LMFDB - Dirichlet character orbit 33957.jc

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33957, base_ring=CyclotomicField(1470)) M = H._module chi = DirichletCharacter(H, M([245,1140,1029])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(29,33957)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

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

First 15 of 336 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{33957}(29,\cdot)$	$1$	$1$	$e\left(\frac{232}{735}\right)$	$e\left(\frac{464}{735}\right)$	$e\left(\frac{181}{1470}\right)$	$e\left(\frac{232}{245}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{79}{1470}\right)$	$e\left(\frac{193}{735}\right)$	$e\left(\frac{46}{245}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1109}{1470}\right)$
$\chi_{33957}(239,\cdot)$	$1$	$1$	$e\left(\frac{173}{735}\right)$	$e\left(\frac{346}{735}\right)$	$e\left(\frac{569}{1470}\right)$	$e\left(\frac{173}{245}\right)$	$e\left(\frac{61}{98}\right)$	$e\left(\frac{1361}{1470}\right)$	$e\left(\frac{692}{735}\right)$	$e\left(\frac{104}{245}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1261}{1470}\right)$
$\chi_{33957}(281,\cdot)$	$1$	$1$	$e\left(\frac{619}{735}\right)$	$e\left(\frac{503}{735}\right)$	$e\left(\frac{277}{1470}\right)$	$e\left(\frac{129}{245}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{1063}{1470}\right)$	$e\left(\frac{271}{735}\right)$	$e\left(\frac{222}{245}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1283}{1470}\right)$
$\chi_{33957}(365,\cdot)$	$1$	$1$	$e\left(\frac{146}{735}\right)$	$e\left(\frac{292}{735}\right)$	$e\left(\frac{323}{1470}\right)$	$e\left(\frac{146}{245}\right)$	$e\left(\frac{41}{98}\right)$	$e\left(\frac{677}{1470}\right)$	$e\left(\frac{584}{735}\right)$	$e\left(\frac{143}{245}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{907}{1470}\right)$
$\chi_{33957}(470,\cdot)$	$1$	$1$	$e\left(\frac{358}{735}\right)$	$e\left(\frac{716}{735}\right)$	$e\left(\frac{349}{1470}\right)$	$e\left(\frac{113}{245}\right)$	$e\left(\frac{71}{98}\right)$	$e\left(\frac{331}{1470}\right)$	$e\left(\frac{697}{735}\right)$	$e\left(\frac{109}{245}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{311}{1470}\right)$
$\chi_{33957}(596,\cdot)$	$1$	$1$	$e\left(\frac{541}{735}\right)$	$e\left(\frac{347}{735}\right)$	$e\left(\frac{1363}{1470}\right)$	$e\left(\frac{51}{245}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{67}{1470}\right)$	$e\left(\frac{694}{735}\right)$	$e\left(\frac{8}{245}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{587}{1470}\right)$
$\chi_{33957}(722,\cdot)$	$1$	$1$	$e\left(\frac{157}{735}\right)$	$e\left(\frac{314}{735}\right)$	$e\left(\frac{151}{1470}\right)$	$e\left(\frac{157}{245}\right)$	$e\left(\frac{31}{98}\right)$	$e\left(\frac{139}{1470}\right)$	$e\left(\frac{628}{735}\right)$	$e\left(\frac{236}{245}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{779}{1470}\right)$
$\chi_{33957}(743,\cdot)$	$1$	$1$	$e\left(\frac{44}{735}\right)$	$e\left(\frac{88}{735}\right)$	$e\left(\frac{47}{1470}\right)$	$e\left(\frac{44}{245}\right)$	$e\left(\frac{9}{98}\right)$	$e\left(\frac{53}{1470}\right)$	$e\left(\frac{176}{735}\right)$	$e\left(\frac{127}{245}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{223}{1470}\right)$
$\chi_{33957}(974,\cdot)$	$1$	$1$	$e\left(\frac{334}{735}\right)$	$e\left(\frac{668}{735}\right)$	$e\left(\frac{457}{1470}\right)$	$e\left(\frac{89}{245}\right)$	$e\left(\frac{75}{98}\right)$	$e\left(\frac{703}{1470}\right)$	$e\left(\frac{601}{735}\right)$	$e\left(\frac{62}{245}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{323}{1470}\right)$
$\chi_{33957}(1058,\cdot)$	$1$	$1$	$e\left(\frac{281}{735}\right)$	$e\left(\frac{562}{735}\right)$	$e\left(\frac{83}{1470}\right)$	$e\left(\frac{36}{245}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{1157}{1470}\right)$	$e\left(\frac{389}{735}\right)$	$e\left(\frac{193}{245}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1207}{1470}\right)$
$\chi_{33957}(1163,\cdot)$	$1$	$1$	$e\left(\frac{283}{735}\right)$	$e\left(\frac{566}{735}\right)$	$e\left(\frac{319}{1470}\right)$	$e\left(\frac{38}{245}\right)$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{391}{1470}\right)$	$e\left(\frac{397}{735}\right)$	$e\left(\frac{54}{245}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1451}{1470}\right)$
$\chi_{33957}(1184,\cdot)$	$1$	$1$	$e\left(\frac{317}{735}\right)$	$e\left(\frac{634}{735}\right)$	$e\left(\frac{1391}{1470}\right)$	$e\left(\frac{72}{245}\right)$	$e\left(\frac{37}{98}\right)$	$e\left(\frac{599}{1470}\right)$	$e\left(\frac{533}{735}\right)$	$e\left(\frac{141}{245}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1189}{1470}\right)$
$\chi_{33957}(1289,\cdot)$	$1$	$1$	$e\left(\frac{361}{735}\right)$	$e\left(\frac{722}{735}\right)$	$e\left(\frac{703}{1470}\right)$	$e\left(\frac{116}{245}\right)$	$e\left(\frac{95}{98}\right)$	$e\left(\frac{1387}{1470}\right)$	$e\left(\frac{709}{735}\right)$	$e\left(\frac{23}{245}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{677}{1470}\right)$
$\chi_{33957}(1415,\cdot)$	$1$	$1$	$e\left(\frac{607}{735}\right)$	$e\left(\frac{479}{735}\right)$	$e\left(\frac{331}{1470}\right)$	$e\left(\frac{117}{245}\right)$	$e\left(\frac{5}{98}\right)$	$e\left(\frac{1249}{1470}\right)$	$e\left(\frac{223}{735}\right)$	$e\left(\frac{76}{245}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1289}{1470}\right)$
$\chi_{33957}(1436,\cdot)$	$1$	$1$	$e\left(\frac{599}{735}\right)$	$e\left(\frac{463}{735}\right)$	$e\left(\frac{857}{1470}\right)$	$e\left(\frac{109}{245}\right)$	$e\left(\frac{39}{98}\right)$	$e\left(\frac{1373}{1470}\right)$	$e\left(\frac{191}{735}\right)$	$e\left(\frac{142}{245}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{313}{1470}\right)$

Overview	Random
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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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{33957}(29,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{232}{735}\right)\)	\(e\left(\frac{464}{735}\right)\)	\(e\left(\frac{181}{1470}\right)\)	\(e\left(\frac{232}{245}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{79}{1470}\right)\)	\(e\left(\frac{193}{735}\right)\)	\(e\left(\frac{46}{245}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1109}{1470}\right)\)
\(\chi_{33957}(239,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{735}\right)\)	\(e\left(\frac{346}{735}\right)\)	\(e\left(\frac{569}{1470}\right)\)	\(e\left(\frac{173}{245}\right)\)	\(e\left(\frac{61}{98}\right)\)	\(e\left(\frac{1361}{1470}\right)\)	\(e\left(\frac{692}{735}\right)\)	\(e\left(\frac{104}{245}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1261}{1470}\right)\)
\(\chi_{33957}(281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{619}{735}\right)\)	\(e\left(\frac{503}{735}\right)\)	\(e\left(\frac{277}{1470}\right)\)	\(e\left(\frac{129}{245}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{1063}{1470}\right)\)	\(e\left(\frac{271}{735}\right)\)	\(e\left(\frac{222}{245}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1283}{1470}\right)\)
\(\chi_{33957}(365,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{146}{735}\right)\)	\(e\left(\frac{292}{735}\right)\)	\(e\left(\frac{323}{1470}\right)\)	\(e\left(\frac{146}{245}\right)\)	\(e\left(\frac{41}{98}\right)\)	\(e\left(\frac{677}{1470}\right)\)	\(e\left(\frac{584}{735}\right)\)	\(e\left(\frac{143}{245}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{907}{1470}\right)\)
\(\chi_{33957}(470,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{358}{735}\right)\)	\(e\left(\frac{716}{735}\right)\)	\(e\left(\frac{349}{1470}\right)\)	\(e\left(\frac{113}{245}\right)\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{331}{1470}\right)\)	\(e\left(\frac{697}{735}\right)\)	\(e\left(\frac{109}{245}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{311}{1470}\right)\)
\(\chi_{33957}(596,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{541}{735}\right)\)	\(e\left(\frac{347}{735}\right)\)	\(e\left(\frac{1363}{1470}\right)\)	\(e\left(\frac{51}{245}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{67}{1470}\right)\)	\(e\left(\frac{694}{735}\right)\)	\(e\left(\frac{8}{245}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{587}{1470}\right)\)
\(\chi_{33957}(722,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{735}\right)\)	\(e\left(\frac{314}{735}\right)\)	\(e\left(\frac{151}{1470}\right)\)	\(e\left(\frac{157}{245}\right)\)	\(e\left(\frac{31}{98}\right)\)	\(e\left(\frac{139}{1470}\right)\)	\(e\left(\frac{628}{735}\right)\)	\(e\left(\frac{236}{245}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{779}{1470}\right)\)
\(\chi_{33957}(743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{735}\right)\)	\(e\left(\frac{88}{735}\right)\)	\(e\left(\frac{47}{1470}\right)\)	\(e\left(\frac{44}{245}\right)\)	\(e\left(\frac{9}{98}\right)\)	\(e\left(\frac{53}{1470}\right)\)	\(e\left(\frac{176}{735}\right)\)	\(e\left(\frac{127}{245}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{223}{1470}\right)\)
\(\chi_{33957}(974,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{334}{735}\right)\)	\(e\left(\frac{668}{735}\right)\)	\(e\left(\frac{457}{1470}\right)\)	\(e\left(\frac{89}{245}\right)\)	\(e\left(\frac{75}{98}\right)\)	\(e\left(\frac{703}{1470}\right)\)	\(e\left(\frac{601}{735}\right)\)	\(e\left(\frac{62}{245}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{323}{1470}\right)\)
\(\chi_{33957}(1058,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{281}{735}\right)\)	\(e\left(\frac{562}{735}\right)\)	\(e\left(\frac{83}{1470}\right)\)	\(e\left(\frac{36}{245}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{1157}{1470}\right)\)	\(e\left(\frac{389}{735}\right)\)	\(e\left(\frac{193}{245}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1207}{1470}\right)\)
\(\chi_{33957}(1163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{283}{735}\right)\)	\(e\left(\frac{566}{735}\right)\)	\(e\left(\frac{319}{1470}\right)\)	\(e\left(\frac{38}{245}\right)\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{391}{1470}\right)\)	\(e\left(\frac{397}{735}\right)\)	\(e\left(\frac{54}{245}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1451}{1470}\right)\)
\(\chi_{33957}(1184,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{317}{735}\right)\)	\(e\left(\frac{634}{735}\right)\)	\(e\left(\frac{1391}{1470}\right)\)	\(e\left(\frac{72}{245}\right)\)	\(e\left(\frac{37}{98}\right)\)	\(e\left(\frac{599}{1470}\right)\)	\(e\left(\frac{533}{735}\right)\)	\(e\left(\frac{141}{245}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1189}{1470}\right)\)
\(\chi_{33957}(1289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{361}{735}\right)\)	\(e\left(\frac{722}{735}\right)\)	\(e\left(\frac{703}{1470}\right)\)	\(e\left(\frac{116}{245}\right)\)	\(e\left(\frac{95}{98}\right)\)	\(e\left(\frac{1387}{1470}\right)\)	\(e\left(\frac{709}{735}\right)\)	\(e\left(\frac{23}{245}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{677}{1470}\right)\)
\(\chi_{33957}(1415,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{607}{735}\right)\)	\(e\left(\frac{479}{735}\right)\)	\(e\left(\frac{331}{1470}\right)\)	\(e\left(\frac{117}{245}\right)\)	\(e\left(\frac{5}{98}\right)\)	\(e\left(\frac{1249}{1470}\right)\)	\(e\left(\frac{223}{735}\right)\)	\(e\left(\frac{76}{245}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1289}{1470}\right)\)
\(\chi_{33957}(1436,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{599}{735}\right)\)	\(e\left(\frac{463}{735}\right)\)	\(e\left(\frac{857}{1470}\right)\)	\(e\left(\frac{109}{245}\right)\)	\(e\left(\frac{39}{98}\right)\)	\(e\left(\frac{1373}{1470}\right)\)	\(e\left(\frac{191}{735}\right)\)	\(e\left(\frac{142}{245}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{313}{1470}\right)\)

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First 15 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.jc
Modulus	$33957$
Conductor	$33957$
Order	$1470$
Real	no
Primitive	yes
Minimal	yes
Parity	even

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