LMFDB - Dirichlet character orbit 2028.bh

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2028, base_ring=CyclotomicField(52)) M = H._module chi = DirichletCharacter(H, M([26,26,21])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(47,2028)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2028$
Conductor:	$2028$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$52$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{52})$
Fixed field:	Number field defined by a degree 52 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{2028}(47,\cdot)$	$-1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{6}{13}\right)$	$-i$	$-1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{2028}(83,\cdot)$	$-1$	$1$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{8}{13}\right)$	$i$	$-1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{2028}(203,\cdot)$	$-1$	$1$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{1}{13}\right)$	$-i$	$-1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{2028}(359,\cdot)$	$-1$	$1$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{9}{13}\right)$	$-i$	$-1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{2028}(395,\cdot)$	$-1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{5}{13}\right)$	$i$	$-1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{2028}(515,\cdot)$	$-1$	$1$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{4}{13}\right)$	$-i$	$-1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{2028}(551,\cdot)$	$-1$	$1$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{10}{13}\right)$	$i$	$-1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{2028}(671,\cdot)$	$-1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{12}{13}\right)$	$-i$	$-1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{2028}(707,\cdot)$	$-1$	$1$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{2}{13}\right)$	$i$	$-1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{2028}(827,\cdot)$	$-1$	$1$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{7}{13}\right)$	$-i$	$-1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{2028}(863,\cdot)$	$-1$	$1$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{7}{13}\right)$	$i$	$-1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{2028}(983,\cdot)$	$-1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{2}{13}\right)$	$-i$	$-1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{2028}(1019,\cdot)$	$-1$	$1$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{12}{13}\right)$	$i$	$-1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{2028}(1139,\cdot)$	$-1$	$1$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{10}{13}\right)$	$-i$	$-1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{2028}(1175,\cdot)$	$-1$	$1$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{4}{13}\right)$	$i$	$-1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{2028}(1295,\cdot)$	$-1$	$1$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{5}{13}\right)$	$-i$	$-1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{2028}(1331,\cdot)$	$-1$	$1$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{9}{13}\right)$	$i$	$-1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{2028}(1487,\cdot)$	$-1$	$1$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{1}{13}\right)$	$i$	$-1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{2028}(1607,\cdot)$	$-1$	$1$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{8}{13}\right)$	$-i$	$-1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{2028}(1643,\cdot)$	$-1$	$1$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{6}{13}\right)$	$i$	$-1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{2028}(1763,\cdot)$	$-1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{3}{13}\right)$	$-i$	$-1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{2028}(1799,\cdot)$	$-1$	$1$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{11}{13}\right)$	$i$	$-1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{2028}(1919,\cdot)$	$-1$	$1$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{11}{13}\right)$	$-i$	$-1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{2028}(1955,\cdot)$	$-1$	$1$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{3}{13}\right)$	$i$	$-1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{12}{13}\right)$

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Character	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{2028}(47,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{2028}(83,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{2028}(203,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{2028}(359,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{2028}(395,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{2028}(515,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{2028}(551,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{2028}(671,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{2028}(707,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{2028}(827,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{2028}(863,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{2028}(983,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{2028}(1019,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{2028}(1139,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{2028}(1175,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{2028}(1295,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{2028}(1331,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{2028}(1487,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{2028}(1607,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{2028}(1643,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{2028}(1763,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{2028}(1799,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{2028}(1919,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{2028}(1955,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)

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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	2028.bh
Modulus	$2028$
Conductor	$2028$
Order	$52$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(2028\)
Conductor:	\(2028\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(52\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)