LMFDB - Dirichlet character orbit 373527.rp

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(373527, base_ring=CyclotomicField(16170)) M = H._module chi = DirichletCharacter(H, M([8085,1375,7203])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(17,373527)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$373527$
Conductor:	$124509$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$16170$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 124509.hd	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:	$\Q(\zeta_{8085})$
Fixed field:	Number field defined by a degree 16170 polynomial (not computed)

First 13 of 3360 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{373527}(17,\cdot)$	$-1$	$1$	$e\left(\frac{3574}{8085}\right)$	$e\left(\frac{7148}{8085}\right)$	$e\left(\frac{7516}{8085}\right)$	$e\left(\frac{879}{2695}\right)$	$e\left(\frac{601}{1617}\right)$	$e\left(\frac{608}{2695}\right)$	$e\left(\frac{6211}{8085}\right)$	$e\left(\frac{7327}{16170}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{2193}{2695}\right)$
$\chi_{373527}(206,\cdot)$	$-1$	$1$	$e\left(\frac{3898}{8085}\right)$	$e\left(\frac{7796}{8085}\right)$	$e\left(\frac{3112}{8085}\right)$	$e\left(\frac{1203}{2695}\right)$	$e\left(\frac{1402}{1617}\right)$	$e\left(\frac{2221}{2695}\right)$	$e\left(\frac{7507}{8085}\right)$	$e\left(\frac{13339}{16170}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{941}{2695}\right)$
$\chi_{373527}(332,\cdot)$	$-1$	$1$	$e\left(\frac{271}{8085}\right)$	$e\left(\frac{542}{8085}\right)$	$e\left(\frac{3004}{8085}\right)$	$e\left(\frac{271}{2695}\right)$	$e\left(\frac{655}{1617}\right)$	$e\left(\frac{1607}{2695}\right)$	$e\left(\frac{1084}{8085}\right)$	$e\left(\frac{8023}{16170}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{1182}{2695}\right)$
$\chi_{373527}(404,\cdot)$	$-1$	$1$	$e\left(\frac{2048}{8085}\right)$	$e\left(\frac{4096}{8085}\right)$	$e\left(\frac{7397}{8085}\right)$	$e\left(\frac{2048}{2695}\right)$	$e\left(\frac{272}{1617}\right)$	$e\left(\frac{181}{2695}\right)$	$e\left(\frac{107}{8085}\right)$	$e\left(\frac{1769}{16170}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{1136}{2695}\right)$
$\chi_{373527}(458,\cdot)$	$-1$	$1$	$e\left(\frac{2272}{8085}\right)$	$e\left(\frac{4544}{8085}\right)$	$e\left(\frac{1258}{8085}\right)$	$e\left(\frac{2272}{2695}\right)$	$e\left(\frac{706}{1617}\right)$	$e\left(\frac{664}{2695}\right)$	$e\left(\frac{1003}{8085}\right)$	$e\left(\frac{13711}{16170}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{1934}{2695}\right)$
$\chi_{373527}(530,\cdot)$	$-1$	$1$	$e\left(\frac{7226}{8085}\right)$	$e\left(\frac{6367}{8085}\right)$	$e\left(\frac{1994}{8085}\right)$	$e\left(\frac{1836}{2695}\right)$	$e\left(\frac{227}{1617}\right)$	$e\left(\frac{157}{2695}\right)$	$e\left(\frac{4649}{8085}\right)$	$e\left(\frac{15203}{16170}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{92}{2695}\right)$
$\chi_{373527}(710,\cdot)$	$-1$	$1$	$e\left(\frac{5959}{8085}\right)$	$e\left(\frac{3833}{8085}\right)$	$e\left(\frac{5641}{8085}\right)$	$e\left(\frac{569}{2695}\right)$	$e\left(\frac{703}{1617}\right)$	$e\left(\frac{878}{2695}\right)$	$e\left(\frac{7666}{8085}\right)$	$e\left(\frac{5767}{16170}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{463}{2695}\right)$
$\chi_{373527}(899,\cdot)$	$-1$	$1$	$e\left(\frac{5233}{8085}\right)$	$e\left(\frac{2381}{8085}\right)$	$e\left(\frac{3232}{8085}\right)$	$e\left(\frac{2538}{2695}\right)$	$e\left(\frac{76}{1617}\right)$	$e\left(\frac{1406}{2695}\right)$	$e\left(\frac{4762}{8085}\right)$	$e\left(\frac{1279}{16170}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{1871}{2695}\right)$
$\chi_{373527}(908,\cdot)$	$-1$	$1$	$e\left(\frac{8039}{8085}\right)$	$e\left(\frac{7993}{8085}\right)$	$e\left(\frac{2921}{8085}\right)$	$e\left(\frac{2649}{2695}\right)$	$e\left(\frac{575}{1617}\right)$	$e\left(\frac{2283}{2695}\right)$	$e\left(\frac{7901}{8085}\right)$	$e\left(\frac{15017}{16170}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{943}{2695}\right)$
$\chi_{373527}(1025,\cdot)$	$-1$	$1$	$e\left(\frac{661}{8085}\right)$	$e\left(\frac{1322}{8085}\right)$	$e\left(\frac{2494}{8085}\right)$	$e\left(\frac{661}{2695}\right)$	$e\left(\frac{631}{1617}\right)$	$e\left(\frac{1702}{2695}\right)$	$e\left(\frac{2644}{8085}\right)$	$e\left(\frac{2683}{16170}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{1272}{2695}\right)$
$\chi_{373527}(1151,\cdot)$	$-1$	$1$	$e\left(\frac{6862}{8085}\right)$	$e\left(\frac{5639}{8085}\right)$	$e\left(\frac{853}{8085}\right)$	$e\left(\frac{1472}{2695}\right)$	$e\left(\frac{1543}{1617}\right)$	$e\left(\frac{2404}{2695}\right)$	$e\left(\frac{3193}{8085}\right)$	$e\left(\frac{1861}{16170}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{2164}{2695}\right)$
$\chi_{373527}(1223,\cdot)$	$-1$	$1$	$e\left(\frac{6956}{8085}\right)$	$e\left(\frac{5827}{8085}\right)$	$e\left(\frac{2969}{8085}\right)$	$e\left(\frac{1566}{2695}\right)$	$e\left(\frac{368}{1617}\right)$	$e\left(\frac{1957}{2695}\right)$	$e\left(\frac{3569}{8085}\right)$	$e\left(\frac{10193}{16170}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{237}{2695}\right)$
$\chi_{373527}(1349,\cdot)$	$-1$	$1$	$e\left(\frac{2642}{8085}\right)$	$e\left(\frac{5284}{8085}\right)$	$e\left(\frac{2018}{8085}\right)$	$e\left(\frac{2642}{2695}\right)$	$e\left(\frac{932}{1617}\right)$	$e\left(\frac{2689}{2695}\right)$	$e\left(\frac{2483}{8085}\right)$	$e\left(\frac{12791}{16170}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{2434}{2695}\right)$

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Character	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{373527}(17,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3574}{8085}\right)\)	\(e\left(\frac{7148}{8085}\right)\)	\(e\left(\frac{7516}{8085}\right)\)	\(e\left(\frac{879}{2695}\right)\)	\(e\left(\frac{601}{1617}\right)\)	\(e\left(\frac{608}{2695}\right)\)	\(e\left(\frac{6211}{8085}\right)\)	\(e\left(\frac{7327}{16170}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{2193}{2695}\right)\)
\(\chi_{373527}(206,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3898}{8085}\right)\)	\(e\left(\frac{7796}{8085}\right)\)	\(e\left(\frac{3112}{8085}\right)\)	\(e\left(\frac{1203}{2695}\right)\)	\(e\left(\frac{1402}{1617}\right)\)	\(e\left(\frac{2221}{2695}\right)\)	\(e\left(\frac{7507}{8085}\right)\)	\(e\left(\frac{13339}{16170}\right)\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{941}{2695}\right)\)
\(\chi_{373527}(332,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{271}{8085}\right)\)	\(e\left(\frac{542}{8085}\right)\)	\(e\left(\frac{3004}{8085}\right)\)	\(e\left(\frac{271}{2695}\right)\)	\(e\left(\frac{655}{1617}\right)\)	\(e\left(\frac{1607}{2695}\right)\)	\(e\left(\frac{1084}{8085}\right)\)	\(e\left(\frac{8023}{16170}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{1182}{2695}\right)\)
\(\chi_{373527}(404,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2048}{8085}\right)\)	\(e\left(\frac{4096}{8085}\right)\)	\(e\left(\frac{7397}{8085}\right)\)	\(e\left(\frac{2048}{2695}\right)\)	\(e\left(\frac{272}{1617}\right)\)	\(e\left(\frac{181}{2695}\right)\)	\(e\left(\frac{107}{8085}\right)\)	\(e\left(\frac{1769}{16170}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{1136}{2695}\right)\)
\(\chi_{373527}(458,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2272}{8085}\right)\)	\(e\left(\frac{4544}{8085}\right)\)	\(e\left(\frac{1258}{8085}\right)\)	\(e\left(\frac{2272}{2695}\right)\)	\(e\left(\frac{706}{1617}\right)\)	\(e\left(\frac{664}{2695}\right)\)	\(e\left(\frac{1003}{8085}\right)\)	\(e\left(\frac{13711}{16170}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{1934}{2695}\right)\)
\(\chi_{373527}(530,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7226}{8085}\right)\)	\(e\left(\frac{6367}{8085}\right)\)	\(e\left(\frac{1994}{8085}\right)\)	\(e\left(\frac{1836}{2695}\right)\)	\(e\left(\frac{227}{1617}\right)\)	\(e\left(\frac{157}{2695}\right)\)	\(e\left(\frac{4649}{8085}\right)\)	\(e\left(\frac{15203}{16170}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{92}{2695}\right)\)
\(\chi_{373527}(710,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5959}{8085}\right)\)	\(e\left(\frac{3833}{8085}\right)\)	\(e\left(\frac{5641}{8085}\right)\)	\(e\left(\frac{569}{2695}\right)\)	\(e\left(\frac{703}{1617}\right)\)	\(e\left(\frac{878}{2695}\right)\)	\(e\left(\frac{7666}{8085}\right)\)	\(e\left(\frac{5767}{16170}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{463}{2695}\right)\)
\(\chi_{373527}(899,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5233}{8085}\right)\)	\(e\left(\frac{2381}{8085}\right)\)	\(e\left(\frac{3232}{8085}\right)\)	\(e\left(\frac{2538}{2695}\right)\)	\(e\left(\frac{76}{1617}\right)\)	\(e\left(\frac{1406}{2695}\right)\)	\(e\left(\frac{4762}{8085}\right)\)	\(e\left(\frac{1279}{16170}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{1871}{2695}\right)\)
\(\chi_{373527}(908,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8039}{8085}\right)\)	\(e\left(\frac{7993}{8085}\right)\)	\(e\left(\frac{2921}{8085}\right)\)	\(e\left(\frac{2649}{2695}\right)\)	\(e\left(\frac{575}{1617}\right)\)	\(e\left(\frac{2283}{2695}\right)\)	\(e\left(\frac{7901}{8085}\right)\)	\(e\left(\frac{15017}{16170}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{943}{2695}\right)\)
\(\chi_{373527}(1025,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{661}{8085}\right)\)	\(e\left(\frac{1322}{8085}\right)\)	\(e\left(\frac{2494}{8085}\right)\)	\(e\left(\frac{661}{2695}\right)\)	\(e\left(\frac{631}{1617}\right)\)	\(e\left(\frac{1702}{2695}\right)\)	\(e\left(\frac{2644}{8085}\right)\)	\(e\left(\frac{2683}{16170}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{1272}{2695}\right)\)
\(\chi_{373527}(1151,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{6862}{8085}\right)\)	\(e\left(\frac{5639}{8085}\right)\)	\(e\left(\frac{853}{8085}\right)\)	\(e\left(\frac{1472}{2695}\right)\)	\(e\left(\frac{1543}{1617}\right)\)	\(e\left(\frac{2404}{2695}\right)\)	\(e\left(\frac{3193}{8085}\right)\)	\(e\left(\frac{1861}{16170}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{2164}{2695}\right)\)
\(\chi_{373527}(1223,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{6956}{8085}\right)\)	\(e\left(\frac{5827}{8085}\right)\)	\(e\left(\frac{2969}{8085}\right)\)	\(e\left(\frac{1566}{2695}\right)\)	\(e\left(\frac{368}{1617}\right)\)	\(e\left(\frac{1957}{2695}\right)\)	\(e\left(\frac{3569}{8085}\right)\)	\(e\left(\frac{10193}{16170}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{237}{2695}\right)\)
\(\chi_{373527}(1349,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2642}{8085}\right)\)	\(e\left(\frac{5284}{8085}\right)\)	\(e\left(\frac{2018}{8085}\right)\)	\(e\left(\frac{2642}{2695}\right)\)	\(e\left(\frac{932}{1617}\right)\)	\(e\left(\frac{2689}{2695}\right)\)	\(e\left(\frac{2483}{8085}\right)\)	\(e\left(\frac{12791}{16170}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{2434}{2695}\right)\)

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First 13 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.rp
Modulus	$373527$
Conductor	$124509$
Order	$16170$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(373527\)
Conductor:	\(124509\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(16170\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 124509.hd	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)