LMFDB - Dirichlet character orbit 309680.cfm

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(309680, base_ring=CyclotomicField(1092)) M = H._module chi = DirichletCharacter(H, M([0,0,273,650,294])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(17,309680)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$309680$
Conductor:	$19355$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$1092$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 19355.jf	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{1092})$
Fixed field:	Number field defined by a degree 1092 polynomial (not computed)

First 31 of 288 characters in Galois orbit

Character	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{309680}(17,\cdot)$	$-1$	$1$	$e\left(\frac{671}{1092}\right)$	$e\left(\frac{125}{546}\right)$	$e\left(\frac{32}{273}\right)$	$e\left(\frac{199}{364}\right)$	$e\left(\frac{857}{1092}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{307}{364}\right)$	$e\left(\frac{16}{91}\right)$	$e\left(\frac{19}{78}\right)$
$\chi_{309680}(33,\cdot)$	$-1$	$1$	$e\left(\frac{121}{1092}\right)$	$e\left(\frac{121}{546}\right)$	$e\left(\frac{55}{273}\right)$	$e\left(\frac{197}{364}\right)$	$e\left(\frac{799}{1092}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{121}{364}\right)$	$e\left(\frac{73}{91}\right)$	$e\left(\frac{29}{78}\right)$
$\chi_{309680}(817,\cdot)$	$-1$	$1$	$e\left(\frac{835}{1092}\right)$	$e\left(\frac{289}{546}\right)$	$e\left(\frac{181}{273}\right)$	$e\left(\frac{99}{364}\right)$	$e\left(\frac{505}{1092}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{107}{364}\right)$	$e\left(\frac{45}{91}\right)$	$e\left(\frac{77}{78}\right)$
$\chi_{309680}(1937,\cdot)$	$-1$	$1$	$e\left(\frac{127}{1092}\right)$	$e\left(\frac{127}{546}\right)$	$e\left(\frac{157}{273}\right)$	$e\left(\frac{291}{364}\right)$	$e\left(\frac{613}{1092}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{127}{364}\right)$	$e\left(\frac{33}{91}\right)$	$e\left(\frac{53}{78}\right)$
$\chi_{309680}(2033,\cdot)$	$-1$	$1$	$e\left(\frac{353}{1092}\right)$	$e\left(\frac{353}{546}\right)$	$e\left(\frac{86}{273}\right)$	$e\left(\frac{313}{364}\right)$	$e\left(\frac{887}{1092}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{353}{364}\right)$	$e\left(\frac{43}{91}\right)$	$e\left(\frac{73}{78}\right)$
$\chi_{309680}(4177,\cdot)$	$-1$	$1$	$e\left(\frac{391}{1092}\right)$	$e\left(\frac{391}{546}\right)$	$e\left(\frac{4}{273}\right)$	$e\left(\frac{59}{364}\right)$	$e\left(\frac{73}{1092}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{27}{364}\right)$	$e\left(\frac{2}{91}\right)$	$e\left(\frac{17}{78}\right)$
$\chi_{309680}(5073,\cdot)$	$-1$	$1$	$e\left(\frac{1009}{1092}\right)$	$e\left(\frac{463}{546}\right)$	$e\left(\frac{136}{273}\right)$	$e\left(\frac{277}{364}\right)$	$e\left(\frac{571}{1092}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{281}{364}\right)$	$e\left(\frac{68}{91}\right)$	$e\left(\frac{71}{78}\right)$
$\chi_{309680}(6177,\cdot)$	$-1$	$1$	$e\left(\frac{635}{1092}\right)$	$e\left(\frac{89}{546}\right)$	$e\left(\frac{239}{273}\right)$	$e\left(\frac{363}{364}\right)$	$e\left(\frac{881}{1092}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{271}{364}\right)$	$e\left(\frac{74}{91}\right)$	$e\left(\frac{31}{78}\right)$
$\chi_{309680}(10657,\cdot)$	$-1$	$1$	$e\left(\frac{311}{1092}\right)$	$e\left(\frac{311}{546}\right)$	$e\left(\frac{191}{273}\right)$	$e\left(\frac{19}{364}\right)$	$e\left(\frac{5}{1092}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{311}{364}\right)$	$e\left(\frac{50}{91}\right)$	$e\left(\frac{61}{78}\right)$
$\chi_{309680}(10993,\cdot)$	$-1$	$1$	$e\left(\frac{1049}{1092}\right)$	$e\left(\frac{503}{546}\right)$	$e\left(\frac{179}{273}\right)$	$e\left(\frac{297}{364}\right)$	$e\left(\frac{59}{1092}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{321}{364}\right)$	$e\left(\frac{44}{91}\right)$	$e\left(\frac{49}{78}\right)$
$\chi_{309680}(11233,\cdot)$	$-1$	$1$	$e\left(\frac{349}{1092}\right)$	$e\left(\frac{349}{546}\right)$	$e\left(\frac{109}{273}\right)$	$e\left(\frac{129}{364}\right)$	$e\left(\frac{283}{1092}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{349}{364}\right)$	$e\left(\frac{9}{91}\right)$	$e\left(\frac{5}{78}\right)$
$\chi_{309680}(14577,\cdot)$	$-1$	$1$	$e\left(\frac{647}{1092}\right)$	$e\left(\frac{101}{546}\right)$	$e\left(\frac{170}{273}\right)$	$e\left(\frac{187}{364}\right)$	$e\left(\frac{509}{1092}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{283}{364}\right)$	$e\left(\frac{85}{91}\right)$	$e\left(\frac{1}{78}\right)$
$\chi_{309680}(14593,\cdot)$	$-1$	$1$	$e\left(\frac{241}{1092}\right)$	$e\left(\frac{241}{546}\right)$	$e\left(\frac{184}{273}\right)$	$e\left(\frac{257}{364}\right)$	$e\left(\frac{355}{1092}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{241}{364}\right)$	$e\left(\frac{1}{91}\right)$	$e\left(\frac{41}{78}\right)$
$\chi_{309680}(14913,\cdot)$	$-1$	$1$	$e\left(\frac{461}{1092}\right)$	$e\left(\frac{461}{546}\right)$	$e\left(\frac{11}{273}\right)$	$e\left(\frac{185}{364}\right)$	$e\left(\frac{815}{1092}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{97}{364}\right)$	$e\left(\frac{51}{91}\right)$	$e\left(\frac{37}{78}\right)$
$\chi_{309680}(15713,\cdot)$	$-1$	$1$	$e\left(\frac{961}{1092}\right)$	$e\left(\frac{415}{546}\right)$	$e\left(\frac{139}{273}\right)$	$e\left(\frac{253}{364}\right)$	$e\left(\frac{967}{1092}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{233}{364}\right)$	$e\left(\frac{24}{91}\right)$	$e\left(\frac{35}{78}\right)$
$\chi_{309680}(15937,\cdot)$	$-1$	$1$	$e\left(\frac{223}{1092}\right)$	$e\left(\frac{223}{546}\right)$	$e\left(\frac{151}{273}\right)$	$e\left(\frac{339}{364}\right)$	$e\left(\frac{913}{1092}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{223}{364}\right)$	$e\left(\frac{30}{91}\right)$	$e\left(\frac{47}{78}\right)$
$\chi_{309680}(16817,\cdot)$	$-1$	$1$	$e\left(\frac{443}{1092}\right)$	$e\left(\frac{443}{546}\right)$	$e\left(\frac{251}{273}\right)$	$e\left(\frac{267}{364}\right)$	$e\left(\frac{281}{1092}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{79}{364}\right)$	$e\left(\frac{80}{91}\right)$	$e\left(\frac{43}{78}\right)$
$\chi_{309680}(17713,\cdot)$	$-1$	$1$	$e\left(\frac{437}{1092}\right)$	$e\left(\frac{437}{546}\right)$	$e\left(\frac{149}{273}\right)$	$e\left(\frac{173}{364}\right)$	$e\left(\frac{467}{1092}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{73}{364}\right)$	$e\left(\frac{29}{91}\right)$	$e\left(\frac{19}{78}\right)$
$\chi_{309680}(18513,\cdot)$	$-1$	$1$	$e\left(\frac{913}{1092}\right)$	$e\left(\frac{367}{546}\right)$	$e\left(\frac{142}{273}\right)$	$e\left(\frac{229}{364}\right)$	$e\left(\frac{271}{1092}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{185}{364}\right)$	$e\left(\frac{71}{91}\right)$	$e\left(\frac{77}{78}\right)$
$\chi_{309680}(19633,\cdot)$	$-1$	$1$	$e\left(\frac{205}{1092}\right)$	$e\left(\frac{205}{546}\right)$	$e\left(\frac{118}{273}\right)$	$e\left(\frac{57}{364}\right)$	$e\left(\frac{379}{1092}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{205}{364}\right)$	$e\left(\frac{59}{91}\right)$	$e\left(\frac{53}{78}\right)$
$\chi_{309680}(23873,\cdot)$	$-1$	$1$	$e\left(\frac{401}{1092}\right)$	$e\left(\frac{401}{546}\right)$	$e\left(\frac{83}{273}\right)$	$e\left(\frac{337}{364}\right)$	$e\left(\frac{491}{1092}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{37}{364}\right)$	$e\left(\frac{87}{91}\right)$	$e\left(\frac{31}{78}\right)$
$\chi_{309680}(24897,\cdot)$	$-1$	$1$	$e\left(\frac{607}{1092}\right)$	$e\left(\frac{61}{546}\right)$	$e\left(\frac{127}{273}\right)$	$e\left(\frac{167}{364}\right)$	$e\left(\frac{1021}{1092}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{243}{364}\right)$	$e\left(\frac{18}{91}\right)$	$e\left(\frac{23}{78}\right)$
$\chi_{309680}(27233,\cdot)$	$-1$	$1$	$e\left(\frac{137}{1092}\right)$	$e\left(\frac{137}{546}\right)$	$e\left(\frac{236}{273}\right)$	$e\left(\frac{205}{364}\right)$	$e\left(\frac{1031}{1092}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{137}{364}\right)$	$e\left(\frac{27}{91}\right)$	$e\left(\frac{67}{78}\right)$
$\chi_{309680}(28577,\cdot)$	$-1$	$1$	$e\left(\frac{275}{1092}\right)$	$e\left(\frac{275}{546}\right)$	$e\left(\frac{125}{273}\right)$	$e\left(\frac{183}{364}\right)$	$e\left(\frac{29}{1092}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{275}{364}\right)$	$e\left(\frac{17}{91}\right)$	$e\left(\frac{73}{78}\right)$
$\chi_{309680}(28817,\cdot)$	$-1$	$1$	$e\left(\frac{19}{1092}\right)$	$e\left(\frac{19}{546}\right)$	$e\left(\frac{232}{273}\right)$	$e\left(\frac{55}{364}\right)$	$e\left(\frac{685}{1092}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{19}{364}\right)$	$e\left(\frac{25}{91}\right)$	$e\left(\frac{11}{78}\right)$
$\chi_{309680}(31153,\cdot)$	$-1$	$1$	$e\left(\frac{809}{1092}\right)$	$e\left(\frac{263}{546}\right)$	$e\left(\frac{194}{273}\right)$	$e\left(\frac{177}{364}\right)$	$e\left(\frac{947}{1092}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{81}{364}\right)$	$e\left(\frac{6}{91}\right)$	$e\left(\frac{25}{78}\right)$
$\chi_{309680}(31377,\cdot)$	$-1$	$1$	$e\left(\frac{83}{1092}\right)$	$e\left(\frac{83}{546}\right)$	$e\left(\frac{137}{273}\right)$	$e\left(\frac{87}{364}\right)$	$e\left(\frac{521}{1092}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{83}{364}\right)$	$e\left(\frac{23}{91}\right)$	$e\left(\frac{7}{78}\right)$
$\chi_{309680}(31617,\cdot)$	$-1$	$1$	$e\left(\frac{307}{1092}\right)$	$e\left(\frac{307}{546}\right)$	$e\left(\frac{214}{273}\right)$	$e\left(\frac{199}{364}\right)$	$e\left(\frac{493}{1092}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{307}{364}\right)$	$e\left(\frac{16}{91}\right)$	$e\left(\frac{71}{78}\right)$
$\chi_{309680}(34513,\cdot)$	$-1$	$1$	$e\left(\frac{209}{1092}\right)$	$e\left(\frac{209}{546}\right)$	$e\left(\frac{95}{273}\right)$	$e\left(\frac{241}{364}\right)$	$e\left(\frac{983}{1092}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{209}{364}\right)$	$e\left(\frac{2}{91}\right)$	$e\left(\frac{43}{78}\right)$
$\chi_{309680}(36433,\cdot)$	$-1$	$1$	$e\left(\frac{421}{1092}\right)$	$e\left(\frac{421}{546}\right)$	$e\left(\frac{241}{273}\right)$	$e\left(\frac{165}{364}\right)$	$e\left(\frac{235}{1092}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{57}{364}\right)$	$e\left(\frac{75}{91}\right)$	$e\left(\frac{59}{78}\right)$
$\chi_{309680}(37537,\cdot)$	$-1$	$1$	$e\left(\frac{971}{1092}\right)$	$e\left(\frac{425}{546}\right)$	$e\left(\frac{218}{273}\right)$	$e\left(\frac{167}{364}\right)$	$e\left(\frac{293}{1092}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{243}{364}\right)$	$e\left(\frac{18}{91}\right)$	$e\left(\frac{49}{78}\right)$

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	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{309680}(17,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{671}{1092}\right)\)	\(e\left(\frac{125}{546}\right)\)	\(e\left(\frac{32}{273}\right)\)	\(e\left(\frac{199}{364}\right)\)	\(e\left(\frac{857}{1092}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{307}{364}\right)\)	\(e\left(\frac{16}{91}\right)\)	\(e\left(\frac{19}{78}\right)\)
\(\chi_{309680}(33,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{1092}\right)\)	\(e\left(\frac{121}{546}\right)\)	\(e\left(\frac{55}{273}\right)\)	\(e\left(\frac{197}{364}\right)\)	\(e\left(\frac{799}{1092}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{121}{364}\right)\)	\(e\left(\frac{73}{91}\right)\)	\(e\left(\frac{29}{78}\right)\)
\(\chi_{309680}(817,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{835}{1092}\right)\)	\(e\left(\frac{289}{546}\right)\)	\(e\left(\frac{181}{273}\right)\)	\(e\left(\frac{99}{364}\right)\)	\(e\left(\frac{505}{1092}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{107}{364}\right)\)	\(e\left(\frac{45}{91}\right)\)	\(e\left(\frac{77}{78}\right)\)
\(\chi_{309680}(1937,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{1092}\right)\)	\(e\left(\frac{127}{546}\right)\)	\(e\left(\frac{157}{273}\right)\)	\(e\left(\frac{291}{364}\right)\)	\(e\left(\frac{613}{1092}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{127}{364}\right)\)	\(e\left(\frac{33}{91}\right)\)	\(e\left(\frac{53}{78}\right)\)
\(\chi_{309680}(2033,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{353}{1092}\right)\)	\(e\left(\frac{353}{546}\right)\)	\(e\left(\frac{86}{273}\right)\)	\(e\left(\frac{313}{364}\right)\)	\(e\left(\frac{887}{1092}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{353}{364}\right)\)	\(e\left(\frac{43}{91}\right)\)	\(e\left(\frac{73}{78}\right)\)
\(\chi_{309680}(4177,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{391}{1092}\right)\)	\(e\left(\frac{391}{546}\right)\)	\(e\left(\frac{4}{273}\right)\)	\(e\left(\frac{59}{364}\right)\)	\(e\left(\frac{73}{1092}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{27}{364}\right)\)	\(e\left(\frac{2}{91}\right)\)	\(e\left(\frac{17}{78}\right)\)
\(\chi_{309680}(5073,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1009}{1092}\right)\)	\(e\left(\frac{463}{546}\right)\)	\(e\left(\frac{136}{273}\right)\)	\(e\left(\frac{277}{364}\right)\)	\(e\left(\frac{571}{1092}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{281}{364}\right)\)	\(e\left(\frac{68}{91}\right)\)	\(e\left(\frac{71}{78}\right)\)
\(\chi_{309680}(6177,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{635}{1092}\right)\)	\(e\left(\frac{89}{546}\right)\)	\(e\left(\frac{239}{273}\right)\)	\(e\left(\frac{363}{364}\right)\)	\(e\left(\frac{881}{1092}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{271}{364}\right)\)	\(e\left(\frac{74}{91}\right)\)	\(e\left(\frac{31}{78}\right)\)
\(\chi_{309680}(10657,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{311}{1092}\right)\)	\(e\left(\frac{311}{546}\right)\)	\(e\left(\frac{191}{273}\right)\)	\(e\left(\frac{19}{364}\right)\)	\(e\left(\frac{5}{1092}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{311}{364}\right)\)	\(e\left(\frac{50}{91}\right)\)	\(e\left(\frac{61}{78}\right)\)
\(\chi_{309680}(10993,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1049}{1092}\right)\)	\(e\left(\frac{503}{546}\right)\)	\(e\left(\frac{179}{273}\right)\)	\(e\left(\frac{297}{364}\right)\)	\(e\left(\frac{59}{1092}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{321}{364}\right)\)	\(e\left(\frac{44}{91}\right)\)	\(e\left(\frac{49}{78}\right)\)
\(\chi_{309680}(11233,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{349}{1092}\right)\)	\(e\left(\frac{349}{546}\right)\)	\(e\left(\frac{109}{273}\right)\)	\(e\left(\frac{129}{364}\right)\)	\(e\left(\frac{283}{1092}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{349}{364}\right)\)	\(e\left(\frac{9}{91}\right)\)	\(e\left(\frac{5}{78}\right)\)
\(\chi_{309680}(14577,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{647}{1092}\right)\)	\(e\left(\frac{101}{546}\right)\)	\(e\left(\frac{170}{273}\right)\)	\(e\left(\frac{187}{364}\right)\)	\(e\left(\frac{509}{1092}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{283}{364}\right)\)	\(e\left(\frac{85}{91}\right)\)	\(e\left(\frac{1}{78}\right)\)
\(\chi_{309680}(14593,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{241}{1092}\right)\)	\(e\left(\frac{241}{546}\right)\)	\(e\left(\frac{184}{273}\right)\)	\(e\left(\frac{257}{364}\right)\)	\(e\left(\frac{355}{1092}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{241}{364}\right)\)	\(e\left(\frac{1}{91}\right)\)	\(e\left(\frac{41}{78}\right)\)
\(\chi_{309680}(14913,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{461}{1092}\right)\)	\(e\left(\frac{461}{546}\right)\)	\(e\left(\frac{11}{273}\right)\)	\(e\left(\frac{185}{364}\right)\)	\(e\left(\frac{815}{1092}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{97}{364}\right)\)	\(e\left(\frac{51}{91}\right)\)	\(e\left(\frac{37}{78}\right)\)
\(\chi_{309680}(15713,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{961}{1092}\right)\)	\(e\left(\frac{415}{546}\right)\)	\(e\left(\frac{139}{273}\right)\)	\(e\left(\frac{253}{364}\right)\)	\(e\left(\frac{967}{1092}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{233}{364}\right)\)	\(e\left(\frac{24}{91}\right)\)	\(e\left(\frac{35}{78}\right)\)
\(\chi_{309680}(15937,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{223}{1092}\right)\)	\(e\left(\frac{223}{546}\right)\)	\(e\left(\frac{151}{273}\right)\)	\(e\left(\frac{339}{364}\right)\)	\(e\left(\frac{913}{1092}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{223}{364}\right)\)	\(e\left(\frac{30}{91}\right)\)	\(e\left(\frac{47}{78}\right)\)
\(\chi_{309680}(16817,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{443}{1092}\right)\)	\(e\left(\frac{443}{546}\right)\)	\(e\left(\frac{251}{273}\right)\)	\(e\left(\frac{267}{364}\right)\)	\(e\left(\frac{281}{1092}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{79}{364}\right)\)	\(e\left(\frac{80}{91}\right)\)	\(e\left(\frac{43}{78}\right)\)
\(\chi_{309680}(17713,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{437}{1092}\right)\)	\(e\left(\frac{437}{546}\right)\)	\(e\left(\frac{149}{273}\right)\)	\(e\left(\frac{173}{364}\right)\)	\(e\left(\frac{467}{1092}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{73}{364}\right)\)	\(e\left(\frac{29}{91}\right)\)	\(e\left(\frac{19}{78}\right)\)
\(\chi_{309680}(18513,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{913}{1092}\right)\)	\(e\left(\frac{367}{546}\right)\)	\(e\left(\frac{142}{273}\right)\)	\(e\left(\frac{229}{364}\right)\)	\(e\left(\frac{271}{1092}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{185}{364}\right)\)	\(e\left(\frac{71}{91}\right)\)	\(e\left(\frac{77}{78}\right)\)
\(\chi_{309680}(19633,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{205}{1092}\right)\)	\(e\left(\frac{205}{546}\right)\)	\(e\left(\frac{118}{273}\right)\)	\(e\left(\frac{57}{364}\right)\)	\(e\left(\frac{379}{1092}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{205}{364}\right)\)	\(e\left(\frac{59}{91}\right)\)	\(e\left(\frac{53}{78}\right)\)
\(\chi_{309680}(23873,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{401}{1092}\right)\)	\(e\left(\frac{401}{546}\right)\)	\(e\left(\frac{83}{273}\right)\)	\(e\left(\frac{337}{364}\right)\)	\(e\left(\frac{491}{1092}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{37}{364}\right)\)	\(e\left(\frac{87}{91}\right)\)	\(e\left(\frac{31}{78}\right)\)
\(\chi_{309680}(24897,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{607}{1092}\right)\)	\(e\left(\frac{61}{546}\right)\)	\(e\left(\frac{127}{273}\right)\)	\(e\left(\frac{167}{364}\right)\)	\(e\left(\frac{1021}{1092}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{243}{364}\right)\)	\(e\left(\frac{18}{91}\right)\)	\(e\left(\frac{23}{78}\right)\)
\(\chi_{309680}(27233,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{1092}\right)\)	\(e\left(\frac{137}{546}\right)\)	\(e\left(\frac{236}{273}\right)\)	\(e\left(\frac{205}{364}\right)\)	\(e\left(\frac{1031}{1092}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{137}{364}\right)\)	\(e\left(\frac{27}{91}\right)\)	\(e\left(\frac{67}{78}\right)\)
\(\chi_{309680}(28577,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{275}{1092}\right)\)	\(e\left(\frac{275}{546}\right)\)	\(e\left(\frac{125}{273}\right)\)	\(e\left(\frac{183}{364}\right)\)	\(e\left(\frac{29}{1092}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{275}{364}\right)\)	\(e\left(\frac{17}{91}\right)\)	\(e\left(\frac{73}{78}\right)\)
\(\chi_{309680}(28817,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{1092}\right)\)	\(e\left(\frac{19}{546}\right)\)	\(e\left(\frac{232}{273}\right)\)	\(e\left(\frac{55}{364}\right)\)	\(e\left(\frac{685}{1092}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{19}{364}\right)\)	\(e\left(\frac{25}{91}\right)\)	\(e\left(\frac{11}{78}\right)\)
\(\chi_{309680}(31153,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{809}{1092}\right)\)	\(e\left(\frac{263}{546}\right)\)	\(e\left(\frac{194}{273}\right)\)	\(e\left(\frac{177}{364}\right)\)	\(e\left(\frac{947}{1092}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{81}{364}\right)\)	\(e\left(\frac{6}{91}\right)\)	\(e\left(\frac{25}{78}\right)\)
\(\chi_{309680}(31377,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{1092}\right)\)	\(e\left(\frac{83}{546}\right)\)	\(e\left(\frac{137}{273}\right)\)	\(e\left(\frac{87}{364}\right)\)	\(e\left(\frac{521}{1092}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{83}{364}\right)\)	\(e\left(\frac{23}{91}\right)\)	\(e\left(\frac{7}{78}\right)\)
\(\chi_{309680}(31617,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{307}{1092}\right)\)	\(e\left(\frac{307}{546}\right)\)	\(e\left(\frac{214}{273}\right)\)	\(e\left(\frac{199}{364}\right)\)	\(e\left(\frac{493}{1092}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{307}{364}\right)\)	\(e\left(\frac{16}{91}\right)\)	\(e\left(\frac{71}{78}\right)\)
\(\chi_{309680}(34513,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{209}{1092}\right)\)	\(e\left(\frac{209}{546}\right)\)	\(e\left(\frac{95}{273}\right)\)	\(e\left(\frac{241}{364}\right)\)	\(e\left(\frac{983}{1092}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{209}{364}\right)\)	\(e\left(\frac{2}{91}\right)\)	\(e\left(\frac{43}{78}\right)\)
\(\chi_{309680}(36433,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{421}{1092}\right)\)	\(e\left(\frac{421}{546}\right)\)	\(e\left(\frac{241}{273}\right)\)	\(e\left(\frac{165}{364}\right)\)	\(e\left(\frac{235}{1092}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{57}{364}\right)\)	\(e\left(\frac{75}{91}\right)\)	\(e\left(\frac{59}{78}\right)\)
\(\chi_{309680}(37537,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{971}{1092}\right)\)	\(e\left(\frac{425}{546}\right)\)	\(e\left(\frac{218}{273}\right)\)	\(e\left(\frac{167}{364}\right)\)	\(e\left(\frac{293}{1092}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{243}{364}\right)\)	\(e\left(\frac{18}{91}\right)\)	\(e\left(\frac{49}{78}\right)\)

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First 31 of 288 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	309680.cfm
Modulus	$309680$
Conductor	$19355$
Order	$1092$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(309680\)
Conductor:	\(19355\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(1092\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 19355.jf	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)