LMFDB - Dirichlet character orbit 8670.bv

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8670, base_ring=CyclotomicField(68)) M = H._module chi = DirichletCharacter(H, M([34,51,2])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(203, 8670)) 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("8670.203"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$8670$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$4335$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$68$	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 4335.bx	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:	$\Q(\zeta_{68})$
Fixed field:	Number field defined by a degree 68 polynomial

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{8670}(203,\cdot)$	$1$	$1$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{61}{68}\right)$
$\chi_{8670}(407,\cdot)$	$1$	$1$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{3}{68}\right)$
$\chi_{8670}(713,\cdot)$	$1$	$1$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{1}{68}\right)$
$\chi_{8670}(917,\cdot)$	$1$	$1$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{11}{68}\right)$
$\chi_{8670}(1223,\cdot)$	$1$	$1$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{9}{68}\right)$
$\chi_{8670}(1427,\cdot)$	$1$	$1$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{19}{68}\right)$
$\chi_{8670}(1937,\cdot)$	$1$	$1$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{27}{68}\right)$
$\chi_{8670}(2243,\cdot)$	$1$	$1$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{25}{68}\right)$
$\chi_{8670}(2447,\cdot)$	$1$	$1$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{35}{68}\right)$
$\chi_{8670}(2753,\cdot)$	$1$	$1$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{33}{68}\right)$
$\chi_{8670}(2957,\cdot)$	$1$	$1$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{43}{68}\right)$
$\chi_{8670}(3263,\cdot)$	$1$	$1$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{41}{68}\right)$
$\chi_{8670}(3773,\cdot)$	$1$	$1$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{49}{68}\right)$
$\chi_{8670}(3977,\cdot)$	$1$	$1$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{59}{68}\right)$
$\chi_{8670}(4283,\cdot)$	$1$	$1$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{57}{68}\right)$
$\chi_{8670}(4487,\cdot)$	$1$	$1$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{67}{68}\right)$
$\chi_{8670}(4793,\cdot)$	$1$	$1$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{65}{68}\right)$
$\chi_{8670}(4997,\cdot)$	$1$	$1$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{7}{68}\right)$
$\chi_{8670}(5303,\cdot)$	$1$	$1$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{5}{68}\right)$
$\chi_{8670}(5507,\cdot)$	$1$	$1$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{15}{68}\right)$
$\chi_{8670}(5813,\cdot)$	$1$	$1$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{13}{68}\right)$
$\chi_{8670}(6017,\cdot)$	$1$	$1$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{23}{68}\right)$
$\chi_{8670}(6323,\cdot)$	$1$	$1$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{21}{68}\right)$
$\chi_{8670}(6527,\cdot)$	$1$	$1$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{31}{68}\right)$
$\chi_{8670}(6833,\cdot)$	$1$	$1$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{29}{68}\right)$
$\chi_{8670}(7037,\cdot)$	$1$	$1$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{39}{68}\right)$
$\chi_{8670}(7343,\cdot)$	$1$	$1$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{37}{68}\right)$
$\chi_{8670}(7547,\cdot)$	$1$	$1$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{47}{68}\right)$
$\chi_{8670}(7853,\cdot)$	$1$	$1$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{45}{68}\right)$
$\chi_{8670}(8057,\cdot)$	$1$	$1$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{55}{68}\right)$
$\chi_{8670}(8363,\cdot)$	$1$	$1$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{53}{68}\right)$

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	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{8670}(203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{61}{68}\right)\)
\(\chi_{8670}(407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{3}{68}\right)\)
\(\chi_{8670}(713,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{1}{68}\right)\)
\(\chi_{8670}(917,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{11}{68}\right)\)
\(\chi_{8670}(1223,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{9}{68}\right)\)
\(\chi_{8670}(1427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{19}{68}\right)\)
\(\chi_{8670}(1937,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{27}{68}\right)\)
\(\chi_{8670}(2243,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{25}{68}\right)\)
\(\chi_{8670}(2447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{35}{68}\right)\)
\(\chi_{8670}(2753,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{33}{68}\right)\)
\(\chi_{8670}(2957,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{43}{68}\right)\)
\(\chi_{8670}(3263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{41}{68}\right)\)
\(\chi_{8670}(3773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{49}{68}\right)\)
\(\chi_{8670}(3977,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{59}{68}\right)\)
\(\chi_{8670}(4283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{57}{68}\right)\)
\(\chi_{8670}(4487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{67}{68}\right)\)
\(\chi_{8670}(4793,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{65}{68}\right)\)
\(\chi_{8670}(4997,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{7}{68}\right)\)
\(\chi_{8670}(5303,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{5}{68}\right)\)
\(\chi_{8670}(5507,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{15}{68}\right)\)
\(\chi_{8670}(5813,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{13}{68}\right)\)
\(\chi_{8670}(6017,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{23}{68}\right)\)
\(\chi_{8670}(6323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{21}{68}\right)\)
\(\chi_{8670}(6527,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{31}{68}\right)\)
\(\chi_{8670}(6833,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{29}{68}\right)\)
\(\chi_{8670}(7037,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{39}{68}\right)\)
\(\chi_{8670}(7343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{37}{68}\right)\)
\(\chi_{8670}(7547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{47}{68}\right)\)
\(\chi_{8670}(7853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{45}{68}\right)\)
\(\chi_{8670}(8057,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{55}{68}\right)\)
\(\chi_{8670}(8363,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{53}{68}\right)\)

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First 31 of 32 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	8670.bv
Modulus	$8670$
Conductor	$4335$
Order	$68$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8670\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(4335\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(68\)	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 4335.bx	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);