LMFDB - Dirichlet character orbit 373527.rg

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(373527, base_ring=CyclotomicField(16170)) M = H._module chi = DirichletCharacter(H, M([10780,3190,5586])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(25,373527)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$373527$
Conductor:	$373527$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$8085$	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:	$\Q(\zeta_{8085})$
Fixed field:	Number field defined by a degree 8085 polynomial (not computed)

First 17 of 3360 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{373527}(25,\cdot)$	$1$	$1$	$e\left(\frac{766}{2695}\right)$	$e\left(\frac{1532}{2695}\right)$	$e\left(\frac{4997}{8085}\right)$	$e\left(\frac{2298}{2695}\right)$	$e\left(\frac{1459}{1617}\right)$	$e\left(\frac{3628}{8085}\right)$	$e\left(\frac{369}{2695}\right)$	$e\left(\frac{6947}{8085}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{1508}{8085}\right)$
$\chi_{373527}(58,\cdot)$	$1$	$1$	$e\left(\frac{2586}{2695}\right)$	$e\left(\frac{2477}{2695}\right)$	$e\left(\frac{3247}{8085}\right)$	$e\left(\frac{2368}{2695}\right)$	$e\left(\frac{584}{1617}\right)$	$e\left(\frac{2228}{8085}\right)$	$e\left(\frac{2259}{2695}\right)$	$e\left(\frac{7297}{8085}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{2593}{8085}\right)$
$\chi_{373527}(247,\cdot)$	$1$	$1$	$e\left(\frac{1978}{2695}\right)$	$e\left(\frac{1261}{2695}\right)$	$e\left(\frac{5881}{8085}\right)$	$e\left(\frac{544}{2695}\right)$	$e\left(\frac{746}{1617}\right)$	$e\left(\frac{3134}{8085}\right)$	$e\left(\frac{2522}{2695}\right)$	$e\left(\frac{256}{8085}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{1579}{8085}\right)$
$\chi_{373527}(466,\cdot)$	$1$	$1$	$e\left(\frac{514}{2695}\right)$	$e\left(\frac{1028}{2695}\right)$	$e\left(\frac{4493}{8085}\right)$	$e\left(\frac{1542}{2695}\right)$	$e\left(\frac{1207}{1617}\right)$	$e\left(\frac{5812}{8085}\right)$	$e\left(\frac{2056}{2695}\right)$	$e\left(\frac{8018}{8085}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{7577}{8085}\right)$
$\chi_{373527}(499,\cdot)$	$1$	$1$	$e\left(\frac{1494}{2695}\right)$	$e\left(\frac{293}{2695}\right)$	$e\left(\frac{1063}{8085}\right)$	$e\left(\frac{1787}{2695}\right)$	$e\left(\frac{1109}{1617}\right)$	$e\left(\frac{6302}{8085}\right)$	$e\left(\frac{586}{2695}\right)$	$e\left(\frac{3853}{8085}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{1942}{8085}\right)$
$\chi_{373527}(592,\cdot)$	$1$	$1$	$e\left(\frac{2612}{2695}\right)$	$e\left(\frac{2529}{2695}\right)$	$e\left(\frac{989}{8085}\right)$	$e\left(\frac{2446}{2695}\right)$	$e\left(\frac{148}{1617}\right)$	$e\left(\frac{4441}{8085}\right)$	$e\left(\frac{2363}{2695}\right)$	$e\left(\frac{6224}{8085}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{491}{8085}\right)$
$\chi_{373527}(625,\cdot)$	$1$	$1$	$e\left(\frac{1532}{2695}\right)$	$e\left(\frac{369}{2695}\right)$	$e\left(\frac{1909}{8085}\right)$	$e\left(\frac{1901}{2695}\right)$	$e\left(\frac{1301}{1617}\right)$	$e\left(\frac{7256}{8085}\right)$	$e\left(\frac{738}{2695}\right)$	$e\left(\frac{5809}{8085}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{3016}{8085}\right)$
$\chi_{373527}(718,\cdot)$	$1$	$1$	$e\left(\frac{706}{2695}\right)$	$e\left(\frac{1412}{2695}\right)$	$e\left(\frac{257}{8085}\right)$	$e\left(\frac{2118}{2695}\right)$	$e\left(\frac{475}{1617}\right)$	$e\left(\frac{7228}{8085}\right)$	$e\left(\frac{129}{2695}\right)$	$e\left(\frac{2582}{8085}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{4493}{8085}\right)$
$\chi_{373527}(751,\cdot)$	$1$	$1$	$e\left(\frac{2361}{2695}\right)$	$e\left(\frac{2027}{2695}\right)$	$e\left(\frac{1642}{8085}\right)$	$e\left(\frac{1693}{2695}\right)$	$e\left(\frac{128}{1617}\right)$	$e\left(\frac{7643}{8085}\right)$	$e\left(\frac{1359}{2695}\right)$	$e\left(\frac{5077}{8085}\right)$	$e\left(\frac{56}{165}\right)$	$e\left(\frac{7723}{8085}\right)$
$\chi_{373527}(907,\cdot)$	$1$	$1$	$e\left(\frac{1928}{2695}\right)$	$e\left(\frac{1161}{2695}\right)$	$e\left(\frac{1931}{8085}\right)$	$e\left(\frac{394}{2695}\right)$	$e\left(\frac{1543}{1617}\right)$	$e\left(\frac{3439}{8085}\right)$	$e\left(\frac{2322}{2695}\right)$	$e\left(\frac{3356}{8085}\right)$	$e\left(\frac{13}{165}\right)$	$e\left(\frac{5414}{8085}\right)$
$\chi_{373527}(940,\cdot)$	$1$	$1$	$e\left(\frac{2558}{2695}\right)$	$e\left(\frac{2421}{2695}\right)$	$e\left(\frac{496}{8085}\right)$	$e\left(\frac{2284}{2695}\right)$	$e\left(\frac{17}{1617}\right)$	$e\left(\frac{674}{8085}\right)$	$e\left(\frac{2147}{2695}\right)$	$e\left(\frac{2026}{8085}\right)$	$e\left(\frac{158}{165}\right)$	$e\left(\frac{7759}{8085}\right)$
$\chi_{373527}(1159,\cdot)$	$1$	$1$	$e\left(\frac{1679}{2695}\right)$	$e\left(\frac{663}{2695}\right)$	$e\left(\frac{4898}{8085}\right)$	$e\left(\frac{2342}{2695}\right)$	$e\left(\frac{370}{1617}\right)$	$e\left(\frac{592}{8085}\right)$	$e\left(\frac{1326}{2695}\right)$	$e\left(\frac{5858}{8085}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{6887}{8085}\right)$
$\chi_{373527}(1192,\cdot)$	$1$	$1$	$e\left(\frac{2494}{2695}\right)$	$e\left(\frac{2293}{2695}\right)$	$e\left(\frac{4603}{8085}\right)$	$e\left(\frac{2092}{2695}\right)$	$e\left(\frac{800}{1617}\right)$	$e\left(\frac{2897}{8085}\right)$	$e\left(\frac{1891}{2695}\right)$	$e\left(\frac{3838}{8085}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{3397}{8085}\right)$
$\chi_{373527}(1285,\cdot)$	$1$	$1$	$e\left(\frac{2482}{2695}\right)$	$e\left(\frac{2269}{2695}\right)$	$e\left(\frac{1499}{8085}\right)$	$e\left(\frac{2056}{2695}\right)$	$e\left(\frac{172}{1617}\right)$	$e\left(\frac{4156}{8085}\right)$	$e\left(\frac{1843}{2695}\right)$	$e\left(\frac{809}{8085}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{221}{8085}\right)$
$\chi_{373527}(1318,\cdot)$	$1$	$1$	$e\left(\frac{2007}{2695}\right)$	$e\left(\frac{1319}{2695}\right)$	$e\left(\frac{4399}{8085}\right)$	$e\left(\frac{631}{2695}\right)$	$e\left(\frac{467}{1617}\right)$	$e\left(\frac{3011}{8085}\right)$	$e\left(\frac{2638}{2695}\right)$	$e\left(\frac{6004}{8085}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{271}{8085}\right)$
$\chi_{373527}(1411,\cdot)$	$1$	$1$	$e\left(\frac{261}{2695}\right)$	$e\left(\frac{522}{2695}\right)$	$e\left(\frac{137}{8085}\right)$	$e\left(\frac{783}{2695}\right)$	$e\left(\frac{184}{1617}\right)$	$e\left(\frac{1588}{8085}\right)$	$e\left(\frac{1044}{2695}\right)$	$e\left(\frac{527}{8085}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{1703}{8085}\right)$
$\chi_{373527}(1444,\cdot)$	$1$	$1$	$e\left(\frac{596}{2695}\right)$	$e\left(\frac{1192}{2695}\right)$	$e\left(\frac{2347}{8085}\right)$	$e\left(\frac{1788}{2695}\right)$	$e\left(\frac{827}{1617}\right)$	$e\left(\frac{353}{8085}\right)$	$e\left(\frac{2384}{2695}\right)$	$e\left(\frac{4012}{8085}\right)$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{5923}{8085}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{373527}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{766}{2695}\right)\)	\(e\left(\frac{1532}{2695}\right)\)	\(e\left(\frac{4997}{8085}\right)\)	\(e\left(\frac{2298}{2695}\right)\)	\(e\left(\frac{1459}{1617}\right)\)	\(e\left(\frac{3628}{8085}\right)\)	\(e\left(\frac{369}{2695}\right)\)	\(e\left(\frac{6947}{8085}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{1508}{8085}\right)\)
\(\chi_{373527}(58,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2586}{2695}\right)\)	\(e\left(\frac{2477}{2695}\right)\)	\(e\left(\frac{3247}{8085}\right)\)	\(e\left(\frac{2368}{2695}\right)\)	\(e\left(\frac{584}{1617}\right)\)	\(e\left(\frac{2228}{8085}\right)\)	\(e\left(\frac{2259}{2695}\right)\)	\(e\left(\frac{7297}{8085}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{2593}{8085}\right)\)
\(\chi_{373527}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1978}{2695}\right)\)	\(e\left(\frac{1261}{2695}\right)\)	\(e\left(\frac{5881}{8085}\right)\)	\(e\left(\frac{544}{2695}\right)\)	\(e\left(\frac{746}{1617}\right)\)	\(e\left(\frac{3134}{8085}\right)\)	\(e\left(\frac{2522}{2695}\right)\)	\(e\left(\frac{256}{8085}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{1579}{8085}\right)\)
\(\chi_{373527}(466,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{514}{2695}\right)\)	\(e\left(\frac{1028}{2695}\right)\)	\(e\left(\frac{4493}{8085}\right)\)	\(e\left(\frac{1542}{2695}\right)\)	\(e\left(\frac{1207}{1617}\right)\)	\(e\left(\frac{5812}{8085}\right)\)	\(e\left(\frac{2056}{2695}\right)\)	\(e\left(\frac{8018}{8085}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{7577}{8085}\right)\)
\(\chi_{373527}(499,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1494}{2695}\right)\)	\(e\left(\frac{293}{2695}\right)\)	\(e\left(\frac{1063}{8085}\right)\)	\(e\left(\frac{1787}{2695}\right)\)	\(e\left(\frac{1109}{1617}\right)\)	\(e\left(\frac{6302}{8085}\right)\)	\(e\left(\frac{586}{2695}\right)\)	\(e\left(\frac{3853}{8085}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{1942}{8085}\right)\)
\(\chi_{373527}(592,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2612}{2695}\right)\)	\(e\left(\frac{2529}{2695}\right)\)	\(e\left(\frac{989}{8085}\right)\)	\(e\left(\frac{2446}{2695}\right)\)	\(e\left(\frac{148}{1617}\right)\)	\(e\left(\frac{4441}{8085}\right)\)	\(e\left(\frac{2363}{2695}\right)\)	\(e\left(\frac{6224}{8085}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{491}{8085}\right)\)
\(\chi_{373527}(625,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1532}{2695}\right)\)	\(e\left(\frac{369}{2695}\right)\)	\(e\left(\frac{1909}{8085}\right)\)	\(e\left(\frac{1901}{2695}\right)\)	\(e\left(\frac{1301}{1617}\right)\)	\(e\left(\frac{7256}{8085}\right)\)	\(e\left(\frac{738}{2695}\right)\)	\(e\left(\frac{5809}{8085}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{3016}{8085}\right)\)
\(\chi_{373527}(718,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{706}{2695}\right)\)	\(e\left(\frac{1412}{2695}\right)\)	\(e\left(\frac{257}{8085}\right)\)	\(e\left(\frac{2118}{2695}\right)\)	\(e\left(\frac{475}{1617}\right)\)	\(e\left(\frac{7228}{8085}\right)\)	\(e\left(\frac{129}{2695}\right)\)	\(e\left(\frac{2582}{8085}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{4493}{8085}\right)\)
\(\chi_{373527}(751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2361}{2695}\right)\)	\(e\left(\frac{2027}{2695}\right)\)	\(e\left(\frac{1642}{8085}\right)\)	\(e\left(\frac{1693}{2695}\right)\)	\(e\left(\frac{128}{1617}\right)\)	\(e\left(\frac{7643}{8085}\right)\)	\(e\left(\frac{1359}{2695}\right)\)	\(e\left(\frac{5077}{8085}\right)\)	\(e\left(\frac{56}{165}\right)\)	\(e\left(\frac{7723}{8085}\right)\)
\(\chi_{373527}(907,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1928}{2695}\right)\)	\(e\left(\frac{1161}{2695}\right)\)	\(e\left(\frac{1931}{8085}\right)\)	\(e\left(\frac{394}{2695}\right)\)	\(e\left(\frac{1543}{1617}\right)\)	\(e\left(\frac{3439}{8085}\right)\)	\(e\left(\frac{2322}{2695}\right)\)	\(e\left(\frac{3356}{8085}\right)\)	\(e\left(\frac{13}{165}\right)\)	\(e\left(\frac{5414}{8085}\right)\)
\(\chi_{373527}(940,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2558}{2695}\right)\)	\(e\left(\frac{2421}{2695}\right)\)	\(e\left(\frac{496}{8085}\right)\)	\(e\left(\frac{2284}{2695}\right)\)	\(e\left(\frac{17}{1617}\right)\)	\(e\left(\frac{674}{8085}\right)\)	\(e\left(\frac{2147}{2695}\right)\)	\(e\left(\frac{2026}{8085}\right)\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{7759}{8085}\right)\)
\(\chi_{373527}(1159,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1679}{2695}\right)\)	\(e\left(\frac{663}{2695}\right)\)	\(e\left(\frac{4898}{8085}\right)\)	\(e\left(\frac{2342}{2695}\right)\)	\(e\left(\frac{370}{1617}\right)\)	\(e\left(\frac{592}{8085}\right)\)	\(e\left(\frac{1326}{2695}\right)\)	\(e\left(\frac{5858}{8085}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{6887}{8085}\right)\)
\(\chi_{373527}(1192,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2494}{2695}\right)\)	\(e\left(\frac{2293}{2695}\right)\)	\(e\left(\frac{4603}{8085}\right)\)	\(e\left(\frac{2092}{2695}\right)\)	\(e\left(\frac{800}{1617}\right)\)	\(e\left(\frac{2897}{8085}\right)\)	\(e\left(\frac{1891}{2695}\right)\)	\(e\left(\frac{3838}{8085}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{3397}{8085}\right)\)
\(\chi_{373527}(1285,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2482}{2695}\right)\)	\(e\left(\frac{2269}{2695}\right)\)	\(e\left(\frac{1499}{8085}\right)\)	\(e\left(\frac{2056}{2695}\right)\)	\(e\left(\frac{172}{1617}\right)\)	\(e\left(\frac{4156}{8085}\right)\)	\(e\left(\frac{1843}{2695}\right)\)	\(e\left(\frac{809}{8085}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{221}{8085}\right)\)
\(\chi_{373527}(1318,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2007}{2695}\right)\)	\(e\left(\frac{1319}{2695}\right)\)	\(e\left(\frac{4399}{8085}\right)\)	\(e\left(\frac{631}{2695}\right)\)	\(e\left(\frac{467}{1617}\right)\)	\(e\left(\frac{3011}{8085}\right)\)	\(e\left(\frac{2638}{2695}\right)\)	\(e\left(\frac{6004}{8085}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{271}{8085}\right)\)
\(\chi_{373527}(1411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{261}{2695}\right)\)	\(e\left(\frac{522}{2695}\right)\)	\(e\left(\frac{137}{8085}\right)\)	\(e\left(\frac{783}{2695}\right)\)	\(e\left(\frac{184}{1617}\right)\)	\(e\left(\frac{1588}{8085}\right)\)	\(e\left(\frac{1044}{2695}\right)\)	\(e\left(\frac{527}{8085}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{1703}{8085}\right)\)
\(\chi_{373527}(1444,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{596}{2695}\right)\)	\(e\left(\frac{1192}{2695}\right)\)	\(e\left(\frac{2347}{8085}\right)\)	\(e\left(\frac{1788}{2695}\right)\)	\(e\left(\frac{827}{1617}\right)\)	\(e\left(\frac{353}{8085}\right)\)	\(e\left(\frac{2384}{2695}\right)\)	\(e\left(\frac{4012}{8085}\right)\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{5923}{8085}\right)\)

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First 17 of 3360 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	373527.rg
Modulus	$373527$
Conductor	$373527$
Order	$8085$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(373527\)
Conductor:	\(373527\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(8085\)	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)