LMFDB - Dirichlet character orbit 42237.li

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42237, base_ring=CyclotomicField(114)) M = H._module chi = DirichletCharacter(H, M([38,76,58])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(1075,42237)) 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:	$57$	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 57 polynomial

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{42237}(1075,\cdot)$	$1$	$1$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{6}{19}\right)$
$\chi_{42237}(1888,\cdot)$	$1$	$1$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{11}{19}\right)$
$\chi_{42237}(3298,\cdot)$	$1$	$1$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{11}{19}\right)$
$\chi_{42237}(4111,\cdot)$	$1$	$1$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{8}{19}\right)$
$\chi_{42237}(5521,\cdot)$	$1$	$1$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{16}{19}\right)$
$\chi_{42237}(6334,\cdot)$	$1$	$1$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{5}{19}\right)$
$\chi_{42237}(7744,\cdot)$	$1$	$1$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{2}{19}\right)$
$\chi_{42237}(8557,\cdot)$	$1$	$1$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{2}{19}\right)$
$\chi_{42237}(9967,\cdot)$	$1$	$1$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{7}{19}\right)$
$\chi_{42237}(10780,\cdot)$	$1$	$1$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{18}{19}\right)$
$\chi_{42237}(12190,\cdot)$	$1$	$1$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{12}{19}\right)$
$\chi_{42237}(13003,\cdot)$	$1$	$1$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{15}{19}\right)$
$\chi_{42237}(14413,\cdot)$	$1$	$1$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{17}{19}\right)$
$\chi_{42237}(15226,\cdot)$	$1$	$1$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{12}{19}\right)$
$\chi_{42237}(16636,\cdot)$	$1$	$1$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{3}{19}\right)$
$\chi_{42237}(17449,\cdot)$	$1$	$1$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{9}{19}\right)$
$\chi_{42237}(18859,\cdot)$	$1$	$1$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{8}{19}\right)$
$\chi_{42237}(19672,\cdot)$	$1$	$1$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{6}{19}\right)$
$\chi_{42237}(21082,\cdot)$	$1$	$1$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{13}{19}\right)$
$\chi_{42237}(21895,\cdot)$	$1$	$1$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{3}{19}\right)$
$\chi_{42237}(23305,\cdot)$	$1$	$1$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{18}{19}\right)$
$\chi_{42237}(25528,\cdot)$	$1$	$1$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{4}{19}\right)$
$\chi_{42237}(26341,\cdot)$	$1$	$1$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{16}{19}\right)$
$\chi_{42237}(27751,\cdot)$	$1$	$1$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{9}{19}\right)$
$\chi_{42237}(28564,\cdot)$	$1$	$1$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{13}{19}\right)$
$\chi_{42237}(29974,\cdot)$	$1$	$1$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{14}{19}\right)$
$\chi_{42237}(30787,\cdot)$	$1$	$1$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{10}{19}\right)$
$\chi_{42237}(33010,\cdot)$	$1$	$1$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{7}{19}\right)$
$\chi_{42237}(34420,\cdot)$	$1$	$1$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{5}{19}\right)$
$\chi_{42237}(35233,\cdot)$	$1$	$1$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{4}{19}\right)$
$\chi_{42237}(36643,\cdot)$	$1$	$1$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{10}{19}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\(\chi_{42237}(1075,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{6}{19}\right)\)
\(\chi_{42237}(1888,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{11}{19}\right)\)
\(\chi_{42237}(3298,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{11}{19}\right)\)
\(\chi_{42237}(4111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{8}{19}\right)\)
\(\chi_{42237}(5521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{16}{19}\right)\)
\(\chi_{42237}(6334,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{5}{19}\right)\)
\(\chi_{42237}(7744,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{2}{19}\right)\)
\(\chi_{42237}(8557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{2}{19}\right)\)
\(\chi_{42237}(9967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{7}{19}\right)\)
\(\chi_{42237}(10780,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{18}{19}\right)\)
\(\chi_{42237}(12190,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{12}{19}\right)\)
\(\chi_{42237}(13003,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{15}{19}\right)\)
\(\chi_{42237}(14413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{17}{19}\right)\)
\(\chi_{42237}(15226,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{12}{19}\right)\)
\(\chi_{42237}(16636,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{3}{19}\right)\)
\(\chi_{42237}(17449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{9}{19}\right)\)
\(\chi_{42237}(18859,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{8}{19}\right)\)
\(\chi_{42237}(19672,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{6}{19}\right)\)
\(\chi_{42237}(21082,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{13}{19}\right)\)
\(\chi_{42237}(21895,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{3}{19}\right)\)
\(\chi_{42237}(23305,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{18}{19}\right)\)
\(\chi_{42237}(25528,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{4}{19}\right)\)
\(\chi_{42237}(26341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{16}{19}\right)\)
\(\chi_{42237}(27751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{9}{19}\right)\)
\(\chi_{42237}(28564,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{13}{19}\right)\)
\(\chi_{42237}(29974,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{14}{19}\right)\)
\(\chi_{42237}(30787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{10}{19}\right)\)
\(\chi_{42237}(33010,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{7}{19}\right)\)
\(\chi_{42237}(34420,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{5}{19}\right)\)
\(\chi_{42237}(35233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{4}{19}\right)\)
\(\chi_{42237}(36643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{10}{19}\right)\)

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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.li
Modulus	$42237$
Conductor	$42237$
Order	$57$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(42237\)
Conductor:	\(42237\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(57\)	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)