LMFDB - Dirichlet character orbit 12138.da

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(12138, base_ring=CyclotomicField(816)) M = H._module chi = DirichletCharacter(H, M([0,136,27])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(31,12138)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$12138$
Conductor:	$2023$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$816$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2023.bn	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:	$\Q(\zeta_{816})$
Fixed field:	Number field defined by a degree 816 polynomial (not computed)

First 31 of 256 characters in Galois orbit

Character	$-1$	$1$	$5$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{12138}(31,\cdot)$	$1$	$1$	$e\left(\frac{335}{816}\right)$	$e\left(\frac{349}{816}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{121}{408}\right)$	$e\left(\frac{581}{816}\right)$	$e\left(\frac{335}{408}\right)$	$e\left(\frac{37}{272}\right)$	$e\left(\frac{379}{816}\right)$	$e\left(\frac{491}{816}\right)$	$e\left(\frac{43}{272}\right)$
$\chi_{12138}(61,\cdot)$	$1$	$1$	$e\left(\frac{181}{816}\right)$	$e\left(\frac{191}{816}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{203}{408}\right)$	$e\left(\frac{7}{816}\right)$	$e\left(\frac{181}{408}\right)$	$e\left(\frac{7}{272}\right)$	$e\left(\frac{329}{816}\right)$	$e\left(\frac{409}{816}\right)$	$e\left(\frac{89}{272}\right)$
$\chi_{12138}(73,\cdot)$	$1$	$1$	$e\left(\frac{611}{816}\right)$	$e\left(\frac{505}{816}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{133}{408}\right)$	$e\left(\frac{497}{816}\right)$	$e\left(\frac{203}{408}\right)$	$e\left(\frac{225}{272}\right)$	$e\left(\frac{511}{816}\right)$	$e\left(\frac{479}{816}\right)$	$e\left(\frac{63}{272}\right)$
$\chi_{12138}(199,\cdot)$	$1$	$1$	$e\left(\frac{635}{816}\right)$	$e\left(\frac{625}{816}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{205}{408}\right)$	$e\left(\frac{809}{816}\right)$	$e\left(\frac{227}{408}\right)$	$e\left(\frac{265}{272}\right)$	$e\left(\frac{487}{816}\right)$	$e\left(\frac{407}{816}\right)$	$e\left(\frac{183}{272}\right)$
$\chi_{12138}(241,\cdot)$	$1$	$1$	$e\left(\frac{23}{816}\right)$	$e\left(\frac{421}{816}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{1}{408}\right)$	$e\left(\frac{605}{816}\right)$	$e\left(\frac{23}{408}\right)$	$e\left(\frac{61}{272}\right)$	$e\left(\frac{691}{816}\right)$	$e\left(\frac{611}{816}\right)$	$e\left(\frac{115}{272}\right)$
$\chi_{12138}(283,\cdot)$	$1$	$1$	$e\left(\frac{113}{816}\right)$	$e\left(\frac{259}{816}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{271}{408}\right)$	$e\left(\frac{347}{816}\right)$	$e\left(\frac{113}{408}\right)$	$e\left(\frac{75}{272}\right)$	$e\left(\frac{805}{816}\right)$	$e\left(\frac{341}{816}\right)$	$e\left(\frac{21}{272}\right)$
$\chi_{12138}(313,\cdot)$	$1$	$1$	$e\left(\frac{733}{816}\right)$	$e\left(\frac{503}{816}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{227}{408}\right)$	$e\left(\frac{655}{816}\right)$	$e\left(\frac{325}{408}\right)$	$e\left(\frac{111}{272}\right)$	$e\left(\frac{593}{816}\right)$	$e\left(\frac{385}{816}\right)$	$e\left(\frac{129}{272}\right)$
$\chi_{12138}(367,\cdot)$	$1$	$1$	$e\left(\frac{533}{816}\right)$	$e\left(\frac{319}{816}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{307}{408}\right)$	$e\left(\frac{503}{816}\right)$	$e\left(\frac{125}{408}\right)$	$e\left(\frac{231}{272}\right)$	$e\left(\frac{793}{816}\right)$	$e\left(\frac{713}{816}\right)$	$e\left(\frac{217}{272}\right)$
$\chi_{12138}(397,\cdot)$	$1$	$1$	$e\left(\frac{505}{816}\right)$	$e\left(\frac{587}{816}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{359}{408}\right)$	$e\left(\frac{547}{816}\right)$	$e\left(\frac{97}{408}\right)$	$e\left(\frac{3}{272}\right)$	$e\left(\frac{413}{816}\right)$	$e\left(\frac{253}{816}\right)$	$e\left(\frac{77}{272}\right)$
$\chi_{12138}(439,\cdot)$	$1$	$1$	$e\left(\frac{463}{816}\right)$	$e\left(\frac{173}{816}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{233}{408}\right)$	$e\left(\frac{613}{816}\right)$	$e\left(\frac{55}{408}\right)$	$e\left(\frac{69}{272}\right)$	$e\left(\frac{251}{816}\right)$	$e\left(\frac{379}{816}\right)$	$e\left(\frac{139}{272}\right)$
$\chi_{12138}(481,\cdot)$	$1$	$1$	$e\left(\frac{643}{816}\right)$	$e\left(\frac{665}{816}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{365}{408}\right)$	$e\left(\frac{97}{816}\right)$	$e\left(\frac{235}{408}\right)$	$e\left(\frac{97}{272}\right)$	$e\left(\frac{479}{816}\right)$	$e\left(\frac{655}{816}\right)$	$e\left(\frac{223}{272}\right)$
$\chi_{12138}(607,\cdot)$	$1$	$1$	$e\left(\frac{331}{816}\right)$	$e\left(\frac{737}{816}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{245}{408}\right)$	$e\left(\frac{121}{816}\right)$	$e\left(\frac{331}{408}\right)$	$e\left(\frac{121}{272}\right)$	$e\left(\frac{791}{816}\right)$	$e\left(\frac{775}{816}\right)$	$e\left(\frac{23}{272}\right)$
$\chi_{12138}(619,\cdot)$	$1$	$1$	$e\left(\frac{653}{816}\right)$	$e\left(\frac{103}{816}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{259}{408}\right)$	$e\left(\frac{431}{816}\right)$	$e\left(\frac{245}{408}\right)$	$e\left(\frac{159}{272}\right)$	$e\left(\frac{673}{816}\right)$	$e\left(\frac{353}{816}\right)$	$e\left(\frac{1}{272}\right)$
$\chi_{12138}(649,\cdot)$	$1$	$1$	$e\left(\frac{439}{816}\right)$	$e\left(\frac{53}{816}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{161}{408}\right)$	$e\left(\frac{301}{816}\right)$	$e\left(\frac{31}{408}\right)$	$e\left(\frac{29}{272}\right)$	$e\left(\frac{275}{816}\right)$	$e\left(\frac{451}{816}\right)$	$e\left(\frac{19}{272}\right)$
$\chi_{12138}(691,\cdot)$	$1$	$1$	$e\left(\frac{721}{816}\right)$	$e\left(\frac{35}{816}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{191}{408}\right)$	$e\left(\frac{91}{816}\right)$	$e\left(\frac{313}{408}\right)$	$e\left(\frac{91}{272}\right)$	$e\left(\frac{197}{816}\right)$	$e\left(\frac{421}{816}\right)$	$e\left(\frac{69}{272}\right)$
$\chi_{12138}(703,\cdot)$	$1$	$1$	$e\left(\frac{185}{816}\right)$	$e\left(\frac{619}{816}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{79}{408}\right)$	$e\left(\frac{467}{816}\right)$	$e\left(\frac{185}{408}\right)$	$e\left(\frac{195}{272}\right)$	$e\left(\frac{733}{816}\right)$	$e\left(\frac{125}{816}\right)$	$e\left(\frac{109}{272}\right)$
$\chi_{12138}(745,\cdot)$	$1$	$1$	$e\left(\frac{287}{816}\right)$	$e\left(\frac{109}{816}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{385}{408}\right)$	$e\left(\frac{773}{816}\right)$	$e\left(\frac{287}{408}\right)$	$e\left(\frac{229}{272}\right)$	$e\left(\frac{427}{816}\right)$	$e\left(\frac{635}{816}\right)$	$e\left(\frac{75}{272}\right)$
$\chi_{12138}(775,\cdot)$	$1$	$1$	$e\left(\frac{277}{816}\right)$	$e\left(\frac{671}{816}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{83}{408}\right)$	$e\left(\frac{439}{816}\right)$	$e\left(\frac{277}{408}\right)$	$e\left(\frac{167}{272}\right)$	$e\left(\frac{233}{816}\right)$	$e\left(\frac{121}{816}\right)$	$e\left(\frac{25}{272}\right)$
$\chi_{12138}(787,\cdot)$	$1$	$1$	$e\left(\frac{803}{816}\right)$	$e\left(\frac{649}{816}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{301}{408}\right)$	$e\left(\frac{545}{816}\right)$	$e\left(\frac{395}{408}\right)$	$e\left(\frac{1}{272}\right)$	$e\left(\frac{319}{816}\right)$	$e\left(\frac{719}{816}\right)$	$e\left(\frac{207}{272}\right)$
$\chi_{12138}(913,\cdot)$	$1$	$1$	$e\left(\frac{443}{816}\right)$	$e\left(\frac{481}{816}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{37}{408}\right)$	$e\left(\frac{761}{816}\right)$	$e\left(\frac{35}{408}\right)$	$e\left(\frac{217}{272}\right)$	$e\left(\frac{679}{816}\right)$	$e\left(\frac{167}{816}\right)$	$e\left(\frac{39}{272}\right)$
$\chi_{12138}(955,\cdot)$	$1$	$1$	$e\left(\frac{71}{816}\right)$	$e\left(\frac{661}{816}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{145}{408}\right)$	$e\left(\frac{413}{816}\right)$	$e\left(\frac{71}{408}\right)$	$e\left(\frac{141}{272}\right)$	$e\left(\frac{643}{816}\right)$	$e\left(\frac{467}{816}\right)$	$e\left(\frac{83}{272}\right)$
$\chi_{12138}(997,\cdot)$	$1$	$1$	$e\left(\frac{497}{816}\right)$	$e\left(\frac{547}{816}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{199}{408}\right)$	$e\left(\frac{443}{816}\right)$	$e\left(\frac{89}{408}\right)$	$e\left(\frac{171}{272}\right)$	$e\left(\frac{421}{816}\right)$	$e\left(\frac{5}{816}\right)$	$e\left(\frac{37}{272}\right)$
$\chi_{12138}(1027,\cdot)$	$1$	$1$	$e\left(\frac{637}{816}\right)$	$e\left(\frac{23}{816}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{347}{408}\right)$	$e\left(\frac{223}{816}\right)$	$e\left(\frac{229}{408}\right)$	$e\left(\frac{223}{272}\right)$	$e\left(\frac{689}{816}\right)$	$e\left(\frac{673}{816}\right)$	$e\left(\frac{193}{272}\right)$
$\chi_{12138}(1111,\cdot)$	$1$	$1$	$e\left(\frac{121}{816}\right)$	$e\left(\frac{299}{816}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{23}{408}\right)$	$e\left(\frac{451}{816}\right)$	$e\left(\frac{121}{408}\right)$	$e\left(\frac{179}{272}\right)$	$e\left(\frac{797}{816}\right)$	$e\left(\frac{589}{816}\right)$	$e\left(\frac{61}{272}\right)$
$\chi_{12138}(1153,\cdot)$	$1$	$1$	$e\left(\frac{415}{816}\right)$	$e\left(\frac{749}{816}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{89}{408}\right)$	$e\left(\frac{805}{816}\right)$	$e\left(\frac{7}{408}\right)$	$e\left(\frac{261}{272}\right)$	$e\left(\frac{299}{816}\right)$	$e\left(\frac{523}{816}\right)$	$e\left(\frac{171}{272}\right)$
$\chi_{12138}(1195,\cdot)$	$1$	$1$	$e\left(\frac{19}{816}\right)$	$e\left(\frac{809}{816}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{125}{408}\right)$	$e\left(\frac{145}{816}\right)$	$e\left(\frac{19}{408}\right)$	$e\left(\frac{145}{272}\right)$	$e\left(\frac{287}{816}\right)$	$e\left(\frac{79}{816}\right)$	$e\left(\frac{95}{272}\right)$
$\chi_{12138}(1321,\cdot)$	$1$	$1$	$e\left(\frac{139}{816}\right)$	$e\left(\frac{593}{816}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{77}{408}\right)$	$e\left(\frac{73}{816}\right)$	$e\left(\frac{139}{408}\right)$	$e\left(\frac{73}{272}\right)$	$e\left(\frac{167}{816}\right)$	$e\left(\frac{535}{816}\right)$	$e\left(\frac{151}{272}\right)$
$\chi_{12138}(1333,\cdot)$	$1$	$1$	$e\left(\frac{557}{816}\right)$	$e\left(\frac{439}{816}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{379}{408}\right)$	$e\left(\frac{815}{816}\right)$	$e\left(\frac{149}{408}\right)$	$e\left(\frac{271}{272}\right)$	$e\left(\frac{769}{816}\right)$	$e\left(\frac{641}{816}\right)$	$e\left(\frac{65}{272}\right)$
$\chi_{12138}(1363,\cdot)$	$1$	$1$	$e\left(\frac{487}{816}\right)$	$e\left(\frac{293}{816}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{305}{408}\right)$	$e\left(\frac{109}{816}\right)$	$e\left(\frac{79}{408}\right)$	$e\left(\frac{109}{272}\right)$	$e\left(\frac{227}{816}\right)$	$e\left(\frac{307}{816}\right)$	$e\left(\frac{259}{272}\right)$
$\chi_{12138}(1417,\cdot)$	$1$	$1$	$e\left(\frac{617}{816}\right)$	$e\left(\frac{331}{816}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{151}{408}\right)$	$e\left(\frac{371}{816}\right)$	$e\left(\frac{209}{408}\right)$	$e\left(\frac{99}{272}\right)$	$e\left(\frac{301}{816}\right)$	$e\left(\frac{461}{816}\right)$	$e\left(\frac{93}{272}\right)$
$\chi_{12138}(1459,\cdot)$	$1$	$1$	$e\left(\frac{239}{816}\right)$	$e\left(\frac{685}{816}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{241}{408}\right)$	$e\left(\frac{149}{816}\right)$	$e\left(\frac{239}{408}\right)$	$e\left(\frac{149}{272}\right)$	$e\left(\frac{475}{816}\right)$	$e\left(\frac{779}{816}\right)$	$e\left(\frac{107}{272}\right)$

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	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{12138}(31,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{335}{816}\right)\)	\(e\left(\frac{349}{816}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{121}{408}\right)\)	\(e\left(\frac{581}{816}\right)\)	\(e\left(\frac{335}{408}\right)\)	\(e\left(\frac{37}{272}\right)\)	\(e\left(\frac{379}{816}\right)\)	\(e\left(\frac{491}{816}\right)\)	\(e\left(\frac{43}{272}\right)\)
\(\chi_{12138}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{816}\right)\)	\(e\left(\frac{191}{816}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{203}{408}\right)\)	\(e\left(\frac{7}{816}\right)\)	\(e\left(\frac{181}{408}\right)\)	\(e\left(\frac{7}{272}\right)\)	\(e\left(\frac{329}{816}\right)\)	\(e\left(\frac{409}{816}\right)\)	\(e\left(\frac{89}{272}\right)\)
\(\chi_{12138}(73,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{611}{816}\right)\)	\(e\left(\frac{505}{816}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{133}{408}\right)\)	\(e\left(\frac{497}{816}\right)\)	\(e\left(\frac{203}{408}\right)\)	\(e\left(\frac{225}{272}\right)\)	\(e\left(\frac{511}{816}\right)\)	\(e\left(\frac{479}{816}\right)\)	\(e\left(\frac{63}{272}\right)\)
\(\chi_{12138}(199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{635}{816}\right)\)	\(e\left(\frac{625}{816}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{205}{408}\right)\)	\(e\left(\frac{809}{816}\right)\)	\(e\left(\frac{227}{408}\right)\)	\(e\left(\frac{265}{272}\right)\)	\(e\left(\frac{487}{816}\right)\)	\(e\left(\frac{407}{816}\right)\)	\(e\left(\frac{183}{272}\right)\)
\(\chi_{12138}(241,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{816}\right)\)	\(e\left(\frac{421}{816}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{1}{408}\right)\)	\(e\left(\frac{605}{816}\right)\)	\(e\left(\frac{23}{408}\right)\)	\(e\left(\frac{61}{272}\right)\)	\(e\left(\frac{691}{816}\right)\)	\(e\left(\frac{611}{816}\right)\)	\(e\left(\frac{115}{272}\right)\)
\(\chi_{12138}(283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{816}\right)\)	\(e\left(\frac{259}{816}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{271}{408}\right)\)	\(e\left(\frac{347}{816}\right)\)	\(e\left(\frac{113}{408}\right)\)	\(e\left(\frac{75}{272}\right)\)	\(e\left(\frac{805}{816}\right)\)	\(e\left(\frac{341}{816}\right)\)	\(e\left(\frac{21}{272}\right)\)
\(\chi_{12138}(313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{733}{816}\right)\)	\(e\left(\frac{503}{816}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{227}{408}\right)\)	\(e\left(\frac{655}{816}\right)\)	\(e\left(\frac{325}{408}\right)\)	\(e\left(\frac{111}{272}\right)\)	\(e\left(\frac{593}{816}\right)\)	\(e\left(\frac{385}{816}\right)\)	\(e\left(\frac{129}{272}\right)\)
\(\chi_{12138}(367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{533}{816}\right)\)	\(e\left(\frac{319}{816}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{307}{408}\right)\)	\(e\left(\frac{503}{816}\right)\)	\(e\left(\frac{125}{408}\right)\)	\(e\left(\frac{231}{272}\right)\)	\(e\left(\frac{793}{816}\right)\)	\(e\left(\frac{713}{816}\right)\)	\(e\left(\frac{217}{272}\right)\)
\(\chi_{12138}(397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{505}{816}\right)\)	\(e\left(\frac{587}{816}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{359}{408}\right)\)	\(e\left(\frac{547}{816}\right)\)	\(e\left(\frac{97}{408}\right)\)	\(e\left(\frac{3}{272}\right)\)	\(e\left(\frac{413}{816}\right)\)	\(e\left(\frac{253}{816}\right)\)	\(e\left(\frac{77}{272}\right)\)
\(\chi_{12138}(439,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{463}{816}\right)\)	\(e\left(\frac{173}{816}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{233}{408}\right)\)	\(e\left(\frac{613}{816}\right)\)	\(e\left(\frac{55}{408}\right)\)	\(e\left(\frac{69}{272}\right)\)	\(e\left(\frac{251}{816}\right)\)	\(e\left(\frac{379}{816}\right)\)	\(e\left(\frac{139}{272}\right)\)
\(\chi_{12138}(481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{643}{816}\right)\)	\(e\left(\frac{665}{816}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{365}{408}\right)\)	\(e\left(\frac{97}{816}\right)\)	\(e\left(\frac{235}{408}\right)\)	\(e\left(\frac{97}{272}\right)\)	\(e\left(\frac{479}{816}\right)\)	\(e\left(\frac{655}{816}\right)\)	\(e\left(\frac{223}{272}\right)\)
\(\chi_{12138}(607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{331}{816}\right)\)	\(e\left(\frac{737}{816}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{245}{408}\right)\)	\(e\left(\frac{121}{816}\right)\)	\(e\left(\frac{331}{408}\right)\)	\(e\left(\frac{121}{272}\right)\)	\(e\left(\frac{791}{816}\right)\)	\(e\left(\frac{775}{816}\right)\)	\(e\left(\frac{23}{272}\right)\)
\(\chi_{12138}(619,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{653}{816}\right)\)	\(e\left(\frac{103}{816}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{259}{408}\right)\)	\(e\left(\frac{431}{816}\right)\)	\(e\left(\frac{245}{408}\right)\)	\(e\left(\frac{159}{272}\right)\)	\(e\left(\frac{673}{816}\right)\)	\(e\left(\frac{353}{816}\right)\)	\(e\left(\frac{1}{272}\right)\)
\(\chi_{12138}(649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{439}{816}\right)\)	\(e\left(\frac{53}{816}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{161}{408}\right)\)	\(e\left(\frac{301}{816}\right)\)	\(e\left(\frac{31}{408}\right)\)	\(e\left(\frac{29}{272}\right)\)	\(e\left(\frac{275}{816}\right)\)	\(e\left(\frac{451}{816}\right)\)	\(e\left(\frac{19}{272}\right)\)
\(\chi_{12138}(691,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{721}{816}\right)\)	\(e\left(\frac{35}{816}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{191}{408}\right)\)	\(e\left(\frac{91}{816}\right)\)	\(e\left(\frac{313}{408}\right)\)	\(e\left(\frac{91}{272}\right)\)	\(e\left(\frac{197}{816}\right)\)	\(e\left(\frac{421}{816}\right)\)	\(e\left(\frac{69}{272}\right)\)
\(\chi_{12138}(703,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{185}{816}\right)\)	\(e\left(\frac{619}{816}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{79}{408}\right)\)	\(e\left(\frac{467}{816}\right)\)	\(e\left(\frac{185}{408}\right)\)	\(e\left(\frac{195}{272}\right)\)	\(e\left(\frac{733}{816}\right)\)	\(e\left(\frac{125}{816}\right)\)	\(e\left(\frac{109}{272}\right)\)
\(\chi_{12138}(745,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{287}{816}\right)\)	\(e\left(\frac{109}{816}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{385}{408}\right)\)	\(e\left(\frac{773}{816}\right)\)	\(e\left(\frac{287}{408}\right)\)	\(e\left(\frac{229}{272}\right)\)	\(e\left(\frac{427}{816}\right)\)	\(e\left(\frac{635}{816}\right)\)	\(e\left(\frac{75}{272}\right)\)
\(\chi_{12138}(775,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{277}{816}\right)\)	\(e\left(\frac{671}{816}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{83}{408}\right)\)	\(e\left(\frac{439}{816}\right)\)	\(e\left(\frac{277}{408}\right)\)	\(e\left(\frac{167}{272}\right)\)	\(e\left(\frac{233}{816}\right)\)	\(e\left(\frac{121}{816}\right)\)	\(e\left(\frac{25}{272}\right)\)
\(\chi_{12138}(787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{803}{816}\right)\)	\(e\left(\frac{649}{816}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{301}{408}\right)\)	\(e\left(\frac{545}{816}\right)\)	\(e\left(\frac{395}{408}\right)\)	\(e\left(\frac{1}{272}\right)\)	\(e\left(\frac{319}{816}\right)\)	\(e\left(\frac{719}{816}\right)\)	\(e\left(\frac{207}{272}\right)\)
\(\chi_{12138}(913,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{443}{816}\right)\)	\(e\left(\frac{481}{816}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{37}{408}\right)\)	\(e\left(\frac{761}{816}\right)\)	\(e\left(\frac{35}{408}\right)\)	\(e\left(\frac{217}{272}\right)\)	\(e\left(\frac{679}{816}\right)\)	\(e\left(\frac{167}{816}\right)\)	\(e\left(\frac{39}{272}\right)\)
\(\chi_{12138}(955,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{816}\right)\)	\(e\left(\frac{661}{816}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{145}{408}\right)\)	\(e\left(\frac{413}{816}\right)\)	\(e\left(\frac{71}{408}\right)\)	\(e\left(\frac{141}{272}\right)\)	\(e\left(\frac{643}{816}\right)\)	\(e\left(\frac{467}{816}\right)\)	\(e\left(\frac{83}{272}\right)\)
\(\chi_{12138}(997,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{497}{816}\right)\)	\(e\left(\frac{547}{816}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{199}{408}\right)\)	\(e\left(\frac{443}{816}\right)\)	\(e\left(\frac{89}{408}\right)\)	\(e\left(\frac{171}{272}\right)\)	\(e\left(\frac{421}{816}\right)\)	\(e\left(\frac{5}{816}\right)\)	\(e\left(\frac{37}{272}\right)\)
\(\chi_{12138}(1027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{637}{816}\right)\)	\(e\left(\frac{23}{816}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{347}{408}\right)\)	\(e\left(\frac{223}{816}\right)\)	\(e\left(\frac{229}{408}\right)\)	\(e\left(\frac{223}{272}\right)\)	\(e\left(\frac{689}{816}\right)\)	\(e\left(\frac{673}{816}\right)\)	\(e\left(\frac{193}{272}\right)\)
\(\chi_{12138}(1111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{816}\right)\)	\(e\left(\frac{299}{816}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{23}{408}\right)\)	\(e\left(\frac{451}{816}\right)\)	\(e\left(\frac{121}{408}\right)\)	\(e\left(\frac{179}{272}\right)\)	\(e\left(\frac{797}{816}\right)\)	\(e\left(\frac{589}{816}\right)\)	\(e\left(\frac{61}{272}\right)\)
\(\chi_{12138}(1153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{415}{816}\right)\)	\(e\left(\frac{749}{816}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{89}{408}\right)\)	\(e\left(\frac{805}{816}\right)\)	\(e\left(\frac{7}{408}\right)\)	\(e\left(\frac{261}{272}\right)\)	\(e\left(\frac{299}{816}\right)\)	\(e\left(\frac{523}{816}\right)\)	\(e\left(\frac{171}{272}\right)\)
\(\chi_{12138}(1195,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{816}\right)\)	\(e\left(\frac{809}{816}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{125}{408}\right)\)	\(e\left(\frac{145}{816}\right)\)	\(e\left(\frac{19}{408}\right)\)	\(e\left(\frac{145}{272}\right)\)	\(e\left(\frac{287}{816}\right)\)	\(e\left(\frac{79}{816}\right)\)	\(e\left(\frac{95}{272}\right)\)
\(\chi_{12138}(1321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{816}\right)\)	\(e\left(\frac{593}{816}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{77}{408}\right)\)	\(e\left(\frac{73}{816}\right)\)	\(e\left(\frac{139}{408}\right)\)	\(e\left(\frac{73}{272}\right)\)	\(e\left(\frac{167}{816}\right)\)	\(e\left(\frac{535}{816}\right)\)	\(e\left(\frac{151}{272}\right)\)
\(\chi_{12138}(1333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{557}{816}\right)\)	\(e\left(\frac{439}{816}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{379}{408}\right)\)	\(e\left(\frac{815}{816}\right)\)	\(e\left(\frac{149}{408}\right)\)	\(e\left(\frac{271}{272}\right)\)	\(e\left(\frac{769}{816}\right)\)	\(e\left(\frac{641}{816}\right)\)	\(e\left(\frac{65}{272}\right)\)
\(\chi_{12138}(1363,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{487}{816}\right)\)	\(e\left(\frac{293}{816}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{305}{408}\right)\)	\(e\left(\frac{109}{816}\right)\)	\(e\left(\frac{79}{408}\right)\)	\(e\left(\frac{109}{272}\right)\)	\(e\left(\frac{227}{816}\right)\)	\(e\left(\frac{307}{816}\right)\)	\(e\left(\frac{259}{272}\right)\)
\(\chi_{12138}(1417,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{617}{816}\right)\)	\(e\left(\frac{331}{816}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{151}{408}\right)\)	\(e\left(\frac{371}{816}\right)\)	\(e\left(\frac{209}{408}\right)\)	\(e\left(\frac{99}{272}\right)\)	\(e\left(\frac{301}{816}\right)\)	\(e\left(\frac{461}{816}\right)\)	\(e\left(\frac{93}{272}\right)\)
\(\chi_{12138}(1459,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{816}\right)\)	\(e\left(\frac{685}{816}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{241}{408}\right)\)	\(e\left(\frac{149}{816}\right)\)	\(e\left(\frac{239}{408}\right)\)	\(e\left(\frac{149}{272}\right)\)	\(e\left(\frac{475}{816}\right)\)	\(e\left(\frac{779}{816}\right)\)	\(e\left(\frac{107}{272}\right)\)

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First 31 of 256 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	12138.da
Modulus	$12138$
Conductor	$2023$
Order	$816$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(12138\)
Conductor:	\(2023\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(816\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2023.bn	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)