LMFDB - Dirichlet character orbit 309680.cds

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(309680, base_ring=CyclotomicField(1092)) M = H._module chi = DirichletCharacter(H, M([546,273,0,1040,952])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(11,309680)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$309680$
Conductor:	$61936$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$1092$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 61936.rg	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:	$\Q(\zeta_{1092})$
Fixed field:	Number field defined by a degree 1092 polynomial (not computed)

First 31 of 288 characters in Galois orbit

Character	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{309680}(11,\cdot)$	$-1$	$1$	$e\left(\frac{27}{364}\right)$	$e\left(\frac{27}{182}\right)$	$e\left(\frac{139}{1092}\right)$	$e\left(\frac{895}{1092}\right)$	$e\left(\frac{32}{273}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{81}{364}\right)$	$e\left(\frac{527}{1092}\right)$	$e\left(\frac{77}{78}\right)$
$\chi_{309680}(51,\cdot)$	$-1$	$1$	$e\left(\frac{237}{364}\right)$	$e\left(\frac{55}{182}\right)$	$e\left(\frac{209}{1092}\right)$	$e\left(\frac{293}{1092}\right)$	$e\left(\frac{109}{273}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{347}{364}\right)$	$e\left(\frac{541}{1092}\right)$	$e\left(\frac{49}{78}\right)$
$\chi_{309680}(1691,\cdot)$	$-1$	$1$	$e\left(\frac{323}{364}\right)$	$e\left(\frac{141}{182}\right)$	$e\left(\frac{463}{1092}\right)$	$e\left(\frac{43}{1092}\right)$	$e\left(\frac{248}{273}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{241}{364}\right)$	$e\left(\frac{467}{1092}\right)$	$e\left(\frac{41}{78}\right)$
$\chi_{309680}(2011,\cdot)$	$-1$	$1$	$e\left(\frac{363}{364}\right)$	$e\left(\frac{181}{182}\right)$	$e\left(\frac{251}{1092}\right)$	$e\left(\frac{587}{1092}\right)$	$e\left(\frac{46}{273}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{361}{364}\right)$	$e\left(\frac{331}{1092}\right)$	$e\left(\frac{1}{78}\right)$
$\chi_{309680}(5651,\cdot)$	$-1$	$1$	$e\left(\frac{353}{364}\right)$	$e\left(\frac{171}{182}\right)$	$e\left(\frac{941}{1092}\right)$	$e\left(\frac{269}{1092}\right)$	$e\left(\frac{142}{273}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{331}{364}\right)$	$e\left(\frac{1}{1092}\right)$	$e\left(\frac{37}{78}\right)$
$\chi_{309680}(6171,\cdot)$	$-1$	$1$	$e\left(\frac{291}{364}\right)$	$e\left(\frac{109}{182}\right)$	$e\left(\frac{487}{1092}\right)$	$e\left(\frac{991}{1092}\right)$	$e\left(\frac{173}{273}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{145}{364}\right)$	$e\left(\frac{503}{1092}\right)$	$e\left(\frac{47}{78}\right)$
$\chi_{309680}(6211,\cdot)$	$-1$	$1$	$e\left(\frac{317}{364}\right)$	$e\left(\frac{135}{182}\right)$	$e\left(\frac{149}{1092}\right)$	$e\left(\frac{653}{1092}\right)$	$e\left(\frac{160}{273}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{223}{364}\right)$	$e\left(\frac{997}{1092}\right)$	$e\left(\frac{73}{78}\right)$
$\chi_{309680}(6491,\cdot)$	$-1$	$1$	$e\left(\frac{215}{364}\right)$	$e\left(\frac{33}{182}\right)$	$e\left(\frac{635}{1092}\right)$	$e\left(\frac{467}{1092}\right)$	$e\left(\frac{211}{273}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{281}{364}\right)$	$e\left(\frac{907}{1092}\right)$	$e\left(\frac{19}{78}\right)$
$\chi_{309680}(7051,\cdot)$	$-1$	$1$	$e\left(\frac{123}{364}\right)$	$e\left(\frac{123}{182}\right)$	$e\left(\frac{431}{1092}\right)$	$e\left(\frac{599}{1092}\right)$	$e\left(\frac{166}{273}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{364}\right)$	$e\left(\frac{55}{1092}\right)$	$e\left(\frac{7}{78}\right)$
$\chi_{309680}(8131,\cdot)$	$-1$	$1$	$e\left(\frac{305}{364}\right)$	$e\left(\frac{123}{182}\right)$	$e\left(\frac{613}{1092}\right)$	$e\left(\frac{781}{1092}\right)$	$e\left(\frac{257}{273}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{187}{364}\right)$	$e\left(\frac{965}{1092}\right)$	$e\left(\frac{59}{78}\right)$
$\chi_{309680}(11211,\cdot)$	$-1$	$1$	$e\left(\frac{87}{364}\right)$	$e\left(\frac{87}{182}\right)$	$e\left(\frac{367}{1092}\right)$	$e\left(\frac{619}{1092}\right)$	$e\left(\frac{2}{273}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{261}{364}\right)$	$e\left(\frac{323}{1092}\right)$	$e\left(\frac{17}{78}\right)$
$\chi_{309680}(11531,\cdot)$	$-1$	$1$	$e\left(\frac{87}{364}\right)$	$e\left(\frac{87}{182}\right)$	$e\left(\frac{731}{1092}\right)$	$e\left(\frac{983}{1092}\right)$	$e\left(\frac{184}{273}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{261}{364}\right)$	$e\left(\frac{1051}{1092}\right)$	$e\left(\frac{43}{78}\right)$
$\chi_{309680}(13771,\cdot)$	$-1$	$1$	$e\left(\frac{167}{364}\right)$	$e\left(\frac{167}{182}\right)$	$e\left(\frac{671}{1092}\right)$	$e\left(\frac{251}{1092}\right)$	$e\left(\frac{235}{273}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{137}{364}\right)$	$e\left(\frac{415}{1092}\right)$	$e\left(\frac{67}{78}\right)$
$\chi_{309680}(18251,\cdot)$	$-1$	$1$	$e\left(\frac{75}{364}\right)$	$e\left(\frac{75}{182}\right)$	$e\left(\frac{467}{1092}\right)$	$e\left(\frac{383}{1092}\right)$	$e\left(\frac{190}{273}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{225}{364}\right)$	$e\left(\frac{655}{1092}\right)$	$e\left(\frac{55}{78}\right)$
$\chi_{309680}(18531,\cdot)$	$-1$	$1$	$e\left(\frac{225}{364}\right)$	$e\left(\frac{43}{182}\right)$	$e\left(\frac{1037}{1092}\right)$	$e\left(\frac{785}{1092}\right)$	$e\left(\frac{115}{273}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{311}{364}\right)$	$e\left(\frac{145}{1092}\right)$	$e\left(\frac{61}{78}\right)$
$\chi_{309680}(19371,\cdot)$	$-1$	$1$	$e\left(\frac{339}{364}\right)$	$e\left(\frac{157}{182}\right)$	$e\left(\frac{815}{1092}\right)$	$e\left(\frac{479}{1092}\right)$	$e\left(\frac{58}{273}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{289}{364}\right)$	$e\left(\frac{631}{1092}\right)$	$e\left(\frac{25}{78}\right)$
$\chi_{309680}(19611,\cdot)$	$-1$	$1$	$e\left(\frac{223}{364}\right)$	$e\left(\frac{41}{182}\right)$	$e\left(\frac{811}{1092}\right)$	$e\left(\frac{139}{1092}\right)$	$e\left(\frac{116}{273}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{305}{364}\right)$	$e\left(\frac{443}{1092}\right)$	$e\left(\frac{11}{78}\right)$
$\chi_{309680}(20171,\cdot)$	$-1$	$1$	$e\left(\frac{303}{364}\right)$	$e\left(\frac{121}{182}\right)$	$e\left(\frac{751}{1092}\right)$	$e\left(\frac{499}{1092}\right)$	$e\left(\frac{167}{273}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{181}{364}\right)$	$e\left(\frac{899}{1092}\right)$	$e\left(\frac{35}{78}\right)$
$\chi_{309680}(21291,\cdot)$	$-1$	$1$	$e\left(\frac{211}{364}\right)$	$e\left(\frac{29}{182}\right)$	$e\left(\frac{547}{1092}\right)$	$e\left(\frac{631}{1092}\right)$	$e\left(\frac{122}{273}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{269}{364}\right)$	$e\left(\frac{47}{1092}\right)$	$e\left(\frac{23}{78}\right)$
$\chi_{309680}(21571,\cdot)$	$-1$	$1$	$e\left(\frac{293}{364}\right)$	$e\left(\frac{111}{182}\right)$	$e\left(\frac{349}{1092}\right)$	$e\left(\frac{181}{1092}\right)$	$e\left(\frac{263}{273}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{151}{364}\right)$	$e\left(\frac{569}{1092}\right)$	$e\left(\frac{71}{78}\right)$
$\chi_{309680}(21611,\cdot)$	$-1$	$1$	$e\left(\frac{307}{364}\right)$	$e\left(\frac{125}{182}\right)$	$e\left(\frac{839}{1092}\right)$	$e\left(\frac{335}{1092}\right)$	$e\left(\frac{256}{273}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{193}{364}\right)$	$e\left(\frac{667}{1092}\right)$	$e\left(\frac{31}{78}\right)$
$\chi_{309680}(22131,\cdot)$	$-1$	$1$	$e\left(\frac{261}{364}\right)$	$e\left(\frac{79}{182}\right)$	$e\left(\frac{373}{1092}\right)$	$e\left(\frac{37}{1092}\right)$	$e\left(\frac{188}{273}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{55}{364}\right)$	$e\left(\frac{605}{1092}\right)$	$e\left(\frac{77}{78}\right)$
$\chi_{309680}(22171,\cdot)$	$-1$	$1$	$e\left(\frac{159}{364}\right)$	$e\left(\frac{159}{182}\right)$	$e\left(\frac{131}{1092}\right)$	$e\left(\frac{215}{1092}\right)$	$e\left(\frac{148}{273}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{113}{364}\right)$	$e\left(\frac{151}{1092}\right)$	$e\left(\frac{49}{78}\right)$
$\chi_{309680}(23811,\cdot)$	$-1$	$1$	$e\left(\frac{193}{364}\right)$	$e\left(\frac{11}{182}\right)$	$e\left(\frac{697}{1092}\right)$	$e\left(\frac{277}{1092}\right)$	$e\left(\frac{131}{273}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{215}{364}\right)$	$e\left(\frac{545}{1092}\right)$	$e\left(\frac{41}{78}\right)$
$\chi_{309680}(24131,\cdot)$	$-1$	$1$	$e\left(\frac{285}{364}\right)$	$e\left(\frac{103}{182}\right)$	$e\left(\frac{173}{1092}\right)$	$e\left(\frac{509}{1092}\right)$	$e\left(\frac{85}{273}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{127}{364}\right)$	$e\left(\frac{1033}{1092}\right)$	$e\left(\frac{1}{78}\right)$
$\chi_{309680}(26891,\cdot)$	$-1$	$1$	$e\left(\frac{283}{364}\right)$	$e\left(\frac{101}{182}\right)$	$e\left(\frac{1039}{1092}\right)$	$e\left(\frac{955}{1092}\right)$	$e\left(\frac{86}{273}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{121}{364}\right)$	$e\left(\frac{239}{1092}\right)$	$e\left(\frac{29}{78}\right)$
$\chi_{309680}(27771,\cdot)$	$-1$	$1$	$e\left(\frac{275}{364}\right)$	$e\left(\frac{93}{182}\right)$	$e\left(\frac{863}{1092}\right)$	$e\left(\frac{191}{1092}\right)$	$e\left(\frac{181}{273}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{97}{364}\right)$	$e\left(\frac{703}{1092}\right)$	$e\left(\frac{37}{78}\right)$
$\chi_{309680}(28331,\cdot)$	$-1$	$1$	$e\left(\frac{239}{364}\right)$	$e\left(\frac{57}{182}\right)$	$e\left(\frac{71}{1092}\right)$	$e\left(\frac{575}{1092}\right)$	$e\left(\frac{199}{273}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{353}{364}\right)$	$e\left(\frac{607}{1092}\right)$	$e\left(\frac{73}{78}\right)$
$\chi_{309680}(28611,\cdot)$	$-1$	$1$	$e\left(\frac{137}{364}\right)$	$e\left(\frac{137}{182}\right)$	$e\left(\frac{557}{1092}\right)$	$e\left(\frac{389}{1092}\right)$	$e\left(\frac{250}{273}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{47}{364}\right)$	$e\left(\frac{517}{1092}\right)$	$e\left(\frac{19}{78}\right)$
$\chi_{309680}(29171,\cdot)$	$-1$	$1$	$e\left(\frac{45}{364}\right)$	$e\left(\frac{45}{182}\right)$	$e\left(\frac{353}{1092}\right)$	$e\left(\frac{521}{1092}\right)$	$e\left(\frac{205}{273}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{135}{364}\right)$	$e\left(\frac{757}{1092}\right)$	$e\left(\frac{7}{78}\right)$
$\chi_{309680}(33331,\cdot)$	$-1$	$1$	$e\left(\frac{321}{364}\right)$	$e\left(\frac{139}{182}\right)$	$e\left(\frac{601}{1092}\right)$	$e\left(\frac{853}{1092}\right)$	$e\left(\frac{158}{273}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{235}{364}\right)$	$e\left(\frac{401}{1092}\right)$	$e\left(\frac{17}{78}\right)$

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	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{309680}(11,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{364}\right)\)	\(e\left(\frac{27}{182}\right)\)	\(e\left(\frac{139}{1092}\right)\)	\(e\left(\frac{895}{1092}\right)\)	\(e\left(\frac{32}{273}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{81}{364}\right)\)	\(e\left(\frac{527}{1092}\right)\)	\(e\left(\frac{77}{78}\right)\)
\(\chi_{309680}(51,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{237}{364}\right)\)	\(e\left(\frac{55}{182}\right)\)	\(e\left(\frac{209}{1092}\right)\)	\(e\left(\frac{293}{1092}\right)\)	\(e\left(\frac{109}{273}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{347}{364}\right)\)	\(e\left(\frac{541}{1092}\right)\)	\(e\left(\frac{49}{78}\right)\)
\(\chi_{309680}(1691,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{323}{364}\right)\)	\(e\left(\frac{141}{182}\right)\)	\(e\left(\frac{463}{1092}\right)\)	\(e\left(\frac{43}{1092}\right)\)	\(e\left(\frac{248}{273}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{241}{364}\right)\)	\(e\left(\frac{467}{1092}\right)\)	\(e\left(\frac{41}{78}\right)\)
\(\chi_{309680}(2011,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{363}{364}\right)\)	\(e\left(\frac{181}{182}\right)\)	\(e\left(\frac{251}{1092}\right)\)	\(e\left(\frac{587}{1092}\right)\)	\(e\left(\frac{46}{273}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{361}{364}\right)\)	\(e\left(\frac{331}{1092}\right)\)	\(e\left(\frac{1}{78}\right)\)
\(\chi_{309680}(5651,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{353}{364}\right)\)	\(e\left(\frac{171}{182}\right)\)	\(e\left(\frac{941}{1092}\right)\)	\(e\left(\frac{269}{1092}\right)\)	\(e\left(\frac{142}{273}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{331}{364}\right)\)	\(e\left(\frac{1}{1092}\right)\)	\(e\left(\frac{37}{78}\right)\)
\(\chi_{309680}(6171,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{291}{364}\right)\)	\(e\left(\frac{109}{182}\right)\)	\(e\left(\frac{487}{1092}\right)\)	\(e\left(\frac{991}{1092}\right)\)	\(e\left(\frac{173}{273}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{145}{364}\right)\)	\(e\left(\frac{503}{1092}\right)\)	\(e\left(\frac{47}{78}\right)\)
\(\chi_{309680}(6211,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{317}{364}\right)\)	\(e\left(\frac{135}{182}\right)\)	\(e\left(\frac{149}{1092}\right)\)	\(e\left(\frac{653}{1092}\right)\)	\(e\left(\frac{160}{273}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{223}{364}\right)\)	\(e\left(\frac{997}{1092}\right)\)	\(e\left(\frac{73}{78}\right)\)
\(\chi_{309680}(6491,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{215}{364}\right)\)	\(e\left(\frac{33}{182}\right)\)	\(e\left(\frac{635}{1092}\right)\)	\(e\left(\frac{467}{1092}\right)\)	\(e\left(\frac{211}{273}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{281}{364}\right)\)	\(e\left(\frac{907}{1092}\right)\)	\(e\left(\frac{19}{78}\right)\)
\(\chi_{309680}(7051,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{123}{364}\right)\)	\(e\left(\frac{123}{182}\right)\)	\(e\left(\frac{431}{1092}\right)\)	\(e\left(\frac{599}{1092}\right)\)	\(e\left(\frac{166}{273}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{364}\right)\)	\(e\left(\frac{55}{1092}\right)\)	\(e\left(\frac{7}{78}\right)\)
\(\chi_{309680}(8131,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{305}{364}\right)\)	\(e\left(\frac{123}{182}\right)\)	\(e\left(\frac{613}{1092}\right)\)	\(e\left(\frac{781}{1092}\right)\)	\(e\left(\frac{257}{273}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{187}{364}\right)\)	\(e\left(\frac{965}{1092}\right)\)	\(e\left(\frac{59}{78}\right)\)
\(\chi_{309680}(11211,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{87}{364}\right)\)	\(e\left(\frac{87}{182}\right)\)	\(e\left(\frac{367}{1092}\right)\)	\(e\left(\frac{619}{1092}\right)\)	\(e\left(\frac{2}{273}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{261}{364}\right)\)	\(e\left(\frac{323}{1092}\right)\)	\(e\left(\frac{17}{78}\right)\)
\(\chi_{309680}(11531,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{87}{364}\right)\)	\(e\left(\frac{87}{182}\right)\)	\(e\left(\frac{731}{1092}\right)\)	\(e\left(\frac{983}{1092}\right)\)	\(e\left(\frac{184}{273}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{261}{364}\right)\)	\(e\left(\frac{1051}{1092}\right)\)	\(e\left(\frac{43}{78}\right)\)
\(\chi_{309680}(13771,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{364}\right)\)	\(e\left(\frac{167}{182}\right)\)	\(e\left(\frac{671}{1092}\right)\)	\(e\left(\frac{251}{1092}\right)\)	\(e\left(\frac{235}{273}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{137}{364}\right)\)	\(e\left(\frac{415}{1092}\right)\)	\(e\left(\frac{67}{78}\right)\)
\(\chi_{309680}(18251,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{75}{364}\right)\)	\(e\left(\frac{75}{182}\right)\)	\(e\left(\frac{467}{1092}\right)\)	\(e\left(\frac{383}{1092}\right)\)	\(e\left(\frac{190}{273}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{225}{364}\right)\)	\(e\left(\frac{655}{1092}\right)\)	\(e\left(\frac{55}{78}\right)\)
\(\chi_{309680}(18531,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{225}{364}\right)\)	\(e\left(\frac{43}{182}\right)\)	\(e\left(\frac{1037}{1092}\right)\)	\(e\left(\frac{785}{1092}\right)\)	\(e\left(\frac{115}{273}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{311}{364}\right)\)	\(e\left(\frac{145}{1092}\right)\)	\(e\left(\frac{61}{78}\right)\)
\(\chi_{309680}(19371,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{339}{364}\right)\)	\(e\left(\frac{157}{182}\right)\)	\(e\left(\frac{815}{1092}\right)\)	\(e\left(\frac{479}{1092}\right)\)	\(e\left(\frac{58}{273}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{289}{364}\right)\)	\(e\left(\frac{631}{1092}\right)\)	\(e\left(\frac{25}{78}\right)\)
\(\chi_{309680}(19611,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{223}{364}\right)\)	\(e\left(\frac{41}{182}\right)\)	\(e\left(\frac{811}{1092}\right)\)	\(e\left(\frac{139}{1092}\right)\)	\(e\left(\frac{116}{273}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{305}{364}\right)\)	\(e\left(\frac{443}{1092}\right)\)	\(e\left(\frac{11}{78}\right)\)
\(\chi_{309680}(20171,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{303}{364}\right)\)	\(e\left(\frac{121}{182}\right)\)	\(e\left(\frac{751}{1092}\right)\)	\(e\left(\frac{499}{1092}\right)\)	\(e\left(\frac{167}{273}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{181}{364}\right)\)	\(e\left(\frac{899}{1092}\right)\)	\(e\left(\frac{35}{78}\right)\)
\(\chi_{309680}(21291,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{211}{364}\right)\)	\(e\left(\frac{29}{182}\right)\)	\(e\left(\frac{547}{1092}\right)\)	\(e\left(\frac{631}{1092}\right)\)	\(e\left(\frac{122}{273}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{269}{364}\right)\)	\(e\left(\frac{47}{1092}\right)\)	\(e\left(\frac{23}{78}\right)\)
\(\chi_{309680}(21571,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{293}{364}\right)\)	\(e\left(\frac{111}{182}\right)\)	\(e\left(\frac{349}{1092}\right)\)	\(e\left(\frac{181}{1092}\right)\)	\(e\left(\frac{263}{273}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{151}{364}\right)\)	\(e\left(\frac{569}{1092}\right)\)	\(e\left(\frac{71}{78}\right)\)
\(\chi_{309680}(21611,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{307}{364}\right)\)	\(e\left(\frac{125}{182}\right)\)	\(e\left(\frac{839}{1092}\right)\)	\(e\left(\frac{335}{1092}\right)\)	\(e\left(\frac{256}{273}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{193}{364}\right)\)	\(e\left(\frac{667}{1092}\right)\)	\(e\left(\frac{31}{78}\right)\)
\(\chi_{309680}(22131,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{261}{364}\right)\)	\(e\left(\frac{79}{182}\right)\)	\(e\left(\frac{373}{1092}\right)\)	\(e\left(\frac{37}{1092}\right)\)	\(e\left(\frac{188}{273}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{55}{364}\right)\)	\(e\left(\frac{605}{1092}\right)\)	\(e\left(\frac{77}{78}\right)\)
\(\chi_{309680}(22171,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{159}{364}\right)\)	\(e\left(\frac{159}{182}\right)\)	\(e\left(\frac{131}{1092}\right)\)	\(e\left(\frac{215}{1092}\right)\)	\(e\left(\frac{148}{273}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{113}{364}\right)\)	\(e\left(\frac{151}{1092}\right)\)	\(e\left(\frac{49}{78}\right)\)
\(\chi_{309680}(23811,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{193}{364}\right)\)	\(e\left(\frac{11}{182}\right)\)	\(e\left(\frac{697}{1092}\right)\)	\(e\left(\frac{277}{1092}\right)\)	\(e\left(\frac{131}{273}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{215}{364}\right)\)	\(e\left(\frac{545}{1092}\right)\)	\(e\left(\frac{41}{78}\right)\)
\(\chi_{309680}(24131,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{285}{364}\right)\)	\(e\left(\frac{103}{182}\right)\)	\(e\left(\frac{173}{1092}\right)\)	\(e\left(\frac{509}{1092}\right)\)	\(e\left(\frac{85}{273}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{127}{364}\right)\)	\(e\left(\frac{1033}{1092}\right)\)	\(e\left(\frac{1}{78}\right)\)
\(\chi_{309680}(26891,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{283}{364}\right)\)	\(e\left(\frac{101}{182}\right)\)	\(e\left(\frac{1039}{1092}\right)\)	\(e\left(\frac{955}{1092}\right)\)	\(e\left(\frac{86}{273}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{121}{364}\right)\)	\(e\left(\frac{239}{1092}\right)\)	\(e\left(\frac{29}{78}\right)\)
\(\chi_{309680}(27771,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{275}{364}\right)\)	\(e\left(\frac{93}{182}\right)\)	\(e\left(\frac{863}{1092}\right)\)	\(e\left(\frac{191}{1092}\right)\)	\(e\left(\frac{181}{273}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{97}{364}\right)\)	\(e\left(\frac{703}{1092}\right)\)	\(e\left(\frac{37}{78}\right)\)
\(\chi_{309680}(28331,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{239}{364}\right)\)	\(e\left(\frac{57}{182}\right)\)	\(e\left(\frac{71}{1092}\right)\)	\(e\left(\frac{575}{1092}\right)\)	\(e\left(\frac{199}{273}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{353}{364}\right)\)	\(e\left(\frac{607}{1092}\right)\)	\(e\left(\frac{73}{78}\right)\)
\(\chi_{309680}(28611,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{364}\right)\)	\(e\left(\frac{137}{182}\right)\)	\(e\left(\frac{557}{1092}\right)\)	\(e\left(\frac{389}{1092}\right)\)	\(e\left(\frac{250}{273}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{47}{364}\right)\)	\(e\left(\frac{517}{1092}\right)\)	\(e\left(\frac{19}{78}\right)\)
\(\chi_{309680}(29171,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{45}{364}\right)\)	\(e\left(\frac{45}{182}\right)\)	\(e\left(\frac{353}{1092}\right)\)	\(e\left(\frac{521}{1092}\right)\)	\(e\left(\frac{205}{273}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{135}{364}\right)\)	\(e\left(\frac{757}{1092}\right)\)	\(e\left(\frac{7}{78}\right)\)
\(\chi_{309680}(33331,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{321}{364}\right)\)	\(e\left(\frac{139}{182}\right)\)	\(e\left(\frac{601}{1092}\right)\)	\(e\left(\frac{853}{1092}\right)\)	\(e\left(\frac{158}{273}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{235}{364}\right)\)	\(e\left(\frac{401}{1092}\right)\)	\(e\left(\frac{17}{78}\right)\)

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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.cds
Modulus	$309680$
Conductor	$61936$
Order	$1092$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(309680\)
Conductor:	\(61936\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(1092\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 61936.rg	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)