LMFDB - Dirichlet character orbit 2890.y

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2890, base_ring=CyclotomicField(68)) M = H._module chi = DirichletCharacter(H, M([0,39])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(21,2890)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2890$
Conductor:	$289$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$68$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 289.h	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:	$\Q(\zeta_{68})$
Fixed field:	Number field defined by a degree 68 polynomial

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{2890}(21,\cdot)$	$1$	$1$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{47}{68}\right)$
$\chi_{2890}(81,\cdot)$	$1$	$1$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{57}{68}\right)$
$\chi_{2890}(191,\cdot)$	$1$	$1$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{19}{68}\right)$
$\chi_{2890}(361,\cdot)$	$1$	$1$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{59}{68}\right)$
$\chi_{2890}(421,\cdot)$	$1$	$1$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{45}{68}\right)$
$\chi_{2890}(531,\cdot)$	$1$	$1$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{31}{68}\right)$
$\chi_{2890}(591,\cdot)$	$1$	$1$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{5}{68}\right)$
$\chi_{2890}(701,\cdot)$	$1$	$1$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{3}{68}\right)$
$\chi_{2890}(761,\cdot)$	$1$	$1$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{33}{68}\right)$
$\chi_{2890}(871,\cdot)$	$1$	$1$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{43}{68}\right)$
$\chi_{2890}(931,\cdot)$	$1$	$1$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{61}{68}\right)$
$\chi_{2890}(1041,\cdot)$	$1$	$1$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{15}{68}\right)$
$\chi_{2890}(1101,\cdot)$	$1$	$1$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{21}{68}\right)$
$\chi_{2890}(1211,\cdot)$	$1$	$1$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{55}{68}\right)$
$\chi_{2890}(1271,\cdot)$	$1$	$1$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{49}{68}\right)$
$\chi_{2890}(1381,\cdot)$	$1$	$1$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{27}{68}\right)$
$\chi_{2890}(1441,\cdot)$	$1$	$1$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{9}{68}\right)$
$\chi_{2890}(1551,\cdot)$	$1$	$1$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{67}{68}\right)$
$\chi_{2890}(1611,\cdot)$	$1$	$1$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{37}{68}\right)$
$\chi_{2890}(1721,\cdot)$	$1$	$1$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{39}{68}\right)$
$\chi_{2890}(1781,\cdot)$	$1$	$1$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{65}{68}\right)$
$\chi_{2890}(1891,\cdot)$	$1$	$1$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{11}{68}\right)$
$\chi_{2890}(1951,\cdot)$	$1$	$1$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{25}{68}\right)$
$\chi_{2890}(2121,\cdot)$	$1$	$1$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{53}{68}\right)$
$\chi_{2890}(2231,\cdot)$	$1$	$1$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{23}{68}\right)$
$\chi_{2890}(2291,\cdot)$	$1$	$1$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{13}{68}\right)$
$\chi_{2890}(2401,\cdot)$	$1$	$1$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{63}{68}\right)$
$\chi_{2890}(2461,\cdot)$	$1$	$1$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{41}{68}\right)$
$\chi_{2890}(2571,\cdot)$	$1$	$1$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{35}{68}\right)$
$\chi_{2890}(2631,\cdot)$	$1$	$1$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{1}{68}\right)$
$\chi_{2890}(2741,\cdot)$	$1$	$1$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{7}{68}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{2890}(21,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{47}{68}\right)\)
\(\chi_{2890}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{57}{68}\right)\)
\(\chi_{2890}(191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{19}{68}\right)\)
\(\chi_{2890}(361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{59}{68}\right)\)
\(\chi_{2890}(421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{45}{68}\right)\)
\(\chi_{2890}(531,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{31}{68}\right)\)
\(\chi_{2890}(591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{5}{68}\right)\)
\(\chi_{2890}(701,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)
\(\chi_{2890}(761,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{33}{68}\right)\)
\(\chi_{2890}(871,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{43}{68}\right)\)
\(\chi_{2890}(931,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{61}{68}\right)\)
\(\chi_{2890}(1041,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{15}{68}\right)\)
\(\chi_{2890}(1101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{21}{68}\right)\)
\(\chi_{2890}(1211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{55}{68}\right)\)
\(\chi_{2890}(1271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{49}{68}\right)\)
\(\chi_{2890}(1381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{27}{68}\right)\)
\(\chi_{2890}(1441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{9}{68}\right)\)
\(\chi_{2890}(1551,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{67}{68}\right)\)
\(\chi_{2890}(1611,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{37}{68}\right)\)
\(\chi_{2890}(1721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{39}{68}\right)\)
\(\chi_{2890}(1781,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{65}{68}\right)\)
\(\chi_{2890}(1891,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{11}{68}\right)\)
\(\chi_{2890}(1951,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{25}{68}\right)\)
\(\chi_{2890}(2121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{53}{68}\right)\)
\(\chi_{2890}(2231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)
\(\chi_{2890}(2291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{13}{68}\right)\)
\(\chi_{2890}(2401,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{63}{68}\right)\)
\(\chi_{2890}(2461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{41}{68}\right)\)
\(\chi_{2890}(2571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{35}{68}\right)\)
\(\chi_{2890}(2631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{1}{68}\right)\)
\(\chi_{2890}(2741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{7}{68}\right)\)

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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	2890.y
Modulus	$2890$
Conductor	$289$
Order	$68$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(2890\)
Conductor:	\(289\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(68\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 289.h	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)