{9}{76}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{71}{76}\right)\)
\(\chi_{1832}(101,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{37}{76}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{33}{76}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{7}{76}\right)\)
\(\chi_{1832}(109,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{51}{76}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{27}{76}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{61}{76}\right)\)
\(\chi_{1832}(141,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{7}{76}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{35}{76}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{65}{76}\right)\)
\(\chi_{1832}(197,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{59}{76}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{67}{76}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{5}{76}\right)\)
\(\chi_{1832}(221,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{5}{76}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{25}{76}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{3}{76}\right)\)
\(\chi_{1832}(237,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{43}{76}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{63}{76}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{41}{76}\right)\)
\(\chi_{1832}(261,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{21}{76}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{29}{76}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{43}{76}\right)\)
\(\chi_{1832}(317,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{45}{76}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{73}{76}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{27}{76}\right)\)
\(\chi_{1832}(349,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{13}{76}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{65}{76}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{23}{76}\right)\)
\(\chi_{1832}(357,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{75}{76}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{71}{76}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{45}{76}\right)\)
\(\chi_{1832}(365,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{55}{76}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{47}{76}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{33}{76}\right)\)
\(\chi_{1832}(437,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{25}{76}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{49}{76}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{15}{76}\right)\)
\(\chi_{1832}(445,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{31}{76}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{3}{76}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{49}{76}\right)\)
\(\chi_{1832}(573,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{11}{76}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{55}{76}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{37}{76}\right)\)
\(\chi_{1832}(581,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{23}{76}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{39}{76}\right)\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{29}{76}\right)\)
\(\chi_{1832}(653,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{39}{76}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{43}{76}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{69}{76}\right)\)
\(\chi_{1832}(685,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{27}{76}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{59}{76}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{1}{76}\right)\)
\(\chi_{1832}(709,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{67}{76}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{31}{76}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{25}{76}\right)\)
\(\chi_{1832}(717,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{35}{76}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{23}{76}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{21}{76}\right)\)
\(\chi_{1832}(741,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{53}{76}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{37}{76}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{47}{76}\right)\)
\(\chi_{1832}(773,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{33}{76}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{13}{76}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{35}{76}\right)\)
\(\chi_{1832}(1061,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{3}{76}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{15}{76}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{17}{76}\right)\)
\(\chi_{1832}(1093,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{9}{76}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{45}{76}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{51}{76}\right)\)
\(\chi_{1832}(1197,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{47}{76}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{7}{76}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{13}{76}\right)\)
\(\chi_{1832}(1229,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{41}{76}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{53}{76}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{55}{76}\right)\)
\(\chi_{1832}(1517,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{71}{76}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{51}{76}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{73}{76}\right)\)
\(\chi_{1832}(1549,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{15}{76}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{75}{76}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{9}{76}\right)\)
\(\chi_{1832}(1573,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{73}{76}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{61}{76}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{59}{76}\right)\)

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Basic properties

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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	1832.bj
Modulus	$1832$
Conductor	$1832$
Order	$76$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(1832\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1832\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(76\)	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:	yes	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);