LMFDB - Dirichlet character orbit 42237.pb

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42237, base_ring=CyclotomicField(114)) M = H._module chi = DirichletCharacter(H, M([76,19,40])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(277,42237)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$42237$
Conductor:	$42237$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$114$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	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 114 polynomial (not computed)

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{42237}(277,\cdot)$	$1$	$1$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{12}{19}\right)$
$\chi_{42237}(634,\cdot)$	$1$	$1$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{1}{19}\right)$
$\chi_{42237}(2500,\cdot)$	$1$	$1$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{17}{19}\right)$
$\chi_{42237}(2857,\cdot)$	$1$	$1$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{17}{19}\right)$
$\chi_{42237}(4723,\cdot)$	$1$	$1$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{3}{19}\right)$
$\chi_{42237}(5080,\cdot)$	$1$	$1$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{14}{19}\right)$
$\chi_{42237}(6946,\cdot)$	$1$	$1$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{8}{19}\right)$
$\chi_{42237}(7303,\cdot)$	$1$	$1$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{11}{19}\right)$
$\chi_{42237}(9169,\cdot)$	$1$	$1$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{13}{19}\right)$
$\chi_{42237}(9526,\cdot)$	$1$	$1$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{8}{19}\right)$
$\chi_{42237}(11392,\cdot)$	$1$	$1$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{18}{19}\right)$
$\chi_{42237}(11749,\cdot)$	$1$	$1$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{5}{19}\right)$
$\chi_{42237}(13615,\cdot)$	$1$	$1$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{11}{114}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{4}{19}\right)$
$\chi_{42237}(13972,\cdot)$	$1$	$1$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{2}{19}\right)$
$\chi_{42237}(15838,\cdot)$	$1$	$1$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{9}{19}\right)$
$\chi_{42237}(16195,\cdot)$	$1$	$1$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{18}{19}\right)$
$\chi_{42237}(18061,\cdot)$	$1$	$1$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{14}{19}\right)$
$\chi_{42237}(18418,\cdot)$	$1$	$1$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{15}{19}\right)$
$\chi_{42237}(20641,\cdot)$	$1$	$1$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{12}{19}\right)$
$\chi_{42237}(22507,\cdot)$	$1$	$1$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{5}{19}\right)$
$\chi_{42237}(22864,\cdot)$	$1$	$1$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{9}{19}\right)$
$\chi_{42237}(24730,\cdot)$	$1$	$1$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{10}{19}\right)$
$\chi_{42237}(25087,\cdot)$	$1$	$1$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{6}{19}\right)$
$\chi_{42237}(26953,\cdot)$	$1$	$1$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{15}{19}\right)$
$\chi_{42237}(27310,\cdot)$	$1$	$1$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{3}{19}\right)$
$\chi_{42237}(29176,\cdot)$	$1$	$1$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{1}{19}\right)$
$\chi_{42237}(31399,\cdot)$	$1$	$1$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{6}{19}\right)$
$\chi_{42237}(31756,\cdot)$	$1$	$1$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{16}{19}\right)$
$\chi_{42237}(33622,\cdot)$	$1$	$1$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{11}{19}\right)$
$\chi_{42237}(33979,\cdot)$	$1$	$1$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{31}{114}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{13}{19}\right)$
$\chi_{42237}(35845,\cdot)$	$1$	$1$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{16}{19}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\(\chi_{42237}(277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)
\(\chi_{42237}(634,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)
\(\chi_{42237}(2500,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)
\(\chi_{42237}(2857,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)
\(\chi_{42237}(4723,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)
\(\chi_{42237}(5080,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)
\(\chi_{42237}(6946,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)
\(\chi_{42237}(7303,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)
\(\chi_{42237}(9169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)
\(\chi_{42237}(9526,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)
\(\chi_{42237}(11392,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)
\(\chi_{42237}(11749,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)
\(\chi_{42237}(13615,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{11}{114}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)
\(\chi_{42237}(13972,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)
\(\chi_{42237}(15838,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)
\(\chi_{42237}(16195,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)
\(\chi_{42237}(18061,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)
\(\chi_{42237}(18418,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)
\(\chi_{42237}(20641,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)
\(\chi_{42237}(22507,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)
\(\chi_{42237}(22864,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)
\(\chi_{42237}(24730,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)
\(\chi_{42237}(25087,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)
\(\chi_{42237}(26953,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)
\(\chi_{42237}(27310,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)
\(\chi_{42237}(29176,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)
\(\chi_{42237}(31399,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)
\(\chi_{42237}(31756,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)
\(\chi_{42237}(33622,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)
\(\chi_{42237}(33979,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{31}{114}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)
\(\chi_{42237}(35845,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)

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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	42237.pb
Modulus	$42237$
Conductor	$42237$
Order	$114$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(42237\)
Conductor:	\(42237\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(114\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)