LMFDB - Dirichlet character orbit 42237.qc

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42237, base_ring=CyclotomicField(228)) M = H._module chi = DirichletCharacter(H, M([114,95,216])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(305,42237)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$42237$
Conductor:	$14079$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$228$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 14079.fs	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:	$\Q(\zeta_{228})$
Fixed field:	Number field defined by a degree 228 polynomial (not computed)

First 31 of 72 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{42237}(305,\cdot)$	$1$	$1$	$e\left(\frac{197}{228}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{3}{76}\right)$	$e\left(\frac{157}{228}\right)$	$e\left(\frac{45}{76}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{11}{228}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{25}{57}\right)$
$\chi_{42237}(1502,\cdot)$	$1$	$1$	$e\left(\frac{107}{228}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{73}{76}\right)$	$e\left(\frac{223}{228}\right)$	$e\left(\frac{31}{76}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{65}{228}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{13}{57}\right)$
$\chi_{42237}(1844,\cdot)$	$1$	$1$	$e\left(\frac{103}{228}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{17}{76}\right)$	$e\left(\frac{155}{228}\right)$	$e\left(\frac{27}{76}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{37}{228}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{53}{57}\right)$
$\chi_{42237}(2186,\cdot)$	$1$	$1$	$e\left(\frac{61}{228}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{75}{76}\right)$	$e\left(\frac{125}{228}\right)$	$e\left(\frac{61}{76}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{199}{228}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{17}{57}\right)$
$\chi_{42237}(3725,\cdot)$	$1$	$1$	$e\left(\frac{119}{228}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{13}{76}\right)$	$e\left(\frac{199}{228}\right)$	$e\left(\frac{43}{76}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{149}{228}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{7}{57}\right)$
$\chi_{42237}(4067,\cdot)$	$1$	$1$	$e\left(\frac{115}{228}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{33}{76}\right)$	$e\left(\frac{131}{228}\right)$	$e\left(\frac{39}{76}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{121}{228}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{47}{57}\right)$
$\chi_{42237}(4409,\cdot)$	$1$	$1$	$e\left(\frac{73}{228}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{15}{76}\right)$	$e\left(\frac{101}{228}\right)$	$e\left(\frac{73}{76}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{55}{228}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{11}{57}\right)$
$\chi_{42237}(4751,\cdot)$	$1$	$1$	$e\left(\frac{221}{228}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{35}{76}\right)$	$e\left(\frac{109}{228}\right)$	$e\left(\frac{69}{76}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{179}{228}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{13}{57}\right)$
$\chi_{42237}(5948,\cdot)$	$1$	$1$	$e\left(\frac{131}{228}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{29}{76}\right)$	$e\left(\frac{175}{228}\right)$	$e\left(\frac{55}{76}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{5}{228}\right)$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{1}{57}\right)$
$\chi_{42237}(6290,\cdot)$	$1$	$1$	$e\left(\frac{127}{228}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{49}{76}\right)$	$e\left(\frac{107}{228}\right)$	$e\left(\frac{51}{76}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{205}{228}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{41}{57}\right)$
$\chi_{42237}(6632,\cdot)$	$1$	$1$	$e\left(\frac{85}{228}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{31}{76}\right)$	$e\left(\frac{77}{228}\right)$	$e\left(\frac{9}{76}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{139}{228}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{5}{57}\right)$
$\chi_{42237}(6974,\cdot)$	$1$	$1$	$e\left(\frac{5}{228}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{51}{76}\right)$	$e\left(\frac{85}{228}\right)$	$e\left(\frac{5}{76}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{35}{228}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{7}{57}\right)$
$\chi_{42237}(8171,\cdot)$	$1$	$1$	$e\left(\frac{143}{228}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{45}{76}\right)$	$e\left(\frac{151}{228}\right)$	$e\left(\frac{67}{76}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{89}{228}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{52}{57}\right)$
$\chi_{42237}(8513,\cdot)$	$1$	$1$	$e\left(\frac{139}{228}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{65}{76}\right)$	$e\left(\frac{83}{228}\right)$	$e\left(\frac{63}{76}\right)$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{61}{228}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{35}{57}\right)$
$\chi_{42237}(8855,\cdot)$	$1$	$1$	$e\left(\frac{97}{228}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{47}{76}\right)$	$e\left(\frac{53}{228}\right)$	$e\left(\frac{21}{76}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{223}{228}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{56}{57}\right)$
$\chi_{42237}(9197,\cdot)$	$1$	$1$	$e\left(\frac{17}{228}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{67}{76}\right)$	$e\left(\frac{61}{228}\right)$	$e\left(\frac{17}{76}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{119}{228}\right)$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{1}{57}\right)$
$\chi_{42237}(10394,\cdot)$	$1$	$1$	$e\left(\frac{155}{228}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{61}{76}\right)$	$e\left(\frac{127}{228}\right)$	$e\left(\frac{3}{76}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{173}{228}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{46}{57}\right)$
$\chi_{42237}(10736,\cdot)$	$1$	$1$	$e\left(\frac{151}{228}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{5}{76}\right)$	$e\left(\frac{59}{228}\right)$	$e\left(\frac{75}{76}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{145}{228}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{29}{57}\right)$
$\chi_{42237}(11078,\cdot)$	$1$	$1$	$e\left(\frac{109}{228}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{63}{76}\right)$	$e\left(\frac{29}{228}\right)$	$e\left(\frac{33}{76}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{79}{228}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{50}{57}\right)$
$\chi_{42237}(11420,\cdot)$	$1$	$1$	$e\left(\frac{29}{228}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{7}{76}\right)$	$e\left(\frac{37}{228}\right)$	$e\left(\frac{29}{76}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{203}{228}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{52}{57}\right)$
$\chi_{42237}(12617,\cdot)$	$1$	$1$	$e\left(\frac{167}{228}\right)$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{1}{76}\right)$	$e\left(\frac{103}{228}\right)$	$e\left(\frac{15}{76}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{29}{228}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{40}{57}\right)$
$\chi_{42237}(12959,\cdot)$	$1$	$1$	$e\left(\frac{163}{228}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{21}{76}\right)$	$e\left(\frac{35}{228}\right)$	$e\left(\frac{11}{76}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{1}{228}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{23}{57}\right)$
$\chi_{42237}(13301,\cdot)$	$1$	$1$	$e\left(\frac{121}{228}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{3}{76}\right)$	$e\left(\frac{5}{228}\right)$	$e\left(\frac{45}{76}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{163}{228}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{44}{57}\right)$
$\chi_{42237}(13643,\cdot)$	$1$	$1$	$e\left(\frac{41}{228}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{23}{76}\right)$	$e\left(\frac{13}{228}\right)$	$e\left(\frac{41}{76}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{59}{228}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{46}{57}\right)$
$\chi_{42237}(14840,\cdot)$	$1$	$1$	$e\left(\frac{179}{228}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{17}{76}\right)$	$e\left(\frac{79}{228}\right)$	$e\left(\frac{27}{76}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{113}{228}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{34}{57}\right)$
$\chi_{42237}(15182,\cdot)$	$1$	$1$	$e\left(\frac{175}{228}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{37}{76}\right)$	$e\left(\frac{11}{228}\right)$	$e\left(\frac{23}{76}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{85}{228}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{17}{57}\right)$
$\chi_{42237}(15866,\cdot)$	$1$	$1$	$e\left(\frac{53}{228}\right)$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{39}{76}\right)$	$e\left(\frac{217}{228}\right)$	$e\left(\frac{53}{76}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{143}{228}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{40}{57}\right)$
$\chi_{42237}(17063,\cdot)$	$1$	$1$	$e\left(\frac{191}{228}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{33}{76}\right)$	$e\left(\frac{55}{228}\right)$	$e\left(\frac{39}{76}\right)$	$e\left(\frac{31}{114}\right)$	$e\left(\frac{197}{228}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{28}{57}\right)$
$\chi_{42237}(17405,\cdot)$	$1$	$1$	$e\left(\frac{187}{228}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{53}{76}\right)$	$e\left(\frac{215}{228}\right)$	$e\left(\frac{35}{76}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{169}{228}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{11}{57}\right)$
$\chi_{42237}(17747,\cdot)$	$1$	$1$	$e\left(\frac{145}{228}\right)$	$e\left(\frac{31}{114}\right)$	$e\left(\frac{35}{76}\right)$	$e\left(\frac{185}{228}\right)$	$e\left(\frac{69}{76}\right)$	$e\left(\frac{11}{114}\right)$	$e\left(\frac{103}{228}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{32}{57}\right)$
$\chi_{42237}(18089,\cdot)$	$1$	$1$	$e\left(\frac{65}{228}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{55}{76}\right)$	$e\left(\frac{193}{228}\right)$	$e\left(\frac{65}{76}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{227}{228}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{34}{57}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\(\chi_{42237}(305,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{228}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{3}{76}\right)\)	\(e\left(\frac{157}{228}\right)\)	\(e\left(\frac{45}{76}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{11}{228}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{25}{57}\right)\)
\(\chi_{42237}(1502,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{228}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{73}{76}\right)\)	\(e\left(\frac{223}{228}\right)\)	\(e\left(\frac{31}{76}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{65}{228}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{13}{57}\right)\)
\(\chi_{42237}(1844,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{228}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{17}{76}\right)\)	\(e\left(\frac{155}{228}\right)\)	\(e\left(\frac{27}{76}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{37}{228}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{53}{57}\right)\)
\(\chi_{42237}(2186,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{228}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{75}{76}\right)\)	\(e\left(\frac{125}{228}\right)\)	\(e\left(\frac{61}{76}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{199}{228}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{17}{57}\right)\)
\(\chi_{42237}(3725,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{228}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{13}{76}\right)\)	\(e\left(\frac{199}{228}\right)\)	\(e\left(\frac{43}{76}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{149}{228}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{7}{57}\right)\)
\(\chi_{42237}(4067,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{228}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{33}{76}\right)\)	\(e\left(\frac{131}{228}\right)\)	\(e\left(\frac{39}{76}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{121}{228}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{47}{57}\right)\)
\(\chi_{42237}(4409,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{228}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{15}{76}\right)\)	\(e\left(\frac{101}{228}\right)\)	\(e\left(\frac{73}{76}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{55}{228}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{11}{57}\right)\)
\(\chi_{42237}(4751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{221}{228}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{35}{76}\right)\)	\(e\left(\frac{109}{228}\right)\)	\(e\left(\frac{69}{76}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{179}{228}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{13}{57}\right)\)
\(\chi_{42237}(5948,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{228}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{29}{76}\right)\)	\(e\left(\frac{175}{228}\right)\)	\(e\left(\frac{55}{76}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{5}{228}\right)\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)
\(\chi_{42237}(6290,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{228}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{49}{76}\right)\)	\(e\left(\frac{107}{228}\right)\)	\(e\left(\frac{51}{76}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{205}{228}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{41}{57}\right)\)
\(\chi_{42237}(6632,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{228}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{31}{76}\right)\)	\(e\left(\frac{77}{228}\right)\)	\(e\left(\frac{9}{76}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{139}{228}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{5}{57}\right)\)
\(\chi_{42237}(6974,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{228}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{51}{76}\right)\)	\(e\left(\frac{85}{228}\right)\)	\(e\left(\frac{5}{76}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{35}{228}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{7}{57}\right)\)
\(\chi_{42237}(8171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{228}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{45}{76}\right)\)	\(e\left(\frac{151}{228}\right)\)	\(e\left(\frac{67}{76}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{89}{228}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{52}{57}\right)\)
\(\chi_{42237}(8513,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{228}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{65}{76}\right)\)	\(e\left(\frac{83}{228}\right)\)	\(e\left(\frac{63}{76}\right)\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{61}{228}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{35}{57}\right)\)
\(\chi_{42237}(8855,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{228}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{47}{76}\right)\)	\(e\left(\frac{53}{228}\right)\)	\(e\left(\frac{21}{76}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{223}{228}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{56}{57}\right)\)
\(\chi_{42237}(9197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{228}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{67}{76}\right)\)	\(e\left(\frac{61}{228}\right)\)	\(e\left(\frac{17}{76}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{119}{228}\right)\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)
\(\chi_{42237}(10394,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{155}{228}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{61}{76}\right)\)	\(e\left(\frac{127}{228}\right)\)	\(e\left(\frac{3}{76}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{173}{228}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{46}{57}\right)\)
\(\chi_{42237}(10736,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{228}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{5}{76}\right)\)	\(e\left(\frac{59}{228}\right)\)	\(e\left(\frac{75}{76}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{145}{228}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{29}{57}\right)\)
\(\chi_{42237}(11078,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{228}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{63}{76}\right)\)	\(e\left(\frac{29}{228}\right)\)	\(e\left(\frac{33}{76}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{79}{228}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{50}{57}\right)\)
\(\chi_{42237}(11420,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{228}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{7}{76}\right)\)	\(e\left(\frac{37}{228}\right)\)	\(e\left(\frac{29}{76}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{203}{228}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{52}{57}\right)\)
\(\chi_{42237}(12617,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{228}\right)\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{1}{76}\right)\)	\(e\left(\frac{103}{228}\right)\)	\(e\left(\frac{15}{76}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{29}{228}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{40}{57}\right)\)
\(\chi_{42237}(12959,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{228}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{21}{76}\right)\)	\(e\left(\frac{35}{228}\right)\)	\(e\left(\frac{11}{76}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{1}{228}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{23}{57}\right)\)
\(\chi_{42237}(13301,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{228}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{3}{76}\right)\)	\(e\left(\frac{5}{228}\right)\)	\(e\left(\frac{45}{76}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{163}{228}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{44}{57}\right)\)
\(\chi_{42237}(13643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{228}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{23}{76}\right)\)	\(e\left(\frac{13}{228}\right)\)	\(e\left(\frac{41}{76}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{59}{228}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{46}{57}\right)\)
\(\chi_{42237}(14840,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{228}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{17}{76}\right)\)	\(e\left(\frac{79}{228}\right)\)	\(e\left(\frac{27}{76}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{113}{228}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{34}{57}\right)\)
\(\chi_{42237}(15182,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{175}{228}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{37}{76}\right)\)	\(e\left(\frac{11}{228}\right)\)	\(e\left(\frac{23}{76}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{85}{228}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{17}{57}\right)\)
\(\chi_{42237}(15866,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{228}\right)\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{39}{76}\right)\)	\(e\left(\frac{217}{228}\right)\)	\(e\left(\frac{53}{76}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{143}{228}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{40}{57}\right)\)
\(\chi_{42237}(17063,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{228}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{33}{76}\right)\)	\(e\left(\frac{55}{228}\right)\)	\(e\left(\frac{39}{76}\right)\)	\(e\left(\frac{31}{114}\right)\)	\(e\left(\frac{197}{228}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{28}{57}\right)\)
\(\chi_{42237}(17405,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{187}{228}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{53}{76}\right)\)	\(e\left(\frac{215}{228}\right)\)	\(e\left(\frac{35}{76}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{169}{228}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{11}{57}\right)\)
\(\chi_{42237}(17747,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{228}\right)\)	\(e\left(\frac{31}{114}\right)\)	\(e\left(\frac{35}{76}\right)\)	\(e\left(\frac{185}{228}\right)\)	\(e\left(\frac{69}{76}\right)\)	\(e\left(\frac{11}{114}\right)\)	\(e\left(\frac{103}{228}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{32}{57}\right)\)
\(\chi_{42237}(18089,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{228}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{55}{76}\right)\)	\(e\left(\frac{193}{228}\right)\)	\(e\left(\frac{65}{76}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{227}{228}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{34}{57}\right)\)

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First 31 of 72 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.qc
Modulus	$42237$
Conductor	$14079$
Order	$228$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(42237\)
Conductor:	\(14079\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(228\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 14079.fs	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)