LMFDB - Dirichlet character orbit 1227.x

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1227, base_ring=CyclotomicField(102)) M = H._module chi = DirichletCharacter(H, M([51,70])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(17, 1227)) 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("1227.17"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$1227$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1227$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$102$	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:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{51})$	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 102 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{1227}(17,\cdot)$	$-1$	$1$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{5}{51}\right)$
$\chi_{1227}(71,\cdot)$	$-1$	$1$	$e\left(\frac{1}{102}\right)$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{2}{51}\right)$
$\chi_{1227}(77,\cdot)$	$-1$	$1$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{31}{51}\right)$
$\chi_{1227}(80,\cdot)$	$-1$	$1$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{25}{51}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{50}{51}\right)$
$\chi_{1227}(98,\cdot)$	$-1$	$1$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{13}{51}\right)$
$\chi_{1227}(101,\cdot)$	$-1$	$1$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{23}{51}\right)$
$\chi_{1227}(167,\cdot)$	$-1$	$1$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{41}{51}\right)$
$\chi_{1227}(179,\cdot)$	$-1$	$1$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{40}{51}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{16}{51}\right)$
$\chi_{1227}(197,\cdot)$	$-1$	$1$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{26}{51}\right)$
$\chi_{1227}(203,\cdot)$	$-1$	$1$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{11}{51}\right)$
$\chi_{1227}(218,\cdot)$	$-1$	$1$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{25}{51}\right)$
$\chi_{1227}(272,\cdot)$	$-1$	$1$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{49}{51}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{40}{51}\right)$
$\chi_{1227}(389,\cdot)$	$-1$	$1$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{7}{51}\right)$
$\chi_{1227}(425,\cdot)$	$-1$	$1$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{35}{51}\right)$
$\chi_{1227}(494,\cdot)$	$-1$	$1$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{20}{51}\right)$
$\chi_{1227}(542,\cdot)$	$-1$	$1$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{4}{51}\right)$
$\chi_{1227}(548,\cdot)$	$-1$	$1$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{32}{51}\right)$
$\chi_{1227}(593,\cdot)$	$-1$	$1$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{44}{51}\right)$
$\chi_{1227}(665,\cdot)$	$-1$	$1$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{19}{51}\right)$
$\chi_{1227}(674,\cdot)$	$-1$	$1$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{49}{51}\right)$
$\chi_{1227}(695,\cdot)$	$-1$	$1$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{49}{51}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{47}{51}\right)$
$\chi_{1227}(698,\cdot)$	$-1$	$1$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{25}{51}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{10}{51}\right)$
$\chi_{1227}(773,\cdot)$	$-1$	$1$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{40}{51}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{29}{51}\right)$
$\chi_{1227}(794,\cdot)$	$-1$	$1$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{46}{51}\right)$
$\chi_{1227}(809,\cdot)$	$-1$	$1$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{14}{51}\right)$
$\chi_{1227}(899,\cdot)$	$-1$	$1$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{28}{51}\right)$
$\chi_{1227}(914,\cdot)$	$-1$	$1$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{38}{51}\right)$
$\chi_{1227}(920,\cdot)$	$-1$	$1$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{8}{51}\right)$
$\chi_{1227}(1127,\cdot)$	$-1$	$1$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{22}{51}\right)$
$\chi_{1227}(1136,\cdot)$	$-1$	$1$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{37}{51}\right)$
$\chi_{1227}(1181,\cdot)$	$-1$	$1$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{1}{51}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{1227}(17,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{5}{51}\right)\)
\(\chi_{1227}(71,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{102}\right)\)	\(e\left(\frac{1}{51}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{2}{51}\right)\)
\(\chi_{1227}(77,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{1}{51}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{31}{51}\right)\)
\(\chi_{1227}(80,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{25}{51}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{23}{51}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{50}{51}\right)\)
\(\chi_{1227}(98,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{13}{51}\right)\)
\(\chi_{1227}(101,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{23}{51}\right)\)
\(\chi_{1227}(167,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{26}{51}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{41}{51}\right)\)
\(\chi_{1227}(179,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{8}{51}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{40}{51}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{16}{51}\right)\)
\(\chi_{1227}(197,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{14}{51}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{26}{51}\right)\)
\(\chi_{1227}(203,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{31}{51}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{11}{51}\right)\)
\(\chi_{1227}(218,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{25}{51}\right)\)
\(\chi_{1227}(272,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{20}{51}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{49}{51}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{40}{51}\right)\)
\(\chi_{1227}(389,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{29}{51}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{43}{51}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{7}{51}\right)\)
\(\chi_{1227}(425,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{43}{51}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{35}{51}\right)\)
\(\chi_{1227}(494,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{10}{51}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{50}{51}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{20}{51}\right)\)
\(\chi_{1227}(542,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{10}{51}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{4}{51}\right)\)
\(\chi_{1227}(548,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{16}{51}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{29}{51}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{32}{51}\right)\)
\(\chi_{1227}(593,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{8}{51}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{44}{51}\right)\)
\(\chi_{1227}(665,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{102}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{19}{51}\right)\)
\(\chi_{1227}(674,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{50}{51}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{49}{51}\right)\)
\(\chi_{1227}(695,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{49}{51}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{47}{51}\right)\)
\(\chi_{1227}(698,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{25}{51}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{10}{51}\right)\)
\(\chi_{1227}(773,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{40}{51}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{29}{51}\right)\)
\(\chi_{1227}(794,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{23}{51}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{46}{51}\right)\)
\(\chi_{1227}(809,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{14}{51}\right)\)
\(\chi_{1227}(899,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{14}{51}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{28}{51}\right)\)
\(\chi_{1227}(914,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{44}{51}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{38}{51}\right)\)
\(\chi_{1227}(920,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{20}{51}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{8}{51}\right)\)
\(\chi_{1227}(1127,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{22}{51}\right)\)
\(\chi_{1227}(1136,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{44}{51}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{16}{51}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{37}{51}\right)\)
\(\chi_{1227}(1181,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{26}{51}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{1}{51}\right)\)

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Basic properties

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First 31 of 32 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	1227.x
Modulus	$1227$
Conductor	$1227$
Order	$102$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(1227\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1227\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(102\)	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:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);