LMFDB - Dirichlet character orbit 2312.bg

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2312, base_ring=CyclotomicField(136)) M = H._module chi = DirichletCharacter(H, M([68,68,7])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(19,2312)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2312$
Conductor:	$2312$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$136$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$19$	$21$	$23$
$\chi_{2312}(19,\cdot)$	$-1$	$1$	$e\left(\frac{7}{136}\right)$	$e\left(\frac{39}{136}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{133}{136}\right)$
$\chi_{2312}(43,\cdot)$	$-1$	$1$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{105}{136}\right)$	$e\left(\frac{39}{136}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{107}{136}\right)$
$\chi_{2312}(59,\cdot)$	$-1$	$1$	$e\left(\frac{117}{136}\right)$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{107}{136}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{47}{136}\right)$
$\chi_{2312}(83,\cdot)$	$-1$	$1$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{101}{136}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{133}{136}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{33}{136}\right)$
$\chi_{2312}(195,\cdot)$	$-1$	$1$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{3}{136}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{103}{136}\right)$
$\chi_{2312}(219,\cdot)$	$-1$	$1$	$e\left(\frac{83}{136}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{81}{136}\right)$
$\chi_{2312}(291,\cdot)$	$-1$	$1$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{105}{136}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{37}{136}\right)$
$\chi_{2312}(315,\cdot)$	$-1$	$1$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{131}{136}\right)$
$\chi_{2312}(331,\cdot)$	$-1$	$1$	$e\left(\frac{37}{136}\right)$	$e\left(\frac{109}{136}\right)$	$e\left(\frac{91}{136}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{23}{136}\right)$
$\chi_{2312}(355,\cdot)$	$-1$	$1$	$e\left(\frac{107}{136}\right)$	$e\left(\frac{91}{136}\right)$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{129}{136}\right)$
$\chi_{2312}(427,\cdot)$	$-1$	$1$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{7}{136}\right)$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{1}{136}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{125}{136}\right)$
$\chi_{2312}(451,\cdot)$	$-1$	$1$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{7}{136}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{75}{136}\right)$
$\chi_{2312}(467,\cdot)$	$-1$	$1$	$e\left(\frac{133}{136}\right)$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{11}{136}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{79}{136}\right)$
$\chi_{2312}(491,\cdot)$	$-1$	$1$	$e\left(\frac{131}{136}\right)$	$e\left(\frac{11}{136}\right)$	$e\left(\frac{109}{136}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{41}{136}\right)$
$\chi_{2312}(563,\cdot)$	$-1$	$1$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{129}{136}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{77}{136}\right)$
$\chi_{2312}(587,\cdot)$	$-1$	$1$	$e\left(\frac{1}{136}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{19}{136}\right)$
$\chi_{2312}(603,\cdot)$	$-1$	$1$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{135}{136}\right)$
$\chi_{2312}(627,\cdot)$	$-1$	$1$	$e\left(\frac{19}{136}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{89}{136}\right)$
$\chi_{2312}(699,\cdot)$	$-1$	$1$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{31}{136}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{29}{136}\right)$
$\chi_{2312}(723,\cdot)$	$-1$	$1$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{73}{136}\right)$	$e\left(\frac{31}{136}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{99}{136}\right)$
$\chi_{2312}(739,\cdot)$	$-1$	$1$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{101}{136}\right)$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{131}{136}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{55}{136}\right)$
$\chi_{2312}(763,\cdot)$	$-1$	$1$	$e\left(\frac{43}{136}\right)$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{37}{136}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{1}{136}\right)$
$\chi_{2312}(835,\cdot)$	$-1$	$1$	$e\left(\frac{135}{136}\right)$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{49}{136}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{117}{136}\right)$
$\chi_{2312}(859,\cdot)$	$-1$	$1$	$e\left(\frac{81}{136}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{43}{136}\right)$
$\chi_{2312}(875,\cdot)$	$-1$	$1$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{43}{136}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{27}{136}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{111}{136}\right)$
$\chi_{2312}(899,\cdot)$	$-1$	$1$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{43}{136}\right)$	$e\left(\frac{117}{136}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{45}{136}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{49}{136}\right)$
$\chi_{2312}(971,\cdot)$	$-1$	$1$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{1}{136}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{105}{136}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{69}{136}\right)$
$\chi_{2312}(995,\cdot)$	$-1$	$1$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{33}{136}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{123}{136}\right)$
$\chi_{2312}(1011,\cdot)$	$-1$	$1$	$e\left(\frac{109}{136}\right)$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{31}{136}\right)$
$\chi_{2312}(1035,\cdot)$	$-1$	$1$	$e\left(\frac{91}{136}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{97}{136}\right)$
$\chi_{2312}(1107,\cdot)$	$-1$	$1$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{135}{136}\right)$	$e\left(\frac{89}{136}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{21}{136}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(21\)	\(23\)
\(\chi_{2312}(19,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{136}\right)\)	\(e\left(\frac{39}{136}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{133}{136}\right)\)
\(\chi_{2312}(43,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{105}{136}\right)\)	\(e\left(\frac{39}{136}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{107}{136}\right)\)
\(\chi_{2312}(59,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{117}{136}\right)\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{107}{136}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{47}{136}\right)\)
\(\chi_{2312}(83,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{101}{136}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{133}{136}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{33}{136}\right)\)
\(\chi_{2312}(195,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{3}{136}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{103}{136}\right)\)
\(\chi_{2312}(219,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{136}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{81}{136}\right)\)
\(\chi_{2312}(291,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{105}{136}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{37}{136}\right)\)
\(\chi_{2312}(315,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{131}{136}\right)\)
\(\chi_{2312}(331,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{136}\right)\)	\(e\left(\frac{109}{136}\right)\)	\(e\left(\frac{91}{136}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{23}{136}\right)\)
\(\chi_{2312}(355,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{107}{136}\right)\)	\(e\left(\frac{91}{136}\right)\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{129}{136}\right)\)
\(\chi_{2312}(427,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{7}{136}\right)\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{1}{136}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{125}{136}\right)\)
\(\chi_{2312}(451,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{7}{136}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{75}{136}\right)\)
\(\chi_{2312}(467,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{136}\right)\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{11}{136}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{79}{136}\right)\)
\(\chi_{2312}(491,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{136}\right)\)	\(e\left(\frac{11}{136}\right)\)	\(e\left(\frac{109}{136}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{41}{136}\right)\)
\(\chi_{2312}(563,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{129}{136}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{77}{136}\right)\)
\(\chi_{2312}(587,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{136}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{19}{136}\right)\)
\(\chi_{2312}(603,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{135}{136}\right)\)
\(\chi_{2312}(627,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{136}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{89}{136}\right)\)
\(\chi_{2312}(699,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{31}{136}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{29}{136}\right)\)
\(\chi_{2312}(723,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{73}{136}\right)\)	\(e\left(\frac{31}{136}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{99}{136}\right)\)
\(\chi_{2312}(739,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{101}{136}\right)\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{131}{136}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{55}{136}\right)\)
\(\chi_{2312}(763,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{136}\right)\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{37}{136}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{1}{136}\right)\)
\(\chi_{2312}(835,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{135}{136}\right)\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{49}{136}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{117}{136}\right)\)
\(\chi_{2312}(859,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{81}{136}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{43}{136}\right)\)
\(\chi_{2312}(875,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{43}{136}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{27}{136}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{111}{136}\right)\)
\(\chi_{2312}(899,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{43}{136}\right)\)	\(e\left(\frac{117}{136}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{45}{136}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{49}{136}\right)\)
\(\chi_{2312}(971,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{1}{136}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{105}{136}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{69}{136}\right)\)
\(\chi_{2312}(995,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{33}{136}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{123}{136}\right)\)
\(\chi_{2312}(1011,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{136}\right)\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{31}{136}\right)\)
\(\chi_{2312}(1035,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{136}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{97}{136}\right)\)
\(\chi_{2312}(1107,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{135}{136}\right)\)	\(e\left(\frac{89}{136}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{21}{136}\right)\)

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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	2312.bg
Modulus	$2312$
Conductor	$2312$
Order	$136$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(2312\)
Conductor:	\(2312\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(136\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)