LMFDB - Dirichlet character orbit 9802.bp

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9802, base_ring=CyclotomicField(52)) M = H._module chi = DirichletCharacter(H, M([51,39])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(655, 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("9802.655"); 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:	$52$	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.bs	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:	$\Q(\zeta_{52})$	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 52 polynomial	comment:Fixed field sage:chi.fixed_field()

Characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{9802}(655,\cdot)$	$1$	$1$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{49}{52}\right)$	$-1$	$e\left(\frac{4}{13}\right)$	$-1$
$\chi_{9802}(853,\cdot)$	$1$	$1$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{3}{52}\right)$	$-1$	$e\left(\frac{9}{13}\right)$	$-1$
$\chi_{9802}(1409,\cdot)$	$1$	$1$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{33}{52}\right)$	$-1$	$e\left(\frac{8}{13}\right)$	$-1$
$\chi_{9802}(1607,\cdot)$	$1$	$1$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{19}{52}\right)$	$-1$	$e\left(\frac{5}{13}\right)$	$-1$
$\chi_{9802}(2163,\cdot)$	$1$	$1$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{17}{52}\right)$	$-1$	$e\left(\frac{12}{13}\right)$	$-1$
$\chi_{9802}(2361,\cdot)$	$1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{35}{52}\right)$	$-1$	$e\left(\frac{1}{13}\right)$	$-1$
$\chi_{9802}(2917,\cdot)$	$1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{1}{52}\right)$	$-1$	$e\left(\frac{3}{13}\right)$	$-1$
$\chi_{9802}(3115,\cdot)$	$1$	$1$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{51}{52}\right)$	$-1$	$e\left(\frac{10}{13}\right)$	$-1$
$\chi_{9802}(3671,\cdot)$	$1$	$1$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{37}{52}\right)$	$-1$	$e\left(\frac{7}{13}\right)$	$-1$
$\chi_{9802}(3869,\cdot)$	$1$	$1$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{15}{52}\right)$	$-1$	$e\left(\frac{6}{13}\right)$	$-1$
$\chi_{9802}(4425,\cdot)$	$1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{21}{52}\right)$	$-1$	$e\left(\frac{11}{13}\right)$	$-1$
$\chi_{9802}(4623,\cdot)$	$1$	$1$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{31}{52}\right)$	$-1$	$e\left(\frac{2}{13}\right)$	$-1$
$\chi_{9802}(5179,\cdot)$	$1$	$1$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{5}{52}\right)$	$-1$	$e\left(\frac{2}{13}\right)$	$-1$
$\chi_{9802}(5377,\cdot)$	$1$	$1$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{47}{52}\right)$	$-1$	$e\left(\frac{11}{13}\right)$	$-1$
$\chi_{9802}(5933,\cdot)$	$1$	$1$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{41}{52}\right)$	$-1$	$e\left(\frac{6}{13}\right)$	$-1$
$\chi_{9802}(6131,\cdot)$	$1$	$1$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{11}{52}\right)$	$-1$	$e\left(\frac{7}{13}\right)$	$-1$
$\chi_{9802}(6687,\cdot)$	$1$	$1$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{25}{52}\right)$	$-1$	$e\left(\frac{10}{13}\right)$	$-1$
$\chi_{9802}(6885,\cdot)$	$1$	$1$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{27}{52}\right)$	$-1$	$e\left(\frac{3}{13}\right)$	$-1$
$\chi_{9802}(7441,\cdot)$	$1$	$1$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{9}{52}\right)$	$-1$	$e\left(\frac{1}{13}\right)$	$-1$
$\chi_{9802}(7639,\cdot)$	$1$	$1$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{43}{52}\right)$	$-1$	$e\left(\frac{12}{13}\right)$	$-1$
$\chi_{9802}(8195,\cdot)$	$1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{45}{52}\right)$	$-1$	$e\left(\frac{5}{13}\right)$	$-1$
$\chi_{9802}(8393,\cdot)$	$1$	$1$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{7}{52}\right)$	$-1$	$e\left(\frac{8}{13}\right)$	$-1$
$\chi_{9802}(8949,\cdot)$	$1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{29}{52}\right)$	$-1$	$e\left(\frac{9}{13}\right)$	$-1$
$\chi_{9802}(9147,\cdot)$	$1$	$1$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{23}{52}\right)$	$-1$	$e\left(\frac{4}{13}\right)$	$-1$

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Character	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{9802}(655,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(-1\)	\(e\left(\frac{4}{13}\right)\)	\(-1\)
\(\chi_{9802}(853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(-1\)	\(e\left(\frac{9}{13}\right)\)	\(-1\)
\(\chi_{9802}(1409,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(-1\)	\(e\left(\frac{8}{13}\right)\)	\(-1\)
\(\chi_{9802}(1607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(-1\)	\(e\left(\frac{5}{13}\right)\)	\(-1\)
\(\chi_{9802}(2163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(-1\)	\(e\left(\frac{12}{13}\right)\)	\(-1\)
\(\chi_{9802}(2361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(-1\)	\(e\left(\frac{1}{13}\right)\)	\(-1\)
\(\chi_{9802}(2917,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(-1\)	\(e\left(\frac{3}{13}\right)\)	\(-1\)
\(\chi_{9802}(3115,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(-1\)	\(e\left(\frac{10}{13}\right)\)	\(-1\)
\(\chi_{9802}(3671,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(-1\)	\(e\left(\frac{7}{13}\right)\)	\(-1\)
\(\chi_{9802}(3869,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(-1\)	\(e\left(\frac{6}{13}\right)\)	\(-1\)
\(\chi_{9802}(4425,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(-1\)	\(e\left(\frac{11}{13}\right)\)	\(-1\)
\(\chi_{9802}(4623,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(-1\)	\(e\left(\frac{2}{13}\right)\)	\(-1\)
\(\chi_{9802}(5179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(-1\)	\(e\left(\frac{2}{13}\right)\)	\(-1\)
\(\chi_{9802}(5377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(-1\)	\(e\left(\frac{11}{13}\right)\)	\(-1\)
\(\chi_{9802}(5933,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(-1\)	\(e\left(\frac{6}{13}\right)\)	\(-1\)
\(\chi_{9802}(6131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(-1\)	\(e\left(\frac{7}{13}\right)\)	\(-1\)
\(\chi_{9802}(6687,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(-1\)	\(e\left(\frac{10}{13}\right)\)	\(-1\)
\(\chi_{9802}(6885,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(-1\)	\(e\left(\frac{3}{13}\right)\)	\(-1\)
\(\chi_{9802}(7441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(-1\)	\(e\left(\frac{1}{13}\right)\)	\(-1\)
\(\chi_{9802}(7639,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(-1\)	\(e\left(\frac{12}{13}\right)\)	\(-1\)
\(\chi_{9802}(8195,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(-1\)	\(e\left(\frac{5}{13}\right)\)	\(-1\)
\(\chi_{9802}(8393,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(-1\)	\(e\left(\frac{8}{13}\right)\)	\(-1\)
\(\chi_{9802}(8949,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(-1\)	\(e\left(\frac{9}{13}\right)\)	\(-1\)
\(\chi_{9802}(9147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(-1\)	\(e\left(\frac{4}{13}\right)\)	\(-1\)

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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.bp
Modulus	$9802$
Conductor	$4901$
Order	$52$
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:	\(52\)	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.bs	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);