LMFDB - Dirichlet character orbit 373527.rv

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(373527, base_ring=CyclotomicField(16170)) M = H._module chi = DirichletCharacter(H, M([10780,4675,15141])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(52,373527)) 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:	$16170$	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 16170 polynomial (not computed)

First 14 of 3360 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{373527}(52,\cdot)$	$1$	$1$	$e\left(\frac{3727}{5390}\right)$	$e\left(\frac{1032}{2695}\right)$	$e\left(\frac{139}{16170}\right)$	$e\left(\frac{401}{5390}\right)$	$e\left(\frac{1132}{1617}\right)$	$e\left(\frac{2458}{8085}\right)$	$e\left(\frac{2064}{2695}\right)$	$e\left(\frac{887}{8085}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{6331}{16170}\right)$
$\chi_{373527}(292,\cdot)$	$1$	$1$	$e\left(\frac{4551}{5390}\right)$	$e\left(\frac{1856}{2695}\right)$	$e\left(\frac{15647}{16170}\right)$	$e\left(\frac{2873}{5390}\right)$	$e\left(\frac{1313}{1617}\right)$	$e\left(\frac{1454}{8085}\right)$	$e\left(\frac{1017}{2695}\right)$	$e\left(\frac{676}{8085}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{10613}{16170}\right)$
$\chi_{373527}(304,\cdot)$	$1$	$1$	$e\left(\frac{963}{5390}\right)$	$e\left(\frac{963}{2695}\right)$	$e\left(\frac{9241}{16170}\right)$	$e\left(\frac{2889}{5390}\right)$	$e\left(\frac{1213}{1617}\right)$	$e\left(\frac{7762}{8085}\right)$	$e\left(\frac{1926}{2695}\right)$	$e\left(\frac{4643}{8085}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{15019}{16170}\right)$
$\chi_{373527}(556,\cdot)$	$1$	$1$	$e\left(\frac{2721}{5390}\right)$	$e\left(\frac{26}{2695}\right)$	$e\left(\frac{5827}{16170}\right)$	$e\left(\frac{2773}{5390}\right)$	$e\left(\frac{1399}{1617}\right)$	$e\left(\frac{5149}{8085}\right)$	$e\left(\frac{52}{2695}\right)$	$e\left(\frac{3506}{8085}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{5983}{16170}\right)$
$\chi_{373527}(733,\cdot)$	$1$	$1$	$e\left(\frac{1443}{5390}\right)$	$e\left(\frac{1443}{2695}\right)$	$e\left(\frac{9431}{16170}\right)$	$e\left(\frac{4329}{5390}\right)$	$e\left(\frac{1376}{1617}\right)$	$e\left(\frac{4142}{8085}\right)$	$e\left(\frac{191}{2695}\right)$	$e\left(\frac{3238}{8085}\right)$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{1919}{16170}\right)$
$\chi_{373527}(745,\cdot)$	$1$	$1$	$e\left(\frac{5387}{5390}\right)$	$e\left(\frac{2692}{2695}\right)$	$e\left(\frac{7309}{16170}\right)$	$e\left(\frac{5381}{5390}\right)$	$e\left(\frac{730}{1617}\right)$	$e\left(\frac{1168}{8085}\right)$	$e\left(\frac{2689}{2695}\right)$	$e\left(\frac{632}{8085}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{7291}{16170}\right)$
$\chi_{373527}(871,\cdot)$	$1$	$1$	$e\left(\frac{2479}{5390}\right)$	$e\left(\frac{2479}{2695}\right)$	$e\left(\frac{11503}{16170}\right)$	$e\left(\frac{2047}{5390}\right)$	$e\left(\frac{277}{1617}\right)$	$e\left(\frac{5941}{8085}\right)$	$e\left(\frac{2263}{2695}\right)$	$e\left(\frac{2384}{8085}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{10207}{16170}\right)$
$\chi_{373527}(985,\cdot)$	$1$	$1$	$e\left(\frac{311}{5390}\right)$	$e\left(\frac{311}{2695}\right)$	$e\left(\frac{14867}{16170}\right)$	$e\left(\frac{933}{5390}\right)$	$e\left(\frac{1580}{1617}\right)$	$e\left(\frac{7379}{8085}\right)$	$e\left(\frac{622}{2695}\right)$	$e\left(\frac{61}{8085}\right)$	$e\left(\frac{23}{165}\right)$	$e\left(\frac{563}{16170}\right)$
$\chi_{373527}(997,\cdot)$	$1$	$1$	$e\left(\frac{4793}{5390}\right)$	$e\left(\frac{2098}{2695}\right)$	$e\left(\frac{15361}{16170}\right)$	$e\left(\frac{3599}{5390}\right)$	$e\left(\frac{1357}{1617}\right)$	$e\left(\frac{6052}{8085}\right)$	$e\left(\frac{1501}{2695}\right)$	$e\left(\frac{4493}{8085}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{11779}{16170}\right)$
$\chi_{373527}(1174,\cdot)$	$1$	$1$	$e\left(\frac{197}{5390}\right)$	$e\left(\frac{197}{2695}\right)$	$e\left(\frac{12329}{16170}\right)$	$e\left(\frac{591}{5390}\right)$	$e\left(\frac{1292}{1617}\right)$	$e\left(\frac{5948}{8085}\right)$	$e\left(\frac{394}{2695}\right)$	$e\left(\frac{5212}{8085}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{13511}{16170}\right)$
$\chi_{373527}(1249,\cdot)$	$1$	$1$	$e\left(\frac{4311}{5390}\right)$	$e\left(\frac{1616}{2695}\right)$	$e\left(\frac{2077}{16170}\right)$	$e\left(\frac{2153}{5390}\right)$	$e\left(\frac{1501}{1617}\right)$	$e\left(\frac{5959}{8085}\right)$	$e\left(\frac{537}{2695}\right)$	$e\left(\frac{2726}{8085}\right)$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{11773}{16170}\right)$
$\chi_{373527}(1300,\cdot)$	$1$	$1$	$e\left(\frac{5259}{5390}\right)$	$e\left(\frac{2564}{2695}\right)$	$e\left(\frac{10133}{16170}\right)$	$e\left(\frac{4997}{5390}\right)$	$e\left(\frac{974}{1617}\right)$	$e\left(\frac{6086}{8085}\right)$	$e\left(\frac{2433}{2695}\right)$	$e\left(\frac{7834}{8085}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{9347}{16170}\right)$
$\chi_{373527}(1426,\cdot)$	$1$	$1$	$e\left(\frac{4063}{5390}\right)$	$e\left(\frac{1368}{2695}\right)$	$e\left(\frac{11591}{16170}\right)$	$e\left(\frac{1409}{5390}\right)$	$e\left(\frac{761}{1617}\right)$	$e\left(\frac{6392}{8085}\right)$	$e\left(\frac{41}{2695}\right)$	$e\left(\frac{5563}{8085}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{3629}{16170}\right)$
$\chi_{373527}(1438,\cdot)$	$1$	$1$	$e\left(\frac{887}{5390}\right)$	$e\left(\frac{887}{2695}\right)$	$e\left(\frac{7549}{16170}\right)$	$e\left(\frac{2661}{5390}\right)$	$e\left(\frac{1021}{1617}\right)$	$e\left(\frac{6808}{8085}\right)$	$e\left(\frac{1774}{2695}\right)$	$e\left(\frac{2687}{8085}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{12871}{16170}\right)$

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Character	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{373527}(52,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3727}{5390}\right)\)	\(e\left(\frac{1032}{2695}\right)\)	\(e\left(\frac{139}{16170}\right)\)	\(e\left(\frac{401}{5390}\right)\)	\(e\left(\frac{1132}{1617}\right)\)	\(e\left(\frac{2458}{8085}\right)\)	\(e\left(\frac{2064}{2695}\right)\)	\(e\left(\frac{887}{8085}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{6331}{16170}\right)\)
\(\chi_{373527}(292,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4551}{5390}\right)\)	\(e\left(\frac{1856}{2695}\right)\)	\(e\left(\frac{15647}{16170}\right)\)	\(e\left(\frac{2873}{5390}\right)\)	\(e\left(\frac{1313}{1617}\right)\)	\(e\left(\frac{1454}{8085}\right)\)	\(e\left(\frac{1017}{2695}\right)\)	\(e\left(\frac{676}{8085}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{10613}{16170}\right)\)
\(\chi_{373527}(304,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{963}{5390}\right)\)	\(e\left(\frac{963}{2695}\right)\)	\(e\left(\frac{9241}{16170}\right)\)	\(e\left(\frac{2889}{5390}\right)\)	\(e\left(\frac{1213}{1617}\right)\)	\(e\left(\frac{7762}{8085}\right)\)	\(e\left(\frac{1926}{2695}\right)\)	\(e\left(\frac{4643}{8085}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{15019}{16170}\right)\)
\(\chi_{373527}(556,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2721}{5390}\right)\)	\(e\left(\frac{26}{2695}\right)\)	\(e\left(\frac{5827}{16170}\right)\)	\(e\left(\frac{2773}{5390}\right)\)	\(e\left(\frac{1399}{1617}\right)\)	\(e\left(\frac{5149}{8085}\right)\)	\(e\left(\frac{52}{2695}\right)\)	\(e\left(\frac{3506}{8085}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{5983}{16170}\right)\)
\(\chi_{373527}(733,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1443}{5390}\right)\)	\(e\left(\frac{1443}{2695}\right)\)	\(e\left(\frac{9431}{16170}\right)\)	\(e\left(\frac{4329}{5390}\right)\)	\(e\left(\frac{1376}{1617}\right)\)	\(e\left(\frac{4142}{8085}\right)\)	\(e\left(\frac{191}{2695}\right)\)	\(e\left(\frac{3238}{8085}\right)\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{1919}{16170}\right)\)
\(\chi_{373527}(745,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5387}{5390}\right)\)	\(e\left(\frac{2692}{2695}\right)\)	\(e\left(\frac{7309}{16170}\right)\)	\(e\left(\frac{5381}{5390}\right)\)	\(e\left(\frac{730}{1617}\right)\)	\(e\left(\frac{1168}{8085}\right)\)	\(e\left(\frac{2689}{2695}\right)\)	\(e\left(\frac{632}{8085}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{7291}{16170}\right)\)
\(\chi_{373527}(871,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2479}{5390}\right)\)	\(e\left(\frac{2479}{2695}\right)\)	\(e\left(\frac{11503}{16170}\right)\)	\(e\left(\frac{2047}{5390}\right)\)	\(e\left(\frac{277}{1617}\right)\)	\(e\left(\frac{5941}{8085}\right)\)	\(e\left(\frac{2263}{2695}\right)\)	\(e\left(\frac{2384}{8085}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{10207}{16170}\right)\)
\(\chi_{373527}(985,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{311}{5390}\right)\)	\(e\left(\frac{311}{2695}\right)\)	\(e\left(\frac{14867}{16170}\right)\)	\(e\left(\frac{933}{5390}\right)\)	\(e\left(\frac{1580}{1617}\right)\)	\(e\left(\frac{7379}{8085}\right)\)	\(e\left(\frac{622}{2695}\right)\)	\(e\left(\frac{61}{8085}\right)\)	\(e\left(\frac{23}{165}\right)\)	\(e\left(\frac{563}{16170}\right)\)
\(\chi_{373527}(997,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4793}{5390}\right)\)	\(e\left(\frac{2098}{2695}\right)\)	\(e\left(\frac{15361}{16170}\right)\)	\(e\left(\frac{3599}{5390}\right)\)	\(e\left(\frac{1357}{1617}\right)\)	\(e\left(\frac{6052}{8085}\right)\)	\(e\left(\frac{1501}{2695}\right)\)	\(e\left(\frac{4493}{8085}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{11779}{16170}\right)\)
\(\chi_{373527}(1174,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{5390}\right)\)	\(e\left(\frac{197}{2695}\right)\)	\(e\left(\frac{12329}{16170}\right)\)	\(e\left(\frac{591}{5390}\right)\)	\(e\left(\frac{1292}{1617}\right)\)	\(e\left(\frac{5948}{8085}\right)\)	\(e\left(\frac{394}{2695}\right)\)	\(e\left(\frac{5212}{8085}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{13511}{16170}\right)\)
\(\chi_{373527}(1249,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4311}{5390}\right)\)	\(e\left(\frac{1616}{2695}\right)\)	\(e\left(\frac{2077}{16170}\right)\)	\(e\left(\frac{2153}{5390}\right)\)	\(e\left(\frac{1501}{1617}\right)\)	\(e\left(\frac{5959}{8085}\right)\)	\(e\left(\frac{537}{2695}\right)\)	\(e\left(\frac{2726}{8085}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{11773}{16170}\right)\)
\(\chi_{373527}(1300,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5259}{5390}\right)\)	\(e\left(\frac{2564}{2695}\right)\)	\(e\left(\frac{10133}{16170}\right)\)	\(e\left(\frac{4997}{5390}\right)\)	\(e\left(\frac{974}{1617}\right)\)	\(e\left(\frac{6086}{8085}\right)\)	\(e\left(\frac{2433}{2695}\right)\)	\(e\left(\frac{7834}{8085}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{9347}{16170}\right)\)
\(\chi_{373527}(1426,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4063}{5390}\right)\)	\(e\left(\frac{1368}{2695}\right)\)	\(e\left(\frac{11591}{16170}\right)\)	\(e\left(\frac{1409}{5390}\right)\)	\(e\left(\frac{761}{1617}\right)\)	\(e\left(\frac{6392}{8085}\right)\)	\(e\left(\frac{41}{2695}\right)\)	\(e\left(\frac{5563}{8085}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{3629}{16170}\right)\)
\(\chi_{373527}(1438,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{887}{5390}\right)\)	\(e\left(\frac{887}{2695}\right)\)	\(e\left(\frac{7549}{16170}\right)\)	\(e\left(\frac{2661}{5390}\right)\)	\(e\left(\frac{1021}{1617}\right)\)	\(e\left(\frac{6808}{8085}\right)\)	\(e\left(\frac{1774}{2695}\right)\)	\(e\left(\frac{2687}{8085}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{12871}{16170}\right)\)

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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.rv
Modulus	$373527$
Conductor	$373527$
Order	$16170$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(373527\)
Conductor:	\(373527\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(16170\)	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)