LMFDB - Dirichlet character orbit 2890.bf

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2890, base_ring=CyclotomicField(136)) M = H._module chi = DirichletCharacter(H, M([0,65])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(111,2890)) 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:	$136$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 289.i	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:	$\Q(\zeta_{136})$
Fixed field:	Number field defined by a degree 136 polynomial (not computed)

First 31 of 64 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{2890}(111,\cdot)$	$1$	$1$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{11}{136}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{135}{136}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{79}{136}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{101}{136}\right)$
$\chi_{2890}(121,\cdot)$	$1$	$1$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{19}{136}\right)$
$\chi_{2890}(151,\cdot)$	$1$	$1$	$e\left(\frac{3}{136}\right)$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{125}{136}\right)$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{103}{136}\right)$
$\chi_{2890}(161,\cdot)$	$1$	$1$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{131}{136}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{97}{136}\right)$
$\chi_{2890}(281,\cdot)$	$1$	$1$	$e\left(\frac{81}{136}\right)$	$e\left(\frac{43}{136}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{107}{136}\right)$	$e\left(\frac{61}{136}\right)$
$\chi_{2890}(291,\cdot)$	$1$	$1$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{37}{136}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{105}{136}\right)$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{43}{136}\right)$
$\chi_{2890}(321,\cdot)$	$1$	$1$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{49}{136}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{45}{136}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{117}{136}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{79}{136}\right)$
$\chi_{2890}(331,\cdot)$	$1$	$1$	$e\left(\frac{37}{136}\right)$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{91}{136}\right)$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{1}{136}\right)$
$\chi_{2890}(451,\cdot)$	$1$	$1$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{75}{136}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{7}{136}\right)$	$e\left(\frac{19}{136}\right)$	$e\left(\frac{21}{136}\right)$
$\chi_{2890}(461,\cdot)$	$1$	$1$	$e\left(\frac{31}{136}\right)$	$e\left(\frac{45}{136}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{33}{136}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{67}{136}\right)$
$\chi_{2890}(491,\cdot)$	$1$	$1$	$e\left(\frac{131}{136}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{109}{136}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{55}{136}\right)$
$\chi_{2890}(501,\cdot)$	$1$	$1$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{75}{136}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{41}{136}\right)$
$\chi_{2890}(621,\cdot)$	$1$	$1$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{107}{136}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{39}{136}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{117}{136}\right)$
$\chi_{2890}(631,\cdot)$	$1$	$1$	$e\left(\frac{103}{136}\right)$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{37}{136}\right)$	$e\left(\frac{91}{136}\right)$
$\chi_{2890}(661,\cdot)$	$1$	$1$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{33}{136}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{133}{136}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{101}{136}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{31}{136}\right)$
$\chi_{2890}(671,\cdot)$	$1$	$1$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{27}{136}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{81}{136}\right)$
$\chi_{2890}(791,\cdot)$	$1$	$1$	$e\left(\frac{129}{136}\right)$	$e\left(\frac{3}{136}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{77}{136}\right)$
$\chi_{2890}(801,\cdot)$	$1$	$1$	$e\left(\frac{39}{136}\right)$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{81}{136}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{129}{136}\right)$	$e\left(\frac{117}{136}\right)$	$e\left(\frac{115}{136}\right)$
$\chi_{2890}(831,\cdot)$	$1$	$1$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{109}{136}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{7}{136}\right)$
$\chi_{2890}(841,\cdot)$	$1$	$1$	$e\left(\frac{125}{136}\right)$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{19}{136}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{131}{136}\right)$	$e\left(\frac{103}{136}\right)$	$e\left(\frac{121}{136}\right)$
$\chi_{2890}(961,\cdot)$	$1$	$1$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{103}{136}\right)$	$e\left(\frac{27}{136}\right)$	$e\left(\frac{37}{136}\right)$
$\chi_{2890}(971,\cdot)$	$1$	$1$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{105}{136}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{1}{136}\right)$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{3}{136}\right)$
$\chi_{2890}(1011,\cdot)$	$1$	$1$	$e\left(\frac{109}{136}\right)$	$e\left(\frac{31}{136}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{25}{136}\right)$
$\chi_{2890}(1131,\cdot)$	$1$	$1$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{31}{136}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{135}{136}\right)$	$e\left(\frac{75}{136}\right)$	$e\left(\frac{133}{136}\right)$
$\chi_{2890}(1141,\cdot)$	$1$	$1$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{129}{136}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{27}{136}\right)$
$\chi_{2890}(1171,\cdot)$	$1$	$1$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{73}{136}\right)$	$e\left(\frac{95}{136}\right)$
$\chi_{2890}(1181,\cdot)$	$1$	$1$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{135}{136}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{7}{136}\right)$	$e\left(\frac{65}{136}\right)$
$\chi_{2890}(1301,\cdot)$	$1$	$1$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{31}{136}\right)$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{93}{136}\right)$
$\chi_{2890}(1341,\cdot)$	$1$	$1$	$e\left(\frac{43}{136}\right)$	$e\left(\frac{1}{136}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{37}{136}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{129}{136}\right)$	$e\left(\frac{71}{136}\right)$
$\chi_{2890}(1351,\cdot)$	$1$	$1$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{103}{136}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{3}{136}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{105}{136}\right)$
$\chi_{2890}(1471,\cdot)$	$1$	$1$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{131}{136}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{53}{136}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{2890}(111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{11}{136}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{135}{136}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{79}{136}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{101}{136}\right)\)
\(\chi_{2890}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{19}{136}\right)\)
\(\chi_{2890}(151,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{136}\right)\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{125}{136}\right)\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{103}{136}\right)\)
\(\chi_{2890}(161,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{131}{136}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{97}{136}\right)\)
\(\chi_{2890}(281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{136}\right)\)	\(e\left(\frac{43}{136}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{107}{136}\right)\)	\(e\left(\frac{61}{136}\right)\)
\(\chi_{2890}(291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{37}{136}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{105}{136}\right)\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{43}{136}\right)\)
\(\chi_{2890}(321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{49}{136}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{45}{136}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{117}{136}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{79}{136}\right)\)
\(\chi_{2890}(331,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{136}\right)\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{91}{136}\right)\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{1}{136}\right)\)
\(\chi_{2890}(451,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{75}{136}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{7}{136}\right)\)	\(e\left(\frac{19}{136}\right)\)	\(e\left(\frac{21}{136}\right)\)
\(\chi_{2890}(461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{136}\right)\)	\(e\left(\frac{45}{136}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{33}{136}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{67}{136}\right)\)
\(\chi_{2890}(491,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{136}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{109}{136}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{55}{136}\right)\)
\(\chi_{2890}(501,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{75}{136}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{41}{136}\right)\)
\(\chi_{2890}(621,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{107}{136}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{39}{136}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{117}{136}\right)\)
\(\chi_{2890}(631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{136}\right)\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{37}{136}\right)\)	\(e\left(\frac{91}{136}\right)\)
\(\chi_{2890}(661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{33}{136}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{133}{136}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{101}{136}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{31}{136}\right)\)
\(\chi_{2890}(671,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{27}{136}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{81}{136}\right)\)
\(\chi_{2890}(791,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{129}{136}\right)\)	\(e\left(\frac{3}{136}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{77}{136}\right)\)
\(\chi_{2890}(801,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{136}\right)\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{81}{136}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{129}{136}\right)\)	\(e\left(\frac{117}{136}\right)\)	\(e\left(\frac{115}{136}\right)\)
\(\chi_{2890}(831,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{109}{136}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{7}{136}\right)\)
\(\chi_{2890}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{136}\right)\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{19}{136}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{131}{136}\right)\)	\(e\left(\frac{103}{136}\right)\)	\(e\left(\frac{121}{136}\right)\)
\(\chi_{2890}(961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{103}{136}\right)\)	\(e\left(\frac{27}{136}\right)\)	\(e\left(\frac{37}{136}\right)\)
\(\chi_{2890}(971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{105}{136}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{1}{136}\right)\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{3}{136}\right)\)
\(\chi_{2890}(1011,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{136}\right)\)	\(e\left(\frac{31}{136}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{25}{136}\right)\)
\(\chi_{2890}(1131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{31}{136}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{135}{136}\right)\)	\(e\left(\frac{75}{136}\right)\)	\(e\left(\frac{133}{136}\right)\)
\(\chi_{2890}(1141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{129}{136}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{27}{136}\right)\)
\(\chi_{2890}(1171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{73}{136}\right)\)	\(e\left(\frac{95}{136}\right)\)
\(\chi_{2890}(1181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{135}{136}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{7}{136}\right)\)	\(e\left(\frac{65}{136}\right)\)
\(\chi_{2890}(1301,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{31}{136}\right)\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{93}{136}\right)\)
\(\chi_{2890}(1341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{136}\right)\)	\(e\left(\frac{1}{136}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{37}{136}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{129}{136}\right)\)	\(e\left(\frac{71}{136}\right)\)
\(\chi_{2890}(1351,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{103}{136}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{3}{136}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{105}{136}\right)\)
\(\chi_{2890}(1471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{131}{136}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{53}{136}\right)\)

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First 31 of 64 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.bf
Modulus	$2890$
Conductor	$289$
Order	$136$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(2890\)
Conductor:	\(289\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(136\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 289.i	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)