LMFDB - Dirichlet character orbit 8464.bi

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8464, base_ring=CyclotomicField(92)) M = H._module chi = DirichletCharacter(H, M([0,69,80])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(93,8464)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8464$
Conductor:	$8464$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$92$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{92})$
Fixed field:	Number field defined by a degree 92 polynomial

First 31 of 44 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8464}(93,\cdot)$	$1$	$1$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{17}{92}\right)$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{77}{92}\right)$
$\chi_{8464}(277,\cdot)$	$1$	$1$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{51}{92}\right)$	$e\left(\frac{37}{92}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{47}{92}\right)$
$\chi_{8464}(461,\cdot)$	$1$	$1$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{17}{92}\right)$
$\chi_{8464}(645,\cdot)$	$1$	$1$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{79}{92}\right)$
$\chi_{8464}(829,\cdot)$	$1$	$1$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{19}{92}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{49}{92}\right)$
$\chi_{8464}(1013,\cdot)$	$1$	$1$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{19}{92}\right)$
$\chi_{8464}(1197,\cdot)$	$1$	$1$	$e\left(\frac{11}{92}\right)$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{37}{92}\right)$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{11}{92}\right)$	$e\left(\frac{81}{92}\right)$
$\chi_{8464}(1381,\cdot)$	$1$	$1$	$e\left(\frac{41}{92}\right)$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{41}{92}\right)$	$e\left(\frac{51}{92}\right)$
$\chi_{8464}(1565,\cdot)$	$1$	$1$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{49}{92}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{87}{92}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{21}{92}\right)$
$\chi_{8464}(1749,\cdot)$	$1$	$1$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{47}{92}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{83}{92}\right)$
$\chi_{8464}(1933,\cdot)$	$1$	$1$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{53}{92}\right)$
$\chi_{8464}(2301,\cdot)$	$1$	$1$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{85}{92}\right)$
$\chi_{8464}(2485,\cdot)$	$1$	$1$	$e\left(\frac{37}{92}\right)$	$e\left(\frac{67}{92}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{91}{92}\right)$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{37}{92}\right)$	$e\left(\frac{55}{92}\right)$
$\chi_{8464}(2669,\cdot)$	$1$	$1$	$e\left(\frac{67}{92}\right)$	$e\left(\frac{89}{92}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{51}{92}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{67}{92}\right)$	$e\left(\frac{25}{92}\right)$
$\chi_{8464}(2853,\cdot)$	$1$	$1$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{19}{92}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{67}{92}\right)$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{87}{92}\right)$
$\chi_{8464}(3037,\cdot)$	$1$	$1$	$e\left(\frac{35}{92}\right)$	$e\left(\frac{41}{92}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{35}{92}\right)$	$e\left(\frac{57}{92}\right)$
$\chi_{8464}(3221,\cdot)$	$1$	$1$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{27}{92}\right)$
$\chi_{8464}(3405,\cdot)$	$1$	$1$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{89}{92}\right)$
$\chi_{8464}(3589,\cdot)$	$1$	$1$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{19}{92}\right)$	$e\left(\frac{21}{92}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{59}{92}\right)$
$\chi_{8464}(3773,\cdot)$	$1$	$1$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{37}{92}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{29}{92}\right)$
$\chi_{8464}(3957,\cdot)$	$1$	$1$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{87}{92}\right)$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{91}{92}\right)$
$\chi_{8464}(4141,\cdot)$	$1$	$1$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{61}{92}\right)$
$\chi_{8464}(4325,\cdot)$	$1$	$1$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{11}{92}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{89}{92}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{31}{92}\right)$
$\chi_{8464}(4509,\cdot)$	$1$	$1$	$e\left(\frac{91}{92}\right)$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{83}{92}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{91}{92}\right)$	$e\left(\frac{1}{92}\right)$
$\chi_{8464}(4693,\cdot)$	$1$	$1$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{55}{92}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{63}{92}\right)$
$\chi_{8464}(4877,\cdot)$	$1$	$1$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{33}{92}\right)$
$\chi_{8464}(5061,\cdot)$	$1$	$1$	$e\left(\frac{89}{92}\right)$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{89}{92}\right)$	$e\left(\frac{3}{92}\right)$
$\chi_{8464}(5245,\cdot)$	$1$	$1$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{49}{92}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{65}{92}\right)$
$\chi_{8464}(5429,\cdot)$	$1$	$1$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{51}{92}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{83}{92}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{35}{92}\right)$
$\chi_{8464}(5613,\cdot)$	$1$	$1$	$e\left(\frac{87}{92}\right)$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{47}{92}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{87}{92}\right)$	$e\left(\frac{5}{92}\right)$
$\chi_{8464}(5797,\cdot)$	$1$	$1$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{41}{92}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{67}{92}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8464}(93,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{17}{92}\right)\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{77}{92}\right)\)
\(\chi_{8464}(277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{51}{92}\right)\)	\(e\left(\frac{37}{92}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{47}{92}\right)\)
\(\chi_{8464}(461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{17}{92}\right)\)
\(\chi_{8464}(645,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{79}{92}\right)\)
\(\chi_{8464}(829,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{19}{92}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{49}{92}\right)\)
\(\chi_{8464}(1013,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{19}{92}\right)\)
\(\chi_{8464}(1197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{92}\right)\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{37}{92}\right)\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{11}{92}\right)\)	\(e\left(\frac{81}{92}\right)\)
\(\chi_{8464}(1381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{92}\right)\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{41}{92}\right)\)	\(e\left(\frac{51}{92}\right)\)
\(\chi_{8464}(1565,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{49}{92}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{87}{92}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{21}{92}\right)\)
\(\chi_{8464}(1749,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{47}{92}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{83}{92}\right)\)
\(\chi_{8464}(1933,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{53}{92}\right)\)
\(\chi_{8464}(2301,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{85}{92}\right)\)
\(\chi_{8464}(2485,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{92}\right)\)	\(e\left(\frac{67}{92}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{91}{92}\right)\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{37}{92}\right)\)	\(e\left(\frac{55}{92}\right)\)
\(\chi_{8464}(2669,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{92}\right)\)	\(e\left(\frac{89}{92}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{51}{92}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{67}{92}\right)\)	\(e\left(\frac{25}{92}\right)\)
\(\chi_{8464}(2853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{19}{92}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{67}{92}\right)\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{87}{92}\right)\)
\(\chi_{8464}(3037,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{92}\right)\)	\(e\left(\frac{41}{92}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{35}{92}\right)\)	\(e\left(\frac{57}{92}\right)\)
\(\chi_{8464}(3221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{27}{92}\right)\)
\(\chi_{8464}(3405,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{89}{92}\right)\)
\(\chi_{8464}(3589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{19}{92}\right)\)	\(e\left(\frac{21}{92}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{59}{92}\right)\)
\(\chi_{8464}(3773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{37}{92}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{29}{92}\right)\)
\(\chi_{8464}(3957,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{87}{92}\right)\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{91}{92}\right)\)
\(\chi_{8464}(4141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{61}{92}\right)\)
\(\chi_{8464}(4325,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{11}{92}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{89}{92}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{31}{92}\right)\)
\(\chi_{8464}(4509,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{92}\right)\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{83}{92}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{91}{92}\right)\)	\(e\left(\frac{1}{92}\right)\)
\(\chi_{8464}(4693,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{55}{92}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{63}{92}\right)\)
\(\chi_{8464}(4877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{33}{92}\right)\)
\(\chi_{8464}(5061,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{92}\right)\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{89}{92}\right)\)	\(e\left(\frac{3}{92}\right)\)
\(\chi_{8464}(5245,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{49}{92}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{65}{92}\right)\)
\(\chi_{8464}(5429,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{51}{92}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{83}{92}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{35}{92}\right)\)
\(\chi_{8464}(5613,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{92}\right)\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{47}{92}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{87}{92}\right)\)	\(e\left(\frac{5}{92}\right)\)
\(\chi_{8464}(5797,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{41}{92}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{67}{92}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

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.bi
Modulus	$8464$
Conductor	$8464$
Order	$92$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(8464\)
Conductor:	\(8464\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(92\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)