LMFDB - Dirichlet character orbit 13254.i

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13254, base_ring=CyclotomicField(94)) M = H._module chi = DirichletCharacter(H, M([0,82])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(283, 13254)) 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("13254.283"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$13254$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$2209$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$47$	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 2209.e	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:	$\Q(\zeta_{47})$
Fixed field:	Number field defined by a degree 47 polynomial

First 31 of 46 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{13254}(283,\cdot)$	$1$	$1$	$e\left(\frac{41}{47}\right)$	$e\left(\frac{13}{47}\right)$	$e\left(\frac{10}{47}\right)$	$e\left(\frac{10}{47}\right)$	$e\left(\frac{14}{47}\right)$	$e\left(\frac{41}{47}\right)$	$e\left(\frac{24}{47}\right)$	$e\left(\frac{35}{47}\right)$	$e\left(\frac{36}{47}\right)$	$e\left(\frac{40}{47}\right)$
$\chi_{13254}(565,\cdot)$	$1$	$1$	$e\left(\frac{35}{47}\right)$	$e\left(\frac{26}{47}\right)$	$e\left(\frac{20}{47}\right)$	$e\left(\frac{20}{47}\right)$	$e\left(\frac{28}{47}\right)$	$e\left(\frac{35}{47}\right)$	$e\left(\frac{1}{47}\right)$	$e\left(\frac{23}{47}\right)$	$e\left(\frac{25}{47}\right)$	$e\left(\frac{33}{47}\right)$
$\chi_{13254}(847,\cdot)$	$1$	$1$	$e\left(\frac{29}{47}\right)$	$e\left(\frac{39}{47}\right)$	$e\left(\frac{30}{47}\right)$	$e\left(\frac{30}{47}\right)$	$e\left(\frac{42}{47}\right)$	$e\left(\frac{29}{47}\right)$	$e\left(\frac{25}{47}\right)$	$e\left(\frac{11}{47}\right)$	$e\left(\frac{14}{47}\right)$	$e\left(\frac{26}{47}\right)$
$\chi_{13254}(1129,\cdot)$	$1$	$1$	$e\left(\frac{23}{47}\right)$	$e\left(\frac{5}{47}\right)$	$e\left(\frac{40}{47}\right)$	$e\left(\frac{40}{47}\right)$	$e\left(\frac{9}{47}\right)$	$e\left(\frac{23}{47}\right)$	$e\left(\frac{2}{47}\right)$	$e\left(\frac{46}{47}\right)$	$e\left(\frac{3}{47}\right)$	$e\left(\frac{19}{47}\right)$
$\chi_{13254}(1411,\cdot)$	$1$	$1$	$e\left(\frac{17}{47}\right)$	$e\left(\frac{18}{47}\right)$	$e\left(\frac{3}{47}\right)$	$e\left(\frac{3}{47}\right)$	$e\left(\frac{23}{47}\right)$	$e\left(\frac{17}{47}\right)$	$e\left(\frac{26}{47}\right)$	$e\left(\frac{34}{47}\right)$	$e\left(\frac{39}{47}\right)$	$e\left(\frac{12}{47}\right)$
$\chi_{13254}(1693,\cdot)$	$1$	$1$	$e\left(\frac{11}{47}\right)$	$e\left(\frac{31}{47}\right)$	$e\left(\frac{13}{47}\right)$	$e\left(\frac{13}{47}\right)$	$e\left(\frac{37}{47}\right)$	$e\left(\frac{11}{47}\right)$	$e\left(\frac{3}{47}\right)$	$e\left(\frac{22}{47}\right)$	$e\left(\frac{28}{47}\right)$	$e\left(\frac{5}{47}\right)$
$\chi_{13254}(1975,\cdot)$	$1$	$1$	$e\left(\frac{5}{47}\right)$	$e\left(\frac{44}{47}\right)$	$e\left(\frac{23}{47}\right)$	$e\left(\frac{23}{47}\right)$	$e\left(\frac{4}{47}\right)$	$e\left(\frac{5}{47}\right)$	$e\left(\frac{27}{47}\right)$	$e\left(\frac{10}{47}\right)$	$e\left(\frac{17}{47}\right)$	$e\left(\frac{45}{47}\right)$
$\chi_{13254}(2257,\cdot)$	$1$	$1$	$e\left(\frac{46}{47}\right)$	$e\left(\frac{10}{47}\right)$	$e\left(\frac{33}{47}\right)$	$e\left(\frac{33}{47}\right)$	$e\left(\frac{18}{47}\right)$	$e\left(\frac{46}{47}\right)$	$e\left(\frac{4}{47}\right)$	$e\left(\frac{45}{47}\right)$	$e\left(\frac{6}{47}\right)$	$e\left(\frac{38}{47}\right)$
$\chi_{13254}(2539,\cdot)$	$1$	$1$	$e\left(\frac{40}{47}\right)$	$e\left(\frac{23}{47}\right)$	$e\left(\frac{43}{47}\right)$	$e\left(\frac{43}{47}\right)$	$e\left(\frac{32}{47}\right)$	$e\left(\frac{40}{47}\right)$	$e\left(\frac{28}{47}\right)$	$e\left(\frac{33}{47}\right)$	$e\left(\frac{42}{47}\right)$	$e\left(\frac{31}{47}\right)$
$\chi_{13254}(2821,\cdot)$	$1$	$1$	$e\left(\frac{34}{47}\right)$	$e\left(\frac{36}{47}\right)$	$e\left(\frac{6}{47}\right)$	$e\left(\frac{6}{47}\right)$	$e\left(\frac{46}{47}\right)$	$e\left(\frac{34}{47}\right)$	$e\left(\frac{5}{47}\right)$	$e\left(\frac{21}{47}\right)$	$e\left(\frac{31}{47}\right)$	$e\left(\frac{24}{47}\right)$
$\chi_{13254}(3103,\cdot)$	$1$	$1$	$e\left(\frac{28}{47}\right)$	$e\left(\frac{2}{47}\right)$	$e\left(\frac{16}{47}\right)$	$e\left(\frac{16}{47}\right)$	$e\left(\frac{13}{47}\right)$	$e\left(\frac{28}{47}\right)$	$e\left(\frac{29}{47}\right)$	$e\left(\frac{9}{47}\right)$	$e\left(\frac{20}{47}\right)$	$e\left(\frac{17}{47}\right)$
$\chi_{13254}(3385,\cdot)$	$1$	$1$	$e\left(\frac{22}{47}\right)$	$e\left(\frac{15}{47}\right)$	$e\left(\frac{26}{47}\right)$	$e\left(\frac{26}{47}\right)$	$e\left(\frac{27}{47}\right)$	$e\left(\frac{22}{47}\right)$	$e\left(\frac{6}{47}\right)$	$e\left(\frac{44}{47}\right)$	$e\left(\frac{9}{47}\right)$	$e\left(\frac{10}{47}\right)$
$\chi_{13254}(3667,\cdot)$	$1$	$1$	$e\left(\frac{16}{47}\right)$	$e\left(\frac{28}{47}\right)$	$e\left(\frac{36}{47}\right)$	$e\left(\frac{36}{47}\right)$	$e\left(\frac{41}{47}\right)$	$e\left(\frac{16}{47}\right)$	$e\left(\frac{30}{47}\right)$	$e\left(\frac{32}{47}\right)$	$e\left(\frac{45}{47}\right)$	$e\left(\frac{3}{47}\right)$
$\chi_{13254}(3949,\cdot)$	$1$	$1$	$e\left(\frac{10}{47}\right)$	$e\left(\frac{41}{47}\right)$	$e\left(\frac{46}{47}\right)$	$e\left(\frac{46}{47}\right)$	$e\left(\frac{8}{47}\right)$	$e\left(\frac{10}{47}\right)$	$e\left(\frac{7}{47}\right)$	$e\left(\frac{20}{47}\right)$	$e\left(\frac{34}{47}\right)$	$e\left(\frac{43}{47}\right)$
$\chi_{13254}(4231,\cdot)$	$1$	$1$	$e\left(\frac{4}{47}\right)$	$e\left(\frac{7}{47}\right)$	$e\left(\frac{9}{47}\right)$	$e\left(\frac{9}{47}\right)$	$e\left(\frac{22}{47}\right)$	$e\left(\frac{4}{47}\right)$	$e\left(\frac{31}{47}\right)$	$e\left(\frac{8}{47}\right)$	$e\left(\frac{23}{47}\right)$	$e\left(\frac{36}{47}\right)$
$\chi_{13254}(4513,\cdot)$	$1$	$1$	$e\left(\frac{45}{47}\right)$	$e\left(\frac{20}{47}\right)$	$e\left(\frac{19}{47}\right)$	$e\left(\frac{19}{47}\right)$	$e\left(\frac{36}{47}\right)$	$e\left(\frac{45}{47}\right)$	$e\left(\frac{8}{47}\right)$	$e\left(\frac{43}{47}\right)$	$e\left(\frac{12}{47}\right)$	$e\left(\frac{29}{47}\right)$
$\chi_{13254}(4795,\cdot)$	$1$	$1$	$e\left(\frac{39}{47}\right)$	$e\left(\frac{33}{47}\right)$	$e\left(\frac{29}{47}\right)$	$e\left(\frac{29}{47}\right)$	$e\left(\frac{3}{47}\right)$	$e\left(\frac{39}{47}\right)$	$e\left(\frac{32}{47}\right)$	$e\left(\frac{31}{47}\right)$	$e\left(\frac{1}{47}\right)$	$e\left(\frac{22}{47}\right)$
$\chi_{13254}(5077,\cdot)$	$1$	$1$	$e\left(\frac{33}{47}\right)$	$e\left(\frac{46}{47}\right)$	$e\left(\frac{39}{47}\right)$	$e\left(\frac{39}{47}\right)$	$e\left(\frac{17}{47}\right)$	$e\left(\frac{33}{47}\right)$	$e\left(\frac{9}{47}\right)$	$e\left(\frac{19}{47}\right)$	$e\left(\frac{37}{47}\right)$	$e\left(\frac{15}{47}\right)$
$\chi_{13254}(5359,\cdot)$	$1$	$1$	$e\left(\frac{27}{47}\right)$	$e\left(\frac{12}{47}\right)$	$e\left(\frac{2}{47}\right)$	$e\left(\frac{2}{47}\right)$	$e\left(\frac{31}{47}\right)$	$e\left(\frac{27}{47}\right)$	$e\left(\frac{33}{47}\right)$	$e\left(\frac{7}{47}\right)$	$e\left(\frac{26}{47}\right)$	$e\left(\frac{8}{47}\right)$
$\chi_{13254}(5641,\cdot)$	$1$	$1$	$e\left(\frac{21}{47}\right)$	$e\left(\frac{25}{47}\right)$	$e\left(\frac{12}{47}\right)$	$e\left(\frac{12}{47}\right)$	$e\left(\frac{45}{47}\right)$	$e\left(\frac{21}{47}\right)$	$e\left(\frac{10}{47}\right)$	$e\left(\frac{42}{47}\right)$	$e\left(\frac{15}{47}\right)$	$e\left(\frac{1}{47}\right)$
$\chi_{13254}(5923,\cdot)$	$1$	$1$	$e\left(\frac{15}{47}\right)$	$e\left(\frac{38}{47}\right)$	$e\left(\frac{22}{47}\right)$	$e\left(\frac{22}{47}\right)$	$e\left(\frac{12}{47}\right)$	$e\left(\frac{15}{47}\right)$	$e\left(\frac{34}{47}\right)$	$e\left(\frac{30}{47}\right)$	$e\left(\frac{4}{47}\right)$	$e\left(\frac{41}{47}\right)$
$\chi_{13254}(6205,\cdot)$	$1$	$1$	$e\left(\frac{9}{47}\right)$	$e\left(\frac{4}{47}\right)$	$e\left(\frac{32}{47}\right)$	$e\left(\frac{32}{47}\right)$	$e\left(\frac{26}{47}\right)$	$e\left(\frac{9}{47}\right)$	$e\left(\frac{11}{47}\right)$	$e\left(\frac{18}{47}\right)$	$e\left(\frac{40}{47}\right)$	$e\left(\frac{34}{47}\right)$
$\chi_{13254}(6487,\cdot)$	$1$	$1$	$e\left(\frac{3}{47}\right)$	$e\left(\frac{17}{47}\right)$	$e\left(\frac{42}{47}\right)$	$e\left(\frac{42}{47}\right)$	$e\left(\frac{40}{47}\right)$	$e\left(\frac{3}{47}\right)$	$e\left(\frac{35}{47}\right)$	$e\left(\frac{6}{47}\right)$	$e\left(\frac{29}{47}\right)$	$e\left(\frac{27}{47}\right)$
$\chi_{13254}(6769,\cdot)$	$1$	$1$	$e\left(\frac{44}{47}\right)$	$e\left(\frac{30}{47}\right)$	$e\left(\frac{5}{47}\right)$	$e\left(\frac{5}{47}\right)$	$e\left(\frac{7}{47}\right)$	$e\left(\frac{44}{47}\right)$	$e\left(\frac{12}{47}\right)$	$e\left(\frac{41}{47}\right)$	$e\left(\frac{18}{47}\right)$	$e\left(\frac{20}{47}\right)$
$\chi_{13254}(7051,\cdot)$	$1$	$1$	$e\left(\frac{38}{47}\right)$	$e\left(\frac{43}{47}\right)$	$e\left(\frac{15}{47}\right)$	$e\left(\frac{15}{47}\right)$	$e\left(\frac{21}{47}\right)$	$e\left(\frac{38}{47}\right)$	$e\left(\frac{36}{47}\right)$	$e\left(\frac{29}{47}\right)$	$e\left(\frac{7}{47}\right)$	$e\left(\frac{13}{47}\right)$
$\chi_{13254}(7333,\cdot)$	$1$	$1$	$e\left(\frac{32}{47}\right)$	$e\left(\frac{9}{47}\right)$	$e\left(\frac{25}{47}\right)$	$e\left(\frac{25}{47}\right)$	$e\left(\frac{35}{47}\right)$	$e\left(\frac{32}{47}\right)$	$e\left(\frac{13}{47}\right)$	$e\left(\frac{17}{47}\right)$	$e\left(\frac{43}{47}\right)$	$e\left(\frac{6}{47}\right)$
$\chi_{13254}(7615,\cdot)$	$1$	$1$	$e\left(\frac{26}{47}\right)$	$e\left(\frac{22}{47}\right)$	$e\left(\frac{35}{47}\right)$	$e\left(\frac{35}{47}\right)$	$e\left(\frac{2}{47}\right)$	$e\left(\frac{26}{47}\right)$	$e\left(\frac{37}{47}\right)$	$e\left(\frac{5}{47}\right)$	$e\left(\frac{32}{47}\right)$	$e\left(\frac{46}{47}\right)$
$\chi_{13254}(7897,\cdot)$	$1$	$1$	$e\left(\frac{20}{47}\right)$	$e\left(\frac{35}{47}\right)$	$e\left(\frac{45}{47}\right)$	$e\left(\frac{45}{47}\right)$	$e\left(\frac{16}{47}\right)$	$e\left(\frac{20}{47}\right)$	$e\left(\frac{14}{47}\right)$	$e\left(\frac{40}{47}\right)$	$e\left(\frac{21}{47}\right)$	$e\left(\frac{39}{47}\right)$
$\chi_{13254}(8179,\cdot)$	$1$	$1$	$e\left(\frac{14}{47}\right)$	$e\left(\frac{1}{47}\right)$	$e\left(\frac{8}{47}\right)$	$e\left(\frac{8}{47}\right)$	$e\left(\frac{30}{47}\right)$	$e\left(\frac{14}{47}\right)$	$e\left(\frac{38}{47}\right)$	$e\left(\frac{28}{47}\right)$	$e\left(\frac{10}{47}\right)$	$e\left(\frac{32}{47}\right)$
$\chi_{13254}(8461,\cdot)$	$1$	$1$	$e\left(\frac{8}{47}\right)$	$e\left(\frac{14}{47}\right)$	$e\left(\frac{18}{47}\right)$	$e\left(\frac{18}{47}\right)$	$e\left(\frac{44}{47}\right)$	$e\left(\frac{8}{47}\right)$	$e\left(\frac{15}{47}\right)$	$e\left(\frac{16}{47}\right)$	$e\left(\frac{46}{47}\right)$	$e\left(\frac{25}{47}\right)$
$\chi_{13254}(8743,\cdot)$	$1$	$1$	$e\left(\frac{2}{47}\right)$	$e\left(\frac{27}{47}\right)$	$e\left(\frac{28}{47}\right)$	$e\left(\frac{28}{47}\right)$	$e\left(\frac{11}{47}\right)$	$e\left(\frac{2}{47}\right)$	$e\left(\frac{39}{47}\right)$	$e\left(\frac{4}{47}\right)$	$e\left(\frac{35}{47}\right)$	$e\left(\frac{18}{47}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{13254}(283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{47}\right)\)	\(e\left(\frac{13}{47}\right)\)	\(e\left(\frac{10}{47}\right)\)	\(e\left(\frac{10}{47}\right)\)	\(e\left(\frac{14}{47}\right)\)	\(e\left(\frac{41}{47}\right)\)	\(e\left(\frac{24}{47}\right)\)	\(e\left(\frac{35}{47}\right)\)	\(e\left(\frac{36}{47}\right)\)	\(e\left(\frac{40}{47}\right)\)
\(\chi_{13254}(565,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{47}\right)\)	\(e\left(\frac{26}{47}\right)\)	\(e\left(\frac{20}{47}\right)\)	\(e\left(\frac{20}{47}\right)\)	\(e\left(\frac{28}{47}\right)\)	\(e\left(\frac{35}{47}\right)\)	\(e\left(\frac{1}{47}\right)\)	\(e\left(\frac{23}{47}\right)\)	\(e\left(\frac{25}{47}\right)\)	\(e\left(\frac{33}{47}\right)\)
\(\chi_{13254}(847,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{47}\right)\)	\(e\left(\frac{39}{47}\right)\)	\(e\left(\frac{30}{47}\right)\)	\(e\left(\frac{30}{47}\right)\)	\(e\left(\frac{42}{47}\right)\)	\(e\left(\frac{29}{47}\right)\)	\(e\left(\frac{25}{47}\right)\)	\(e\left(\frac{11}{47}\right)\)	\(e\left(\frac{14}{47}\right)\)	\(e\left(\frac{26}{47}\right)\)
\(\chi_{13254}(1129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{47}\right)\)	\(e\left(\frac{5}{47}\right)\)	\(e\left(\frac{40}{47}\right)\)	\(e\left(\frac{40}{47}\right)\)	\(e\left(\frac{9}{47}\right)\)	\(e\left(\frac{23}{47}\right)\)	\(e\left(\frac{2}{47}\right)\)	\(e\left(\frac{46}{47}\right)\)	\(e\left(\frac{3}{47}\right)\)	\(e\left(\frac{19}{47}\right)\)
\(\chi_{13254}(1411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{47}\right)\)	\(e\left(\frac{18}{47}\right)\)	\(e\left(\frac{3}{47}\right)\)	\(e\left(\frac{3}{47}\right)\)	\(e\left(\frac{23}{47}\right)\)	\(e\left(\frac{17}{47}\right)\)	\(e\left(\frac{26}{47}\right)\)	\(e\left(\frac{34}{47}\right)\)	\(e\left(\frac{39}{47}\right)\)	\(e\left(\frac{12}{47}\right)\)
\(\chi_{13254}(1693,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{47}\right)\)	\(e\left(\frac{31}{47}\right)\)	\(e\left(\frac{13}{47}\right)\)	\(e\left(\frac{13}{47}\right)\)	\(e\left(\frac{37}{47}\right)\)	\(e\left(\frac{11}{47}\right)\)	\(e\left(\frac{3}{47}\right)\)	\(e\left(\frac{22}{47}\right)\)	\(e\left(\frac{28}{47}\right)\)	\(e\left(\frac{5}{47}\right)\)
\(\chi_{13254}(1975,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{47}\right)\)	\(e\left(\frac{44}{47}\right)\)	\(e\left(\frac{23}{47}\right)\)	\(e\left(\frac{23}{47}\right)\)	\(e\left(\frac{4}{47}\right)\)	\(e\left(\frac{5}{47}\right)\)	\(e\left(\frac{27}{47}\right)\)	\(e\left(\frac{10}{47}\right)\)	\(e\left(\frac{17}{47}\right)\)	\(e\left(\frac{45}{47}\right)\)
\(\chi_{13254}(2257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{47}\right)\)	\(e\left(\frac{10}{47}\right)\)	\(e\left(\frac{33}{47}\right)\)	\(e\left(\frac{33}{47}\right)\)	\(e\left(\frac{18}{47}\right)\)	\(e\left(\frac{46}{47}\right)\)	\(e\left(\frac{4}{47}\right)\)	\(e\left(\frac{45}{47}\right)\)	\(e\left(\frac{6}{47}\right)\)	\(e\left(\frac{38}{47}\right)\)
\(\chi_{13254}(2539,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{40}{47}\right)\)	\(e\left(\frac{23}{47}\right)\)	\(e\left(\frac{43}{47}\right)\)	\(e\left(\frac{43}{47}\right)\)	\(e\left(\frac{32}{47}\right)\)	\(e\left(\frac{40}{47}\right)\)	\(e\left(\frac{28}{47}\right)\)	\(e\left(\frac{33}{47}\right)\)	\(e\left(\frac{42}{47}\right)\)	\(e\left(\frac{31}{47}\right)\)
\(\chi_{13254}(2821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{47}\right)\)	\(e\left(\frac{36}{47}\right)\)	\(e\left(\frac{6}{47}\right)\)	\(e\left(\frac{6}{47}\right)\)	\(e\left(\frac{46}{47}\right)\)	\(e\left(\frac{34}{47}\right)\)	\(e\left(\frac{5}{47}\right)\)	\(e\left(\frac{21}{47}\right)\)	\(e\left(\frac{31}{47}\right)\)	\(e\left(\frac{24}{47}\right)\)
\(\chi_{13254}(3103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{47}\right)\)	\(e\left(\frac{2}{47}\right)\)	\(e\left(\frac{16}{47}\right)\)	\(e\left(\frac{16}{47}\right)\)	\(e\left(\frac{13}{47}\right)\)	\(e\left(\frac{28}{47}\right)\)	\(e\left(\frac{29}{47}\right)\)	\(e\left(\frac{9}{47}\right)\)	\(e\left(\frac{20}{47}\right)\)	\(e\left(\frac{17}{47}\right)\)
\(\chi_{13254}(3385,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{47}\right)\)	\(e\left(\frac{15}{47}\right)\)	\(e\left(\frac{26}{47}\right)\)	\(e\left(\frac{26}{47}\right)\)	\(e\left(\frac{27}{47}\right)\)	\(e\left(\frac{22}{47}\right)\)	\(e\left(\frac{6}{47}\right)\)	\(e\left(\frac{44}{47}\right)\)	\(e\left(\frac{9}{47}\right)\)	\(e\left(\frac{10}{47}\right)\)
\(\chi_{13254}(3667,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{47}\right)\)	\(e\left(\frac{28}{47}\right)\)	\(e\left(\frac{36}{47}\right)\)	\(e\left(\frac{36}{47}\right)\)	\(e\left(\frac{41}{47}\right)\)	\(e\left(\frac{16}{47}\right)\)	\(e\left(\frac{30}{47}\right)\)	\(e\left(\frac{32}{47}\right)\)	\(e\left(\frac{45}{47}\right)\)	\(e\left(\frac{3}{47}\right)\)
\(\chi_{13254}(3949,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{47}\right)\)	\(e\left(\frac{41}{47}\right)\)	\(e\left(\frac{46}{47}\right)\)	\(e\left(\frac{46}{47}\right)\)	\(e\left(\frac{8}{47}\right)\)	\(e\left(\frac{10}{47}\right)\)	\(e\left(\frac{7}{47}\right)\)	\(e\left(\frac{20}{47}\right)\)	\(e\left(\frac{34}{47}\right)\)	\(e\left(\frac{43}{47}\right)\)
\(\chi_{13254}(4231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{47}\right)\)	\(e\left(\frac{7}{47}\right)\)	\(e\left(\frac{9}{47}\right)\)	\(e\left(\frac{9}{47}\right)\)	\(e\left(\frac{22}{47}\right)\)	\(e\left(\frac{4}{47}\right)\)	\(e\left(\frac{31}{47}\right)\)	\(e\left(\frac{8}{47}\right)\)	\(e\left(\frac{23}{47}\right)\)	\(e\left(\frac{36}{47}\right)\)
\(\chi_{13254}(4513,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{47}\right)\)	\(e\left(\frac{20}{47}\right)\)	\(e\left(\frac{19}{47}\right)\)	\(e\left(\frac{19}{47}\right)\)	\(e\left(\frac{36}{47}\right)\)	\(e\left(\frac{45}{47}\right)\)	\(e\left(\frac{8}{47}\right)\)	\(e\left(\frac{43}{47}\right)\)	\(e\left(\frac{12}{47}\right)\)	\(e\left(\frac{29}{47}\right)\)
\(\chi_{13254}(4795,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{47}\right)\)	\(e\left(\frac{33}{47}\right)\)	\(e\left(\frac{29}{47}\right)\)	\(e\left(\frac{29}{47}\right)\)	\(e\left(\frac{3}{47}\right)\)	\(e\left(\frac{39}{47}\right)\)	\(e\left(\frac{32}{47}\right)\)	\(e\left(\frac{31}{47}\right)\)	\(e\left(\frac{1}{47}\right)\)	\(e\left(\frac{22}{47}\right)\)
\(\chi_{13254}(5077,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{47}\right)\)	\(e\left(\frac{46}{47}\right)\)	\(e\left(\frac{39}{47}\right)\)	\(e\left(\frac{39}{47}\right)\)	\(e\left(\frac{17}{47}\right)\)	\(e\left(\frac{33}{47}\right)\)	\(e\left(\frac{9}{47}\right)\)	\(e\left(\frac{19}{47}\right)\)	\(e\left(\frac{37}{47}\right)\)	\(e\left(\frac{15}{47}\right)\)
\(\chi_{13254}(5359,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{47}\right)\)	\(e\left(\frac{12}{47}\right)\)	\(e\left(\frac{2}{47}\right)\)	\(e\left(\frac{2}{47}\right)\)	\(e\left(\frac{31}{47}\right)\)	\(e\left(\frac{27}{47}\right)\)	\(e\left(\frac{33}{47}\right)\)	\(e\left(\frac{7}{47}\right)\)	\(e\left(\frac{26}{47}\right)\)	\(e\left(\frac{8}{47}\right)\)
\(\chi_{13254}(5641,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{47}\right)\)	\(e\left(\frac{25}{47}\right)\)	\(e\left(\frac{12}{47}\right)\)	\(e\left(\frac{12}{47}\right)\)	\(e\left(\frac{45}{47}\right)\)	\(e\left(\frac{21}{47}\right)\)	\(e\left(\frac{10}{47}\right)\)	\(e\left(\frac{42}{47}\right)\)	\(e\left(\frac{15}{47}\right)\)	\(e\left(\frac{1}{47}\right)\)
\(\chi_{13254}(5923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{47}\right)\)	\(e\left(\frac{38}{47}\right)\)	\(e\left(\frac{22}{47}\right)\)	\(e\left(\frac{22}{47}\right)\)	\(e\left(\frac{12}{47}\right)\)	\(e\left(\frac{15}{47}\right)\)	\(e\left(\frac{34}{47}\right)\)	\(e\left(\frac{30}{47}\right)\)	\(e\left(\frac{4}{47}\right)\)	\(e\left(\frac{41}{47}\right)\)
\(\chi_{13254}(6205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{47}\right)\)	\(e\left(\frac{4}{47}\right)\)	\(e\left(\frac{32}{47}\right)\)	\(e\left(\frac{32}{47}\right)\)	\(e\left(\frac{26}{47}\right)\)	\(e\left(\frac{9}{47}\right)\)	\(e\left(\frac{11}{47}\right)\)	\(e\left(\frac{18}{47}\right)\)	\(e\left(\frac{40}{47}\right)\)	\(e\left(\frac{34}{47}\right)\)
\(\chi_{13254}(6487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{47}\right)\)	\(e\left(\frac{17}{47}\right)\)	\(e\left(\frac{42}{47}\right)\)	\(e\left(\frac{42}{47}\right)\)	\(e\left(\frac{40}{47}\right)\)	\(e\left(\frac{3}{47}\right)\)	\(e\left(\frac{35}{47}\right)\)	\(e\left(\frac{6}{47}\right)\)	\(e\left(\frac{29}{47}\right)\)	\(e\left(\frac{27}{47}\right)\)
\(\chi_{13254}(6769,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{47}\right)\)	\(e\left(\frac{30}{47}\right)\)	\(e\left(\frac{5}{47}\right)\)	\(e\left(\frac{5}{47}\right)\)	\(e\left(\frac{7}{47}\right)\)	\(e\left(\frac{44}{47}\right)\)	\(e\left(\frac{12}{47}\right)\)	\(e\left(\frac{41}{47}\right)\)	\(e\left(\frac{18}{47}\right)\)	\(e\left(\frac{20}{47}\right)\)
\(\chi_{13254}(7051,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{47}\right)\)	\(e\left(\frac{43}{47}\right)\)	\(e\left(\frac{15}{47}\right)\)	\(e\left(\frac{15}{47}\right)\)	\(e\left(\frac{21}{47}\right)\)	\(e\left(\frac{38}{47}\right)\)	\(e\left(\frac{36}{47}\right)\)	\(e\left(\frac{29}{47}\right)\)	\(e\left(\frac{7}{47}\right)\)	\(e\left(\frac{13}{47}\right)\)
\(\chi_{13254}(7333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{47}\right)\)	\(e\left(\frac{9}{47}\right)\)	\(e\left(\frac{25}{47}\right)\)	\(e\left(\frac{25}{47}\right)\)	\(e\left(\frac{35}{47}\right)\)	\(e\left(\frac{32}{47}\right)\)	\(e\left(\frac{13}{47}\right)\)	\(e\left(\frac{17}{47}\right)\)	\(e\left(\frac{43}{47}\right)\)	\(e\left(\frac{6}{47}\right)\)
\(\chi_{13254}(7615,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{47}\right)\)	\(e\left(\frac{22}{47}\right)\)	\(e\left(\frac{35}{47}\right)\)	\(e\left(\frac{35}{47}\right)\)	\(e\left(\frac{2}{47}\right)\)	\(e\left(\frac{26}{47}\right)\)	\(e\left(\frac{37}{47}\right)\)	\(e\left(\frac{5}{47}\right)\)	\(e\left(\frac{32}{47}\right)\)	\(e\left(\frac{46}{47}\right)\)
\(\chi_{13254}(7897,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{47}\right)\)	\(e\left(\frac{35}{47}\right)\)	\(e\left(\frac{45}{47}\right)\)	\(e\left(\frac{45}{47}\right)\)	\(e\left(\frac{16}{47}\right)\)	\(e\left(\frac{20}{47}\right)\)	\(e\left(\frac{14}{47}\right)\)	\(e\left(\frac{40}{47}\right)\)	\(e\left(\frac{21}{47}\right)\)	\(e\left(\frac{39}{47}\right)\)
\(\chi_{13254}(8179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{47}\right)\)	\(e\left(\frac{1}{47}\right)\)	\(e\left(\frac{8}{47}\right)\)	\(e\left(\frac{8}{47}\right)\)	\(e\left(\frac{30}{47}\right)\)	\(e\left(\frac{14}{47}\right)\)	\(e\left(\frac{38}{47}\right)\)	\(e\left(\frac{28}{47}\right)\)	\(e\left(\frac{10}{47}\right)\)	\(e\left(\frac{32}{47}\right)\)
\(\chi_{13254}(8461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{47}\right)\)	\(e\left(\frac{14}{47}\right)\)	\(e\left(\frac{18}{47}\right)\)	\(e\left(\frac{18}{47}\right)\)	\(e\left(\frac{44}{47}\right)\)	\(e\left(\frac{8}{47}\right)\)	\(e\left(\frac{15}{47}\right)\)	\(e\left(\frac{16}{47}\right)\)	\(e\left(\frac{46}{47}\right)\)	\(e\left(\frac{25}{47}\right)\)
\(\chi_{13254}(8743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{47}\right)\)	\(e\left(\frac{27}{47}\right)\)	\(e\left(\frac{28}{47}\right)\)	\(e\left(\frac{28}{47}\right)\)	\(e\left(\frac{11}{47}\right)\)	\(e\left(\frac{2}{47}\right)\)	\(e\left(\frac{39}{47}\right)\)	\(e\left(\frac{4}{47}\right)\)	\(e\left(\frac{35}{47}\right)\)	\(e\left(\frac{18}{47}\right)\)

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First 31 of 46 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	13254.i
Modulus	$13254$
Conductor	$2209$
Order	$47$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(13254\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(2209\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(47\)	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 2209.e	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);