LMFDB - Dirichlet character orbit 42237.lv

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42237, base_ring=CyclotomicField(114)) M = H._module chi = DirichletCharacter(H, M([95,76,45])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(113,42237)) 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{42237}(113,\cdot)$	$1$	$1$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{5}{114}\right)$
$\chi_{42237}(2336,\cdot)$	$1$	$1$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{17}{114}\right)$
$\chi_{42237}(3305,\cdot)$	$1$	$1$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{31}{114}\right)$
$\chi_{42237}(4559,\cdot)$	$1$	$1$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{29}{114}\right)$
$\chi_{42237}(5528,\cdot)$	$1$	$1$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{43}{114}\right)$
$\chi_{42237}(6782,\cdot)$	$1$	$1$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{41}{114}\right)$
$\chi_{42237}(7751,\cdot)$	$1$	$1$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{55}{114}\right)$
$\chi_{42237}(9005,\cdot)$	$1$	$1$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{53}{114}\right)$
$\chi_{42237}(9974,\cdot)$	$1$	$1$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{67}{114}\right)$
$\chi_{42237}(11228,\cdot)$	$1$	$1$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{65}{114}\right)$
$\chi_{42237}(12197,\cdot)$	$1$	$1$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{79}{114}\right)$
$\chi_{42237}(13451,\cdot)$	$1$	$1$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{77}{114}\right)$
$\chi_{42237}(14420,\cdot)$	$1$	$1$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{91}{114}\right)$
$\chi_{42237}(15674,\cdot)$	$1$	$1$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{31}{114}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{89}{114}\right)$
$\chi_{42237}(16643,\cdot)$	$1$	$1$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{103}{114}\right)$
$\chi_{42237}(17897,\cdot)$	$1$	$1$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{101}{114}\right)$
$\chi_{42237}(18866,\cdot)$	$1$	$1$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{1}{114}\right)$
$\chi_{42237}(20120,\cdot)$	$1$	$1$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{31}{114}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{113}{114}\right)$
$\chi_{42237}(21089,\cdot)$	$1$	$1$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{13}{114}\right)$
$\chi_{42237}(22343,\cdot)$	$1$	$1$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{11}{114}\right)$
$\chi_{42237}(23312,\cdot)$	$1$	$1$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{25}{114}\right)$
$\chi_{42237}(24566,\cdot)$	$1$	$1$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{23}{114}\right)$
$\chi_{42237}(25535,\cdot)$	$1$	$1$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{37}{114}\right)$
$\chi_{42237}(26789,\cdot)$	$1$	$1$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{35}{114}\right)$
$\chi_{42237}(27758,\cdot)$	$1$	$1$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{49}{114}\right)$
$\chi_{42237}(29012,\cdot)$	$1$	$1$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{47}{114}\right)$
$\chi_{42237}(29981,\cdot)$	$1$	$1$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{11}{114}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{61}{114}\right)$
$\chi_{42237}(31235,\cdot)$	$1$	$1$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{59}{114}\right)$
$\chi_{42237}(32204,\cdot)$	$1$	$1$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{73}{114}\right)$
$\chi_{42237}(33458,\cdot)$	$1$	$1$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{71}{114}\right)$
$\chi_{42237}(34427,\cdot)$	$1$	$1$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{85}{114}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\(\chi_{42237}(113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{5}{114}\right)\)
\(\chi_{42237}(2336,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{17}{114}\right)\)
\(\chi_{42237}(3305,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{31}{114}\right)\)
\(\chi_{42237}(4559,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{29}{114}\right)\)
\(\chi_{42237}(5528,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{43}{114}\right)\)
\(\chi_{42237}(6782,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{41}{114}\right)\)
\(\chi_{42237}(7751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{55}{114}\right)\)
\(\chi_{42237}(9005,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{53}{114}\right)\)
\(\chi_{42237}(9974,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{67}{114}\right)\)
\(\chi_{42237}(11228,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{65}{114}\right)\)
\(\chi_{42237}(12197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{79}{114}\right)\)
\(\chi_{42237}(13451,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{77}{114}\right)\)
\(\chi_{42237}(14420,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{91}{114}\right)\)
\(\chi_{42237}(15674,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{31}{114}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{89}{114}\right)\)
\(\chi_{42237}(16643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{103}{114}\right)\)
\(\chi_{42237}(17897,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{101}{114}\right)\)
\(\chi_{42237}(18866,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{1}{114}\right)\)
\(\chi_{42237}(20120,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{31}{114}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{113}{114}\right)\)
\(\chi_{42237}(21089,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{13}{114}\right)\)
\(\chi_{42237}(22343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{11}{114}\right)\)
\(\chi_{42237}(23312,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{25}{114}\right)\)
\(\chi_{42237}(24566,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{23}{114}\right)\)
\(\chi_{42237}(25535,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{37}{114}\right)\)
\(\chi_{42237}(26789,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{35}{114}\right)\)
\(\chi_{42237}(27758,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{49}{114}\right)\)
\(\chi_{42237}(29012,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{47}{114}\right)\)
\(\chi_{42237}(29981,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{11}{114}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{61}{114}\right)\)
\(\chi_{42237}(31235,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{59}{114}\right)\)
\(\chi_{42237}(32204,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{73}{114}\right)\)
\(\chi_{42237}(33458,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{71}{114}\right)\)
\(\chi_{42237}(34427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{85}{114}\right)\)

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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.lv
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)