LMFDB - Dirichlet character orbit 379045.ob

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(379045, base_ring=CyclotomicField(3010)) M = H._module chi = DirichletCharacter(H, M([1505,903,2525])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(414, 379045)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("379045.414"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$379045$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$379045$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$3010$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{1505})$
Fixed field:	Number field defined by a degree 3010 polynomial (not computed)

First 31 of 1008 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{379045}(414,\cdot)$	$-1$	$1$	$e\left(\frac{484}{1505}\right)$	$e\left(\frac{505}{602}\right)$	$e\left(\frac{968}{1505}\right)$	$e\left(\frac{69}{430}\right)$	$e\left(\frac{311}{430}\right)$	$e\left(\frac{1452}{1505}\right)$	$e\left(\frac{204}{301}\right)$	$e\left(\frac{2929}{3010}\right)$	$e\left(\frac{1451}{3010}\right)$	$e\left(\frac{339}{1505}\right)$
$\chi_{379045}(1384,\cdot)$	$-1$	$1$	$e\left(\frac{1056}{1505}\right)$	$e\left(\frac{363}{602}\right)$	$e\left(\frac{607}{1505}\right)$	$e\left(\frac{131}{430}\right)$	$e\left(\frac{229}{430}\right)$	$e\left(\frac{158}{1505}\right)$	$e\left(\frac{62}{301}\right)$	$e\left(\frac{781}{3010}\right)$	$e\left(\frac{19}{3010}\right)$	$e\left(\frac{466}{1505}\right)$
$\chi_{379045}(1704,\cdot)$	$-1$	$1$	$e\left(\frac{1212}{1505}\right)$	$e\left(\frac{379}{602}\right)$	$e\left(\frac{919}{1505}\right)$	$e\left(\frac{187}{430}\right)$	$e\left(\frac{363}{430}\right)$	$e\left(\frac{626}{1505}\right)$	$e\left(\frac{78}{301}\right)$	$e\left(\frac{1837}{3010}\right)$	$e\left(\frac{723}{3010}\right)$	$e\left(\frac{227}{1505}\right)$
$\chi_{379045}(3264,\cdot)$	$-1$	$1$	$e\left(\frac{53}{1505}\right)$	$e\left(\frac{291}{602}\right)$	$e\left(\frac{106}{1505}\right)$	$e\left(\frac{223}{430}\right)$	$e\left(\frac{357}{430}\right)$	$e\left(\frac{159}{1505}\right)$	$e\left(\frac{291}{301}\right)$	$e\left(\frac{243}{3010}\right)$	$e\left(\frac{1667}{3010}\right)$	$e\left(\frac{488}{1505}\right)$
$\chi_{379045}(3639,\cdot)$	$-1$	$1$	$e\left(\frac{1401}{1505}\right)$	$e\left(\frac{491}{602}\right)$	$e\left(\frac{1297}{1505}\right)$	$e\left(\frac{321}{430}\right)$	$e\left(\frac{269}{430}\right)$	$e\left(\frac{1193}{1505}\right)$	$e\left(\frac{190}{301}\right)$	$e\left(\frac{801}{3010}\right)$	$e\left(\frac{2039}{3010}\right)$	$e\left(\frac{661}{1505}\right)$
$\chi_{379045}(3694,\cdot)$	$-1$	$1$	$e\left(\frac{1124}{1505}\right)$	$e\left(\frac{123}{602}\right)$	$e\left(\frac{743}{1505}\right)$	$e\left(\frac{409}{430}\right)$	$e\left(\frac{111}{430}\right)$	$e\left(\frac{362}{1505}\right)$	$e\left(\frac{123}{301}\right)$	$e\left(\frac{2399}{3010}\right)$	$e\left(\frac{2101}{3010}\right)$	$e\left(\frac{439}{1505}\right)$
$\chi_{379045}(4289,\cdot)$	$-1$	$1$	$e\left(\frac{1368}{1505}\right)$	$e\left(\frac{395}{602}\right)$	$e\left(\frac{1231}{1505}\right)$	$e\left(\frac{243}{430}\right)$	$e\left(\frac{67}{430}\right)$	$e\left(\frac{1094}{1505}\right)$	$e\left(\frac{94}{301}\right)$	$e\left(\frac{2893}{3010}\right)$	$e\left(\frac{1427}{3010}\right)$	$e\left(\frac{1493}{1505}\right)$
$\chi_{379045}(4494,\cdot)$	$-1$	$1$	$e\left(\frac{383}{1505}\right)$	$e\left(\frac{47}{602}\right)$	$e\left(\frac{766}{1505}\right)$	$e\left(\frac{143}{430}\right)$	$e\left(\frac{227}{430}\right)$	$e\left(\frac{1149}{1505}\right)$	$e\left(\frac{47}{301}\right)$	$e\left(\frac{393}{3010}\right)$	$e\left(\frac{1767}{3010}\right)$	$e\left(\frac{1198}{1505}\right)$
$\chi_{379045}(4719,\cdot)$	$-1$	$1$	$e\left(\frac{444}{1505}\right)$	$e\left(\frac{115}{602}\right)$	$e\left(\frac{888}{1505}\right)$	$e\left(\frac{209}{430}\right)$	$e\left(\frac{1}{430}\right)$	$e\left(\frac{1332}{1505}\right)$	$e\left(\frac{115}{301}\right)$	$e\left(\frac{1269}{3010}\right)$	$e\left(\frac{2351}{3010}\right)$	$e\left(\frac{709}{1505}\right)$
$\chi_{379045}(4904,\cdot)$	$-1$	$1$	$e\left(\frac{163}{1505}\right)$	$e\left(\frac{9}{602}\right)$	$e\left(\frac{326}{1505}\right)$	$e\left(\frac{53}{430}\right)$	$e\left(\frac{27}{430}\right)$	$e\left(\frac{489}{1505}\right)$	$e\left(\frac{9}{301}\right)$	$e\left(\frac{293}{3010}\right)$	$e\left(\frac{697}{3010}\right)$	$e\left(\frac{223}{1505}\right)$
$\chi_{379045}(4924,\cdot)$	$-1$	$1$	$e\left(\frac{544}{1505}\right)$	$e\left(\frac{187}{602}\right)$	$e\left(\frac{1088}{1505}\right)$	$e\left(\frac{289}{430}\right)$	$e\left(\frac{131}{430}\right)$	$e\left(\frac{127}{1505}\right)$	$e\left(\frac{187}{301}\right)$	$e\left(\frac{2409}{3010}\right)$	$e\left(\frac{101}{3010}\right)$	$e\left(\frac{1289}{1505}\right)$
$\chi_{379045}(4984,\cdot)$	$-1$	$1$	$e\left(\frac{1327}{1505}\right)$	$e\left(\frac{221}{602}\right)$	$e\left(\frac{1149}{1505}\right)$	$e\left(\frac{107}{430}\right)$	$e\left(\frac{233}{430}\right)$	$e\left(\frac{971}{1505}\right)$	$e\left(\frac{221}{301}\right)$	$e\left(\frac{2847}{3010}\right)$	$e\left(\frac{393}{3010}\right)$	$e\left(\frac{292}{1505}\right)$
$\chi_{379045}(5334,\cdot)$	$-1$	$1$	$e\left(\frac{429}{1505}\right)$	$e\left(\frac{345}{602}\right)$	$e\left(\frac{858}{1505}\right)$	$e\left(\frac{369}{430}\right)$	$e\left(\frac{261}{430}\right)$	$e\left(\frac{1287}{1505}\right)$	$e\left(\frac{44}{301}\right)$	$e\left(\frac{1399}{3010}\right)$	$e\left(\frac{431}{3010}\right)$	$e\left(\frac{1224}{1505}\right)$
$\chi_{379045}(6009,\cdot)$	$-1$	$1$	$e\left(\frac{682}{1505}\right)$	$e\left(\frac{479}{602}\right)$	$e\left(\frac{1364}{1505}\right)$	$e\left(\frac{107}{430}\right)$	$e\left(\frac{233}{430}\right)$	$e\left(\frac{541}{1505}\right)$	$e\left(\frac{178}{301}\right)$	$e\left(\frac{2417}{3010}\right)$	$e\left(\frac{2113}{3010}\right)$	$e\left(\frac{1367}{1505}\right)$
$\chi_{379045}(6214,\cdot)$	$-1$	$1$	$e\left(\frac{1027}{1505}\right)$	$e\left(\frac{5}{602}\right)$	$e\left(\frac{549}{1505}\right)$	$e\left(\frac{297}{430}\right)$	$e\left(\frac{273}{430}\right)$	$e\left(\frac{71}{1505}\right)$	$e\left(\frac{5}{301}\right)$	$e\left(\frac{2437}{3010}\right)$	$e\left(\frac{1123}{3010}\right)$	$e\left(\frac{57}{1505}\right)$
$\chi_{379045}(6544,\cdot)$	$-1$	$1$	$e\left(\frac{48}{1505}\right)$	$e\left(\frac{167}{602}\right)$	$e\left(\frac{96}{1505}\right)$	$e\left(\frac{133}{430}\right)$	$e\left(\frac{157}{430}\right)$	$e\left(\frac{144}{1505}\right)$	$e\left(\frac{167}{301}\right)$	$e\left(\frac{2293}{3010}\right)$	$e\left(\frac{1027}{3010}\right)$	$e\left(\frac{158}{1505}\right)$
$\chi_{379045}(6624,\cdot)$	$-1$	$1$	$e\left(\frac{1227}{1505}\right)$	$e\left(\frac{149}{602}\right)$	$e\left(\frac{949}{1505}\right)$	$e\left(\frac{27}{430}\right)$	$e\left(\frac{103}{430}\right)$	$e\left(\frac{671}{1505}\right)$	$e\left(\frac{149}{301}\right)$	$e\left(\frac{1707}{3010}\right)$	$e\left(\frac{2643}{3010}\right)$	$e\left(\frac{1217}{1505}\right)$
$\chi_{379045}(6919,\cdot)$	$-1$	$1$	$e\left(\frac{1481}{1505}\right)$	$e\left(\frac{67}{602}\right)$	$e\left(\frac{1457}{1505}\right)$	$e\left(\frac{41}{430}\right)$	$e\left(\frac{29}{430}\right)$	$e\left(\frac{1433}{1505}\right)$	$e\left(\frac{67}{301}\right)$	$e\left(\frac{1111}{3010}\right)$	$e\left(\frac{239}{3010}\right)$	$e\left(\frac{1426}{1505}\right)$
$\chi_{379045}(6974,\cdot)$	$-1$	$1$	$e\left(\frac{1469}{1505}\right)$	$e\left(\frac{251}{602}\right)$	$e\left(\frac{1433}{1505}\right)$	$e\left(\frac{169}{430}\right)$	$e\left(\frac{151}{430}\right)$	$e\left(\frac{1397}{1505}\right)$	$e\left(\frac{251}{301}\right)$	$e\left(\frac{2419}{3010}\right)$	$e\left(\frac{1111}{3010}\right)$	$e\left(\frac{634}{1505}\right)$
$\chi_{379045}(7944,\cdot)$	$-1$	$1$	$e\left(\frac{136}{1505}\right)$	$e\left(\frac{423}{602}\right)$	$e\left(\frac{272}{1505}\right)$	$e\left(\frac{341}{430}\right)$	$e\left(\frac{409}{430}\right)$	$e\left(\frac{408}{1505}\right)$	$e\left(\frac{122}{301}\right)$	$e\left(\frac{1731}{3010}\right)$	$e\left(\frac{2659}{3010}\right)$	$e\left(\frac{1451}{1505}\right)$
$\chi_{379045}(8149,\cdot)$	$-1$	$1$	$e\left(\frac{96}{1505}\right)$	$e\left(\frac{33}{602}\right)$	$e\left(\frac{192}{1505}\right)$	$e\left(\frac{51}{430}\right)$	$e\left(\frac{99}{430}\right)$	$e\left(\frac{288}{1505}\right)$	$e\left(\frac{33}{301}\right)$	$e\left(\frac{71}{3010}\right)$	$e\left(\frac{549}{3010}\right)$	$e\left(\frac{316}{1505}\right)$
$\chi_{379045}(8264,\cdot)$	$-1$	$1$	$e\left(\frac{1217}{1505}\right)$	$e\left(\frac{503}{602}\right)$	$e\left(\frac{929}{1505}\right)$	$e\left(\frac{277}{430}\right)$	$e\left(\frac{133}{430}\right)$	$e\left(\frac{641}{1505}\right)$	$e\left(\frac{202}{301}\right)$	$e\left(\frac{2797}{3010}\right)$	$e\left(\frac{1363}{3010}\right)$	$e\left(\frac{557}{1505}\right)$
$\chi_{379045}(8559,\cdot)$	$-1$	$1$	$e\left(\frac{16}{1505}\right)$	$e\left(\frac{457}{602}\right)$	$e\left(\frac{32}{1505}\right)$	$e\left(\frac{331}{430}\right)$	$e\left(\frac{339}{430}\right)$	$e\left(\frac{48}{1505}\right)$	$e\left(\frac{156}{301}\right)$	$e\left(\frac{2771}{3010}\right)$	$e\left(\frac{2349}{3010}\right)$	$e\left(\frac{1056}{1505}\right)$
$\chi_{379045}(8799,\cdot)$	$-1$	$1$	$e\left(\frac{1303}{1505}\right)$	$e\left(\frac{589}{602}\right)$	$e\left(\frac{1101}{1505}\right)$	$e\left(\frac{363}{430}\right)$	$e\left(\frac{47}{430}\right)$	$e\left(\frac{899}{1505}\right)$	$e\left(\frac{288}{301}\right)$	$e\left(\frac{2453}{3010}\right)$	$e\left(\frac{2137}{3010}\right)$	$e\left(\frac{213}{1505}\right)$
$\chi_{379045}(9229,\cdot)$	$-1$	$1$	$e\left(\frac{1044}{1505}\right)$	$e\left(\frac{547}{602}\right)$	$e\left(\frac{583}{1505}\right)$	$e\left(\frac{259}{430}\right)$	$e\left(\frac{351}{430}\right)$	$e\left(\frac{122}{1505}\right)$	$e\left(\frac{246}{301}\right)$	$e\left(\frac{2089}{3010}\right)$	$e\left(\frac{891}{3010}\right)$	$e\left(\frac{1179}{1505}\right)$
$\chi_{379045}(10199,\cdot)$	$-1$	$1$	$e\left(\frac{1441}{1505}\right)$	$e\left(\frac{279}{602}\right)$	$e\left(\frac{1377}{1505}\right)$	$e\left(\frac{181}{430}\right)$	$e\left(\frac{149}{430}\right)$	$e\left(\frac{1313}{1505}\right)$	$e\left(\frac{279}{301}\right)$	$e\left(\frac{2461}{3010}\right)$	$e\left(\frac{1139}{3010}\right)$	$e\left(\frac{291}{1505}\right)$
$\chi_{379045}(10519,\cdot)$	$-1$	$1$	$e\left(\frac{267}{1505}\right)$	$e\left(\frac{421}{602}\right)$	$e\left(\frac{534}{1505}\right)$	$e\left(\frac{377}{430}\right)$	$e\left(\frac{403}{430}\right)$	$e\left(\frac{801}{1505}\right)$	$e\left(\frac{120}{301}\right)$	$e\left(\frac{997}{3010}\right)$	$e\left(\frac{163}{3010}\right)$	$e\left(\frac{1067}{1505}\right)$
$\chi_{379045}(12079,\cdot)$	$-1$	$1$	$e\left(\frac{788}{1505}\right)$	$e\left(\frac{459}{602}\right)$	$e\left(\frac{71}{1505}\right)$	$e\left(\frac{123}{430}\right)$	$e\left(\frac{87}{430}\right)$	$e\left(\frac{859}{1505}\right)$	$e\left(\frac{158}{301}\right)$	$e\left(\frac{2903}{3010}\right)$	$e\left(\frac{2437}{3010}\right)$	$e\left(\frac{838}{1505}\right)$
$\chi_{379045}(12454,\cdot)$	$-1$	$1$	$e\left(\frac{456}{1505}\right)$	$e\left(\frac{533}{602}\right)$	$e\left(\frac{912}{1505}\right)$	$e\left(\frac{81}{430}\right)$	$e\left(\frac{309}{430}\right)$	$e\left(\frac{1368}{1505}\right)$	$e\left(\frac{232}{301}\right)$	$e\left(\frac{2971}{3010}\right)$	$e\left(\frac{1479}{3010}\right)$	$e\left(\frac{1501}{1505}\right)$
$\chi_{379045}(12509,\cdot)$	$-1$	$1$	$e\left(\frac{354}{1505}\right)$	$e\left(\frac{291}{602}\right)$	$e\left(\frac{708}{1505}\right)$	$e\left(\frac{309}{430}\right)$	$e\left(\frac{271}{430}\right)$	$e\left(\frac{1062}{1505}\right)$	$e\left(\frac{291}{301}\right)$	$e\left(\frac{2049}{3010}\right)$	$e\left(\frac{2871}{3010}\right)$	$e\left(\frac{789}{1505}\right)$
$\chi_{379045}(13104,\cdot)$	$-1$	$1$	$e\left(\frac{1088}{1505}\right)$	$e\left(\frac{73}{602}\right)$	$e\left(\frac{671}{1505}\right)$	$e\left(\frac{363}{430}\right)$	$e\left(\frac{47}{430}\right)$	$e\left(\frac{254}{1505}\right)$	$e\left(\frac{73}{301}\right)$	$e\left(\frac{303}{3010}\right)$	$e\left(\frac{1707}{3010}\right)$	$e\left(\frac{1073}{1505}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{379045}(414,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{484}{1505}\right)\)	\(e\left(\frac{505}{602}\right)\)	\(e\left(\frac{968}{1505}\right)\)	\(e\left(\frac{69}{430}\right)\)	\(e\left(\frac{311}{430}\right)\)	\(e\left(\frac{1452}{1505}\right)\)	\(e\left(\frac{204}{301}\right)\)	\(e\left(\frac{2929}{3010}\right)\)	\(e\left(\frac{1451}{3010}\right)\)	\(e\left(\frac{339}{1505}\right)\)
\(\chi_{379045}(1384,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1056}{1505}\right)\)	\(e\left(\frac{363}{602}\right)\)	\(e\left(\frac{607}{1505}\right)\)	\(e\left(\frac{131}{430}\right)\)	\(e\left(\frac{229}{430}\right)\)	\(e\left(\frac{158}{1505}\right)\)	\(e\left(\frac{62}{301}\right)\)	\(e\left(\frac{781}{3010}\right)\)	\(e\left(\frac{19}{3010}\right)\)	\(e\left(\frac{466}{1505}\right)\)
\(\chi_{379045}(1704,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1212}{1505}\right)\)	\(e\left(\frac{379}{602}\right)\)	\(e\left(\frac{919}{1505}\right)\)	\(e\left(\frac{187}{430}\right)\)	\(e\left(\frac{363}{430}\right)\)	\(e\left(\frac{626}{1505}\right)\)	\(e\left(\frac{78}{301}\right)\)	\(e\left(\frac{1837}{3010}\right)\)	\(e\left(\frac{723}{3010}\right)\)	\(e\left(\frac{227}{1505}\right)\)
\(\chi_{379045}(3264,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{1505}\right)\)	\(e\left(\frac{291}{602}\right)\)	\(e\left(\frac{106}{1505}\right)\)	\(e\left(\frac{223}{430}\right)\)	\(e\left(\frac{357}{430}\right)\)	\(e\left(\frac{159}{1505}\right)\)	\(e\left(\frac{291}{301}\right)\)	\(e\left(\frac{243}{3010}\right)\)	\(e\left(\frac{1667}{3010}\right)\)	\(e\left(\frac{488}{1505}\right)\)
\(\chi_{379045}(3639,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1401}{1505}\right)\)	\(e\left(\frac{491}{602}\right)\)	\(e\left(\frac{1297}{1505}\right)\)	\(e\left(\frac{321}{430}\right)\)	\(e\left(\frac{269}{430}\right)\)	\(e\left(\frac{1193}{1505}\right)\)	\(e\left(\frac{190}{301}\right)\)	\(e\left(\frac{801}{3010}\right)\)	\(e\left(\frac{2039}{3010}\right)\)	\(e\left(\frac{661}{1505}\right)\)
\(\chi_{379045}(3694,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1124}{1505}\right)\)	\(e\left(\frac{123}{602}\right)\)	\(e\left(\frac{743}{1505}\right)\)	\(e\left(\frac{409}{430}\right)\)	\(e\left(\frac{111}{430}\right)\)	\(e\left(\frac{362}{1505}\right)\)	\(e\left(\frac{123}{301}\right)\)	\(e\left(\frac{2399}{3010}\right)\)	\(e\left(\frac{2101}{3010}\right)\)	\(e\left(\frac{439}{1505}\right)\)
\(\chi_{379045}(4289,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1368}{1505}\right)\)	\(e\left(\frac{395}{602}\right)\)	\(e\left(\frac{1231}{1505}\right)\)	\(e\left(\frac{243}{430}\right)\)	\(e\left(\frac{67}{430}\right)\)	\(e\left(\frac{1094}{1505}\right)\)	\(e\left(\frac{94}{301}\right)\)	\(e\left(\frac{2893}{3010}\right)\)	\(e\left(\frac{1427}{3010}\right)\)	\(e\left(\frac{1493}{1505}\right)\)
\(\chi_{379045}(4494,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{383}{1505}\right)\)	\(e\left(\frac{47}{602}\right)\)	\(e\left(\frac{766}{1505}\right)\)	\(e\left(\frac{143}{430}\right)\)	\(e\left(\frac{227}{430}\right)\)	\(e\left(\frac{1149}{1505}\right)\)	\(e\left(\frac{47}{301}\right)\)	\(e\left(\frac{393}{3010}\right)\)	\(e\left(\frac{1767}{3010}\right)\)	\(e\left(\frac{1198}{1505}\right)\)
\(\chi_{379045}(4719,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{444}{1505}\right)\)	\(e\left(\frac{115}{602}\right)\)	\(e\left(\frac{888}{1505}\right)\)	\(e\left(\frac{209}{430}\right)\)	\(e\left(\frac{1}{430}\right)\)	\(e\left(\frac{1332}{1505}\right)\)	\(e\left(\frac{115}{301}\right)\)	\(e\left(\frac{1269}{3010}\right)\)	\(e\left(\frac{2351}{3010}\right)\)	\(e\left(\frac{709}{1505}\right)\)
\(\chi_{379045}(4904,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{163}{1505}\right)\)	\(e\left(\frac{9}{602}\right)\)	\(e\left(\frac{326}{1505}\right)\)	\(e\left(\frac{53}{430}\right)\)	\(e\left(\frac{27}{430}\right)\)	\(e\left(\frac{489}{1505}\right)\)	\(e\left(\frac{9}{301}\right)\)	\(e\left(\frac{293}{3010}\right)\)	\(e\left(\frac{697}{3010}\right)\)	\(e\left(\frac{223}{1505}\right)\)
\(\chi_{379045}(4924,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{544}{1505}\right)\)	\(e\left(\frac{187}{602}\right)\)	\(e\left(\frac{1088}{1505}\right)\)	\(e\left(\frac{289}{430}\right)\)	\(e\left(\frac{131}{430}\right)\)	\(e\left(\frac{127}{1505}\right)\)	\(e\left(\frac{187}{301}\right)\)	\(e\left(\frac{2409}{3010}\right)\)	\(e\left(\frac{101}{3010}\right)\)	\(e\left(\frac{1289}{1505}\right)\)
\(\chi_{379045}(4984,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1327}{1505}\right)\)	\(e\left(\frac{221}{602}\right)\)	\(e\left(\frac{1149}{1505}\right)\)	\(e\left(\frac{107}{430}\right)\)	\(e\left(\frac{233}{430}\right)\)	\(e\left(\frac{971}{1505}\right)\)	\(e\left(\frac{221}{301}\right)\)	\(e\left(\frac{2847}{3010}\right)\)	\(e\left(\frac{393}{3010}\right)\)	\(e\left(\frac{292}{1505}\right)\)
\(\chi_{379045}(5334,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{429}{1505}\right)\)	\(e\left(\frac{345}{602}\right)\)	\(e\left(\frac{858}{1505}\right)\)	\(e\left(\frac{369}{430}\right)\)	\(e\left(\frac{261}{430}\right)\)	\(e\left(\frac{1287}{1505}\right)\)	\(e\left(\frac{44}{301}\right)\)	\(e\left(\frac{1399}{3010}\right)\)	\(e\left(\frac{431}{3010}\right)\)	\(e\left(\frac{1224}{1505}\right)\)
\(\chi_{379045}(6009,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{682}{1505}\right)\)	\(e\left(\frac{479}{602}\right)\)	\(e\left(\frac{1364}{1505}\right)\)	\(e\left(\frac{107}{430}\right)\)	\(e\left(\frac{233}{430}\right)\)	\(e\left(\frac{541}{1505}\right)\)	\(e\left(\frac{178}{301}\right)\)	\(e\left(\frac{2417}{3010}\right)\)	\(e\left(\frac{2113}{3010}\right)\)	\(e\left(\frac{1367}{1505}\right)\)
\(\chi_{379045}(6214,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1027}{1505}\right)\)	\(e\left(\frac{5}{602}\right)\)	\(e\left(\frac{549}{1505}\right)\)	\(e\left(\frac{297}{430}\right)\)	\(e\left(\frac{273}{430}\right)\)	\(e\left(\frac{71}{1505}\right)\)	\(e\left(\frac{5}{301}\right)\)	\(e\left(\frac{2437}{3010}\right)\)	\(e\left(\frac{1123}{3010}\right)\)	\(e\left(\frac{57}{1505}\right)\)
\(\chi_{379045}(6544,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{48}{1505}\right)\)	\(e\left(\frac{167}{602}\right)\)	\(e\left(\frac{96}{1505}\right)\)	\(e\left(\frac{133}{430}\right)\)	\(e\left(\frac{157}{430}\right)\)	\(e\left(\frac{144}{1505}\right)\)	\(e\left(\frac{167}{301}\right)\)	\(e\left(\frac{2293}{3010}\right)\)	\(e\left(\frac{1027}{3010}\right)\)	\(e\left(\frac{158}{1505}\right)\)
\(\chi_{379045}(6624,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1227}{1505}\right)\)	\(e\left(\frac{149}{602}\right)\)	\(e\left(\frac{949}{1505}\right)\)	\(e\left(\frac{27}{430}\right)\)	\(e\left(\frac{103}{430}\right)\)	\(e\left(\frac{671}{1505}\right)\)	\(e\left(\frac{149}{301}\right)\)	\(e\left(\frac{1707}{3010}\right)\)	\(e\left(\frac{2643}{3010}\right)\)	\(e\left(\frac{1217}{1505}\right)\)
\(\chi_{379045}(6919,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1481}{1505}\right)\)	\(e\left(\frac{67}{602}\right)\)	\(e\left(\frac{1457}{1505}\right)\)	\(e\left(\frac{41}{430}\right)\)	\(e\left(\frac{29}{430}\right)\)	\(e\left(\frac{1433}{1505}\right)\)	\(e\left(\frac{67}{301}\right)\)	\(e\left(\frac{1111}{3010}\right)\)	\(e\left(\frac{239}{3010}\right)\)	\(e\left(\frac{1426}{1505}\right)\)
\(\chi_{379045}(6974,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1469}{1505}\right)\)	\(e\left(\frac{251}{602}\right)\)	\(e\left(\frac{1433}{1505}\right)\)	\(e\left(\frac{169}{430}\right)\)	\(e\left(\frac{151}{430}\right)\)	\(e\left(\frac{1397}{1505}\right)\)	\(e\left(\frac{251}{301}\right)\)	\(e\left(\frac{2419}{3010}\right)\)	\(e\left(\frac{1111}{3010}\right)\)	\(e\left(\frac{634}{1505}\right)\)
\(\chi_{379045}(7944,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{136}{1505}\right)\)	\(e\left(\frac{423}{602}\right)\)	\(e\left(\frac{272}{1505}\right)\)	\(e\left(\frac{341}{430}\right)\)	\(e\left(\frac{409}{430}\right)\)	\(e\left(\frac{408}{1505}\right)\)	\(e\left(\frac{122}{301}\right)\)	\(e\left(\frac{1731}{3010}\right)\)	\(e\left(\frac{2659}{3010}\right)\)	\(e\left(\frac{1451}{1505}\right)\)
\(\chi_{379045}(8149,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{96}{1505}\right)\)	\(e\left(\frac{33}{602}\right)\)	\(e\left(\frac{192}{1505}\right)\)	\(e\left(\frac{51}{430}\right)\)	\(e\left(\frac{99}{430}\right)\)	\(e\left(\frac{288}{1505}\right)\)	\(e\left(\frac{33}{301}\right)\)	\(e\left(\frac{71}{3010}\right)\)	\(e\left(\frac{549}{3010}\right)\)	\(e\left(\frac{316}{1505}\right)\)
\(\chi_{379045}(8264,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1217}{1505}\right)\)	\(e\left(\frac{503}{602}\right)\)	\(e\left(\frac{929}{1505}\right)\)	\(e\left(\frac{277}{430}\right)\)	\(e\left(\frac{133}{430}\right)\)	\(e\left(\frac{641}{1505}\right)\)	\(e\left(\frac{202}{301}\right)\)	\(e\left(\frac{2797}{3010}\right)\)	\(e\left(\frac{1363}{3010}\right)\)	\(e\left(\frac{557}{1505}\right)\)
\(\chi_{379045}(8559,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{16}{1505}\right)\)	\(e\left(\frac{457}{602}\right)\)	\(e\left(\frac{32}{1505}\right)\)	\(e\left(\frac{331}{430}\right)\)	\(e\left(\frac{339}{430}\right)\)	\(e\left(\frac{48}{1505}\right)\)	\(e\left(\frac{156}{301}\right)\)	\(e\left(\frac{2771}{3010}\right)\)	\(e\left(\frac{2349}{3010}\right)\)	\(e\left(\frac{1056}{1505}\right)\)
\(\chi_{379045}(8799,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1303}{1505}\right)\)	\(e\left(\frac{589}{602}\right)\)	\(e\left(\frac{1101}{1505}\right)\)	\(e\left(\frac{363}{430}\right)\)	\(e\left(\frac{47}{430}\right)\)	\(e\left(\frac{899}{1505}\right)\)	\(e\left(\frac{288}{301}\right)\)	\(e\left(\frac{2453}{3010}\right)\)	\(e\left(\frac{2137}{3010}\right)\)	\(e\left(\frac{213}{1505}\right)\)
\(\chi_{379045}(9229,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1044}{1505}\right)\)	\(e\left(\frac{547}{602}\right)\)	\(e\left(\frac{583}{1505}\right)\)	\(e\left(\frac{259}{430}\right)\)	\(e\left(\frac{351}{430}\right)\)	\(e\left(\frac{122}{1505}\right)\)	\(e\left(\frac{246}{301}\right)\)	\(e\left(\frac{2089}{3010}\right)\)	\(e\left(\frac{891}{3010}\right)\)	\(e\left(\frac{1179}{1505}\right)\)
\(\chi_{379045}(10199,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1441}{1505}\right)\)	\(e\left(\frac{279}{602}\right)\)	\(e\left(\frac{1377}{1505}\right)\)	\(e\left(\frac{181}{430}\right)\)	\(e\left(\frac{149}{430}\right)\)	\(e\left(\frac{1313}{1505}\right)\)	\(e\left(\frac{279}{301}\right)\)	\(e\left(\frac{2461}{3010}\right)\)	\(e\left(\frac{1139}{3010}\right)\)	\(e\left(\frac{291}{1505}\right)\)
\(\chi_{379045}(10519,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{267}{1505}\right)\)	\(e\left(\frac{421}{602}\right)\)	\(e\left(\frac{534}{1505}\right)\)	\(e\left(\frac{377}{430}\right)\)	\(e\left(\frac{403}{430}\right)\)	\(e\left(\frac{801}{1505}\right)\)	\(e\left(\frac{120}{301}\right)\)	\(e\left(\frac{997}{3010}\right)\)	\(e\left(\frac{163}{3010}\right)\)	\(e\left(\frac{1067}{1505}\right)\)
\(\chi_{379045}(12079,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{788}{1505}\right)\)	\(e\left(\frac{459}{602}\right)\)	\(e\left(\frac{71}{1505}\right)\)	\(e\left(\frac{123}{430}\right)\)	\(e\left(\frac{87}{430}\right)\)	\(e\left(\frac{859}{1505}\right)\)	\(e\left(\frac{158}{301}\right)\)	\(e\left(\frac{2903}{3010}\right)\)	\(e\left(\frac{2437}{3010}\right)\)	\(e\left(\frac{838}{1505}\right)\)
\(\chi_{379045}(12454,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{456}{1505}\right)\)	\(e\left(\frac{533}{602}\right)\)	\(e\left(\frac{912}{1505}\right)\)	\(e\left(\frac{81}{430}\right)\)	\(e\left(\frac{309}{430}\right)\)	\(e\left(\frac{1368}{1505}\right)\)	\(e\left(\frac{232}{301}\right)\)	\(e\left(\frac{2971}{3010}\right)\)	\(e\left(\frac{1479}{3010}\right)\)	\(e\left(\frac{1501}{1505}\right)\)
\(\chi_{379045}(12509,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{354}{1505}\right)\)	\(e\left(\frac{291}{602}\right)\)	\(e\left(\frac{708}{1505}\right)\)	\(e\left(\frac{309}{430}\right)\)	\(e\left(\frac{271}{430}\right)\)	\(e\left(\frac{1062}{1505}\right)\)	\(e\left(\frac{291}{301}\right)\)	\(e\left(\frac{2049}{3010}\right)\)	\(e\left(\frac{2871}{3010}\right)\)	\(e\left(\frac{789}{1505}\right)\)
\(\chi_{379045}(13104,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1088}{1505}\right)\)	\(e\left(\frac{73}{602}\right)\)	\(e\left(\frac{671}{1505}\right)\)	\(e\left(\frac{363}{430}\right)\)	\(e\left(\frac{47}{430}\right)\)	\(e\left(\frac{254}{1505}\right)\)	\(e\left(\frac{73}{301}\right)\)	\(e\left(\frac{303}{3010}\right)\)	\(e\left(\frac{1707}{3010}\right)\)	\(e\left(\frac{1073}{1505}\right)\)

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Basic properties

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First 31 of 1008 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	379045.ob
Modulus	$379045$
Conductor	$379045$
Order	$3010$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(379045\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(379045\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(3010\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);