LMFDB - Dirichlet character orbit 837.ca

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(837, base_ring=CyclotomicField(90)) M = H._module chi = DirichletCharacter(H, M([80,84])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(7, 837)) 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("837.7"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$837$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$837$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$45$	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:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{45})$	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 45 polynomial	comment:Fixed field sage:chi.fixed_field()

Characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{837}(7,\cdot)$	$1$	$1$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{837}(40,\cdot)$	$1$	$1$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{837}(49,\cdot)$	$1$	$1$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{14}{45}\right)$
$\chi_{837}(103,\cdot)$	$1$	$1$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{41}{45}\right)$
$\chi_{837}(169,\cdot)$	$1$	$1$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{837}(175,\cdot)$	$1$	$1$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{837}(205,\cdot)$	$1$	$1$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{31}{45}\right)$
$\chi_{837}(214,\cdot)$	$1$	$1$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{19}{45}\right)$
$\chi_{837}(286,\cdot)$	$1$	$1$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{837}(319,\cdot)$	$1$	$1$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{23}{45}\right)$
$\chi_{837}(328,\cdot)$	$1$	$1$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{837}(382,\cdot)$	$1$	$1$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{11}{45}\right)$
$\chi_{837}(448,\cdot)$	$1$	$1$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{13}{45}\right)$
$\chi_{837}(454,\cdot)$	$1$	$1$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{837}(484,\cdot)$	$1$	$1$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{837}(493,\cdot)$	$1$	$1$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{34}{45}\right)$
$\chi_{837}(565,\cdot)$	$1$	$1$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{37}{45}\right)$
$\chi_{837}(598,\cdot)$	$1$	$1$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{38}{45}\right)$
$\chi_{837}(607,\cdot)$	$1$	$1$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{837}(661,\cdot)$	$1$	$1$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{837}(727,\cdot)$	$1$	$1$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{837}(733,\cdot)$	$1$	$1$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{2}{45}\right)$
$\chi_{837}(763,\cdot)$	$1$	$1$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{837}(772,\cdot)$	$1$	$1$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{4}{45}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{837}(7,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)
\(\chi_{837}(40,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)
\(\chi_{837}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)
\(\chi_{837}(103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)
\(\chi_{837}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)
\(\chi_{837}(175,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)
\(\chi_{837}(205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)
\(\chi_{837}(214,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)
\(\chi_{837}(286,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{837}(319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)
\(\chi_{837}(328,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)
\(\chi_{837}(382,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)
\(\chi_{837}(448,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)
\(\chi_{837}(454,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)
\(\chi_{837}(484,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{837}(493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)
\(\chi_{837}(565,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)
\(\chi_{837}(598,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)
\(\chi_{837}(607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{837}(661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)
\(\chi_{837}(727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{837}(733,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)
\(\chi_{837}(763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{837}(772,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)

Introduction

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Groups

Database

Properties

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Basic properties

Related number fields

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	837.ca
Modulus	$837$
Conductor	$837$
Order	$45$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(837\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(837\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(45\)	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:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);