LMFDB - Dirichlet character orbit 6253.fa

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6253, base_ring=CyclotomicField(156)) M = H._module chi = DirichletCharacter(H, M([55,117])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(154, 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("6253.154"); 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:	$156$	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:	$\Q(\zeta_{156})$	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 156 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{6253}(154,\cdot)$	$1$	$1$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{127}{156}\right)$
$\chi_{6253}(228,\cdot)$	$1$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{95}{156}\right)$
$\chi_{6253}(253,\cdot)$	$1$	$1$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{53}{156}\right)$
$\chi_{6253}(327,\cdot)$	$1$	$1$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{1}{156}\right)$
$\chi_{6253}(635,\cdot)$	$1$	$1$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{19}{156}\right)$
$\chi_{6253}(709,\cdot)$	$1$	$1$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{59}{156}\right)$
$\chi_{6253}(734,\cdot)$	$1$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{89}{156}\right)$
$\chi_{6253}(808,\cdot)$	$1$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{109}{156}\right)$
$\chi_{6253}(1116,\cdot)$	$1$	$1$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{67}{156}\right)$
$\chi_{6253}(1190,\cdot)$	$1$	$1$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{23}{156}\right)$
$\chi_{6253}(1215,\cdot)$	$1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{125}{156}\right)$
$\chi_{6253}(1289,\cdot)$	$1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{61}{156}\right)$
$\chi_{6253}(1597,\cdot)$	$1$	$1$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{115}{156}\right)$
$\chi_{6253}(1696,\cdot)$	$1$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{5}{156}\right)$
$\chi_{6253}(2078,\cdot)$	$1$	$1$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{7}{156}\right)$
$\chi_{6253}(2152,\cdot)$	$1$	$1$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{107}{156}\right)$
$\chi_{6253}(2177,\cdot)$	$1$	$1$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{41}{156}\right)$
$\chi_{6253}(2251,\cdot)$	$1$	$1$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{121}{156}\right)$
$\chi_{6253}(2559,\cdot)$	$1$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{55}{156}\right)$
$\chi_{6253}(2633,\cdot)$	$1$	$1$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{71}{156}\right)$
$\chi_{6253}(2658,\cdot)$	$1$	$1$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{77}{156}\right)$
$\chi_{6253}(2732,\cdot)$	$1$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{73}{156}\right)$
$\chi_{6253}(3040,\cdot)$	$1$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{103}{156}\right)$
$\chi_{6253}(3114,\cdot)$	$1$	$1$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{35}{156}\right)$
$\chi_{6253}(3139,\cdot)$	$1$	$1$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{113}{156}\right)$
$\chi_{6253}(3213,\cdot)$	$1$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{25}{156}\right)$
$\chi_{6253}(3521,\cdot)$	$1$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{151}{156}\right)$
$\chi_{6253}(3595,\cdot)$	$1$	$1$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{155}{156}\right)$
$\chi_{6253}(3620,\cdot)$	$1$	$1$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{149}{156}\right)$
$\chi_{6253}(3694,\cdot)$	$1$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{133}{156}\right)$
$\chi_{6253}(4002,\cdot)$	$1$	$1$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{43}{156}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{6253}(154,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{127}{156}\right)\)
\(\chi_{6253}(228,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{95}{156}\right)\)
\(\chi_{6253}(253,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{53}{156}\right)\)
\(\chi_{6253}(327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{1}{156}\right)\)
\(\chi_{6253}(635,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{19}{156}\right)\)
\(\chi_{6253}(709,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{59}{156}\right)\)
\(\chi_{6253}(734,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{89}{156}\right)\)
\(\chi_{6253}(808,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{109}{156}\right)\)
\(\chi_{6253}(1116,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{67}{156}\right)\)
\(\chi_{6253}(1190,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{23}{156}\right)\)
\(\chi_{6253}(1215,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{125}{156}\right)\)
\(\chi_{6253}(1289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{61}{156}\right)\)
\(\chi_{6253}(1597,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{115}{156}\right)\)
\(\chi_{6253}(1696,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{5}{156}\right)\)
\(\chi_{6253}(2078,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{7}{156}\right)\)
\(\chi_{6253}(2152,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{107}{156}\right)\)
\(\chi_{6253}(2177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{41}{156}\right)\)
\(\chi_{6253}(2251,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{121}{156}\right)\)
\(\chi_{6253}(2559,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{55}{156}\right)\)
\(\chi_{6253}(2633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{71}{156}\right)\)
\(\chi_{6253}(2658,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{77}{156}\right)\)
\(\chi_{6253}(2732,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{73}{156}\right)\)
\(\chi_{6253}(3040,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{103}{156}\right)\)
\(\chi_{6253}(3114,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{35}{156}\right)\)
\(\chi_{6253}(3139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{113}{156}\right)\)
\(\chi_{6253}(3213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{25}{156}\right)\)
\(\chi_{6253}(3521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{151}{156}\right)\)
\(\chi_{6253}(3595,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{155}{156}\right)\)
\(\chi_{6253}(3620,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{149}{156}\right)\)
\(\chi_{6253}(3694,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{133}{156}\right)\)
\(\chi_{6253}(4002,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{43}{156}\right)\)

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First 31 of 48 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.fa
Modulus	$6253$
Conductor	$6253$
Order	$156$
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:	\(156\)	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);