LMFDB - Dirichlet character orbit 9802.bt

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9802, base_ring=CyclotomicField(78)) M = H._module chi = DirichletCharacter(H, M([68,39])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(289, 9802)) 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("9802.289"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$9802$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$4901$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$78$	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 4901.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:	$\Q(\zeta_{39})$	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 78 polynomial	comment:Fixed field sage:chi.fixed_field()

Characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{9802}(289,\cdot)$	$1$	$1$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{9802}(347,\cdot)$	$1$	$1$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{9802}(1043,\cdot)$	$1$	$1$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{9802}(1101,\cdot)$	$1$	$1$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{9802}(1797,\cdot)$	$1$	$1$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{9802}(1855,\cdot)$	$1$	$1$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{9802}(2551,\cdot)$	$1$	$1$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{9802}(2609,\cdot)$	$1$	$1$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{9802}(3305,\cdot)$	$1$	$1$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{9802}(3363,\cdot)$	$1$	$1$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{9802}(4059,\cdot)$	$1$	$1$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{9802}(4117,\cdot)$	$1$	$1$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{9802}(4813,\cdot)$	$1$	$1$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{9802}(4871,\cdot)$	$1$	$1$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{9802}(5567,\cdot)$	$1$	$1$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{9802}(5625,\cdot)$	$1$	$1$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{9802}(6321,\cdot)$	$1$	$1$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{9802}(6379,\cdot)$	$1$	$1$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{9802}(7133,\cdot)$	$1$	$1$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{9802}(7829,\cdot)$	$1$	$1$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{9802}(7887,\cdot)$	$1$	$1$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{9802}(8583,\cdot)$	$1$	$1$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{9802}(9337,\cdot)$	$1$	$1$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{9802}(9395,\cdot)$	$1$	$1$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{2}{3}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{9802}(289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{9802}(347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{9802}(1043,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{9802}(1101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{9802}(1797,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{9802}(1855,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{9802}(2551,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{9802}(2609,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{9802}(3305,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{9802}(3363,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{9802}(4059,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{9802}(4117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{9802}(4813,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{9802}(4871,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{9802}(5567,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{9802}(5625,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{9802}(6321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{9802}(6379,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{9802}(7133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{9802}(7829,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{9802}(7887,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{9802}(8583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{9802}(9337,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{9802}(9395,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)

Introduction

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Groups

Database

Properties

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Basic properties

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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	9802.bt
Modulus	$9802$
Conductor	$4901$
Order	$78$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(9802\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(4901\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(78\)	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 4901.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);