LMFDB - Dirichlet character orbit 373527.qd

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(373527, base_ring=CyclotomicField(3234)) M = H._module chi = DirichletCharacter(H, M([2695,968,147])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(32,373527)) 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:	$3234$	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:	$\Q(\zeta_{1617})$
Fixed field:	Number field defined by a degree 3234 polynomial (not computed)

First 31 of 840 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{373527}(32,\cdot)$	$1$	$1$	$e\left(\frac{1531}{1617}\right)$	$e\left(\frac{1445}{1617}\right)$	$e\left(\frac{227}{1078}\right)$	$e\left(\frac{453}{539}\right)$	$e\left(\frac{509}{3234}\right)$	$e\left(\frac{1823}{3234}\right)$	$e\left(\frac{1273}{1617}\right)$	$e\left(\frac{340}{1617}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{337}{3234}\right)$
$\chi_{373527}(65,\cdot)$	$1$	$1$	$e\left(\frac{1544}{1617}\right)$	$e\left(\frac{1471}{1617}\right)$	$e\left(\frac{575}{1078}\right)$	$e\left(\frac{466}{539}\right)$	$e\left(\frac{1579}{3234}\right)$	$e\left(\frac{1303}{3234}\right)$	$e\left(\frac{1325}{1617}\right)$	$e\left(\frac{251}{1617}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{1433}{3234}\right)$
$\chi_{373527}(758,\cdot)$	$1$	$1$	$e\left(\frac{926}{1617}\right)$	$e\left(\frac{235}{1617}\right)$	$e\left(\frac{865}{1078}\right)$	$e\left(\frac{387}{539}\right)$	$e\left(\frac{1213}{3234}\right)$	$e\left(\frac{151}{3234}\right)$	$e\left(\frac{470}{1617}\right)$	$e\left(\frac{626}{1617}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{3065}{3234}\right)$
$\chi_{373527}(1418,\cdot)$	$1$	$1$	$e\left(\frac{31}{1617}\right)$	$e\left(\frac{62}{1617}\right)$	$e\left(\frac{125}{1078}\right)$	$e\left(\frac{31}{539}\right)$	$e\left(\frac{437}{3234}\right)$	$e\left(\frac{377}{3234}\right)$	$e\left(\frac{124}{1617}\right)$	$e\left(\frac{1156}{1617}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{499}{3234}\right)$
$\chi_{373527}(2111,\cdot)$	$1$	$1$	$e\left(\frac{1360}{1617}\right)$	$e\left(\frac{1103}{1617}\right)$	$e\left(\frac{459}{1078}\right)$	$e\left(\frac{282}{539}\right)$	$e\left(\frac{863}{3234}\right)$	$e\left(\frac{2195}{3234}\right)$	$e\left(\frac{589}{1617}\right)$	$e\left(\frac{640}{1617}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{349}{3234}\right)$
$\chi_{373527}(2144,\cdot)$	$1$	$1$	$e\left(\frac{152}{1617}\right)$	$e\left(\frac{304}{1617}\right)$	$e\left(\frac{213}{1078}\right)$	$e\left(\frac{152}{539}\right)$	$e\left(\frac{943}{3234}\right)$	$e\left(\frac{2005}{3234}\right)$	$e\left(\frac{608}{1617}\right)$	$e\left(\frac{452}{1617}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{1247}{3234}\right)$
$\chi_{373527}(2804,\cdot)$	$1$	$1$	$e\left(\frac{841}{1617}\right)$	$e\left(\frac{65}{1617}\right)$	$e\left(\frac{331}{1078}\right)$	$e\left(\frac{302}{539}\right)$	$e\left(\frac{2675}{3234}\right)$	$e\left(\frac{317}{3234}\right)$	$e\left(\frac{130}{1617}\right)$	$e\left(\frac{586}{1617}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{1123}{3234}\right)$
$\chi_{373527}(2837,\cdot)$	$1$	$1$	$e\left(\frac{1613}{1617}\right)$	$e\left(\frac{1609}{1617}\right)$	$e\left(\frac{349}{1078}\right)$	$e\left(\frac{535}{539}\right)$	$e\left(\frac{1039}{3234}\right)$	$e\left(\frac{1777}{3234}\right)$	$e\left(\frac{1601}{1617}\right)$	$e\left(\frac{1520}{1617}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{1031}{3234}\right)$
$\chi_{373527}(3530,\cdot)$	$1$	$1$	$e\left(\frac{533}{1617}\right)$	$e\left(\frac{1066}{1617}\right)$	$e\left(\frac{793}{1078}\right)$	$e\left(\frac{533}{539}\right)$	$e\left(\frac{211}{3234}\right)$	$e\left(\frac{2935}{3234}\right)$	$e\left(\frac{515}{1617}\right)$	$e\left(\frac{1202}{1617}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{1277}{3234}\right)$
$\chi_{373527}(4190,\cdot)$	$1$	$1$	$e\left(\frac{727}{1617}\right)$	$e\left(\frac{1454}{1617}\right)$	$e\left(\frac{845}{1078}\right)$	$e\left(\frac{188}{539}\right)$	$e\left(\frac{755}{3234}\right)$	$e\left(\frac{1643}{3234}\right)$	$e\left(\frac{1291}{1617}\right)$	$e\left(\frac{247}{1617}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{2209}{3234}\right)$
$\chi_{373527}(4223,\cdot)$	$1$	$1$	$e\left(\frac{146}{1617}\right)$	$e\left(\frac{292}{1617}\right)$	$e\left(\frac{467}{1078}\right)$	$e\left(\frac{146}{539}\right)$	$e\left(\frac{1693}{3234}\right)$	$e\left(\frac{2245}{3234}\right)$	$e\left(\frac{584}{1617}\right)$	$e\left(\frac{1115}{1617}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{1985}{3234}\right)$
$\chi_{373527}(4883,\cdot)$	$1$	$1$	$e\left(\frac{1132}{1617}\right)$	$e\left(\frac{647}{1617}\right)$	$e\left(\frac{409}{1078}\right)$	$e\left(\frac{54}{539}\right)$	$e\left(\frac{257}{3234}\right)$	$e\left(\frac{1613}{3234}\right)$	$e\left(\frac{1294}{1617}\right)$	$e\left(\frac{1579}{1617}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{2521}{3234}\right)$
$\chi_{373527}(4916,\cdot)$	$1$	$1$	$e\left(\frac{452}{1617}\right)$	$e\left(\frac{904}{1617}\right)$	$e\left(\frac{449}{1078}\right)$	$e\left(\frac{452}{539}\right)$	$e\left(\frac{2251}{3234}\right)$	$e\left(\frac{2941}{3234}\right)$	$e\left(\frac{191}{1617}\right)$	$e\left(\frac{1259}{1617}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{3155}{3234}\right)$
$\chi_{373527}(5576,\cdot)$	$1$	$1$	$e\left(\frac{1306}{1617}\right)$	$e\left(\frac{995}{1617}\right)$	$e\left(\frac{589}{1078}\right)$	$e\left(\frac{228}{539}\right)$	$e\left(\frac{1145}{3234}\right)$	$e\left(\frac{1121}{3234}\right)$	$e\left(\frac{373}{1617}\right)$	$e\left(\frac{139}{1617}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{523}{3234}\right)$
$\chi_{373527}(5609,\cdot)$	$1$	$1$	$e\left(\frac{1451}{1617}\right)$	$e\left(\frac{1285}{1617}\right)$	$e\left(\frac{739}{1078}\right)$	$e\left(\frac{373}{539}\right)$	$e\left(\frac{1885}{3234}\right)$	$e\left(\frac{1789}{3234}\right)$	$e\left(\frac{953}{1617}\right)$	$e\left(\frac{17}{1617}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{1553}{3234}\right)$
$\chi_{373527}(6269,\cdot)$	$1$	$1$	$e\left(\frac{1249}{1617}\right)$	$e\left(\frac{881}{1617}\right)$	$e\left(\frac{307}{1078}\right)$	$e\left(\frac{171}{539}\right)$	$e\left(\frac{185}{3234}\right)$	$e\left(\frac{167}{3234}\right)$	$e\left(\frac{145}{1617}\right)$	$e\left(\frac{778}{1617}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{2683}{3234}\right)$
$\chi_{373527}(6962,\cdot)$	$1$	$1$	$e\left(\frac{961}{1617}\right)$	$e\left(\frac{305}{1617}\right)$	$e\left(\frac{641}{1078}\right)$	$e\left(\frac{422}{539}\right)$	$e\left(\frac{611}{3234}\right)$	$e\left(\frac{1985}{3234}\right)$	$e\left(\frac{610}{1617}\right)$	$e\left(\frac{262}{1617}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{2533}{3234}\right)$
$\chi_{373527}(6995,\cdot)$	$1$	$1$	$e\left(\frac{677}{1617}\right)$	$e\left(\frac{1354}{1617}\right)$	$e\left(\frac{87}{1078}\right)$	$e\left(\frac{138}{539}\right)$	$e\left(\frac{1615}{3234}\right)$	$e\left(\frac{409}{3234}\right)$	$e\left(\frac{1091}{1617}\right)$	$e\left(\frac{1460}{1617}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{2969}{3234}\right)$
$\chi_{373527}(7655,\cdot)$	$1$	$1$	$e\left(\frac{442}{1617}\right)$	$e\left(\frac{884}{1617}\right)$	$e\left(\frac{513}{1078}\right)$	$e\left(\frac{442}{539}\right)$	$e\left(\frac{2423}{3234}\right)$	$e\left(\frac{107}{3234}\right)$	$e\left(\frac{151}{1617}\right)$	$e\left(\frac{208}{1617}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{73}{3234}\right)$
$\chi_{373527}(7688,\cdot)$	$1$	$1$	$e\left(\frac{521}{1617}\right)$	$e\left(\frac{1042}{1617}\right)$	$e\left(\frac{223}{1078}\right)$	$e\left(\frac{521}{539}\right)$	$e\left(\frac{1711}{3234}\right)$	$e\left(\frac{181}{3234}\right)$	$e\left(\frac{467}{1617}\right)$	$e\left(\frac{911}{1617}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{2753}{3234}\right)$
$\chi_{373527}(8381,\cdot)$	$1$	$1$	$e\left(\frac{1058}{1617}\right)$	$e\left(\frac{499}{1617}\right)$	$e\left(\frac{667}{1078}\right)$	$e\left(\frac{519}{539}\right)$	$e\left(\frac{883}{3234}\right)$	$e\left(\frac{1339}{3234}\right)$	$e\left(\frac{998}{1617}\right)$	$e\left(\frac{593}{1617}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{2999}{3234}\right)$
$\chi_{373527}(9041,\cdot)$	$1$	$1$	$e\left(\frac{328}{1617}\right)$	$e\left(\frac{656}{1617}\right)$	$e\left(\frac{1027}{1078}\right)$	$e\left(\frac{328}{539}\right)$	$e\left(\frac{503}{3234}\right)$	$e\left(\frac{1433}{3234}\right)$	$e\left(\frac{1312}{1617}\right)$	$e\left(\frac{1486}{1617}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{1159}{3234}\right)$
$\chi_{373527}(9734,\cdot)$	$1$	$1$	$e\left(\frac{733}{1617}\right)$	$e\left(\frac{1466}{1617}\right)$	$e\left(\frac{591}{1078}\right)$	$e\left(\frac{194}{539}\right)$	$e\left(\frac{5}{3234}\right)$	$e\left(\frac{1403}{3234}\right)$	$e\left(\frac{1315}{1617}\right)$	$e\left(\frac{1201}{1617}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{1471}{3234}\right)$
$\chi_{373527}(9767,\cdot)$	$1$	$1$	$e\left(\frac{977}{1617}\right)$	$e\left(\frac{337}{1617}\right)$	$e\left(\frac{323}{1078}\right)$	$e\left(\frac{438}{539}\right)$	$e\left(\frac{2923}{3234}\right)$	$e\left(\frac{1345}{3234}\right)$	$e\left(\frac{674}{1617}\right)$	$e\left(\frac{650}{1617}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{1643}{3234}\right)$
$\chi_{373527}(10427,\cdot)$	$1$	$1$	$e\left(\frac{907}{1617}\right)$	$e\left(\frac{197}{1617}\right)$	$e\left(\frac{771}{1078}\right)$	$e\left(\frac{368}{539}\right)$	$e\left(\frac{893}{3234}\right)$	$e\left(\frac{911}{3234}\right)$	$e\left(\frac{394}{1617}\right)$	$e\left(\frac{1378}{1617}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{2707}{3234}\right)$
$\chi_{373527}(10460,\cdot)$	$1$	$1$	$e\left(\frac{359}{1617}\right)$	$e\left(\frac{718}{1617}\right)$	$e\left(\frac{613}{1078}\right)$	$e\left(\frac{359}{539}\right)$	$e\left(\frac{2557}{3234}\right)$	$e\left(\frac{193}{3234}\right)$	$e\left(\frac{1436}{1617}\right)$	$e\left(\frac{1025}{1617}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{41}{3234}\right)$
$\chi_{373527}(11120,\cdot)$	$1$	$1$	$e\left(\frac{850}{1617}\right)$	$e\left(\frac{83}{1617}\right)$	$e\left(\frac{489}{1078}\right)$	$e\left(\frac{311}{539}\right)$	$e\left(\frac{3167}{3234}\right)$	$e\left(\frac{3191}{3234}\right)$	$e\left(\frac{166}{1617}\right)$	$e\left(\frac{400}{1617}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{1633}{3234}\right)$
$\chi_{373527}(11813,\cdot)$	$1$	$1$	$e\left(\frac{562}{1617}\right)$	$e\left(\frac{1124}{1617}\right)$	$e\left(\frac{823}{1078}\right)$	$e\left(\frac{23}{539}\right)$	$e\left(\frac{359}{3234}\right)$	$e\left(\frac{1775}{3234}\right)$	$e\left(\frac{631}{1617}\right)$	$e\left(\frac{1501}{1617}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{1483}{3234}\right)$
$\chi_{373527}(11846,\cdot)$	$1$	$1$	$e\left(\frac{1202}{1617}\right)$	$e\left(\frac{787}{1617}\right)$	$e\left(\frac{1039}{1078}\right)$	$e\left(\frac{124}{539}\right)$	$e\left(\frac{2287}{3234}\right)$	$e\left(\frac{2047}{3234}\right)$	$e\left(\frac{1574}{1617}\right)$	$e\left(\frac{851}{1617}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{1457}{3234}\right)$
$\chi_{373527}(12506,\cdot)$	$1$	$1$	$e\left(\frac{43}{1617}\right)$	$e\left(\frac{86}{1617}\right)$	$e\left(\frac{695}{1078}\right)$	$e\left(\frac{43}{539}\right)$	$e\left(\frac{2171}{3234}\right)$	$e\left(\frac{3131}{3234}\right)$	$e\left(\frac{172}{1617}\right)$	$e\left(\frac{1447}{1617}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{2257}{3234}\right)$
$\chi_{373527}(12539,\cdot)$	$1$	$1$	$e\left(\frac{1046}{1617}\right)$	$e\left(\frac{475}{1617}\right)$	$e\left(\frac{97}{1078}\right)$	$e\left(\frac{507}{539}\right)$	$e\left(\frac{2383}{3234}\right)$	$e\left(\frac{1819}{3234}\right)$	$e\left(\frac{950}{1617}\right)$	$e\left(\frac{302}{1617}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{1241}{3234}\right)$

Overview	Random
Universe	Knowledge

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{373527}(32,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1531}{1617}\right)\)	\(e\left(\frac{1445}{1617}\right)\)	\(e\left(\frac{227}{1078}\right)\)	\(e\left(\frac{453}{539}\right)\)	\(e\left(\frac{509}{3234}\right)\)	\(e\left(\frac{1823}{3234}\right)\)	\(e\left(\frac{1273}{1617}\right)\)	\(e\left(\frac{340}{1617}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{337}{3234}\right)\)
\(\chi_{373527}(65,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1544}{1617}\right)\)	\(e\left(\frac{1471}{1617}\right)\)	\(e\left(\frac{575}{1078}\right)\)	\(e\left(\frac{466}{539}\right)\)	\(e\left(\frac{1579}{3234}\right)\)	\(e\left(\frac{1303}{3234}\right)\)	\(e\left(\frac{1325}{1617}\right)\)	\(e\left(\frac{251}{1617}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{1433}{3234}\right)\)
\(\chi_{373527}(758,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{926}{1617}\right)\)	\(e\left(\frac{235}{1617}\right)\)	\(e\left(\frac{865}{1078}\right)\)	\(e\left(\frac{387}{539}\right)\)	\(e\left(\frac{1213}{3234}\right)\)	\(e\left(\frac{151}{3234}\right)\)	\(e\left(\frac{470}{1617}\right)\)	\(e\left(\frac{626}{1617}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{3065}{3234}\right)\)
\(\chi_{373527}(1418,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{1617}\right)\)	\(e\left(\frac{62}{1617}\right)\)	\(e\left(\frac{125}{1078}\right)\)	\(e\left(\frac{31}{539}\right)\)	\(e\left(\frac{437}{3234}\right)\)	\(e\left(\frac{377}{3234}\right)\)	\(e\left(\frac{124}{1617}\right)\)	\(e\left(\frac{1156}{1617}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{499}{3234}\right)\)
\(\chi_{373527}(2111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1360}{1617}\right)\)	\(e\left(\frac{1103}{1617}\right)\)	\(e\left(\frac{459}{1078}\right)\)	\(e\left(\frac{282}{539}\right)\)	\(e\left(\frac{863}{3234}\right)\)	\(e\left(\frac{2195}{3234}\right)\)	\(e\left(\frac{589}{1617}\right)\)	\(e\left(\frac{640}{1617}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{349}{3234}\right)\)
\(\chi_{373527}(2144,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{152}{1617}\right)\)	\(e\left(\frac{304}{1617}\right)\)	\(e\left(\frac{213}{1078}\right)\)	\(e\left(\frac{152}{539}\right)\)	\(e\left(\frac{943}{3234}\right)\)	\(e\left(\frac{2005}{3234}\right)\)	\(e\left(\frac{608}{1617}\right)\)	\(e\left(\frac{452}{1617}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{1247}{3234}\right)\)
\(\chi_{373527}(2804,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{841}{1617}\right)\)	\(e\left(\frac{65}{1617}\right)\)	\(e\left(\frac{331}{1078}\right)\)	\(e\left(\frac{302}{539}\right)\)	\(e\left(\frac{2675}{3234}\right)\)	\(e\left(\frac{317}{3234}\right)\)	\(e\left(\frac{130}{1617}\right)\)	\(e\left(\frac{586}{1617}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{1123}{3234}\right)\)
\(\chi_{373527}(2837,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1613}{1617}\right)\)	\(e\left(\frac{1609}{1617}\right)\)	\(e\left(\frac{349}{1078}\right)\)	\(e\left(\frac{535}{539}\right)\)	\(e\left(\frac{1039}{3234}\right)\)	\(e\left(\frac{1777}{3234}\right)\)	\(e\left(\frac{1601}{1617}\right)\)	\(e\left(\frac{1520}{1617}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{1031}{3234}\right)\)
\(\chi_{373527}(3530,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{533}{1617}\right)\)	\(e\left(\frac{1066}{1617}\right)\)	\(e\left(\frac{793}{1078}\right)\)	\(e\left(\frac{533}{539}\right)\)	\(e\left(\frac{211}{3234}\right)\)	\(e\left(\frac{2935}{3234}\right)\)	\(e\left(\frac{515}{1617}\right)\)	\(e\left(\frac{1202}{1617}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{1277}{3234}\right)\)
\(\chi_{373527}(4190,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{727}{1617}\right)\)	\(e\left(\frac{1454}{1617}\right)\)	\(e\left(\frac{845}{1078}\right)\)	\(e\left(\frac{188}{539}\right)\)	\(e\left(\frac{755}{3234}\right)\)	\(e\left(\frac{1643}{3234}\right)\)	\(e\left(\frac{1291}{1617}\right)\)	\(e\left(\frac{247}{1617}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{2209}{3234}\right)\)
\(\chi_{373527}(4223,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{146}{1617}\right)\)	\(e\left(\frac{292}{1617}\right)\)	\(e\left(\frac{467}{1078}\right)\)	\(e\left(\frac{146}{539}\right)\)	\(e\left(\frac{1693}{3234}\right)\)	\(e\left(\frac{2245}{3234}\right)\)	\(e\left(\frac{584}{1617}\right)\)	\(e\left(\frac{1115}{1617}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{1985}{3234}\right)\)
\(\chi_{373527}(4883,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1132}{1617}\right)\)	\(e\left(\frac{647}{1617}\right)\)	\(e\left(\frac{409}{1078}\right)\)	\(e\left(\frac{54}{539}\right)\)	\(e\left(\frac{257}{3234}\right)\)	\(e\left(\frac{1613}{3234}\right)\)	\(e\left(\frac{1294}{1617}\right)\)	\(e\left(\frac{1579}{1617}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{2521}{3234}\right)\)
\(\chi_{373527}(4916,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{452}{1617}\right)\)	\(e\left(\frac{904}{1617}\right)\)	\(e\left(\frac{449}{1078}\right)\)	\(e\left(\frac{452}{539}\right)\)	\(e\left(\frac{2251}{3234}\right)\)	\(e\left(\frac{2941}{3234}\right)\)	\(e\left(\frac{191}{1617}\right)\)	\(e\left(\frac{1259}{1617}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{3155}{3234}\right)\)
\(\chi_{373527}(5576,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1306}{1617}\right)\)	\(e\left(\frac{995}{1617}\right)\)	\(e\left(\frac{589}{1078}\right)\)	\(e\left(\frac{228}{539}\right)\)	\(e\left(\frac{1145}{3234}\right)\)	\(e\left(\frac{1121}{3234}\right)\)	\(e\left(\frac{373}{1617}\right)\)	\(e\left(\frac{139}{1617}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{523}{3234}\right)\)
\(\chi_{373527}(5609,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1451}{1617}\right)\)	\(e\left(\frac{1285}{1617}\right)\)	\(e\left(\frac{739}{1078}\right)\)	\(e\left(\frac{373}{539}\right)\)	\(e\left(\frac{1885}{3234}\right)\)	\(e\left(\frac{1789}{3234}\right)\)	\(e\left(\frac{953}{1617}\right)\)	\(e\left(\frac{17}{1617}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{1553}{3234}\right)\)
\(\chi_{373527}(6269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1249}{1617}\right)\)	\(e\left(\frac{881}{1617}\right)\)	\(e\left(\frac{307}{1078}\right)\)	\(e\left(\frac{171}{539}\right)\)	\(e\left(\frac{185}{3234}\right)\)	\(e\left(\frac{167}{3234}\right)\)	\(e\left(\frac{145}{1617}\right)\)	\(e\left(\frac{778}{1617}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{2683}{3234}\right)\)
\(\chi_{373527}(6962,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{961}{1617}\right)\)	\(e\left(\frac{305}{1617}\right)\)	\(e\left(\frac{641}{1078}\right)\)	\(e\left(\frac{422}{539}\right)\)	\(e\left(\frac{611}{3234}\right)\)	\(e\left(\frac{1985}{3234}\right)\)	\(e\left(\frac{610}{1617}\right)\)	\(e\left(\frac{262}{1617}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{2533}{3234}\right)\)
\(\chi_{373527}(6995,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{677}{1617}\right)\)	\(e\left(\frac{1354}{1617}\right)\)	\(e\left(\frac{87}{1078}\right)\)	\(e\left(\frac{138}{539}\right)\)	\(e\left(\frac{1615}{3234}\right)\)	\(e\left(\frac{409}{3234}\right)\)	\(e\left(\frac{1091}{1617}\right)\)	\(e\left(\frac{1460}{1617}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{2969}{3234}\right)\)
\(\chi_{373527}(7655,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{442}{1617}\right)\)	\(e\left(\frac{884}{1617}\right)\)	\(e\left(\frac{513}{1078}\right)\)	\(e\left(\frac{442}{539}\right)\)	\(e\left(\frac{2423}{3234}\right)\)	\(e\left(\frac{107}{3234}\right)\)	\(e\left(\frac{151}{1617}\right)\)	\(e\left(\frac{208}{1617}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{73}{3234}\right)\)
\(\chi_{373527}(7688,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{521}{1617}\right)\)	\(e\left(\frac{1042}{1617}\right)\)	\(e\left(\frac{223}{1078}\right)\)	\(e\left(\frac{521}{539}\right)\)	\(e\left(\frac{1711}{3234}\right)\)	\(e\left(\frac{181}{3234}\right)\)	\(e\left(\frac{467}{1617}\right)\)	\(e\left(\frac{911}{1617}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{2753}{3234}\right)\)
\(\chi_{373527}(8381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1058}{1617}\right)\)	\(e\left(\frac{499}{1617}\right)\)	\(e\left(\frac{667}{1078}\right)\)	\(e\left(\frac{519}{539}\right)\)	\(e\left(\frac{883}{3234}\right)\)	\(e\left(\frac{1339}{3234}\right)\)	\(e\left(\frac{998}{1617}\right)\)	\(e\left(\frac{593}{1617}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{2999}{3234}\right)\)
\(\chi_{373527}(9041,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{328}{1617}\right)\)	\(e\left(\frac{656}{1617}\right)\)	\(e\left(\frac{1027}{1078}\right)\)	\(e\left(\frac{328}{539}\right)\)	\(e\left(\frac{503}{3234}\right)\)	\(e\left(\frac{1433}{3234}\right)\)	\(e\left(\frac{1312}{1617}\right)\)	\(e\left(\frac{1486}{1617}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{1159}{3234}\right)\)
\(\chi_{373527}(9734,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{733}{1617}\right)\)	\(e\left(\frac{1466}{1617}\right)\)	\(e\left(\frac{591}{1078}\right)\)	\(e\left(\frac{194}{539}\right)\)	\(e\left(\frac{5}{3234}\right)\)	\(e\left(\frac{1403}{3234}\right)\)	\(e\left(\frac{1315}{1617}\right)\)	\(e\left(\frac{1201}{1617}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{1471}{3234}\right)\)
\(\chi_{373527}(9767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{977}{1617}\right)\)	\(e\left(\frac{337}{1617}\right)\)	\(e\left(\frac{323}{1078}\right)\)	\(e\left(\frac{438}{539}\right)\)	\(e\left(\frac{2923}{3234}\right)\)	\(e\left(\frac{1345}{3234}\right)\)	\(e\left(\frac{674}{1617}\right)\)	\(e\left(\frac{650}{1617}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{1643}{3234}\right)\)
\(\chi_{373527}(10427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{907}{1617}\right)\)	\(e\left(\frac{197}{1617}\right)\)	\(e\left(\frac{771}{1078}\right)\)	\(e\left(\frac{368}{539}\right)\)	\(e\left(\frac{893}{3234}\right)\)	\(e\left(\frac{911}{3234}\right)\)	\(e\left(\frac{394}{1617}\right)\)	\(e\left(\frac{1378}{1617}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{2707}{3234}\right)\)
\(\chi_{373527}(10460,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{359}{1617}\right)\)	\(e\left(\frac{718}{1617}\right)\)	\(e\left(\frac{613}{1078}\right)\)	\(e\left(\frac{359}{539}\right)\)	\(e\left(\frac{2557}{3234}\right)\)	\(e\left(\frac{193}{3234}\right)\)	\(e\left(\frac{1436}{1617}\right)\)	\(e\left(\frac{1025}{1617}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{41}{3234}\right)\)
\(\chi_{373527}(11120,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{850}{1617}\right)\)	\(e\left(\frac{83}{1617}\right)\)	\(e\left(\frac{489}{1078}\right)\)	\(e\left(\frac{311}{539}\right)\)	\(e\left(\frac{3167}{3234}\right)\)	\(e\left(\frac{3191}{3234}\right)\)	\(e\left(\frac{166}{1617}\right)\)	\(e\left(\frac{400}{1617}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{1633}{3234}\right)\)
\(\chi_{373527}(11813,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{562}{1617}\right)\)	\(e\left(\frac{1124}{1617}\right)\)	\(e\left(\frac{823}{1078}\right)\)	\(e\left(\frac{23}{539}\right)\)	\(e\left(\frac{359}{3234}\right)\)	\(e\left(\frac{1775}{3234}\right)\)	\(e\left(\frac{631}{1617}\right)\)	\(e\left(\frac{1501}{1617}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{1483}{3234}\right)\)
\(\chi_{373527}(11846,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1202}{1617}\right)\)	\(e\left(\frac{787}{1617}\right)\)	\(e\left(\frac{1039}{1078}\right)\)	\(e\left(\frac{124}{539}\right)\)	\(e\left(\frac{2287}{3234}\right)\)	\(e\left(\frac{2047}{3234}\right)\)	\(e\left(\frac{1574}{1617}\right)\)	\(e\left(\frac{851}{1617}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{1457}{3234}\right)\)
\(\chi_{373527}(12506,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{1617}\right)\)	\(e\left(\frac{86}{1617}\right)\)	\(e\left(\frac{695}{1078}\right)\)	\(e\left(\frac{43}{539}\right)\)	\(e\left(\frac{2171}{3234}\right)\)	\(e\left(\frac{3131}{3234}\right)\)	\(e\left(\frac{172}{1617}\right)\)	\(e\left(\frac{1447}{1617}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{2257}{3234}\right)\)
\(\chi_{373527}(12539,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1046}{1617}\right)\)	\(e\left(\frac{475}{1617}\right)\)	\(e\left(\frac{97}{1078}\right)\)	\(e\left(\frac{507}{539}\right)\)	\(e\left(\frac{2383}{3234}\right)\)	\(e\left(\frac{1819}{3234}\right)\)	\(e\left(\frac{950}{1617}\right)\)	\(e\left(\frac{302}{1617}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{1241}{3234}\right)\)

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First 31 of 840 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.qd
Modulus	$373527$
Conductor	$373527$
Order	$3234$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(373527\)
Conductor:	\(373527\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(3234\)	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)