LMFDB - Dirichlet character orbit 58492.hi

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(58492, base_ring=CyclotomicField(348)) M = H._module chi = DirichletCharacter(H, M([0,58,165])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(45, 58492)) 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("58492.45"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$58492$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$14623$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$348$	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 14623.dt	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:	$\Q(\zeta_{348})$	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 348 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 112 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{58492}(45,\cdot)$	$-1$	$1$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{115}{348}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{173}{348}\right)$	$e\left(\frac{221}{348}\right)$	$e\left(\frac{7}{87}\right)$
$\chi_{58492}(61,\cdot)$	$-1$	$1$	$e\left(\frac{62}{87}\right)$	$e\left(\frac{43}{87}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{83}{348}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{348}\right)$	$e\left(\frac{217}{348}\right)$	$e\left(\frac{86}{87}\right)$
$\chi_{58492}(325,\cdot)$	$-1$	$1$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{49}{348}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{107}{348}\right)$	$e\left(\frac{191}{348}\right)$	$e\left(\frac{34}{87}\right)$
$\chi_{58492}(649,\cdot)$	$-1$	$1$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{65}{348}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{348}\right)$	$e\left(\frac{19}{348}\right)$	$e\left(\frac{38}{87}\right)$
$\chi_{58492}(1265,\cdot)$	$-1$	$1$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{311}{348}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{253}{348}\right)$	$e\left(\frac{289}{348}\right)$	$e\left(\frac{56}{87}\right)$
$\chi_{58492}(1601,\cdot)$	$-1$	$1$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{10}{87}\right)$	$e\left(\frac{53}{348}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{343}{348}\right)$	$e\left(\frac{235}{348}\right)$	$e\left(\frac{35}{87}\right)$
$\chi_{58492}(1909,\cdot)$	$-1$	$1$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{269}{348}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{211}{348}\right)$	$e\left(\frac{175}{348}\right)$	$e\left(\frac{2}{87}\right)$
$\chi_{58492}(2637,\cdot)$	$-1$	$1$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{245}{348}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{187}{348}\right)$	$e\left(\frac{259}{348}\right)$	$e\left(\frac{83}{87}\right)$
$\chi_{58492}(3853,\cdot)$	$-1$	$1$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{223}{348}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{281}{348}\right)$	$e\left(\frac{17}{348}\right)$	$e\left(\frac{34}{87}\right)$
$\chi_{58492}(4133,\cdot)$	$-1$	$1$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{289}{348}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{347}{348}\right)$	$e\left(\frac{47}{348}\right)$	$e\left(\frac{7}{87}\right)$
$\chi_{58492}(5253,\cdot)$	$-1$	$1$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{151}{348}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{209}{348}\right)$	$e\left(\frac{269}{348}\right)$	$e\left(\frac{16}{87}\right)$
$\chi_{58492}(5617,\cdot)$	$-1$	$1$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{38}{87}\right)$	$e\left(\frac{271}{348}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{329}{348}\right)$	$e\left(\frac{197}{348}\right)$	$e\left(\frac{46}{87}\right)$
$\chi_{58492}(6177,\cdot)$	$-1$	$1$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{337}{348}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{47}{348}\right)$	$e\left(\frac{227}{348}\right)$	$e\left(\frac{19}{87}\right)$
$\chi_{58492}(6389,\cdot)$	$-1$	$1$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{131}{348}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{73}{348}\right)$	$e\left(\frac{49}{348}\right)$	$e\left(\frac{11}{87}\right)$
$\chi_{58492}(6473,\cdot)$	$-1$	$1$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{41}{348}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{331}{348}\right)$	$e\left(\frac{103}{348}\right)$	$e\left(\frac{32}{87}\right)$
$\chi_{58492}(6541,\cdot)$	$-1$	$1$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{41}{87}\right)$	$e\left(\frac{313}{348}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{348}\right)$	$e\left(\frac{311}{348}\right)$	$e\left(\frac{13}{87}\right)$
$\chi_{58492}(7565,\cdot)$	$-1$	$1$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{113}{348}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{55}{348}\right)$	$e\left(\frac{199}{348}\right)$	$e\left(\frac{50}{87}\right)$
$\chi_{58492}(7845,\cdot)$	$-1$	$1$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{251}{348}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{193}{348}\right)$	$e\left(\frac{325}{348}\right)$	$e\left(\frac{41}{87}\right)$
$\chi_{58492}(8417,\cdot)$	$-1$	$1$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{199}{348}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{257}{348}\right)$	$e\left(\frac{101}{348}\right)$	$e\left(\frac{28}{87}\right)$
$\chi_{58492}(8797,\cdot)$	$-1$	$1$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{11}{348}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{301}{348}\right)$	$e\left(\frac{121}{348}\right)$	$e\left(\frac{68}{87}\right)$
$\chi_{58492}(9005,\cdot)$	$-1$	$1$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{77}{87}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{181}{348}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{239}{348}\right)$	$e\left(\frac{251}{348}\right)$	$e\left(\frac{67}{87}\right)$
$\chi_{58492}(9469,\cdot)$	$-1$	$1$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{101}{348}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{43}{348}\right)$	$e\left(\frac{67}{348}\right)$	$e\left(\frac{47}{87}\right)$
$\chi_{58492}(9621,\cdot)$	$-1$	$1$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{79}{348}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{137}{348}\right)$	$e\left(\frac{173}{348}\right)$	$e\left(\frac{85}{87}\right)$
$\chi_{58492}(9957,\cdot)$	$-1$	$1$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{169}{348}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{227}{348}\right)$	$e\left(\frac{119}{348}\right)$	$e\left(\frac{64}{87}\right)$
$\chi_{58492}(10085,\cdot)$	$-1$	$1$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{317}{348}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{259}{348}\right)$	$e\left(\frac{7}{348}\right)$	$e\left(\frac{14}{87}\right)$
$\chi_{58492}(10265,\cdot)$	$-1$	$1$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{59}{87}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{37}{348}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{95}{348}\right)$	$e\left(\frac{59}{348}\right)$	$e\left(\frac{31}{87}\right)$
$\chi_{58492}(10993,\cdot)$	$-1$	$1$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{13}{348}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{71}{348}\right)$	$e\left(\frac{143}{348}\right)$	$e\left(\frac{25}{87}\right)$
$\chi_{58492}(11541,\cdot)$	$-1$	$1$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{293}{348}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{235}{348}\right)$	$e\left(\frac{91}{348}\right)$	$e\left(\frac{8}{87}\right)$
$\chi_{58492}(14745,\cdot)$	$-1$	$1$	$e\left(\frac{43}{87}\right)$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{247}{348}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{305}{348}\right)$	$e\left(\frac{281}{348}\right)$	$e\left(\frac{40}{87}\right)$
$\chi_{58492}(14829,\cdot)$	$-1$	$1$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{157}{348}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{215}{348}\right)$	$e\left(\frac{335}{348}\right)$	$e\left(\frac{61}{87}\right)$
$\chi_{58492}(15921,\cdot)$	$-1$	$1$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{35}{87}\right)$	$e\left(\frac{229}{348}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{287}{348}\right)$	$e\left(\frac{83}{348}\right)$	$e\left(\frac{79}{87}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{58492}(45,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{115}{348}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{173}{348}\right)\)	\(e\left(\frac{221}{348}\right)\)	\(e\left(\frac{7}{87}\right)\)
\(\chi_{58492}(61,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{62}{87}\right)\)	\(e\left(\frac{43}{87}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{83}{348}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{25}{348}\right)\)	\(e\left(\frac{217}{348}\right)\)	\(e\left(\frac{86}{87}\right)\)
\(\chi_{58492}(325,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{49}{348}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{107}{348}\right)\)	\(e\left(\frac{191}{348}\right)\)	\(e\left(\frac{34}{87}\right)\)
\(\chi_{58492}(649,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{65}{348}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{348}\right)\)	\(e\left(\frac{19}{348}\right)\)	\(e\left(\frac{38}{87}\right)\)
\(\chi_{58492}(1265,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{311}{348}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{253}{348}\right)\)	\(e\left(\frac{289}{348}\right)\)	\(e\left(\frac{56}{87}\right)\)
\(\chi_{58492}(1601,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{10}{87}\right)\)	\(e\left(\frac{53}{348}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{343}{348}\right)\)	\(e\left(\frac{235}{348}\right)\)	\(e\left(\frac{35}{87}\right)\)
\(\chi_{58492}(1909,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{269}{348}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{211}{348}\right)\)	\(e\left(\frac{175}{348}\right)\)	\(e\left(\frac{2}{87}\right)\)
\(\chi_{58492}(2637,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{245}{348}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{187}{348}\right)\)	\(e\left(\frac{259}{348}\right)\)	\(e\left(\frac{83}{87}\right)\)
\(\chi_{58492}(3853,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{223}{348}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{281}{348}\right)\)	\(e\left(\frac{17}{348}\right)\)	\(e\left(\frac{34}{87}\right)\)
\(\chi_{58492}(4133,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{289}{348}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{347}{348}\right)\)	\(e\left(\frac{47}{348}\right)\)	\(e\left(\frac{7}{87}\right)\)
\(\chi_{58492}(5253,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{151}{348}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{209}{348}\right)\)	\(e\left(\frac{269}{348}\right)\)	\(e\left(\frac{16}{87}\right)\)
\(\chi_{58492}(5617,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{38}{87}\right)\)	\(e\left(\frac{271}{348}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{329}{348}\right)\)	\(e\left(\frac{197}{348}\right)\)	\(e\left(\frac{46}{87}\right)\)
\(\chi_{58492}(6177,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{337}{348}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{47}{348}\right)\)	\(e\left(\frac{227}{348}\right)\)	\(e\left(\frac{19}{87}\right)\)
\(\chi_{58492}(6389,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{131}{348}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{73}{348}\right)\)	\(e\left(\frac{49}{348}\right)\)	\(e\left(\frac{11}{87}\right)\)
\(\chi_{58492}(6473,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{41}{348}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{331}{348}\right)\)	\(e\left(\frac{103}{348}\right)\)	\(e\left(\frac{32}{87}\right)\)
\(\chi_{58492}(6541,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{41}{87}\right)\)	\(e\left(\frac{313}{348}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{348}\right)\)	\(e\left(\frac{311}{348}\right)\)	\(e\left(\frac{13}{87}\right)\)
\(\chi_{58492}(7565,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{113}{348}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{55}{348}\right)\)	\(e\left(\frac{199}{348}\right)\)	\(e\left(\frac{50}{87}\right)\)
\(\chi_{58492}(7845,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{251}{348}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{193}{348}\right)\)	\(e\left(\frac{325}{348}\right)\)	\(e\left(\frac{41}{87}\right)\)
\(\chi_{58492}(8417,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{199}{348}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{257}{348}\right)\)	\(e\left(\frac{101}{348}\right)\)	\(e\left(\frac{28}{87}\right)\)
\(\chi_{58492}(8797,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{11}{348}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{301}{348}\right)\)	\(e\left(\frac{121}{348}\right)\)	\(e\left(\frac{68}{87}\right)\)
\(\chi_{58492}(9005,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{77}{87}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{181}{348}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{239}{348}\right)\)	\(e\left(\frac{251}{348}\right)\)	\(e\left(\frac{67}{87}\right)\)
\(\chi_{58492}(9469,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{101}{348}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{43}{348}\right)\)	\(e\left(\frac{67}{348}\right)\)	\(e\left(\frac{47}{87}\right)\)
\(\chi_{58492}(9621,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{79}{348}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{137}{348}\right)\)	\(e\left(\frac{173}{348}\right)\)	\(e\left(\frac{85}{87}\right)\)
\(\chi_{58492}(9957,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{169}{348}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{227}{348}\right)\)	\(e\left(\frac{119}{348}\right)\)	\(e\left(\frac{64}{87}\right)\)
\(\chi_{58492}(10085,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{317}{348}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{259}{348}\right)\)	\(e\left(\frac{7}{348}\right)\)	\(e\left(\frac{14}{87}\right)\)
\(\chi_{58492}(10265,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{59}{87}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{37}{348}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{95}{348}\right)\)	\(e\left(\frac{59}{348}\right)\)	\(e\left(\frac{31}{87}\right)\)
\(\chi_{58492}(10993,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{13}{348}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{71}{348}\right)\)	\(e\left(\frac{143}{348}\right)\)	\(e\left(\frac{25}{87}\right)\)
\(\chi_{58492}(11541,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{293}{348}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{235}{348}\right)\)	\(e\left(\frac{91}{348}\right)\)	\(e\left(\frac{8}{87}\right)\)
\(\chi_{58492}(14745,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{87}\right)\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{247}{348}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{305}{348}\right)\)	\(e\left(\frac{281}{348}\right)\)	\(e\left(\frac{40}{87}\right)\)
\(\chi_{58492}(14829,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{157}{348}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{215}{348}\right)\)	\(e\left(\frac{335}{348}\right)\)	\(e\left(\frac{61}{87}\right)\)
\(\chi_{58492}(15921,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{35}{87}\right)\)	\(e\left(\frac{229}{348}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{287}{348}\right)\)	\(e\left(\frac{83}{348}\right)\)	\(e\left(\frac{79}{87}\right)\)

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First 31 of 112 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	58492.hi
Modulus	$58492$
Conductor	$14623$
Order	$348$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(58492\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(14623\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(348\)	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 14623.dt	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);