LMFDB - Dirichlet character orbit 6253.fm

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6253, base_ring=CyclotomicField(468)) M = H._module chi = DirichletCharacter(H, M([27,299])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(5, 6253)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("6253.5"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$6253$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$6253$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$468$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{468})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 468 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 144 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{6253}(5,\cdot)$	$1$	$1$	$e\left(\frac{163}{234}\right)$	$e\left(\frac{179}{234}\right)$	$e\left(\frac{46}{117}\right)$	$e\left(\frac{25}{117}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{289}{468}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{62}{117}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{17}{156}\right)$
$\chi_{6253}(96,\cdot)$	$1$	$1$	$e\left(\frac{161}{234}\right)$	$e\left(\frac{217}{234}\right)$	$e\left(\frac{44}{117}\right)$	$e\left(\frac{29}{117}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{17}{468}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{100}{117}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{1}{156}\right)$
$\chi_{6253}(109,\cdot)$	$1$	$1$	$e\left(\frac{209}{234}\right)$	$e\left(\frac{7}{234}\right)$	$e\left(\frac{92}{117}\right)$	$e\left(\frac{50}{117}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{461}{468}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{7}{117}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{73}{156}\right)$
$\chi_{6253}(161,\cdot)$	$1$	$1$	$e\left(\frac{193}{234}\right)$	$e\left(\frac{77}{234}\right)$	$e\left(\frac{76}{117}\right)$	$e\left(\frac{82}{117}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{157}{468}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{77}{117}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{101}{156}\right)$
$\chi_{6253}(203,\cdot)$	$1$	$1$	$e\left(\frac{97}{234}\right)$	$e\left(\frac{29}{234}\right)$	$e\left(\frac{97}{117}\right)$	$e\left(\frac{40}{117}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{439}{468}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{29}{117}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{35}{156}\right)$
$\chi_{6253}(242,\cdot)$	$1$	$1$	$e\left(\frac{5}{234}\right)$	$e\left(\frac{139}{234}\right)$	$e\left(\frac{5}{117}\right)$	$e\left(\frac{107}{117}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{95}{468}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{22}{117}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{79}{156}\right)$
$\chi_{6253}(278,\cdot)$	$1$	$1$	$e\left(\frac{79}{234}\right)$	$e\left(\frac{137}{234}\right)$	$e\left(\frac{79}{117}\right)$	$e\left(\frac{76}{117}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{97}{468}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{20}{117}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{125}{156}\right)$
$\chi_{6253}(320,\cdot)$	$1$	$1$	$e\left(\frac{211}{234}\right)$	$e\left(\frac{203}{234}\right)$	$e\left(\frac{94}{117}\right)$	$e\left(\frac{46}{117}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{31}{468}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{86}{117}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{11}{156}\right)$
$\chi_{6253}(372,\cdot)$	$1$	$1$	$e\left(\frac{227}{234}\right)$	$e\left(\frac{133}{234}\right)$	$e\left(\frac{110}{117}\right)$	$e\left(\frac{14}{117}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{335}{468}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{16}{117}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{139}{156}\right)$
$\chi_{6253}(385,\cdot)$	$1$	$1$	$e\left(\frac{179}{234}\right)$	$e\left(\frac{109}{234}\right)$	$e\left(\frac{62}{117}\right)$	$e\left(\frac{110}{117}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{359}{468}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{109}{117}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{67}{156}\right)$
$\chi_{6253}(476,\cdot)$	$1$	$1$	$e\left(\frac{181}{234}\right)$	$e\left(\frac{71}{234}\right)$	$e\left(\frac{64}{117}\right)$	$e\left(\frac{106}{117}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{163}{468}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{71}{117}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{83}{156}\right)$
$\chi_{6253}(486,\cdot)$	$1$	$1$	$e\left(\frac{145}{234}\right)$	$e\left(\frac{53}{234}\right)$	$e\left(\frac{28}{117}\right)$	$e\left(\frac{61}{117}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{181}{468}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{53}{117}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{29}{156}\right)$
$\chi_{6253}(590,\cdot)$	$1$	$1$	$e\left(\frac{191}{234}\right)$	$e\left(\frac{115}{234}\right)$	$e\left(\frac{74}{117}\right)$	$e\left(\frac{86}{117}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{353}{468}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{115}{117}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{85}{156}\right)$
$\chi_{6253}(642,\cdot)$	$1$	$1$	$e\left(\frac{175}{234}\right)$	$e\left(\frac{185}{234}\right)$	$e\left(\frac{58}{117}\right)$	$e\left(\frac{1}{117}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{49}{468}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{68}{117}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{113}{156}\right)$
$\chi_{6253}(684,\cdot)$	$1$	$1$	$e\left(\frac{115}{234}\right)$	$e\left(\frac{155}{234}\right)$	$e\left(\frac{115}{117}\right)$	$e\left(\frac{4}{117}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{79}{468}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{38}{117}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{23}{156}\right)$
$\chi_{6253}(720,\cdot)$	$1$	$1$	$e\left(\frac{203}{234}\right)$	$e\left(\frac{121}{234}\right)$	$e\left(\frac{86}{117}\right)$	$e\left(\frac{62}{117}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{113}{468}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{4}{117}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{25}{156}\right)$
$\chi_{6253}(723,\cdot)$	$1$	$1$	$e\left(\frac{23}{234}\right)$	$e\left(\frac{31}{234}\right)$	$e\left(\frac{23}{117}\right)$	$e\left(\frac{71}{117}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{203}{468}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{31}{117}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{67}{156}\right)$
$\chi_{6253}(759,\cdot)$	$1$	$1$	$e\left(\frac{61}{234}\right)$	$e\left(\frac{11}{234}\right)$	$e\left(\frac{61}{117}\right)$	$e\left(\frac{112}{117}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{457}{468}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{11}{117}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{137}{156}\right)$
$\chi_{6253}(801,\cdot)$	$1$	$1$	$e\left(\frac{229}{234}\right)$	$e\left(\frac{95}{234}\right)$	$e\left(\frac{112}{117}\right)$	$e\left(\frac{10}{117}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{139}{468}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{95}{117}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{155}{156}\right)$
$\chi_{6253}(853,\cdot)$	$1$	$1$	$e\left(\frac{11}{234}\right)$	$e\left(\frac{25}{234}\right)$	$e\left(\frac{11}{117}\right)$	$e\left(\frac{95}{117}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{443}{468}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{25}{117}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{127}{156}\right)$
$\chi_{6253}(866,\cdot)$	$1$	$1$	$e\left(\frac{197}{234}\right)$	$e\left(\frac{1}{234}\right)$	$e\left(\frac{80}{117}\right)$	$e\left(\frac{74}{117}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{467}{468}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{1}{117}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{55}{156}\right)$
$\chi_{6253}(957,\cdot)$	$1$	$1$	$e\left(\frac{199}{234}\right)$	$e\left(\frac{197}{234}\right)$	$e\left(\frac{82}{117}\right)$	$e\left(\frac{70}{117}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{271}{468}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{80}{117}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{71}{156}\right)$
$\chi_{6253}(967,\cdot)$	$1$	$1$	$e\left(\frac{127}{234}\right)$	$e\left(\frac{161}{234}\right)$	$e\left(\frac{10}{117}\right)$	$e\left(\frac{97}{117}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{73}{468}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{44}{117}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{41}{156}\right)$
$\chi_{6253}(1058,\cdot)$	$1$	$1$	$e\left(\frac{125}{234}\right)$	$e\left(\frac{199}{234}\right)$	$e\left(\frac{8}{117}\right)$	$e\left(\frac{101}{117}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{269}{468}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{82}{117}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{25}{156}\right)$
$\chi_{6253}(1071,\cdot)$	$1$	$1$	$e\left(\frac{173}{234}\right)$	$e\left(\frac{223}{234}\right)$	$e\left(\frac{56}{117}\right)$	$e\left(\frac{5}{117}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{245}{468}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{106}{117}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{97}{156}\right)$
$\chi_{6253}(1123,\cdot)$	$1$	$1$	$e\left(\frac{157}{234}\right)$	$e\left(\frac{59}{234}\right)$	$e\left(\frac{40}{117}\right)$	$e\left(\frac{37}{117}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{409}{468}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{59}{117}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{125}{156}\right)$
$\chi_{6253}(1165,\cdot)$	$1$	$1$	$e\left(\frac{133}{234}\right)$	$e\left(\frac{47}{234}\right)$	$e\left(\frac{16}{117}\right)$	$e\left(\frac{85}{117}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{187}{468}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{47}{117}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{11}{156}\right)$
$\chi_{6253}(1201,\cdot)$	$1$	$1$	$e\left(\frac{185}{234}\right)$	$e\left(\frac{229}{234}\right)$	$e\left(\frac{68}{117}\right)$	$e\left(\frac{98}{117}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{5}{468}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{112}{117}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{37}{156}\right)$
$\chi_{6253}(1204,\cdot)$	$1$	$1$	$e\left(\frac{41}{234}\right)$	$e\left(\frac{157}{234}\right)$	$e\left(\frac{41}{117}\right)$	$e\left(\frac{35}{117}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{311}{468}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{40}{117}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{55}{156}\right)$
$\chi_{6253}(1240,\cdot)$	$1$	$1$	$e\left(\frac{43}{234}\right)$	$e\left(\frac{119}{234}\right)$	$e\left(\frac{43}{117}\right)$	$e\left(\frac{31}{117}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{349}{468}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{2}{117}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{149}{156}\right)$
$\chi_{6253}(1334,\cdot)$	$1$	$1$	$e\left(\frac{29}{234}\right)$	$e\left(\frac{151}{234}\right)$	$e\left(\frac{29}{117}\right)$	$e\left(\frac{59}{117}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{83}{468}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{34}{117}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{115}{156}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{6253}(5,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{234}\right)\)	\(e\left(\frac{179}{234}\right)\)	\(e\left(\frac{46}{117}\right)\)	\(e\left(\frac{25}{117}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{289}{468}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{62}{117}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{17}{156}\right)\)
\(\chi_{6253}(96,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{234}\right)\)	\(e\left(\frac{217}{234}\right)\)	\(e\left(\frac{44}{117}\right)\)	\(e\left(\frac{29}{117}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{17}{468}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{100}{117}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{1}{156}\right)\)
\(\chi_{6253}(109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{209}{234}\right)\)	\(e\left(\frac{7}{234}\right)\)	\(e\left(\frac{92}{117}\right)\)	\(e\left(\frac{50}{117}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{461}{468}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{7}{117}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{73}{156}\right)\)
\(\chi_{6253}(161,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{234}\right)\)	\(e\left(\frac{77}{234}\right)\)	\(e\left(\frac{76}{117}\right)\)	\(e\left(\frac{82}{117}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{157}{468}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{77}{117}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{101}{156}\right)\)
\(\chi_{6253}(203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{234}\right)\)	\(e\left(\frac{29}{234}\right)\)	\(e\left(\frac{97}{117}\right)\)	\(e\left(\frac{40}{117}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{439}{468}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{29}{117}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{35}{156}\right)\)
\(\chi_{6253}(242,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{234}\right)\)	\(e\left(\frac{139}{234}\right)\)	\(e\left(\frac{5}{117}\right)\)	\(e\left(\frac{107}{117}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{95}{468}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{22}{117}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{79}{156}\right)\)
\(\chi_{6253}(278,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{234}\right)\)	\(e\left(\frac{137}{234}\right)\)	\(e\left(\frac{79}{117}\right)\)	\(e\left(\frac{76}{117}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{97}{468}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{20}{117}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{125}{156}\right)\)
\(\chi_{6253}(320,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{211}{234}\right)\)	\(e\left(\frac{203}{234}\right)\)	\(e\left(\frac{94}{117}\right)\)	\(e\left(\frac{46}{117}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{31}{468}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{86}{117}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{11}{156}\right)\)
\(\chi_{6253}(372,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{234}\right)\)	\(e\left(\frac{133}{234}\right)\)	\(e\left(\frac{110}{117}\right)\)	\(e\left(\frac{14}{117}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{335}{468}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{16}{117}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{139}{156}\right)\)
\(\chi_{6253}(385,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{234}\right)\)	\(e\left(\frac{109}{234}\right)\)	\(e\left(\frac{62}{117}\right)\)	\(e\left(\frac{110}{117}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{359}{468}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{109}{117}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{67}{156}\right)\)
\(\chi_{6253}(476,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{234}\right)\)	\(e\left(\frac{71}{234}\right)\)	\(e\left(\frac{64}{117}\right)\)	\(e\left(\frac{106}{117}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{163}{468}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{71}{117}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{83}{156}\right)\)
\(\chi_{6253}(486,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{234}\right)\)	\(e\left(\frac{53}{234}\right)\)	\(e\left(\frac{28}{117}\right)\)	\(e\left(\frac{61}{117}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{181}{468}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{53}{117}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{29}{156}\right)\)
\(\chi_{6253}(590,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{234}\right)\)	\(e\left(\frac{115}{234}\right)\)	\(e\left(\frac{74}{117}\right)\)	\(e\left(\frac{86}{117}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{353}{468}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{115}{117}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{85}{156}\right)\)
\(\chi_{6253}(642,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{175}{234}\right)\)	\(e\left(\frac{185}{234}\right)\)	\(e\left(\frac{58}{117}\right)\)	\(e\left(\frac{1}{117}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{49}{468}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{68}{117}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{113}{156}\right)\)
\(\chi_{6253}(684,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{234}\right)\)	\(e\left(\frac{155}{234}\right)\)	\(e\left(\frac{115}{117}\right)\)	\(e\left(\frac{4}{117}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{79}{468}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{38}{117}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{23}{156}\right)\)
\(\chi_{6253}(720,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{234}\right)\)	\(e\left(\frac{121}{234}\right)\)	\(e\left(\frac{86}{117}\right)\)	\(e\left(\frac{62}{117}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{113}{468}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{4}{117}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{25}{156}\right)\)
\(\chi_{6253}(723,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{234}\right)\)	\(e\left(\frac{31}{234}\right)\)	\(e\left(\frac{23}{117}\right)\)	\(e\left(\frac{71}{117}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{203}{468}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{31}{117}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{67}{156}\right)\)
\(\chi_{6253}(759,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{234}\right)\)	\(e\left(\frac{11}{234}\right)\)	\(e\left(\frac{61}{117}\right)\)	\(e\left(\frac{112}{117}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{457}{468}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{11}{117}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{137}{156}\right)\)
\(\chi_{6253}(801,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{229}{234}\right)\)	\(e\left(\frac{95}{234}\right)\)	\(e\left(\frac{112}{117}\right)\)	\(e\left(\frac{10}{117}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{139}{468}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{95}{117}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{155}{156}\right)\)
\(\chi_{6253}(853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{234}\right)\)	\(e\left(\frac{25}{234}\right)\)	\(e\left(\frac{11}{117}\right)\)	\(e\left(\frac{95}{117}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{443}{468}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{25}{117}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{127}{156}\right)\)
\(\chi_{6253}(866,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{234}\right)\)	\(e\left(\frac{1}{234}\right)\)	\(e\left(\frac{80}{117}\right)\)	\(e\left(\frac{74}{117}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{467}{468}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{1}{117}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{55}{156}\right)\)
\(\chi_{6253}(957,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{234}\right)\)	\(e\left(\frac{197}{234}\right)\)	\(e\left(\frac{82}{117}\right)\)	\(e\left(\frac{70}{117}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{271}{468}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{80}{117}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{71}{156}\right)\)
\(\chi_{6253}(967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{234}\right)\)	\(e\left(\frac{161}{234}\right)\)	\(e\left(\frac{10}{117}\right)\)	\(e\left(\frac{97}{117}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{73}{468}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{44}{117}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{41}{156}\right)\)
\(\chi_{6253}(1058,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{234}\right)\)	\(e\left(\frac{199}{234}\right)\)	\(e\left(\frac{8}{117}\right)\)	\(e\left(\frac{101}{117}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{269}{468}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{82}{117}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{25}{156}\right)\)
\(\chi_{6253}(1071,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{234}\right)\)	\(e\left(\frac{223}{234}\right)\)	\(e\left(\frac{56}{117}\right)\)	\(e\left(\frac{5}{117}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{245}{468}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{106}{117}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{97}{156}\right)\)
\(\chi_{6253}(1123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{234}\right)\)	\(e\left(\frac{59}{234}\right)\)	\(e\left(\frac{40}{117}\right)\)	\(e\left(\frac{37}{117}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{409}{468}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{59}{117}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{125}{156}\right)\)
\(\chi_{6253}(1165,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{234}\right)\)	\(e\left(\frac{47}{234}\right)\)	\(e\left(\frac{16}{117}\right)\)	\(e\left(\frac{85}{117}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{187}{468}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{47}{117}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{11}{156}\right)\)
\(\chi_{6253}(1201,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{185}{234}\right)\)	\(e\left(\frac{229}{234}\right)\)	\(e\left(\frac{68}{117}\right)\)	\(e\left(\frac{98}{117}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{5}{468}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{112}{117}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{37}{156}\right)\)
\(\chi_{6253}(1204,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{234}\right)\)	\(e\left(\frac{157}{234}\right)\)	\(e\left(\frac{41}{117}\right)\)	\(e\left(\frac{35}{117}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{311}{468}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{40}{117}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{55}{156}\right)\)
\(\chi_{6253}(1240,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{234}\right)\)	\(e\left(\frac{119}{234}\right)\)	\(e\left(\frac{43}{117}\right)\)	\(e\left(\frac{31}{117}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{349}{468}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{2}{117}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{149}{156}\right)\)
\(\chi_{6253}(1334,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{234}\right)\)	\(e\left(\frac{151}{234}\right)\)	\(e\left(\frac{29}{117}\right)\)	\(e\left(\frac{59}{117}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{83}{468}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{34}{117}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{115}{156}\right)\)

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First 31 of 144 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	6253.fm
Modulus	$6253$
Conductor	$6253$
Order	$468$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(6253\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(6253\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(468\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);