LMFDB - Dirichlet character orbit 20181.dl

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(20181, base_ring=CyclotomicField(186)) M = H._module chi = DirichletCharacter(H, M([0,124,176])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(25, 20181)) 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("20181.25"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$20181$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$6727$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$93$	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:	no, induced from 6727.bt	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:	$\Q(\zeta_{93})$	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 93 polynomial	comment:Fixed field sage:chi.fixed_field()

First 31 of 60 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{20181}(25,\cdot)$	$1$	$1$	$e\left(\frac{73}{93}\right)$	$e\left(\frac{53}{93}\right)$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{43}{93}\right)$	$e\left(\frac{28}{93}\right)$	$e\left(\frac{41}{93}\right)$	$e\left(\frac{13}{93}\right)$	$e\left(\frac{18}{31}\right)$	$e\left(\frac{77}{93}\right)$
$\chi_{20181}(625,\cdot)$	$1$	$1$	$e\left(\frac{53}{93}\right)$	$e\left(\frac{13}{93}\right)$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{22}{31}\right)$	$e\left(\frac{86}{93}\right)$	$e\left(\frac{56}{93}\right)$	$e\left(\frac{82}{93}\right)$	$e\left(\frac{26}{93}\right)$	$e\left(\frac{5}{31}\right)$	$e\left(\frac{61}{93}\right)$
$\chi_{20181}(676,\cdot)$	$1$	$1$	$e\left(\frac{76}{93}\right)$	$e\left(\frac{59}{93}\right)$	$e\left(\frac{7}{31}\right)$	$e\left(\frac{14}{31}\right)$	$e\left(\frac{4}{93}\right)$	$e\left(\frac{61}{93}\right)$	$e\left(\frac{86}{93}\right)$	$e\left(\frac{25}{93}\right)$	$e\left(\frac{6}{31}\right)$	$e\left(\frac{5}{93}\right)$
$\chi_{20181}(1276,\cdot)$	$1$	$1$	$e\left(\frac{68}{93}\right)$	$e\left(\frac{43}{93}\right)$	$e\left(\frac{3}{31}\right)$	$e\left(\frac{6}{31}\right)$	$e\left(\frac{77}{93}\right)$	$e\left(\frac{35}{93}\right)$	$e\left(\frac{28}{93}\right)$	$e\left(\frac{86}{93}\right)$	$e\left(\frac{7}{31}\right)$	$e\left(\frac{73}{93}\right)$
$\chi_{20181}(1327,\cdot)$	$1$	$1$	$e\left(\frac{79}{93}\right)$	$e\left(\frac{65}{93}\right)$	$e\left(\frac{24}{31}\right)$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{58}{93}\right)$	$e\left(\frac{1}{93}\right)$	$e\left(\frac{38}{93}\right)$	$e\left(\frac{37}{93}\right)$	$e\left(\frac{25}{31}\right)$	$e\left(\frac{26}{93}\right)$
$\chi_{20181}(1927,\cdot)$	$1$	$1$	$e\left(\frac{83}{93}\right)$	$e\left(\frac{73}{93}\right)$	$e\left(\frac{26}{31}\right)$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{68}{93}\right)$	$e\left(\frac{14}{93}\right)$	$e\left(\frac{67}{93}\right)$	$e\left(\frac{53}{93}\right)$	$e\left(\frac{9}{31}\right)$	$e\left(\frac{85}{93}\right)$
$\chi_{20181}(1978,\cdot)$	$1$	$1$	$e\left(\frac{82}{93}\right)$	$e\left(\frac{71}{93}\right)$	$e\left(\frac{10}{31}\right)$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{19}{93}\right)$	$e\left(\frac{34}{93}\right)$	$e\left(\frac{83}{93}\right)$	$e\left(\frac{49}{93}\right)$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{47}{93}\right)$
$\chi_{20181}(2578,\cdot)$	$1$	$1$	$e\left(\frac{5}{93}\right)$	$e\left(\frac{10}{93}\right)$	$e\left(\frac{18}{31}\right)$	$e\left(\frac{5}{31}\right)$	$e\left(\frac{59}{93}\right)$	$e\left(\frac{86}{93}\right)$	$e\left(\frac{13}{93}\right)$	$e\left(\frac{20}{93}\right)$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{4}{93}\right)$
$\chi_{20181}(2629,\cdot)$	$1$	$1$	$e\left(\frac{85}{93}\right)$	$e\left(\frac{77}{93}\right)$	$e\left(\frac{27}{31}\right)$	$e\left(\frac{23}{31}\right)$	$e\left(\frac{73}{93}\right)$	$e\left(\frac{67}{93}\right)$	$e\left(\frac{35}{93}\right)$	$e\left(\frac{61}{93}\right)$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{68}{93}\right)$
$\chi_{20181}(3229,\cdot)$	$1$	$1$	$e\left(\frac{20}{93}\right)$	$e\left(\frac{40}{93}\right)$	$e\left(\frac{10}{31}\right)$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{50}{93}\right)$	$e\left(\frac{65}{93}\right)$	$e\left(\frac{52}{93}\right)$	$e\left(\frac{80}{93}\right)$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{16}{93}\right)$
$\chi_{20181}(3280,\cdot)$	$1$	$1$	$e\left(\frac{88}{93}\right)$	$e\left(\frac{83}{93}\right)$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{26}{31}\right)$	$e\left(\frac{34}{93}\right)$	$e\left(\frac{7}{93}\right)$	$e\left(\frac{80}{93}\right)$	$e\left(\frac{73}{93}\right)$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{89}{93}\right)$
$\chi_{20181}(3880,\cdot)$	$1$	$1$	$e\left(\frac{35}{93}\right)$	$e\left(\frac{70}{93}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{41}{93}\right)$	$e\left(\frac{44}{93}\right)$	$e\left(\frac{91}{93}\right)$	$e\left(\frac{47}{93}\right)$	$e\left(\frac{15}{31}\right)$	$e\left(\frac{28}{93}\right)$
$\chi_{20181}(3931,\cdot)$	$1$	$1$	$e\left(\frac{91}{93}\right)$	$e\left(\frac{89}{93}\right)$	$e\left(\frac{30}{31}\right)$	$e\left(\frac{29}{31}\right)$	$e\left(\frac{88}{93}\right)$	$e\left(\frac{40}{93}\right)$	$e\left(\frac{32}{93}\right)$	$e\left(\frac{85}{93}\right)$	$e\left(\frac{8}{31}\right)$	$e\left(\frac{17}{93}\right)$
$\chi_{20181}(4531,\cdot)$	$1$	$1$	$e\left(\frac{50}{93}\right)$	$e\left(\frac{7}{93}\right)$	$e\left(\frac{25}{31}\right)$	$e\left(\frac{19}{31}\right)$	$e\left(\frac{32}{93}\right)$	$e\left(\frac{23}{93}\right)$	$e\left(\frac{37}{93}\right)$	$e\left(\frac{14}{93}\right)$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{40}{93}\right)$
$\chi_{20181}(4582,\cdot)$	$1$	$1$	$e\left(\frac{1}{93}\right)$	$e\left(\frac{2}{93}\right)$	$e\left(\frac{16}{31}\right)$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{49}{93}\right)$	$e\left(\frac{73}{93}\right)$	$e\left(\frac{77}{93}\right)$	$e\left(\frac{4}{93}\right)$	$e\left(\frac{27}{31}\right)$	$e\left(\frac{38}{93}\right)$
$\chi_{20181}(5182,\cdot)$	$1$	$1$	$e\left(\frac{65}{93}\right)$	$e\left(\frac{37}{93}\right)$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{3}{31}\right)$	$e\left(\frac{23}{93}\right)$	$e\left(\frac{2}{93}\right)$	$e\left(\frac{76}{93}\right)$	$e\left(\frac{74}{93}\right)$	$e\left(\frac{19}{31}\right)$	$e\left(\frac{52}{93}\right)$
$\chi_{20181}(5233,\cdot)$	$1$	$1$	$e\left(\frac{4}{93}\right)$	$e\left(\frac{8}{93}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{10}{93}\right)$	$e\left(\frac{13}{93}\right)$	$e\left(\frac{29}{93}\right)$	$e\left(\frac{16}{93}\right)$	$e\left(\frac{15}{31}\right)$	$e\left(\frac{59}{93}\right)$
$\chi_{20181}(5833,\cdot)$	$1$	$1$	$e\left(\frac{80}{93}\right)$	$e\left(\frac{67}{93}\right)$	$e\left(\frac{9}{31}\right)$	$e\left(\frac{18}{31}\right)$	$e\left(\frac{14}{93}\right)$	$e\left(\frac{74}{93}\right)$	$e\left(\frac{22}{93}\right)$	$e\left(\frac{41}{93}\right)$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{64}{93}\right)$
$\chi_{20181}(5884,\cdot)$	$1$	$1$	$e\left(\frac{7}{93}\right)$	$e\left(\frac{14}{93}\right)$	$e\left(\frac{19}{31}\right)$	$e\left(\frac{7}{31}\right)$	$e\left(\frac{64}{93}\right)$	$e\left(\frac{46}{93}\right)$	$e\left(\frac{74}{93}\right)$	$e\left(\frac{28}{93}\right)$	$e\left(\frac{3}{31}\right)$	$e\left(\frac{80}{93}\right)$
$\chi_{20181}(6484,\cdot)$	$1$	$1$	$e\left(\frac{2}{93}\right)$	$e\left(\frac{4}{93}\right)$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{5}{93}\right)$	$e\left(\frac{53}{93}\right)$	$e\left(\frac{61}{93}\right)$	$e\left(\frac{8}{93}\right)$	$e\left(\frac{23}{31}\right)$	$e\left(\frac{76}{93}\right)$
$\chi_{20181}(6535,\cdot)$	$1$	$1$	$e\left(\frac{10}{93}\right)$	$e\left(\frac{20}{93}\right)$	$e\left(\frac{5}{31}\right)$	$e\left(\frac{10}{31}\right)$	$e\left(\frac{25}{93}\right)$	$e\left(\frac{79}{93}\right)$	$e\left(\frac{26}{93}\right)$	$e\left(\frac{40}{93}\right)$	$e\left(\frac{22}{31}\right)$	$e\left(\frac{8}{93}\right)$
$\chi_{20181}(7135,\cdot)$	$1$	$1$	$e\left(\frac{17}{93}\right)$	$e\left(\frac{34}{93}\right)$	$e\left(\frac{24}{31}\right)$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{89}{93}\right)$	$e\left(\frac{32}{93}\right)$	$e\left(\frac{7}{93}\right)$	$e\left(\frac{68}{93}\right)$	$e\left(\frac{25}{31}\right)$	$e\left(\frac{88}{93}\right)$
$\chi_{20181}(7186,\cdot)$	$1$	$1$	$e\left(\frac{13}{93}\right)$	$e\left(\frac{26}{93}\right)$	$e\left(\frac{22}{31}\right)$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{79}{93}\right)$	$e\left(\frac{19}{93}\right)$	$e\left(\frac{71}{93}\right)$	$e\left(\frac{52}{93}\right)$	$e\left(\frac{10}{31}\right)$	$e\left(\frac{29}{93}\right)$
$\chi_{20181}(7786,\cdot)$	$1$	$1$	$e\left(\frac{32}{93}\right)$	$e\left(\frac{64}{93}\right)$	$e\left(\frac{16}{31}\right)$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{80}{93}\right)$	$e\left(\frac{11}{93}\right)$	$e\left(\frac{46}{93}\right)$	$e\left(\frac{35}{93}\right)$	$e\left(\frac{27}{31}\right)$	$e\left(\frac{7}{93}\right)$
$\chi_{20181}(7837,\cdot)$	$1$	$1$	$e\left(\frac{16}{93}\right)$	$e\left(\frac{32}{93}\right)$	$e\left(\frac{8}{31}\right)$	$e\left(\frac{16}{31}\right)$	$e\left(\frac{40}{93}\right)$	$e\left(\frac{52}{93}\right)$	$e\left(\frac{23}{93}\right)$	$e\left(\frac{64}{93}\right)$	$e\left(\frac{29}{31}\right)$	$e\left(\frac{50}{93}\right)$
$\chi_{20181}(8437,\cdot)$	$1$	$1$	$e\left(\frac{47}{93}\right)$	$e\left(\frac{1}{93}\right)$	$e\left(\frac{8}{31}\right)$	$e\left(\frac{16}{31}\right)$	$e\left(\frac{71}{93}\right)$	$e\left(\frac{83}{93}\right)$	$e\left(\frac{85}{93}\right)$	$e\left(\frac{2}{93}\right)$	$e\left(\frac{29}{31}\right)$	$e\left(\frac{19}{93}\right)$
$\chi_{20181}(8488,\cdot)$	$1$	$1$	$e\left(\frac{19}{93}\right)$	$e\left(\frac{38}{93}\right)$	$e\left(\frac{25}{31}\right)$	$e\left(\frac{19}{31}\right)$	$e\left(\frac{1}{93}\right)$	$e\left(\frac{85}{93}\right)$	$e\left(\frac{68}{93}\right)$	$e\left(\frac{76}{93}\right)$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{71}{93}\right)$
$\chi_{20181}(9139,\cdot)$	$1$	$1$	$e\left(\frac{22}{93}\right)$	$e\left(\frac{44}{93}\right)$	$e\left(\frac{11}{31}\right)$	$e\left(\frac{22}{31}\right)$	$e\left(\frac{55}{93}\right)$	$e\left(\frac{25}{93}\right)$	$e\left(\frac{20}{93}\right)$	$e\left(\frac{88}{93}\right)$	$e\left(\frac{5}{31}\right)$	$e\left(\frac{92}{93}\right)$
$\chi_{20181}(9739,\cdot)$	$1$	$1$	$e\left(\frac{77}{93}\right)$	$e\left(\frac{61}{93}\right)$	$e\left(\frac{23}{31}\right)$	$e\left(\frac{15}{31}\right)$	$e\left(\frac{53}{93}\right)$	$e\left(\frac{41}{93}\right)$	$e\left(\frac{70}{93}\right)$	$e\left(\frac{29}{93}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{43}{93}\right)$
$\chi_{20181}(9790,\cdot)$	$1$	$1$	$e\left(\frac{25}{93}\right)$	$e\left(\frac{50}{93}\right)$	$e\left(\frac{28}{31}\right)$	$e\left(\frac{25}{31}\right)$	$e\left(\frac{16}{93}\right)$	$e\left(\frac{58}{93}\right)$	$e\left(\frac{65}{93}\right)$	$e\left(\frac{7}{93}\right)$	$e\left(\frac{24}{31}\right)$	$e\left(\frac{20}{93}\right)$
$\chi_{20181}(10390,\cdot)$	$1$	$1$	$e\left(\frac{92}{93}\right)$	$e\left(\frac{91}{93}\right)$	$e\left(\frac{15}{31}\right)$	$e\left(\frac{30}{31}\right)$	$e\left(\frac{44}{93}\right)$	$e\left(\frac{20}{93}\right)$	$e\left(\frac{16}{93}\right)$	$e\left(\frac{89}{93}\right)$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{55}{93}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{20181}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{93}\right)\)	\(e\left(\frac{53}{93}\right)\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{43}{93}\right)\)	\(e\left(\frac{28}{93}\right)\)	\(e\left(\frac{41}{93}\right)\)	\(e\left(\frac{13}{93}\right)\)	\(e\left(\frac{18}{31}\right)\)	\(e\left(\frac{77}{93}\right)\)
\(\chi_{20181}(625,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{93}\right)\)	\(e\left(\frac{13}{93}\right)\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{22}{31}\right)\)	\(e\left(\frac{86}{93}\right)\)	\(e\left(\frac{56}{93}\right)\)	\(e\left(\frac{82}{93}\right)\)	\(e\left(\frac{26}{93}\right)\)	\(e\left(\frac{5}{31}\right)\)	\(e\left(\frac{61}{93}\right)\)
\(\chi_{20181}(676,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{76}{93}\right)\)	\(e\left(\frac{59}{93}\right)\)	\(e\left(\frac{7}{31}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(e\left(\frac{4}{93}\right)\)	\(e\left(\frac{61}{93}\right)\)	\(e\left(\frac{86}{93}\right)\)	\(e\left(\frac{25}{93}\right)\)	\(e\left(\frac{6}{31}\right)\)	\(e\left(\frac{5}{93}\right)\)
\(\chi_{20181}(1276,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{93}\right)\)	\(e\left(\frac{43}{93}\right)\)	\(e\left(\frac{3}{31}\right)\)	\(e\left(\frac{6}{31}\right)\)	\(e\left(\frac{77}{93}\right)\)	\(e\left(\frac{35}{93}\right)\)	\(e\left(\frac{28}{93}\right)\)	\(e\left(\frac{86}{93}\right)\)	\(e\left(\frac{7}{31}\right)\)	\(e\left(\frac{73}{93}\right)\)
\(\chi_{20181}(1327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{93}\right)\)	\(e\left(\frac{65}{93}\right)\)	\(e\left(\frac{24}{31}\right)\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{58}{93}\right)\)	\(e\left(\frac{1}{93}\right)\)	\(e\left(\frac{38}{93}\right)\)	\(e\left(\frac{37}{93}\right)\)	\(e\left(\frac{25}{31}\right)\)	\(e\left(\frac{26}{93}\right)\)
\(\chi_{20181}(1927,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{93}\right)\)	\(e\left(\frac{73}{93}\right)\)	\(e\left(\frac{26}{31}\right)\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{68}{93}\right)\)	\(e\left(\frac{14}{93}\right)\)	\(e\left(\frac{67}{93}\right)\)	\(e\left(\frac{53}{93}\right)\)	\(e\left(\frac{9}{31}\right)\)	\(e\left(\frac{85}{93}\right)\)
\(\chi_{20181}(1978,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{93}\right)\)	\(e\left(\frac{71}{93}\right)\)	\(e\left(\frac{10}{31}\right)\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{19}{93}\right)\)	\(e\left(\frac{34}{93}\right)\)	\(e\left(\frac{83}{93}\right)\)	\(e\left(\frac{49}{93}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{47}{93}\right)\)
\(\chi_{20181}(2578,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{93}\right)\)	\(e\left(\frac{10}{93}\right)\)	\(e\left(\frac{18}{31}\right)\)	\(e\left(\frac{5}{31}\right)\)	\(e\left(\frac{59}{93}\right)\)	\(e\left(\frac{86}{93}\right)\)	\(e\left(\frac{13}{93}\right)\)	\(e\left(\frac{20}{93}\right)\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{4}{93}\right)\)
\(\chi_{20181}(2629,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{93}\right)\)	\(e\left(\frac{77}{93}\right)\)	\(e\left(\frac{27}{31}\right)\)	\(e\left(\frac{23}{31}\right)\)	\(e\left(\frac{73}{93}\right)\)	\(e\left(\frac{67}{93}\right)\)	\(e\left(\frac{35}{93}\right)\)	\(e\left(\frac{61}{93}\right)\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{68}{93}\right)\)
\(\chi_{20181}(3229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{93}\right)\)	\(e\left(\frac{40}{93}\right)\)	\(e\left(\frac{10}{31}\right)\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{50}{93}\right)\)	\(e\left(\frac{65}{93}\right)\)	\(e\left(\frac{52}{93}\right)\)	\(e\left(\frac{80}{93}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{16}{93}\right)\)
\(\chi_{20181}(3280,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{88}{93}\right)\)	\(e\left(\frac{83}{93}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{26}{31}\right)\)	\(e\left(\frac{34}{93}\right)\)	\(e\left(\frac{7}{93}\right)\)	\(e\left(\frac{80}{93}\right)\)	\(e\left(\frac{73}{93}\right)\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{89}{93}\right)\)
\(\chi_{20181}(3880,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{93}\right)\)	\(e\left(\frac{70}{93}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{41}{93}\right)\)	\(e\left(\frac{44}{93}\right)\)	\(e\left(\frac{91}{93}\right)\)	\(e\left(\frac{47}{93}\right)\)	\(e\left(\frac{15}{31}\right)\)	\(e\left(\frac{28}{93}\right)\)
\(\chi_{20181}(3931,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{93}\right)\)	\(e\left(\frac{89}{93}\right)\)	\(e\left(\frac{30}{31}\right)\)	\(e\left(\frac{29}{31}\right)\)	\(e\left(\frac{88}{93}\right)\)	\(e\left(\frac{40}{93}\right)\)	\(e\left(\frac{32}{93}\right)\)	\(e\left(\frac{85}{93}\right)\)	\(e\left(\frac{8}{31}\right)\)	\(e\left(\frac{17}{93}\right)\)
\(\chi_{20181}(4531,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{50}{93}\right)\)	\(e\left(\frac{7}{93}\right)\)	\(e\left(\frac{25}{31}\right)\)	\(e\left(\frac{19}{31}\right)\)	\(e\left(\frac{32}{93}\right)\)	\(e\left(\frac{23}{93}\right)\)	\(e\left(\frac{37}{93}\right)\)	\(e\left(\frac{14}{93}\right)\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{40}{93}\right)\)
\(\chi_{20181}(4582,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{93}\right)\)	\(e\left(\frac{2}{93}\right)\)	\(e\left(\frac{16}{31}\right)\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{49}{93}\right)\)	\(e\left(\frac{73}{93}\right)\)	\(e\left(\frac{77}{93}\right)\)	\(e\left(\frac{4}{93}\right)\)	\(e\left(\frac{27}{31}\right)\)	\(e\left(\frac{38}{93}\right)\)
\(\chi_{20181}(5182,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{93}\right)\)	\(e\left(\frac{37}{93}\right)\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{3}{31}\right)\)	\(e\left(\frac{23}{93}\right)\)	\(e\left(\frac{2}{93}\right)\)	\(e\left(\frac{76}{93}\right)\)	\(e\left(\frac{74}{93}\right)\)	\(e\left(\frac{19}{31}\right)\)	\(e\left(\frac{52}{93}\right)\)
\(\chi_{20181}(5233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{93}\right)\)	\(e\left(\frac{8}{93}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{10}{93}\right)\)	\(e\left(\frac{13}{93}\right)\)	\(e\left(\frac{29}{93}\right)\)	\(e\left(\frac{16}{93}\right)\)	\(e\left(\frac{15}{31}\right)\)	\(e\left(\frac{59}{93}\right)\)
\(\chi_{20181}(5833,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{80}{93}\right)\)	\(e\left(\frac{67}{93}\right)\)	\(e\left(\frac{9}{31}\right)\)	\(e\left(\frac{18}{31}\right)\)	\(e\left(\frac{14}{93}\right)\)	\(e\left(\frac{74}{93}\right)\)	\(e\left(\frac{22}{93}\right)\)	\(e\left(\frac{41}{93}\right)\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{64}{93}\right)\)
\(\chi_{20181}(5884,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{93}\right)\)	\(e\left(\frac{14}{93}\right)\)	\(e\left(\frac{19}{31}\right)\)	\(e\left(\frac{7}{31}\right)\)	\(e\left(\frac{64}{93}\right)\)	\(e\left(\frac{46}{93}\right)\)	\(e\left(\frac{74}{93}\right)\)	\(e\left(\frac{28}{93}\right)\)	\(e\left(\frac{3}{31}\right)\)	\(e\left(\frac{80}{93}\right)\)
\(\chi_{20181}(6484,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{93}\right)\)	\(e\left(\frac{4}{93}\right)\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{5}{93}\right)\)	\(e\left(\frac{53}{93}\right)\)	\(e\left(\frac{61}{93}\right)\)	\(e\left(\frac{8}{93}\right)\)	\(e\left(\frac{23}{31}\right)\)	\(e\left(\frac{76}{93}\right)\)
\(\chi_{20181}(6535,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{93}\right)\)	\(e\left(\frac{20}{93}\right)\)	\(e\left(\frac{5}{31}\right)\)	\(e\left(\frac{10}{31}\right)\)	\(e\left(\frac{25}{93}\right)\)	\(e\left(\frac{79}{93}\right)\)	\(e\left(\frac{26}{93}\right)\)	\(e\left(\frac{40}{93}\right)\)	\(e\left(\frac{22}{31}\right)\)	\(e\left(\frac{8}{93}\right)\)
\(\chi_{20181}(7135,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{93}\right)\)	\(e\left(\frac{34}{93}\right)\)	\(e\left(\frac{24}{31}\right)\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{89}{93}\right)\)	\(e\left(\frac{32}{93}\right)\)	\(e\left(\frac{7}{93}\right)\)	\(e\left(\frac{68}{93}\right)\)	\(e\left(\frac{25}{31}\right)\)	\(e\left(\frac{88}{93}\right)\)
\(\chi_{20181}(7186,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{93}\right)\)	\(e\left(\frac{26}{93}\right)\)	\(e\left(\frac{22}{31}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{79}{93}\right)\)	\(e\left(\frac{19}{93}\right)\)	\(e\left(\frac{71}{93}\right)\)	\(e\left(\frac{52}{93}\right)\)	\(e\left(\frac{10}{31}\right)\)	\(e\left(\frac{29}{93}\right)\)
\(\chi_{20181}(7786,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{93}\right)\)	\(e\left(\frac{64}{93}\right)\)	\(e\left(\frac{16}{31}\right)\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{80}{93}\right)\)	\(e\left(\frac{11}{93}\right)\)	\(e\left(\frac{46}{93}\right)\)	\(e\left(\frac{35}{93}\right)\)	\(e\left(\frac{27}{31}\right)\)	\(e\left(\frac{7}{93}\right)\)
\(\chi_{20181}(7837,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{93}\right)\)	\(e\left(\frac{32}{93}\right)\)	\(e\left(\frac{8}{31}\right)\)	\(e\left(\frac{16}{31}\right)\)	\(e\left(\frac{40}{93}\right)\)	\(e\left(\frac{52}{93}\right)\)	\(e\left(\frac{23}{93}\right)\)	\(e\left(\frac{64}{93}\right)\)	\(e\left(\frac{29}{31}\right)\)	\(e\left(\frac{50}{93}\right)\)
\(\chi_{20181}(8437,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{93}\right)\)	\(e\left(\frac{1}{93}\right)\)	\(e\left(\frac{8}{31}\right)\)	\(e\left(\frac{16}{31}\right)\)	\(e\left(\frac{71}{93}\right)\)	\(e\left(\frac{83}{93}\right)\)	\(e\left(\frac{85}{93}\right)\)	\(e\left(\frac{2}{93}\right)\)	\(e\left(\frac{29}{31}\right)\)	\(e\left(\frac{19}{93}\right)\)
\(\chi_{20181}(8488,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{93}\right)\)	\(e\left(\frac{38}{93}\right)\)	\(e\left(\frac{25}{31}\right)\)	\(e\left(\frac{19}{31}\right)\)	\(e\left(\frac{1}{93}\right)\)	\(e\left(\frac{85}{93}\right)\)	\(e\left(\frac{68}{93}\right)\)	\(e\left(\frac{76}{93}\right)\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{71}{93}\right)\)
\(\chi_{20181}(9139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{93}\right)\)	\(e\left(\frac{44}{93}\right)\)	\(e\left(\frac{11}{31}\right)\)	\(e\left(\frac{22}{31}\right)\)	\(e\left(\frac{55}{93}\right)\)	\(e\left(\frac{25}{93}\right)\)	\(e\left(\frac{20}{93}\right)\)	\(e\left(\frac{88}{93}\right)\)	\(e\left(\frac{5}{31}\right)\)	\(e\left(\frac{92}{93}\right)\)
\(\chi_{20181}(9739,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{93}\right)\)	\(e\left(\frac{61}{93}\right)\)	\(e\left(\frac{23}{31}\right)\)	\(e\left(\frac{15}{31}\right)\)	\(e\left(\frac{53}{93}\right)\)	\(e\left(\frac{41}{93}\right)\)	\(e\left(\frac{70}{93}\right)\)	\(e\left(\frac{29}{93}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{43}{93}\right)\)
\(\chi_{20181}(9790,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{93}\right)\)	\(e\left(\frac{50}{93}\right)\)	\(e\left(\frac{28}{31}\right)\)	\(e\left(\frac{25}{31}\right)\)	\(e\left(\frac{16}{93}\right)\)	\(e\left(\frac{58}{93}\right)\)	\(e\left(\frac{65}{93}\right)\)	\(e\left(\frac{7}{93}\right)\)	\(e\left(\frac{24}{31}\right)\)	\(e\left(\frac{20}{93}\right)\)
\(\chi_{20181}(10390,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{92}{93}\right)\)	\(e\left(\frac{91}{93}\right)\)	\(e\left(\frac{15}{31}\right)\)	\(e\left(\frac{30}{31}\right)\)	\(e\left(\frac{44}{93}\right)\)	\(e\left(\frac{20}{93}\right)\)	\(e\left(\frac{16}{93}\right)\)	\(e\left(\frac{89}{93}\right)\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{55}{93}\right)\)

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First 31 of 60 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	20181.dl
Modulus	$20181$
Conductor	$6727$
Order	$93$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(20181\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(6727\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(93\)	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:	no, induced from 6727.bt	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);