LMFDB - Dirichlet character orbit 8464.bh

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8464, base_ring=CyclotomicField(92)) M = H._module chi = DirichletCharacter(H, M([0,69,6])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(45, 8464)) 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("8464.45"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$8464$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$8464$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$92$	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:	yes	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:	$\Q(\zeta_{92})$	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 92 polynomial	comment:Fixed field sage:chi.fixed_field()

First 31 of 44 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8464}(45,\cdot)$	$-1$	$1$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{19}{92}\right)$
$\chi_{8464}(229,\cdot)$	$-1$	$1$	$e\left(\frac{89}{92}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{49}{92}\right)$
$\chi_{8464}(413,\cdot)$	$-1$	$1$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{79}{92}\right)$
$\chi_{8464}(597,\cdot)$	$-1$	$1$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{17}{92}\right)$
$\chi_{8464}(781,\cdot)$	$-1$	$1$	$e\left(\frac{91}{92}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{51}{92}\right)$	$e\left(\frac{83}{92}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{47}{92}\right)$
$\chi_{8464}(965,\cdot)$	$-1$	$1$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{17}{92}\right)$	$e\left(\frac{89}{92}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{77}{92}\right)$
$\chi_{8464}(1149,\cdot)$	$-1$	$1$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{35}{92}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{15}{92}\right)$
$\chi_{8464}(1333,\cdot)$	$-1$	$1$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{41}{92}\right)$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{47}{92}\right)$	$e\left(\frac{45}{92}\right)$
$\chi_{8464}(1517,\cdot)$	$-1$	$1$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{83}{92}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{17}{92}\right)$	$e\left(\frac{75}{92}\right)$
$\chi_{8464}(1701,\cdot)$	$-1$	$1$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{21}{92}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{13}{92}\right)$
$\chi_{8464}(1885,\cdot)$	$-1$	$1$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{49}{92}\right)$	$e\left(\frac{43}{92}\right)$
$\chi_{8464}(2069,\cdot)$	$-1$	$1$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{17}{92}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{89}{92}\right)$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{19}{92}\right)$	$e\left(\frac{73}{92}\right)$
$\chi_{8464}(2253,\cdot)$	$-1$	$1$	$e\left(\frac{35}{92}\right)$	$e\left(\frac{87}{92}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{55}{92}\right)$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{11}{92}\right)$
$\chi_{8464}(2437,\cdot)$	$-1$	$1$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{21}{92}\right)$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{51}{92}\right)$	$e\left(\frac{41}{92}\right)$
$\chi_{8464}(2621,\cdot)$	$-1$	$1$	$e\left(\frac{67}{92}\right)$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{51}{92}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{21}{92}\right)$	$e\left(\frac{71}{92}\right)$
$\chi_{8464}(2805,\cdot)$	$-1$	$1$	$e\left(\frac{37}{92}\right)$	$e\left(\frac{21}{92}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{83}{92}\right)$	$e\left(\frac{9}{92}\right)$
$\chi_{8464}(2989,\cdot)$	$-1$	$1$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{91}{92}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{11}{92}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{39}{92}\right)$
$\chi_{8464}(3357,\cdot)$	$-1$	$1$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{47}{92}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{35}{92}\right)$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{7}{92}\right)$
$\chi_{8464}(3541,\cdot)$	$-1$	$1$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{55}{92}\right)$	$e\left(\frac{37}{92}\right)$
$\chi_{8464}(3725,\cdot)$	$-1$	$1$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{87}{92}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{67}{92}\right)$
$\chi_{8464}(3909,\cdot)$	$-1$	$1$	$e\left(\frac{41}{92}\right)$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{87}{92}\right)$	$e\left(\frac{5}{92}\right)$
$\chi_{8464}(4093,\cdot)$	$-1$	$1$	$e\left(\frac{11}{92}\right)$	$e\left(\frac{51}{92}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{83}{92}\right)$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{35}{92}\right)$
$\chi_{8464}(4277,\cdot)$	$-1$	$1$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{49}{92}\right)$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{65}{92}\right)$
$\chi_{8464}(4461,\cdot)$	$-1$	$1$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{19}{92}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{89}{92}\right)$	$e\left(\frac{3}{92}\right)$
$\chi_{8464}(4645,\cdot)$	$-1$	$1$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{33}{92}\right)$
$\chi_{8464}(4829,\cdot)$	$-1$	$1$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{55}{92}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{63}{92}\right)$
$\chi_{8464}(5013,\cdot)$	$-1$	$1$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{37}{92}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{91}{92}\right)$	$e\left(\frac{1}{92}\right)$
$\chi_{8464}(5197,\cdot)$	$-1$	$1$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{11}{92}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{31}{92}\right)$
$\chi_{8464}(5381,\cdot)$	$-1$	$1$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{49}{92}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{61}{92}\right)$
$\chi_{8464}(5565,\cdot)$	$-1$	$1$	$e\left(\frac{47}{92}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{87}{92}\right)$	$e\left(\frac{55}{92}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{91}{92}\right)$
$\chi_{8464}(5749,\cdot)$	$-1$	$1$	$e\left(\frac{17}{92}\right)$	$e\left(\frac{37}{92}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{29}{92}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8464}(45,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{19}{92}\right)\)
\(\chi_{8464}(229,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{92}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{49}{92}\right)\)
\(\chi_{8464}(413,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{79}{92}\right)\)
\(\chi_{8464}(597,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{17}{92}\right)\)
\(\chi_{8464}(781,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{92}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{51}{92}\right)\)	\(e\left(\frac{83}{92}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{47}{92}\right)\)
\(\chi_{8464}(965,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{17}{92}\right)\)	\(e\left(\frac{89}{92}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{77}{92}\right)\)
\(\chi_{8464}(1149,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{35}{92}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{15}{92}\right)\)
\(\chi_{8464}(1333,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{41}{92}\right)\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{47}{92}\right)\)	\(e\left(\frac{45}{92}\right)\)
\(\chi_{8464}(1517,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{83}{92}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{17}{92}\right)\)	\(e\left(\frac{75}{92}\right)\)
\(\chi_{8464}(1701,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{21}{92}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{13}{92}\right)\)
\(\chi_{8464}(1885,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{49}{92}\right)\)	\(e\left(\frac{43}{92}\right)\)
\(\chi_{8464}(2069,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{17}{92}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{89}{92}\right)\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{19}{92}\right)\)	\(e\left(\frac{73}{92}\right)\)
\(\chi_{8464}(2253,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{92}\right)\)	\(e\left(\frac{87}{92}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{55}{92}\right)\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{11}{92}\right)\)
\(\chi_{8464}(2437,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{21}{92}\right)\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{51}{92}\right)\)	\(e\left(\frac{41}{92}\right)\)
\(\chi_{8464}(2621,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{92}\right)\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{51}{92}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{21}{92}\right)\)	\(e\left(\frac{71}{92}\right)\)
\(\chi_{8464}(2805,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{92}\right)\)	\(e\left(\frac{21}{92}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{83}{92}\right)\)	\(e\left(\frac{9}{92}\right)\)
\(\chi_{8464}(2989,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{91}{92}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{11}{92}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{39}{92}\right)\)
\(\chi_{8464}(3357,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{47}{92}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{35}{92}\right)\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{7}{92}\right)\)
\(\chi_{8464}(3541,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{55}{92}\right)\)	\(e\left(\frac{37}{92}\right)\)
\(\chi_{8464}(3725,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{87}{92}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{67}{92}\right)\)
\(\chi_{8464}(3909,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{92}\right)\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{87}{92}\right)\)	\(e\left(\frac{5}{92}\right)\)
\(\chi_{8464}(4093,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{92}\right)\)	\(e\left(\frac{51}{92}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{83}{92}\right)\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{35}{92}\right)\)
\(\chi_{8464}(4277,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{49}{92}\right)\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{65}{92}\right)\)
\(\chi_{8464}(4461,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{19}{92}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{89}{92}\right)\)	\(e\left(\frac{3}{92}\right)\)
\(\chi_{8464}(4645,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{33}{92}\right)\)
\(\chi_{8464}(4829,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{55}{92}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{63}{92}\right)\)
\(\chi_{8464}(5013,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{37}{92}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{91}{92}\right)\)	\(e\left(\frac{1}{92}\right)\)
\(\chi_{8464}(5197,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{11}{92}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{31}{92}\right)\)
\(\chi_{8464}(5381,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{49}{92}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{61}{92}\right)\)
\(\chi_{8464}(5565,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{92}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{87}{92}\right)\)	\(e\left(\frac{55}{92}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{91}{92}\right)\)
\(\chi_{8464}(5749,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{92}\right)\)	\(e\left(\frac{37}{92}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{29}{92}\right)\)

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First 31 of 44 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	8464.bh
Modulus	$8464$
Conductor	$8464$
Order	$92$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(8464\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(8464\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(92\)	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:	yes	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);