LMFDB - Dirichlet character orbit 373527.ru

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(373527, base_ring=CyclotomicField(16170)) M = H._module chi = DirichletCharacter(H, M([8085,550,15582])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(53,373527)) 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.hf	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 14 of 3360 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{373527}(53,\cdot)$	$-1$	$1$	$e\left(\frac{1007}{16170}\right)$	$e\left(\frac{1007}{8085}\right)$	$e\left(\frac{12863}{16170}\right)$	$e\left(\frac{1007}{5390}\right)$	$e\left(\frac{1387}{1617}\right)$	$e\left(\frac{57}{2695}\right)$	$e\left(\frac{2014}{8085}\right)$	$e\left(\frac{9193}{16170}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{4959}{5390}\right)$
$\chi_{373527}(170,\cdot)$	$-1$	$1$	$e\left(\frac{4423}{16170}\right)$	$e\left(\frac{4423}{8085}\right)$	$e\left(\frac{6157}{16170}\right)$	$e\left(\frac{4423}{5390}\right)$	$e\left(\frac{1058}{1617}\right)$	$e\left(\frac{708}{2695}\right)$	$e\left(\frac{761}{8085}\right)$	$e\left(\frac{13337}{16170}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{5001}{5390}\right)$
$\chi_{373527}(179,\cdot)$	$-1$	$1$	$e\left(\frac{7211}{16170}\right)$	$e\left(\frac{7211}{8085}\right)$	$e\left(\frac{6989}{16170}\right)$	$e\left(\frac{1821}{5390}\right)$	$e\left(\frac{1420}{1617}\right)$	$e\left(\frac{1476}{2695}\right)$	$e\left(\frac{6337}{8085}\right)$	$e\left(\frac{9259}{16170}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{1747}{5390}\right)$
$\chi_{373527}(368,\cdot)$	$-1$	$1$	$e\left(\frac{7193}{16170}\right)$	$e\left(\frac{7193}{8085}\right)$	$e\left(\frac{47}{16170}\right)$	$e\left(\frac{1803}{5390}\right)$	$e\left(\frac{724}{1617}\right)$	$e\left(\frac{458}{2695}\right)$	$e\left(\frac{6301}{8085}\right)$	$e\left(\frac{6397}{16170}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{4811}{5390}\right)$
$\chi_{373527}(548,\cdot)$	$-1$	$1$	$e\left(\frac{7207}{16170}\right)$	$e\left(\frac{7207}{8085}\right)$	$e\left(\frac{7243}{16170}\right)$	$e\left(\frac{1817}{5390}\right)$	$e\left(\frac{1445}{1617}\right)$	$e\left(\frac{52}{2695}\right)$	$e\left(\frac{6329}{8085}\right)$	$e\left(\frac{3233}{16170}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{1829}{5390}\right)$
$\chi_{373527}(620,\cdot)$	$-1$	$1$	$e\left(\frac{14519}{16170}\right)$	$e\left(\frac{6434}{8085}\right)$	$e\left(\frac{11861}{16170}\right)$	$e\left(\frac{3739}{5390}\right)$	$e\left(\frac{1021}{1617}\right)$	$e\left(\frac{2449}{2695}\right)$	$e\left(\frac{4783}{8085}\right)$	$e\left(\frac{6991}{16170}\right)$	$e\left(\frac{94}{165}\right)$	$e\left(\frac{2853}{5390}\right)$
$\chi_{373527}(674,\cdot)$	$-1$	$1$	$e\left(\frac{10081}{16170}\right)$	$e\left(\frac{1996}{8085}\right)$	$e\left(\frac{10699}{16170}\right)$	$e\left(\frac{4691}{5390}\right)$	$e\left(\frac{461}{1617}\right)$	$e\left(\frac{1791}{2695}\right)$	$e\left(\frac{3992}{8085}\right)$	$e\left(\frac{7439}{16170}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{4897}{5390}\right)$
$\chi_{373527}(746,\cdot)$	$-1$	$1$	$e\left(\frac{227}{16170}\right)$	$e\left(\frac{227}{8085}\right)$	$e\left(\frac{13883}{16170}\right)$	$e\left(\frac{227}{5390}\right)$	$e\left(\frac{1411}{1617}\right)$	$e\left(\frac{2657}{2695}\right)$	$e\left(\frac{454}{8085}\right)$	$e\left(\frac{14533}{16170}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{4779}{5390}\right)$
$\chi_{373527}(872,\cdot)$	$-1$	$1$	$e\left(\frac{4541}{16170}\right)$	$e\left(\frac{4541}{8085}\right)$	$e\left(\frac{6749}{16170}\right)$	$e\left(\frac{4541}{5390}\right)$	$e\left(\frac{1129}{1617}\right)$	$e\left(\frac{2291}{2695}\right)$	$e\left(\frac{997}{8085}\right)$	$e\left(\frac{5149}{16170}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{5277}{5390}\right)$
$\chi_{373527}(1061,\cdot)$	$-1$	$1$	$e\left(\frac{2423}{16170}\right)$	$e\left(\frac{2423}{8085}\right)$	$e\left(\frac{3797}{16170}\right)$	$e\left(\frac{2423}{5390}\right)$	$e\left(\frac{622}{1617}\right)$	$e\left(\frac{188}{2695}\right)$	$e\left(\frac{4846}{8085}\right)$	$e\left(\frac{7957}{16170}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{2881}{5390}\right)$
$\chi_{373527}(1115,\cdot)$	$-1$	$1$	$e\left(\frac{6469}{16170}\right)$	$e\left(\frac{6469}{8085}\right)$	$e\left(\frac{13681}{16170}\right)$	$e\left(\frac{1079}{5390}\right)$	$e\left(\frac{398}{1617}\right)$	$e\left(\frac{1434}{2695}\right)$	$e\left(\frac{4853}{8085}\right)$	$e\left(\frac{15251}{16170}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{3483}{5390}\right)$
$\chi_{373527}(1241,\cdot)$	$-1$	$1$	$e\left(\frac{14677}{16170}\right)$	$e\left(\frac{6592}{8085}\right)$	$e\left(\frac{9913}{16170}\right)$	$e\left(\frac{3897}{5390}\right)$	$e\left(\frac{842}{1617}\right)$	$e\left(\frac{2102}{2695}\right)$	$e\left(\frac{5099}{8085}\right)$	$e\left(\frac{10553}{16170}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{2309}{5390}\right)$
$\chi_{373527}(1313,\cdot)$	$-1$	$1$	$e\left(\frac{3029}{16170}\right)$	$e\left(\frac{3029}{8085}\right)$	$e\left(\frac{5741}{16170}\right)$	$e\left(\frac{3029}{5390}\right)$	$e\left(\frac{877}{1617}\right)$	$e\left(\frac{324}{2695}\right)$	$e\left(\frac{6058}{8085}\right)$	$e\left(\frac{7291}{16170}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{3933}{5390}\right)$
$\chi_{373527}(1367,\cdot)$	$-1$	$1$	$e\left(\frac{4111}{16170}\right)$	$e\left(\frac{4111}{8085}\right)$	$e\left(\frac{9799}{16170}\right)$	$e\left(\frac{4111}{5390}\right)$	$e\left(\frac{1391}{1617}\right)$	$e\left(\frac{131}{2695}\right)$	$e\left(\frac{137}{8085}\right)$	$e\left(\frac{12239}{16170}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{617}{5390}\right)$

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Character	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{373527}(53,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1007}{16170}\right)\)	\(e\left(\frac{1007}{8085}\right)\)	\(e\left(\frac{12863}{16170}\right)\)	\(e\left(\frac{1007}{5390}\right)\)	\(e\left(\frac{1387}{1617}\right)\)	\(e\left(\frac{57}{2695}\right)\)	\(e\left(\frac{2014}{8085}\right)\)	\(e\left(\frac{9193}{16170}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{4959}{5390}\right)\)
\(\chi_{373527}(170,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4423}{16170}\right)\)	\(e\left(\frac{4423}{8085}\right)\)	\(e\left(\frac{6157}{16170}\right)\)	\(e\left(\frac{4423}{5390}\right)\)	\(e\left(\frac{1058}{1617}\right)\)	\(e\left(\frac{708}{2695}\right)\)	\(e\left(\frac{761}{8085}\right)\)	\(e\left(\frac{13337}{16170}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{5001}{5390}\right)\)
\(\chi_{373527}(179,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7211}{16170}\right)\)	\(e\left(\frac{7211}{8085}\right)\)	\(e\left(\frac{6989}{16170}\right)\)	\(e\left(\frac{1821}{5390}\right)\)	\(e\left(\frac{1420}{1617}\right)\)	\(e\left(\frac{1476}{2695}\right)\)	\(e\left(\frac{6337}{8085}\right)\)	\(e\left(\frac{9259}{16170}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{1747}{5390}\right)\)
\(\chi_{373527}(368,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7193}{16170}\right)\)	\(e\left(\frac{7193}{8085}\right)\)	\(e\left(\frac{47}{16170}\right)\)	\(e\left(\frac{1803}{5390}\right)\)	\(e\left(\frac{724}{1617}\right)\)	\(e\left(\frac{458}{2695}\right)\)	\(e\left(\frac{6301}{8085}\right)\)	\(e\left(\frac{6397}{16170}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{4811}{5390}\right)\)
\(\chi_{373527}(548,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7207}{16170}\right)\)	\(e\left(\frac{7207}{8085}\right)\)	\(e\left(\frac{7243}{16170}\right)\)	\(e\left(\frac{1817}{5390}\right)\)	\(e\left(\frac{1445}{1617}\right)\)	\(e\left(\frac{52}{2695}\right)\)	\(e\left(\frac{6329}{8085}\right)\)	\(e\left(\frac{3233}{16170}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{1829}{5390}\right)\)
\(\chi_{373527}(620,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{14519}{16170}\right)\)	\(e\left(\frac{6434}{8085}\right)\)	\(e\left(\frac{11861}{16170}\right)\)	\(e\left(\frac{3739}{5390}\right)\)	\(e\left(\frac{1021}{1617}\right)\)	\(e\left(\frac{2449}{2695}\right)\)	\(e\left(\frac{4783}{8085}\right)\)	\(e\left(\frac{6991}{16170}\right)\)	\(e\left(\frac{94}{165}\right)\)	\(e\left(\frac{2853}{5390}\right)\)
\(\chi_{373527}(674,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{10081}{16170}\right)\)	\(e\left(\frac{1996}{8085}\right)\)	\(e\left(\frac{10699}{16170}\right)\)	\(e\left(\frac{4691}{5390}\right)\)	\(e\left(\frac{461}{1617}\right)\)	\(e\left(\frac{1791}{2695}\right)\)	\(e\left(\frac{3992}{8085}\right)\)	\(e\left(\frac{7439}{16170}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{4897}{5390}\right)\)
\(\chi_{373527}(746,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{227}{16170}\right)\)	\(e\left(\frac{227}{8085}\right)\)	\(e\left(\frac{13883}{16170}\right)\)	\(e\left(\frac{227}{5390}\right)\)	\(e\left(\frac{1411}{1617}\right)\)	\(e\left(\frac{2657}{2695}\right)\)	\(e\left(\frac{454}{8085}\right)\)	\(e\left(\frac{14533}{16170}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{4779}{5390}\right)\)
\(\chi_{373527}(872,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4541}{16170}\right)\)	\(e\left(\frac{4541}{8085}\right)\)	\(e\left(\frac{6749}{16170}\right)\)	\(e\left(\frac{4541}{5390}\right)\)	\(e\left(\frac{1129}{1617}\right)\)	\(e\left(\frac{2291}{2695}\right)\)	\(e\left(\frac{997}{8085}\right)\)	\(e\left(\frac{5149}{16170}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{5277}{5390}\right)\)
\(\chi_{373527}(1061,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2423}{16170}\right)\)	\(e\left(\frac{2423}{8085}\right)\)	\(e\left(\frac{3797}{16170}\right)\)	\(e\left(\frac{2423}{5390}\right)\)	\(e\left(\frac{622}{1617}\right)\)	\(e\left(\frac{188}{2695}\right)\)	\(e\left(\frac{4846}{8085}\right)\)	\(e\left(\frac{7957}{16170}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{2881}{5390}\right)\)
\(\chi_{373527}(1115,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{6469}{16170}\right)\)	\(e\left(\frac{6469}{8085}\right)\)	\(e\left(\frac{13681}{16170}\right)\)	\(e\left(\frac{1079}{5390}\right)\)	\(e\left(\frac{398}{1617}\right)\)	\(e\left(\frac{1434}{2695}\right)\)	\(e\left(\frac{4853}{8085}\right)\)	\(e\left(\frac{15251}{16170}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{3483}{5390}\right)\)
\(\chi_{373527}(1241,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{14677}{16170}\right)\)	\(e\left(\frac{6592}{8085}\right)\)	\(e\left(\frac{9913}{16170}\right)\)	\(e\left(\frac{3897}{5390}\right)\)	\(e\left(\frac{842}{1617}\right)\)	\(e\left(\frac{2102}{2695}\right)\)	\(e\left(\frac{5099}{8085}\right)\)	\(e\left(\frac{10553}{16170}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{2309}{5390}\right)\)
\(\chi_{373527}(1313,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3029}{16170}\right)\)	\(e\left(\frac{3029}{8085}\right)\)	\(e\left(\frac{5741}{16170}\right)\)	\(e\left(\frac{3029}{5390}\right)\)	\(e\left(\frac{877}{1617}\right)\)	\(e\left(\frac{324}{2695}\right)\)	\(e\left(\frac{6058}{8085}\right)\)	\(e\left(\frac{7291}{16170}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{3933}{5390}\right)\)
\(\chi_{373527}(1367,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4111}{16170}\right)\)	\(e\left(\frac{4111}{8085}\right)\)	\(e\left(\frac{9799}{16170}\right)\)	\(e\left(\frac{4111}{5390}\right)\)	\(e\left(\frac{1391}{1617}\right)\)	\(e\left(\frac{131}{2695}\right)\)	\(e\left(\frac{137}{8085}\right)\)	\(e\left(\frac{12239}{16170}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{617}{5390}\right)\)

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First 14 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.ru
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.hf	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)