LMFDB - Dirichlet character orbit 6043.k

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6043, base_ring=CyclotomicField(318)) M = H._module chi = DirichletCharacter(H, M([182])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(4,6043)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$6043$
Conductor:	$6043$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$159$	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:	$\Q(\zeta_{159})$
Fixed field:	Number field defined by a degree 159 polynomial (not computed)

First 31 of 104 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{6043}(4,\cdot)$	$1$	$1$	$e\left(\frac{88}{159}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{17}{159}\right)$	$e\left(\frac{91}{159}\right)$	$e\left(\frac{76}{159}\right)$	$e\left(\frac{5}{159}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{20}{159}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6043}(16,\cdot)$	$1$	$1$	$e\left(\frac{17}{159}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{34}{159}\right)$	$e\left(\frac{23}{159}\right)$	$e\left(\frac{152}{159}\right)$	$e\left(\frac{10}{159}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{40}{159}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6043}(256,\cdot)$	$1$	$1$	$e\left(\frac{34}{159}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{68}{159}\right)$	$e\left(\frac{46}{159}\right)$	$e\left(\frac{145}{159}\right)$	$e\left(\frac{20}{159}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{80}{159}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6043}(462,\cdot)$	$1$	$1$	$e\left(\frac{14}{159}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{28}{159}\right)$	$e\left(\frac{47}{159}\right)$	$e\left(\frac{41}{159}\right)$	$e\left(\frac{55}{159}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{61}{159}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6043}(467,\cdot)$	$1$	$1$	$e\left(\frac{40}{159}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{80}{159}\right)$	$e\left(\frac{157}{159}\right)$	$e\left(\frac{49}{159}\right)$	$e\left(\frac{89}{159}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{38}{159}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6043}(483,\cdot)$	$1$	$1$	$e\left(\frac{121}{159}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{83}{159}\right)$	$e\left(\frac{145}{159}\right)$	$e\left(\frac{25}{159}\right)$	$e\left(\frac{146}{159}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{107}{159}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6043}(513,\cdot)$	$1$	$1$	$e\left(\frac{55}{159}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{110}{159}\right)$	$e\left(\frac{37}{159}\right)$	$e\left(\frac{127}{159}\right)$	$e\left(\frac{23}{159}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{92}{159}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6043}(525,\cdot)$	$1$	$1$	$e\left(\frac{8}{159}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{16}{159}\right)$	$e\left(\frac{95}{159}\right)$	$e\left(\frac{137}{159}\right)$	$e\left(\frac{145}{159}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{103}{159}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6043}(541,\cdot)$	$1$	$1$	$e\left(\frac{80}{159}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{1}{159}\right)$	$e\left(\frac{155}{159}\right)$	$e\left(\frac{98}{159}\right)$	$e\left(\frac{19}{159}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{76}{159}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6043}(695,\cdot)$	$1$	$1$	$e\left(\frac{148}{159}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{137}{159}\right)$	$e\left(\frac{88}{159}\right)$	$e\left(\frac{70}{159}\right)$	$e\left(\frac{59}{159}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{77}{159}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6043}(697,\cdot)$	$1$	$1$	$e\left(\frac{67}{159}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{134}{159}\right)$	$e\left(\frac{100}{159}\right)$	$e\left(\frac{94}{159}\right)$	$e\left(\frac{2}{159}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{8}{159}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6043}(830,\cdot)$	$1$	$1$	$e\left(\frac{22}{159}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{44}{159}\right)$	$e\left(\frac{142}{159}\right)$	$e\left(\frac{19}{159}\right)$	$e\left(\frac{41}{159}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{5}{159}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6043}(858,\cdot)$	$1$	$1$	$e\left(\frac{62}{159}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{124}{159}\right)$	$e\left(\frac{140}{159}\right)$	$e\left(\frac{68}{159}\right)$	$e\left(\frac{130}{159}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{43}{159}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6043}(890,\cdot)$	$1$	$1$	$e\left(\frac{20}{159}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{40}{159}\right)$	$e\left(\frac{158}{159}\right)$	$e\left(\frac{104}{159}\right)$	$e\left(\frac{124}{159}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{19}{159}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6043}(893,\cdot)$	$1$	$1$	$e\left(\frac{65}{159}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{130}{159}\right)$	$e\left(\frac{116}{159}\right)$	$e\left(\frac{20}{159}\right)$	$e\left(\frac{85}{159}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{22}{159}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6043}(897,\cdot)$	$1$	$1$	$e\left(\frac{10}{159}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{20}{159}\right)$	$e\left(\frac{79}{159}\right)$	$e\left(\frac{52}{159}\right)$	$e\left(\frac{62}{159}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{89}{159}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6043}(975,\cdot)$	$1$	$1$	$e\left(\frac{56}{159}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{112}{159}\right)$	$e\left(\frac{29}{159}\right)$	$e\left(\frac{5}{159}\right)$	$e\left(\frac{61}{159}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{85}{159}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6043}(986,\cdot)$	$1$	$1$	$e\left(\frac{158}{159}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{157}{159}\right)$	$e\left(\frac{8}{159}\right)$	$e\left(\frac{122}{159}\right)$	$e\left(\frac{121}{159}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{7}{159}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6043}(1024,\cdot)$	$1$	$1$	$e\left(\frac{122}{159}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{85}{159}\right)$	$e\left(\frac{137}{159}\right)$	$e\left(\frac{62}{159}\right)$	$e\left(\frac{25}{159}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{100}{159}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6043}(1221,\cdot)$	$1$	$1$	$e\left(\frac{32}{159}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{64}{159}\right)$	$e\left(\frac{62}{159}\right)$	$e\left(\frac{71}{159}\right)$	$e\left(\frac{103}{159}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{94}{159}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6043}(1294,\cdot)$	$1$	$1$	$e\left(\frac{4}{159}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{8}{159}\right)$	$e\left(\frac{127}{159}\right)$	$e\left(\frac{148}{159}\right)$	$e\left(\frac{152}{159}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{131}{159}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6043}(1305,\cdot)$	$1$	$1$	$e\left(\frac{19}{159}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{38}{159}\right)$	$e\left(\frac{7}{159}\right)$	$e\left(\frac{67}{159}\right)$	$e\left(\frac{86}{159}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{26}{159}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6043}(1349,\cdot)$	$1$	$1$	$e\left(\frac{31}{159}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{62}{159}\right)$	$e\left(\frac{70}{159}\right)$	$e\left(\frac{34}{159}\right)$	$e\left(\frac{65}{159}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{101}{159}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6043}(1407,\cdot)$	$1$	$1$	$e\left(\frac{49}{159}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{98}{159}\right)$	$e\left(\frac{85}{159}\right)$	$e\left(\frac{64}{159}\right)$	$e\left(\frac{113}{159}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{134}{159}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6043}(1453,\cdot)$	$1$	$1$	$e\left(\frac{41}{159}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{82}{159}\right)$	$e\left(\frac{149}{159}\right)$	$e\left(\frac{86}{159}\right)$	$e\left(\frac{127}{159}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{31}{159}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6043}(1511,\cdot)$	$1$	$1$	$e\left(\frac{71}{159}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{142}{159}\right)$	$e\left(\frac{68}{159}\right)$	$e\left(\frac{83}{159}\right)$	$e\left(\frac{154}{159}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{139}{159}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6043}(1642,\cdot)$	$1$	$1$	$e\left(\frac{79}{159}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{158}{159}\right)$	$e\left(\frac{4}{159}\right)$	$e\left(\frac{61}{159}\right)$	$e\left(\frac{140}{159}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{83}{159}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6043}(1646,\cdot)$	$1$	$1$	$e\left(\frac{151}{159}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{143}{159}\right)$	$e\left(\frac{64}{159}\right)$	$e\left(\frac{22}{159}\right)$	$e\left(\frac{14}{159}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{56}{159}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6043}(1713,\cdot)$	$1$	$1$	$e\left(\frac{116}{159}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{73}{159}\right)$	$e\left(\frac{26}{159}\right)$	$e\left(\frac{158}{159}\right)$	$e\left(\frac{115}{159}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{142}{159}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6043}(1734,\cdot)$	$1$	$1$	$e\left(\frac{136}{159}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{113}{159}\right)$	$e\left(\frac{25}{159}\right)$	$e\left(\frac{103}{159}\right)$	$e\left(\frac{80}{159}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{2}{159}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6043}(1816,\cdot)$	$1$	$1$	$e\left(\frac{103}{159}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{47}{159}\right)$	$e\left(\frac{130}{159}\right)$	$e\left(\frac{154}{159}\right)$	$e\left(\frac{98}{159}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{74}{159}\right)$	$e\left(\frac{2}{3}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{6043}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{88}{159}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{17}{159}\right)\)	\(e\left(\frac{91}{159}\right)\)	\(e\left(\frac{76}{159}\right)\)	\(e\left(\frac{5}{159}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{20}{159}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6043}(16,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{159}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{34}{159}\right)\)	\(e\left(\frac{23}{159}\right)\)	\(e\left(\frac{152}{159}\right)\)	\(e\left(\frac{10}{159}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{40}{159}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6043}(256,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{159}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{68}{159}\right)\)	\(e\left(\frac{46}{159}\right)\)	\(e\left(\frac{145}{159}\right)\)	\(e\left(\frac{20}{159}\right)\)	\(e\left(\frac{34}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{80}{159}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6043}(462,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{159}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{28}{159}\right)\)	\(e\left(\frac{47}{159}\right)\)	\(e\left(\frac{41}{159}\right)\)	\(e\left(\frac{55}{159}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{61}{159}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6043}(467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{40}{159}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{80}{159}\right)\)	\(e\left(\frac{157}{159}\right)\)	\(e\left(\frac{49}{159}\right)\)	\(e\left(\frac{89}{159}\right)\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{38}{159}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6043}(483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{159}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{83}{159}\right)\)	\(e\left(\frac{145}{159}\right)\)	\(e\left(\frac{25}{159}\right)\)	\(e\left(\frac{146}{159}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{107}{159}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6043}(513,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{159}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{110}{159}\right)\)	\(e\left(\frac{37}{159}\right)\)	\(e\left(\frac{127}{159}\right)\)	\(e\left(\frac{23}{159}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{92}{159}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6043}(525,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{159}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{16}{159}\right)\)	\(e\left(\frac{95}{159}\right)\)	\(e\left(\frac{137}{159}\right)\)	\(e\left(\frac{145}{159}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{103}{159}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6043}(541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{80}{159}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{1}{159}\right)\)	\(e\left(\frac{155}{159}\right)\)	\(e\left(\frac{98}{159}\right)\)	\(e\left(\frac{19}{159}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{76}{159}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6043}(695,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{148}{159}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{137}{159}\right)\)	\(e\left(\frac{88}{159}\right)\)	\(e\left(\frac{70}{159}\right)\)	\(e\left(\frac{59}{159}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{77}{159}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6043}(697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{159}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{134}{159}\right)\)	\(e\left(\frac{100}{159}\right)\)	\(e\left(\frac{94}{159}\right)\)	\(e\left(\frac{2}{159}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{8}{159}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6043}(830,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{159}\right)\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{44}{159}\right)\)	\(e\left(\frac{142}{159}\right)\)	\(e\left(\frac{19}{159}\right)\)	\(e\left(\frac{41}{159}\right)\)	\(e\left(\frac{22}{53}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{5}{159}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6043}(858,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{159}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{124}{159}\right)\)	\(e\left(\frac{140}{159}\right)\)	\(e\left(\frac{68}{159}\right)\)	\(e\left(\frac{130}{159}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{43}{159}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6043}(890,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{159}\right)\)	\(e\left(\frac{28}{53}\right)\)	\(e\left(\frac{40}{159}\right)\)	\(e\left(\frac{158}{159}\right)\)	\(e\left(\frac{104}{159}\right)\)	\(e\left(\frac{124}{159}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{19}{159}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6043}(893,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{159}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{130}{159}\right)\)	\(e\left(\frac{116}{159}\right)\)	\(e\left(\frac{20}{159}\right)\)	\(e\left(\frac{85}{159}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{22}{159}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6043}(897,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{159}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{20}{159}\right)\)	\(e\left(\frac{79}{159}\right)\)	\(e\left(\frac{52}{159}\right)\)	\(e\left(\frac{62}{159}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{28}{53}\right)\)	\(e\left(\frac{89}{159}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6043}(975,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{56}{159}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{112}{159}\right)\)	\(e\left(\frac{29}{159}\right)\)	\(e\left(\frac{5}{159}\right)\)	\(e\left(\frac{61}{159}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{85}{159}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6043}(986,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{158}{159}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{157}{159}\right)\)	\(e\left(\frac{8}{159}\right)\)	\(e\left(\frac{122}{159}\right)\)	\(e\left(\frac{121}{159}\right)\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{29}{53}\right)\)	\(e\left(\frac{7}{159}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6043}(1024,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{122}{159}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{85}{159}\right)\)	\(e\left(\frac{137}{159}\right)\)	\(e\left(\frac{62}{159}\right)\)	\(e\left(\frac{25}{159}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{100}{159}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6043}(1221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{159}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{64}{159}\right)\)	\(e\left(\frac{62}{159}\right)\)	\(e\left(\frac{71}{159}\right)\)	\(e\left(\frac{103}{159}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{94}{159}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6043}(1294,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{159}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{8}{159}\right)\)	\(e\left(\frac{127}{159}\right)\)	\(e\left(\frac{148}{159}\right)\)	\(e\left(\frac{152}{159}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{131}{159}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6043}(1305,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{159}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{38}{159}\right)\)	\(e\left(\frac{7}{159}\right)\)	\(e\left(\frac{67}{159}\right)\)	\(e\left(\frac{86}{159}\right)\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{26}{159}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6043}(1349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{159}\right)\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{62}{159}\right)\)	\(e\left(\frac{70}{159}\right)\)	\(e\left(\frac{34}{159}\right)\)	\(e\left(\frac{65}{159}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{101}{159}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6043}(1407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{159}\right)\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{98}{159}\right)\)	\(e\left(\frac{85}{159}\right)\)	\(e\left(\frac{64}{159}\right)\)	\(e\left(\frac{113}{159}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{134}{159}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6043}(1453,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{159}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{82}{159}\right)\)	\(e\left(\frac{149}{159}\right)\)	\(e\left(\frac{86}{159}\right)\)	\(e\left(\frac{127}{159}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{31}{159}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6043}(1511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{159}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{142}{159}\right)\)	\(e\left(\frac{68}{159}\right)\)	\(e\left(\frac{83}{159}\right)\)	\(e\left(\frac{154}{159}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{139}{159}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6043}(1642,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{159}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{158}{159}\right)\)	\(e\left(\frac{4}{159}\right)\)	\(e\left(\frac{61}{159}\right)\)	\(e\left(\frac{140}{159}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{83}{159}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6043}(1646,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{159}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{143}{159}\right)\)	\(e\left(\frac{64}{159}\right)\)	\(e\left(\frac{22}{159}\right)\)	\(e\left(\frac{14}{159}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{56}{159}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6043}(1713,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{116}{159}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{73}{159}\right)\)	\(e\left(\frac{26}{159}\right)\)	\(e\left(\frac{158}{159}\right)\)	\(e\left(\frac{115}{159}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{28}{53}\right)\)	\(e\left(\frac{142}{159}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6043}(1734,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{136}{159}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{113}{159}\right)\)	\(e\left(\frac{25}{159}\right)\)	\(e\left(\frac{103}{159}\right)\)	\(e\left(\frac{80}{159}\right)\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{2}{159}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6043}(1816,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{159}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{47}{159}\right)\)	\(e\left(\frac{130}{159}\right)\)	\(e\left(\frac{154}{159}\right)\)	\(e\left(\frac{98}{159}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{34}{53}\right)\)	\(e\left(\frac{74}{159}\right)\)	\(e\left(\frac{2}{3}\right)\)

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First 31 of 104 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	6043.k
Modulus	$6043$
Conductor	$6043$
Order	$159$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(6043\)
Conductor:	\(6043\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(159\)	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)