LMFDB - Dirichlet character orbit 33957.ja

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33957, base_ring=CyclotomicField(1470)) M = H._module chi = DirichletCharacter(H, M([735,125,1323])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(17,33957)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$33957$
Conductor:	$11319$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$1470$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 11319.dr	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:	$\Q(\zeta_{735})$
Fixed field:	Number field defined by a degree 1470 polynomial (not computed)

First 13 of 336 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{33957}(17,\cdot)$	$-1$	$1$	$e\left(\frac{659}{735}\right)$	$e\left(\frac{583}{735}\right)$	$e\left(\frac{416}{735}\right)$	$e\left(\frac{169}{245}\right)$	$e\left(\frac{68}{147}\right)$	$e\left(\frac{33}{245}\right)$	$e\left(\frac{431}{735}\right)$	$e\left(\frac{1067}{1470}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{88}{245}\right)$
$\chi_{33957}(206,\cdot)$	$-1$	$1$	$e\left(\frac{488}{735}\right)$	$e\left(\frac{241}{735}\right)$	$e\left(\frac{617}{735}\right)$	$e\left(\frac{243}{245}\right)$	$e\left(\frac{74}{147}\right)$	$e\left(\frac{46}{245}\right)$	$e\left(\frac{482}{735}\right)$	$e\left(\frac{1079}{1470}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{41}{245}\right)$
$\chi_{33957}(332,\cdot)$	$-1$	$1$	$e\left(\frac{626}{735}\right)$	$e\left(\frac{517}{735}\right)$	$e\left(\frac{674}{735}\right)$	$e\left(\frac{136}{245}\right)$	$e\left(\frac{113}{147}\right)$	$e\left(\frac{57}{245}\right)$	$e\left(\frac{299}{735}\right)$	$e\left(\frac{863}{1470}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{152}{245}\right)$
$\chi_{33957}(404,\cdot)$	$-1$	$1$	$e\left(\frac{253}{735}\right)$	$e\left(\frac{506}{735}\right)$	$e\left(\frac{472}{735}\right)$	$e\left(\frac{8}{245}\right)$	$e\left(\frac{145}{147}\right)$	$e\left(\frac{61}{245}\right)$	$e\left(\frac{277}{735}\right)$	$e\left(\frac{829}{1470}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{81}{245}\right)$
$\chi_{33957}(458,\cdot)$	$-1$	$1$	$e\left(\frac{407}{735}\right)$	$e\left(\frac{79}{735}\right)$	$e\left(\frac{248}{735}\right)$	$e\left(\frac{162}{245}\right)$	$e\left(\frac{131}{147}\right)$	$e\left(\frac{194}{245}\right)$	$e\left(\frac{158}{735}\right)$	$e\left(\frac{311}{1470}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{109}{245}\right)$
$\chi_{33957}(530,\cdot)$	$-1$	$1$	$e\left(\frac{256}{735}\right)$	$e\left(\frac{512}{735}\right)$	$e\left(\frac{649}{735}\right)$	$e\left(\frac{11}{245}\right)$	$e\left(\frac{34}{147}\right)$	$e\left(\frac{237}{245}\right)$	$e\left(\frac{289}{735}\right)$	$e\left(\frac{313}{1470}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{142}{245}\right)$
$\chi_{33957}(710,\cdot)$	$-1$	$1$	$e\left(\frac{74}{735}\right)$	$e\left(\frac{148}{735}\right)$	$e\left(\frac{446}{735}\right)$	$e\left(\frac{74}{245}\right)$	$e\left(\frac{104}{147}\right)$	$e\left(\frac{13}{245}\right)$	$e\left(\frac{296}{735}\right)$	$e\left(\frac{257}{1470}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{198}{245}\right)$
$\chi_{33957}(899,\cdot)$	$-1$	$1$	$e\left(\frac{8}{735}\right)$	$e\left(\frac{16}{735}\right)$	$e\left(\frac{227}{735}\right)$	$e\left(\frac{8}{245}\right)$	$e\left(\frac{47}{147}\right)$	$e\left(\frac{61}{245}\right)$	$e\left(\frac{32}{735}\right)$	$e\left(\frac{1319}{1470}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{81}{245}\right)$
$\chi_{33957}(908,\cdot)$	$-1$	$1$	$e\left(\frac{664}{735}\right)$	$e\left(\frac{593}{735}\right)$	$e\left(\frac{466}{735}\right)$	$e\left(\frac{174}{245}\right)$	$e\left(\frac{79}{147}\right)$	$e\left(\frac{163}{245}\right)$	$e\left(\frac{451}{735}\right)$	$e\left(\frac{697}{1470}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{108}{245}\right)$
$\chi_{33957}(1025,\cdot)$	$-1$	$1$	$e\left(\frac{461}{735}\right)$	$e\left(\frac{187}{735}\right)$	$e\left(\frac{494}{735}\right)$	$e\left(\frac{216}{245}\right)$	$e\left(\frac{44}{147}\right)$	$e\left(\frac{177}{245}\right)$	$e\left(\frac{374}{735}\right)$	$e\left(\frac{1313}{1470}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{227}{245}\right)$
$\chi_{33957}(1151,\cdot)$	$-1$	$1$	$e\left(\frac{557}{735}\right)$	$e\left(\frac{379}{735}\right)$	$e\left(\frac{278}{735}\right)$	$e\left(\frac{67}{245}\right)$	$e\left(\frac{20}{147}\right)$	$e\left(\frac{174}{245}\right)$	$e\left(\frac{23}{735}\right)$	$e\left(\frac{971}{1470}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{219}{245}\right)$
$\chi_{33957}(1223,\cdot)$	$-1$	$1$	$e\left(\frac{31}{735}\right)$	$e\left(\frac{62}{735}\right)$	$e\left(\frac{604}{735}\right)$	$e\left(\frac{31}{245}\right)$	$e\left(\frac{127}{147}\right)$	$e\left(\frac{22}{245}\right)$	$e\left(\frac{124}{735}\right)$	$e\left(\frac{793}{1470}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{222}{245}\right)$
$\chi_{33957}(1349,\cdot)$	$-1$	$1$	$e\left(\frac{307}{735}\right)$	$e\left(\frac{614}{735}\right)$	$e\left(\frac{718}{735}\right)$	$e\left(\frac{62}{245}\right)$	$e\left(\frac{58}{147}\right)$	$e\left(\frac{44}{245}\right)$	$e\left(\frac{493}{735}\right)$	$e\left(\frac{361}{1470}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{199}{245}\right)$

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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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{33957}(17,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{659}{735}\right)\)	\(e\left(\frac{583}{735}\right)\)	\(e\left(\frac{416}{735}\right)\)	\(e\left(\frac{169}{245}\right)\)	\(e\left(\frac{68}{147}\right)\)	\(e\left(\frac{33}{245}\right)\)	\(e\left(\frac{431}{735}\right)\)	\(e\left(\frac{1067}{1470}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{88}{245}\right)\)
\(\chi_{33957}(206,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{488}{735}\right)\)	\(e\left(\frac{241}{735}\right)\)	\(e\left(\frac{617}{735}\right)\)	\(e\left(\frac{243}{245}\right)\)	\(e\left(\frac{74}{147}\right)\)	\(e\left(\frac{46}{245}\right)\)	\(e\left(\frac{482}{735}\right)\)	\(e\left(\frac{1079}{1470}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{41}{245}\right)\)
\(\chi_{33957}(332,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{626}{735}\right)\)	\(e\left(\frac{517}{735}\right)\)	\(e\left(\frac{674}{735}\right)\)	\(e\left(\frac{136}{245}\right)\)	\(e\left(\frac{113}{147}\right)\)	\(e\left(\frac{57}{245}\right)\)	\(e\left(\frac{299}{735}\right)\)	\(e\left(\frac{863}{1470}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{152}{245}\right)\)
\(\chi_{33957}(404,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{253}{735}\right)\)	\(e\left(\frac{506}{735}\right)\)	\(e\left(\frac{472}{735}\right)\)	\(e\left(\frac{8}{245}\right)\)	\(e\left(\frac{145}{147}\right)\)	\(e\left(\frac{61}{245}\right)\)	\(e\left(\frac{277}{735}\right)\)	\(e\left(\frac{829}{1470}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{81}{245}\right)\)
\(\chi_{33957}(458,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{407}{735}\right)\)	\(e\left(\frac{79}{735}\right)\)	\(e\left(\frac{248}{735}\right)\)	\(e\left(\frac{162}{245}\right)\)	\(e\left(\frac{131}{147}\right)\)	\(e\left(\frac{194}{245}\right)\)	\(e\left(\frac{158}{735}\right)\)	\(e\left(\frac{311}{1470}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{109}{245}\right)\)
\(\chi_{33957}(530,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{256}{735}\right)\)	\(e\left(\frac{512}{735}\right)\)	\(e\left(\frac{649}{735}\right)\)	\(e\left(\frac{11}{245}\right)\)	\(e\left(\frac{34}{147}\right)\)	\(e\left(\frac{237}{245}\right)\)	\(e\left(\frac{289}{735}\right)\)	\(e\left(\frac{313}{1470}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{142}{245}\right)\)
\(\chi_{33957}(710,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{74}{735}\right)\)	\(e\left(\frac{148}{735}\right)\)	\(e\left(\frac{446}{735}\right)\)	\(e\left(\frac{74}{245}\right)\)	\(e\left(\frac{104}{147}\right)\)	\(e\left(\frac{13}{245}\right)\)	\(e\left(\frac{296}{735}\right)\)	\(e\left(\frac{257}{1470}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{198}{245}\right)\)
\(\chi_{33957}(899,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{735}\right)\)	\(e\left(\frac{16}{735}\right)\)	\(e\left(\frac{227}{735}\right)\)	\(e\left(\frac{8}{245}\right)\)	\(e\left(\frac{47}{147}\right)\)	\(e\left(\frac{61}{245}\right)\)	\(e\left(\frac{32}{735}\right)\)	\(e\left(\frac{1319}{1470}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{81}{245}\right)\)
\(\chi_{33957}(908,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{664}{735}\right)\)	\(e\left(\frac{593}{735}\right)\)	\(e\left(\frac{466}{735}\right)\)	\(e\left(\frac{174}{245}\right)\)	\(e\left(\frac{79}{147}\right)\)	\(e\left(\frac{163}{245}\right)\)	\(e\left(\frac{451}{735}\right)\)	\(e\left(\frac{697}{1470}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{108}{245}\right)\)
\(\chi_{33957}(1025,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{461}{735}\right)\)	\(e\left(\frac{187}{735}\right)\)	\(e\left(\frac{494}{735}\right)\)	\(e\left(\frac{216}{245}\right)\)	\(e\left(\frac{44}{147}\right)\)	\(e\left(\frac{177}{245}\right)\)	\(e\left(\frac{374}{735}\right)\)	\(e\left(\frac{1313}{1470}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{227}{245}\right)\)
\(\chi_{33957}(1151,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{557}{735}\right)\)	\(e\left(\frac{379}{735}\right)\)	\(e\left(\frac{278}{735}\right)\)	\(e\left(\frac{67}{245}\right)\)	\(e\left(\frac{20}{147}\right)\)	\(e\left(\frac{174}{245}\right)\)	\(e\left(\frac{23}{735}\right)\)	\(e\left(\frac{971}{1470}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{219}{245}\right)\)
\(\chi_{33957}(1223,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{735}\right)\)	\(e\left(\frac{62}{735}\right)\)	\(e\left(\frac{604}{735}\right)\)	\(e\left(\frac{31}{245}\right)\)	\(e\left(\frac{127}{147}\right)\)	\(e\left(\frac{22}{245}\right)\)	\(e\left(\frac{124}{735}\right)\)	\(e\left(\frac{793}{1470}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{222}{245}\right)\)
\(\chi_{33957}(1349,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{307}{735}\right)\)	\(e\left(\frac{614}{735}\right)\)	\(e\left(\frac{718}{735}\right)\)	\(e\left(\frac{62}{245}\right)\)	\(e\left(\frac{58}{147}\right)\)	\(e\left(\frac{44}{245}\right)\)	\(e\left(\frac{493}{735}\right)\)	\(e\left(\frac{361}{1470}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{199}{245}\right)\)

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Basic properties

Related number fields

First 13 of 336 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	33957.ja
Modulus	$33957$
Conductor	$11319$
Order	$1470$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(33957\)
Conductor:	\(11319\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(1470\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 11319.dr	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)