LMFDB - Dirichlet character orbit 416000.brd

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416000, base_ring=CyclotomicField(1600)) M = H._module chi = DirichletCharacter(H, M([800,975,688,1200])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(83, 416000)) 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("416000.83"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$416000$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$416000$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$1600$	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:	$\Q(\zeta_{1600})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 1600 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 640 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{416000}(83,\cdot)$	$-1$	$1$	$e\left(\frac{1341}{1600}\right)$	$e\left(\frac{63}{160}\right)$	$e\left(\frac{541}{800}\right)$	$e\left(\frac{363}{1600}\right)$	$e\left(\frac{381}{400}\right)$	$e\left(\frac{9}{1600}\right)$	$e\left(\frac{371}{1600}\right)$	$e\left(\frac{689}{800}\right)$	$e\left(\frac{823}{1600}\right)$	$e\left(\frac{981}{1600}\right)$
$\chi_{416000}(827,\cdot)$	$-1$	$1$	$e\left(\frac{107}{1600}\right)$	$e\left(\frac{121}{160}\right)$	$e\left(\frac{107}{800}\right)$	$e\left(\frac{301}{1600}\right)$	$e\left(\frac{187}{400}\right)$	$e\left(\frac{1343}{1600}\right)$	$e\left(\frac{1317}{1600}\right)$	$e\left(\frac{503}{800}\right)$	$e\left(\frac{321}{1600}\right)$	$e\left(\frac{787}{1600}\right)$
$\chi_{416000}(1123,\cdot)$	$-1$	$1$	$e\left(\frac{1337}{1600}\right)$	$e\left(\frac{51}{160}\right)$	$e\left(\frac{537}{800}\right)$	$e\left(\frac{591}{1600}\right)$	$e\left(\frac{217}{400}\right)$	$e\left(\frac{213}{1600}\right)$	$e\left(\frac{247}{1600}\right)$	$e\left(\frac{573}{800}\right)$	$e\left(\frac{811}{1600}\right)$	$e\left(\frac{817}{1600}\right)$
$\chi_{416000}(1867,\cdot)$	$-1$	$1$	$e\left(\frac{711}{1600}\right)$	$e\left(\frac{13}{160}\right)$	$e\left(\frac{711}{800}\right)$	$e\left(\frac{1073}{1600}\right)$	$e\left(\frac{151}{400}\right)$	$e\left(\frac{939}{1600}\right)$	$e\left(\frac{841}{1600}\right)$	$e\left(\frac{419}{800}\right)$	$e\left(\frac{533}{1600}\right)$	$e\left(\frac{1551}{1600}\right)$
$\chi_{416000}(2163,\cdot)$	$-1$	$1$	$e\left(\frac{53}{1600}\right)$	$e\left(\frac{39}{160}\right)$	$e\left(\frac{53}{800}\right)$	$e\left(\frac{179}{1600}\right)$	$e\left(\frac{373}{400}\right)$	$e\left(\frac{97}{1600}\right)$	$e\left(\frac{443}{1600}\right)$	$e\left(\frac{137}{800}\right)$	$e\left(\frac{159}{1600}\right)$	$e\left(\frac{973}{1600}\right)$
$\chi_{416000}(3203,\cdot)$	$-1$	$1$	$e\left(\frac{689}{1600}\right)$	$e\left(\frac{27}{160}\right)$	$e\left(\frac{689}{800}\right)$	$e\left(\frac{727}{1600}\right)$	$e\left(\frac{49}{400}\right)$	$e\left(\frac{1261}{1600}\right)$	$e\left(\frac{959}{1600}\right)$	$e\left(\frac{181}{800}\right)$	$e\left(\frac{467}{1600}\right)$	$e\left(\frac{1449}{1600}\right)$
$\chi_{416000}(3947,\cdot)$	$-1$	$1$	$e\left(\frac{1279}{1600}\right)$	$e\left(\frac{117}{160}\right)$	$e\left(\frac{479}{800}\right)$	$e\left(\frac{697}{1600}\right)$	$e\left(\frac{239}{400}\right)$	$e\left(\frac{771}{1600}\right)$	$e\left(\frac{849}{1600}\right)$	$e\left(\frac{91}{800}\right)$	$e\left(\frac{637}{1600}\right)$	$e\left(\frac{839}{1600}\right)$
$\chi_{416000}(4987,\cdot)$	$-1$	$1$	$e\left(\frac{1243}{1600}\right)$	$e\left(\frac{9}{160}\right)$	$e\left(\frac{443}{800}\right)$	$e\left(\frac{1149}{1600}\right)$	$e\left(\frac{363}{400}\right)$	$e\left(\frac{1007}{1600}\right)$	$e\left(\frac{1333}{1600}\right)$	$e\left(\frac{647}{800}\right)$	$e\left(\frac{529}{1600}\right)$	$e\left(\frac{963}{1600}\right)$
$\chi_{416000}(5283,\cdot)$	$-1$	$1$	$e\left(\frac{1321}{1600}\right)$	$e\left(\frac{3}{160}\right)$	$e\left(\frac{521}{800}\right)$	$e\left(\frac{1503}{1600}\right)$	$e\left(\frac{361}{400}\right)$	$e\left(\frac{1029}{1600}\right)$	$e\left(\frac{1351}{1600}\right)$	$e\left(\frac{109}{800}\right)$	$e\left(\frac{763}{1600}\right)$	$e\left(\frac{161}{1600}\right)$
$\chi_{416000}(6027,\cdot)$	$-1$	$1$	$e\left(\frac{1527}{1600}\right)$	$e\left(\frac{61}{160}\right)$	$e\left(\frac{727}{800}\right)$	$e\left(\frac{961}{1600}\right)$	$e\left(\frac{7}{400}\right)$	$e\left(\frac{923}{1600}\right)$	$e\left(\frac{537}{1600}\right)$	$e\left(\frac{83}{800}\right)$	$e\left(\frac{1381}{1600}\right)$	$e\left(\frac{1407}{1600}\right)$
$\chi_{416000}(6323,\cdot)$	$-1$	$1$	$e\left(\frac{1317}{1600}\right)$	$e\left(\frac{151}{160}\right)$	$e\left(\frac{517}{800}\right)$	$e\left(\frac{131}{1600}\right)$	$e\left(\frac{197}{400}\right)$	$e\left(\frac{1233}{1600}\right)$	$e\left(\frac{1227}{1600}\right)$	$e\left(\frac{793}{800}\right)$	$e\left(\frac{751}{1600}\right)$	$e\left(\frac{1597}{1600}\right)$
$\chi_{416000}(7067,\cdot)$	$-1$	$1$	$e\left(\frac{531}{1600}\right)$	$e\left(\frac{113}{160}\right)$	$e\left(\frac{531}{800}\right)$	$e\left(\frac{133}{1600}\right)$	$e\left(\frac{371}{400}\right)$	$e\left(\frac{519}{1600}\right)$	$e\left(\frac{61}{1600}\right)$	$e\left(\frac{799}{800}\right)$	$e\left(\frac{1593}{1600}\right)$	$e\left(\frac{571}{1600}\right)$
$\chi_{416000}(7363,\cdot)$	$-1$	$1$	$e\left(\frac{33}{1600}\right)$	$e\left(\frac{139}{160}\right)$	$e\left(\frac{33}{800}\right)$	$e\left(\frac{1319}{1600}\right)$	$e\left(\frac{353}{400}\right)$	$e\left(\frac{1117}{1600}\right)$	$e\left(\frac{1423}{1600}\right)$	$e\left(\frac{357}{800}\right)$	$e\left(\frac{99}{1600}\right)$	$e\left(\frac{153}{1600}\right)$
$\chi_{416000}(8403,\cdot)$	$-1$	$1$	$e\left(\frac{669}{1600}\right)$	$e\left(\frac{127}{160}\right)$	$e\left(\frac{669}{800}\right)$	$e\left(\frac{267}{1600}\right)$	$e\left(\frac{29}{400}\right)$	$e\left(\frac{681}{1600}\right)$	$e\left(\frac{339}{1600}\right)$	$e\left(\frac{401}{800}\right)$	$e\left(\frac{407}{1600}\right)$	$e\left(\frac{629}{1600}\right)$
$\chi_{416000}(9147,\cdot)$	$-1$	$1$	$e\left(\frac{1099}{1600}\right)$	$e\left(\frac{57}{160}\right)$	$e\left(\frac{299}{800}\right)$	$e\left(\frac{1357}{1600}\right)$	$e\left(\frac{59}{400}\right)$	$e\left(\frac{351}{1600}\right)$	$e\left(\frac{69}{1600}\right)$	$e\left(\frac{471}{800}\right)$	$e\left(\frac{97}{1600}\right)$	$e\left(\frac{1459}{1600}\right)$
$\chi_{416000}(10187,\cdot)$	$-1$	$1$	$e\left(\frac{1063}{1600}\right)$	$e\left(\frac{109}{160}\right)$	$e\left(\frac{263}{800}\right)$	$e\left(\frac{209}{1600}\right)$	$e\left(\frac{183}{400}\right)$	$e\left(\frac{587}{1600}\right)$	$e\left(\frac{553}{1600}\right)$	$e\left(\frac{227}{800}\right)$	$e\left(\frac{1589}{1600}\right)$	$e\left(\frac{1583}{1600}\right)$
$\chi_{416000}(10483,\cdot)$	$-1$	$1$	$e\left(\frac{1301}{1600}\right)$	$e\left(\frac{103}{160}\right)$	$e\left(\frac{501}{800}\right)$	$e\left(\frac{1043}{1600}\right)$	$e\left(\frac{341}{400}\right)$	$e\left(\frac{449}{1600}\right)$	$e\left(\frac{731}{1600}\right)$	$e\left(\frac{329}{800}\right)$	$e\left(\frac{703}{1600}\right)$	$e\left(\frac{941}{1600}\right)$
$\chi_{416000}(11227,\cdot)$	$-1$	$1$	$e\left(\frac{1347}{1600}\right)$	$e\left(\frac{1}{160}\right)$	$e\left(\frac{547}{800}\right)$	$e\left(\frac{21}{1600}\right)$	$e\left(\frac{227}{400}\right)$	$e\left(\frac{503}{1600}\right)$	$e\left(\frac{1357}{1600}\right)$	$e\left(\frac{463}{800}\right)$	$e\left(\frac{841}{1600}\right)$	$e\left(\frac{427}{1600}\right)$
$\chi_{416000}(11523,\cdot)$	$-1$	$1$	$e\left(\frac{1297}{1600}\right)$	$e\left(\frac{91}{160}\right)$	$e\left(\frac{497}{800}\right)$	$e\left(\frac{1271}{1600}\right)$	$e\left(\frac{177}{400}\right)$	$e\left(\frac{653}{1600}\right)$	$e\left(\frac{607}{1600}\right)$	$e\left(\frac{213}{800}\right)$	$e\left(\frac{691}{1600}\right)$	$e\left(\frac{777}{1600}\right)$
$\chi_{416000}(12267,\cdot)$	$-1$	$1$	$e\left(\frac{351}{1600}\right)$	$e\left(\frac{53}{160}\right)$	$e\left(\frac{351}{800}\right)$	$e\left(\frac{793}{1600}\right)$	$e\left(\frac{191}{400}\right)$	$e\left(\frac{99}{1600}\right)$	$e\left(\frac{881}{1600}\right)$	$e\left(\frac{379}{800}\right)$	$e\left(\frac{1053}{1600}\right)$	$e\left(\frac{1191}{1600}\right)$
$\chi_{416000}(12563,\cdot)$	$-1$	$1$	$e\left(\frac{13}{1600}\right)$	$e\left(\frac{79}{160}\right)$	$e\left(\frac{13}{800}\right)$	$e\left(\frac{859}{1600}\right)$	$e\left(\frac{333}{400}\right)$	$e\left(\frac{537}{1600}\right)$	$e\left(\frac{803}{1600}\right)$	$e\left(\frac{577}{800}\right)$	$e\left(\frac{39}{1600}\right)$	$e\left(\frac{933}{1600}\right)$
$\chi_{416000}(13603,\cdot)$	$-1$	$1$	$e\left(\frac{649}{1600}\right)$	$e\left(\frac{67}{160}\right)$	$e\left(\frac{649}{800}\right)$	$e\left(\frac{1407}{1600}\right)$	$e\left(\frac{9}{400}\right)$	$e\left(\frac{101}{1600}\right)$	$e\left(\frac{1319}{1600}\right)$	$e\left(\frac{621}{800}\right)$	$e\left(\frac{347}{1600}\right)$	$e\left(\frac{1409}{1600}\right)$
$\chi_{416000}(14347,\cdot)$	$-1$	$1$	$e\left(\frac{919}{1600}\right)$	$e\left(\frac{157}{160}\right)$	$e\left(\frac{119}{800}\right)$	$e\left(\frac{417}{1600}\right)$	$e\left(\frac{279}{400}\right)$	$e\left(\frac{1531}{1600}\right)$	$e\left(\frac{889}{1600}\right)$	$e\left(\frac{51}{800}\right)$	$e\left(\frac{1157}{1600}\right)$	$e\left(\frac{479}{1600}\right)$
$\chi_{416000}(15387,\cdot)$	$-1$	$1$	$e\left(\frac{883}{1600}\right)$	$e\left(\frac{49}{160}\right)$	$e\left(\frac{83}{800}\right)$	$e\left(\frac{869}{1600}\right)$	$e\left(\frac{3}{400}\right)$	$e\left(\frac{167}{1600}\right)$	$e\left(\frac{1373}{1600}\right)$	$e\left(\frac{607}{800}\right)$	$e\left(\frac{1049}{1600}\right)$	$e\left(\frac{603}{1600}\right)$
$\chi_{416000}(15683,\cdot)$	$-1$	$1$	$e\left(\frac{1281}{1600}\right)$	$e\left(\frac{43}{160}\right)$	$e\left(\frac{481}{800}\right)$	$e\left(\frac{583}{1600}\right)$	$e\left(\frac{321}{400}\right)$	$e\left(\frac{1469}{1600}\right)$	$e\left(\frac{111}{1600}\right)$	$e\left(\frac{549}{800}\right)$	$e\left(\frac{643}{1600}\right)$	$e\left(\frac{121}{1600}\right)$
$\chi_{416000}(16427,\cdot)$	$-1$	$1$	$e\left(\frac{1167}{1600}\right)$	$e\left(\frac{101}{160}\right)$	$e\left(\frac{367}{800}\right)$	$e\left(\frac{681}{1600}\right)$	$e\left(\frac{47}{400}\right)$	$e\left(\frac{83}{1600}\right)$	$e\left(\frac{577}{1600}\right)$	$e\left(\frac{43}{800}\right)$	$e\left(\frac{301}{1600}\right)$	$e\left(\frac{1047}{1600}\right)$
$\chi_{416000}(16723,\cdot)$	$-1$	$1$	$e\left(\frac{1277}{1600}\right)$	$e\left(\frac{31}{160}\right)$	$e\left(\frac{477}{800}\right)$	$e\left(\frac{811}{1600}\right)$	$e\left(\frac{157}{400}\right)$	$e\left(\frac{73}{1600}\right)$	$e\left(\frac{1587}{1600}\right)$	$e\left(\frac{433}{800}\right)$	$e\left(\frac{631}{1600}\right)$	$e\left(\frac{1557}{1600}\right)$
$\chi_{416000}(17467,\cdot)$	$-1$	$1$	$e\left(\frac{171}{1600}\right)$	$e\left(\frac{153}{160}\right)$	$e\left(\frac{171}{800}\right)$	$e\left(\frac{1453}{1600}\right)$	$e\left(\frac{11}{400}\right)$	$e\left(\frac{1279}{1600}\right)$	$e\left(\frac{101}{1600}\right)$	$e\left(\frac{759}{800}\right)$	$e\left(\frac{513}{1600}\right)$	$e\left(\frac{211}{1600}\right)$
$\chi_{416000}(17763,\cdot)$	$-1$	$1$	$e\left(\frac{1593}{1600}\right)$	$e\left(\frac{19}{160}\right)$	$e\left(\frac{793}{800}\right)$	$e\left(\frac{399}{1600}\right)$	$e\left(\frac{313}{400}\right)$	$e\left(\frac{1557}{1600}\right)$	$e\left(\frac{183}{1600}\right)$	$e\left(\frac{797}{800}\right)$	$e\left(\frac{1579}{1600}\right)$	$e\left(\frac{113}{1600}\right)$
$\chi_{416000}(18803,\cdot)$	$-1$	$1$	$e\left(\frac{629}{1600}\right)$	$e\left(\frac{7}{160}\right)$	$e\left(\frac{629}{800}\right)$	$e\left(\frac{947}{1600}\right)$	$e\left(\frac{389}{400}\right)$	$e\left(\frac{1121}{1600}\right)$	$e\left(\frac{699}{1600}\right)$	$e\left(\frac{41}{800}\right)$	$e\left(\frac{287}{1600}\right)$	$e\left(\frac{589}{1600}\right)$
$\chi_{416000}(19547,\cdot)$	$-1$	$1$	$e\left(\frac{739}{1600}\right)$	$e\left(\frac{97}{160}\right)$	$e\left(\frac{739}{800}\right)$	$e\left(\frac{1077}{1600}\right)$	$e\left(\frac{99}{400}\right)$	$e\left(\frac{1111}{1600}\right)$	$e\left(\frac{109}{1600}\right)$	$e\left(\frac{431}{800}\right)$	$e\left(\frac{617}{1600}\right)$	$e\left(\frac{1099}{1600}\right)$

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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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{416000}(83,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1341}{1600}\right)\)	\(e\left(\frac{63}{160}\right)\)	\(e\left(\frac{541}{800}\right)\)	\(e\left(\frac{363}{1600}\right)\)	\(e\left(\frac{381}{400}\right)\)	\(e\left(\frac{9}{1600}\right)\)	\(e\left(\frac{371}{1600}\right)\)	\(e\left(\frac{689}{800}\right)\)	\(e\left(\frac{823}{1600}\right)\)	\(e\left(\frac{981}{1600}\right)\)
\(\chi_{416000}(827,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{107}{1600}\right)\)	\(e\left(\frac{121}{160}\right)\)	\(e\left(\frac{107}{800}\right)\)	\(e\left(\frac{301}{1600}\right)\)	\(e\left(\frac{187}{400}\right)\)	\(e\left(\frac{1343}{1600}\right)\)	\(e\left(\frac{1317}{1600}\right)\)	\(e\left(\frac{503}{800}\right)\)	\(e\left(\frac{321}{1600}\right)\)	\(e\left(\frac{787}{1600}\right)\)
\(\chi_{416000}(1123,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1337}{1600}\right)\)	\(e\left(\frac{51}{160}\right)\)	\(e\left(\frac{537}{800}\right)\)	\(e\left(\frac{591}{1600}\right)\)	\(e\left(\frac{217}{400}\right)\)	\(e\left(\frac{213}{1600}\right)\)	\(e\left(\frac{247}{1600}\right)\)	\(e\left(\frac{573}{800}\right)\)	\(e\left(\frac{811}{1600}\right)\)	\(e\left(\frac{817}{1600}\right)\)
\(\chi_{416000}(1867,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{711}{1600}\right)\)	\(e\left(\frac{13}{160}\right)\)	\(e\left(\frac{711}{800}\right)\)	\(e\left(\frac{1073}{1600}\right)\)	\(e\left(\frac{151}{400}\right)\)	\(e\left(\frac{939}{1600}\right)\)	\(e\left(\frac{841}{1600}\right)\)	\(e\left(\frac{419}{800}\right)\)	\(e\left(\frac{533}{1600}\right)\)	\(e\left(\frac{1551}{1600}\right)\)
\(\chi_{416000}(2163,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{1600}\right)\)	\(e\left(\frac{39}{160}\right)\)	\(e\left(\frac{53}{800}\right)\)	\(e\left(\frac{179}{1600}\right)\)	\(e\left(\frac{373}{400}\right)\)	\(e\left(\frac{97}{1600}\right)\)	\(e\left(\frac{443}{1600}\right)\)	\(e\left(\frac{137}{800}\right)\)	\(e\left(\frac{159}{1600}\right)\)	\(e\left(\frac{973}{1600}\right)\)
\(\chi_{416000}(3203,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{689}{1600}\right)\)	\(e\left(\frac{27}{160}\right)\)	\(e\left(\frac{689}{800}\right)\)	\(e\left(\frac{727}{1600}\right)\)	\(e\left(\frac{49}{400}\right)\)	\(e\left(\frac{1261}{1600}\right)\)	\(e\left(\frac{959}{1600}\right)\)	\(e\left(\frac{181}{800}\right)\)	\(e\left(\frac{467}{1600}\right)\)	\(e\left(\frac{1449}{1600}\right)\)
\(\chi_{416000}(3947,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1279}{1600}\right)\)	\(e\left(\frac{117}{160}\right)\)	\(e\left(\frac{479}{800}\right)\)	\(e\left(\frac{697}{1600}\right)\)	\(e\left(\frac{239}{400}\right)\)	\(e\left(\frac{771}{1600}\right)\)	\(e\left(\frac{849}{1600}\right)\)	\(e\left(\frac{91}{800}\right)\)	\(e\left(\frac{637}{1600}\right)\)	\(e\left(\frac{839}{1600}\right)\)
\(\chi_{416000}(4987,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1243}{1600}\right)\)	\(e\left(\frac{9}{160}\right)\)	\(e\left(\frac{443}{800}\right)\)	\(e\left(\frac{1149}{1600}\right)\)	\(e\left(\frac{363}{400}\right)\)	\(e\left(\frac{1007}{1600}\right)\)	\(e\left(\frac{1333}{1600}\right)\)	\(e\left(\frac{647}{800}\right)\)	\(e\left(\frac{529}{1600}\right)\)	\(e\left(\frac{963}{1600}\right)\)
\(\chi_{416000}(5283,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1321}{1600}\right)\)	\(e\left(\frac{3}{160}\right)\)	\(e\left(\frac{521}{800}\right)\)	\(e\left(\frac{1503}{1600}\right)\)	\(e\left(\frac{361}{400}\right)\)	\(e\left(\frac{1029}{1600}\right)\)	\(e\left(\frac{1351}{1600}\right)\)	\(e\left(\frac{109}{800}\right)\)	\(e\left(\frac{763}{1600}\right)\)	\(e\left(\frac{161}{1600}\right)\)
\(\chi_{416000}(6027,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1527}{1600}\right)\)	\(e\left(\frac{61}{160}\right)\)	\(e\left(\frac{727}{800}\right)\)	\(e\left(\frac{961}{1600}\right)\)	\(e\left(\frac{7}{400}\right)\)	\(e\left(\frac{923}{1600}\right)\)	\(e\left(\frac{537}{1600}\right)\)	\(e\left(\frac{83}{800}\right)\)	\(e\left(\frac{1381}{1600}\right)\)	\(e\left(\frac{1407}{1600}\right)\)
\(\chi_{416000}(6323,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1317}{1600}\right)\)	\(e\left(\frac{151}{160}\right)\)	\(e\left(\frac{517}{800}\right)\)	\(e\left(\frac{131}{1600}\right)\)	\(e\left(\frac{197}{400}\right)\)	\(e\left(\frac{1233}{1600}\right)\)	\(e\left(\frac{1227}{1600}\right)\)	\(e\left(\frac{793}{800}\right)\)	\(e\left(\frac{751}{1600}\right)\)	\(e\left(\frac{1597}{1600}\right)\)
\(\chi_{416000}(7067,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{531}{1600}\right)\)	\(e\left(\frac{113}{160}\right)\)	\(e\left(\frac{531}{800}\right)\)	\(e\left(\frac{133}{1600}\right)\)	\(e\left(\frac{371}{400}\right)\)	\(e\left(\frac{519}{1600}\right)\)	\(e\left(\frac{61}{1600}\right)\)	\(e\left(\frac{799}{800}\right)\)	\(e\left(\frac{1593}{1600}\right)\)	\(e\left(\frac{571}{1600}\right)\)
\(\chi_{416000}(7363,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{1600}\right)\)	\(e\left(\frac{139}{160}\right)\)	\(e\left(\frac{33}{800}\right)\)	\(e\left(\frac{1319}{1600}\right)\)	\(e\left(\frac{353}{400}\right)\)	\(e\left(\frac{1117}{1600}\right)\)	\(e\left(\frac{1423}{1600}\right)\)	\(e\left(\frac{357}{800}\right)\)	\(e\left(\frac{99}{1600}\right)\)	\(e\left(\frac{153}{1600}\right)\)
\(\chi_{416000}(8403,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{669}{1600}\right)\)	\(e\left(\frac{127}{160}\right)\)	\(e\left(\frac{669}{800}\right)\)	\(e\left(\frac{267}{1600}\right)\)	\(e\left(\frac{29}{400}\right)\)	\(e\left(\frac{681}{1600}\right)\)	\(e\left(\frac{339}{1600}\right)\)	\(e\left(\frac{401}{800}\right)\)	\(e\left(\frac{407}{1600}\right)\)	\(e\left(\frac{629}{1600}\right)\)
\(\chi_{416000}(9147,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1099}{1600}\right)\)	\(e\left(\frac{57}{160}\right)\)	\(e\left(\frac{299}{800}\right)\)	\(e\left(\frac{1357}{1600}\right)\)	\(e\left(\frac{59}{400}\right)\)	\(e\left(\frac{351}{1600}\right)\)	\(e\left(\frac{69}{1600}\right)\)	\(e\left(\frac{471}{800}\right)\)	\(e\left(\frac{97}{1600}\right)\)	\(e\left(\frac{1459}{1600}\right)\)
\(\chi_{416000}(10187,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1063}{1600}\right)\)	\(e\left(\frac{109}{160}\right)\)	\(e\left(\frac{263}{800}\right)\)	\(e\left(\frac{209}{1600}\right)\)	\(e\left(\frac{183}{400}\right)\)	\(e\left(\frac{587}{1600}\right)\)	\(e\left(\frac{553}{1600}\right)\)	\(e\left(\frac{227}{800}\right)\)	\(e\left(\frac{1589}{1600}\right)\)	\(e\left(\frac{1583}{1600}\right)\)
\(\chi_{416000}(10483,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1301}{1600}\right)\)	\(e\left(\frac{103}{160}\right)\)	\(e\left(\frac{501}{800}\right)\)	\(e\left(\frac{1043}{1600}\right)\)	\(e\left(\frac{341}{400}\right)\)	\(e\left(\frac{449}{1600}\right)\)	\(e\left(\frac{731}{1600}\right)\)	\(e\left(\frac{329}{800}\right)\)	\(e\left(\frac{703}{1600}\right)\)	\(e\left(\frac{941}{1600}\right)\)
\(\chi_{416000}(11227,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1347}{1600}\right)\)	\(e\left(\frac{1}{160}\right)\)	\(e\left(\frac{547}{800}\right)\)	\(e\left(\frac{21}{1600}\right)\)	\(e\left(\frac{227}{400}\right)\)	\(e\left(\frac{503}{1600}\right)\)	\(e\left(\frac{1357}{1600}\right)\)	\(e\left(\frac{463}{800}\right)\)	\(e\left(\frac{841}{1600}\right)\)	\(e\left(\frac{427}{1600}\right)\)
\(\chi_{416000}(11523,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1297}{1600}\right)\)	\(e\left(\frac{91}{160}\right)\)	\(e\left(\frac{497}{800}\right)\)	\(e\left(\frac{1271}{1600}\right)\)	\(e\left(\frac{177}{400}\right)\)	\(e\left(\frac{653}{1600}\right)\)	\(e\left(\frac{607}{1600}\right)\)	\(e\left(\frac{213}{800}\right)\)	\(e\left(\frac{691}{1600}\right)\)	\(e\left(\frac{777}{1600}\right)\)
\(\chi_{416000}(12267,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{351}{1600}\right)\)	\(e\left(\frac{53}{160}\right)\)	\(e\left(\frac{351}{800}\right)\)	\(e\left(\frac{793}{1600}\right)\)	\(e\left(\frac{191}{400}\right)\)	\(e\left(\frac{99}{1600}\right)\)	\(e\left(\frac{881}{1600}\right)\)	\(e\left(\frac{379}{800}\right)\)	\(e\left(\frac{1053}{1600}\right)\)	\(e\left(\frac{1191}{1600}\right)\)
\(\chi_{416000}(12563,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{1600}\right)\)	\(e\left(\frac{79}{160}\right)\)	\(e\left(\frac{13}{800}\right)\)	\(e\left(\frac{859}{1600}\right)\)	\(e\left(\frac{333}{400}\right)\)	\(e\left(\frac{537}{1600}\right)\)	\(e\left(\frac{803}{1600}\right)\)	\(e\left(\frac{577}{800}\right)\)	\(e\left(\frac{39}{1600}\right)\)	\(e\left(\frac{933}{1600}\right)\)
\(\chi_{416000}(13603,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{649}{1600}\right)\)	\(e\left(\frac{67}{160}\right)\)	\(e\left(\frac{649}{800}\right)\)	\(e\left(\frac{1407}{1600}\right)\)	\(e\left(\frac{9}{400}\right)\)	\(e\left(\frac{101}{1600}\right)\)	\(e\left(\frac{1319}{1600}\right)\)	\(e\left(\frac{621}{800}\right)\)	\(e\left(\frac{347}{1600}\right)\)	\(e\left(\frac{1409}{1600}\right)\)
\(\chi_{416000}(14347,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{919}{1600}\right)\)	\(e\left(\frac{157}{160}\right)\)	\(e\left(\frac{119}{800}\right)\)	\(e\left(\frac{417}{1600}\right)\)	\(e\left(\frac{279}{400}\right)\)	\(e\left(\frac{1531}{1600}\right)\)	\(e\left(\frac{889}{1600}\right)\)	\(e\left(\frac{51}{800}\right)\)	\(e\left(\frac{1157}{1600}\right)\)	\(e\left(\frac{479}{1600}\right)\)
\(\chi_{416000}(15387,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{883}{1600}\right)\)	\(e\left(\frac{49}{160}\right)\)	\(e\left(\frac{83}{800}\right)\)	\(e\left(\frac{869}{1600}\right)\)	\(e\left(\frac{3}{400}\right)\)	\(e\left(\frac{167}{1600}\right)\)	\(e\left(\frac{1373}{1600}\right)\)	\(e\left(\frac{607}{800}\right)\)	\(e\left(\frac{1049}{1600}\right)\)	\(e\left(\frac{603}{1600}\right)\)
\(\chi_{416000}(15683,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1281}{1600}\right)\)	\(e\left(\frac{43}{160}\right)\)	\(e\left(\frac{481}{800}\right)\)	\(e\left(\frac{583}{1600}\right)\)	\(e\left(\frac{321}{400}\right)\)	\(e\left(\frac{1469}{1600}\right)\)	\(e\left(\frac{111}{1600}\right)\)	\(e\left(\frac{549}{800}\right)\)	\(e\left(\frac{643}{1600}\right)\)	\(e\left(\frac{121}{1600}\right)\)
\(\chi_{416000}(16427,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1167}{1600}\right)\)	\(e\left(\frac{101}{160}\right)\)	\(e\left(\frac{367}{800}\right)\)	\(e\left(\frac{681}{1600}\right)\)	\(e\left(\frac{47}{400}\right)\)	\(e\left(\frac{83}{1600}\right)\)	\(e\left(\frac{577}{1600}\right)\)	\(e\left(\frac{43}{800}\right)\)	\(e\left(\frac{301}{1600}\right)\)	\(e\left(\frac{1047}{1600}\right)\)
\(\chi_{416000}(16723,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1277}{1600}\right)\)	\(e\left(\frac{31}{160}\right)\)	\(e\left(\frac{477}{800}\right)\)	\(e\left(\frac{811}{1600}\right)\)	\(e\left(\frac{157}{400}\right)\)	\(e\left(\frac{73}{1600}\right)\)	\(e\left(\frac{1587}{1600}\right)\)	\(e\left(\frac{433}{800}\right)\)	\(e\left(\frac{631}{1600}\right)\)	\(e\left(\frac{1557}{1600}\right)\)
\(\chi_{416000}(17467,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{171}{1600}\right)\)	\(e\left(\frac{153}{160}\right)\)	\(e\left(\frac{171}{800}\right)\)	\(e\left(\frac{1453}{1600}\right)\)	\(e\left(\frac{11}{400}\right)\)	\(e\left(\frac{1279}{1600}\right)\)	\(e\left(\frac{101}{1600}\right)\)	\(e\left(\frac{759}{800}\right)\)	\(e\left(\frac{513}{1600}\right)\)	\(e\left(\frac{211}{1600}\right)\)
\(\chi_{416000}(17763,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1593}{1600}\right)\)	\(e\left(\frac{19}{160}\right)\)	\(e\left(\frac{793}{800}\right)\)	\(e\left(\frac{399}{1600}\right)\)	\(e\left(\frac{313}{400}\right)\)	\(e\left(\frac{1557}{1600}\right)\)	\(e\left(\frac{183}{1600}\right)\)	\(e\left(\frac{797}{800}\right)\)	\(e\left(\frac{1579}{1600}\right)\)	\(e\left(\frac{113}{1600}\right)\)
\(\chi_{416000}(18803,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{629}{1600}\right)\)	\(e\left(\frac{7}{160}\right)\)	\(e\left(\frac{629}{800}\right)\)	\(e\left(\frac{947}{1600}\right)\)	\(e\left(\frac{389}{400}\right)\)	\(e\left(\frac{1121}{1600}\right)\)	\(e\left(\frac{699}{1600}\right)\)	\(e\left(\frac{41}{800}\right)\)	\(e\left(\frac{287}{1600}\right)\)	\(e\left(\frac{589}{1600}\right)\)
\(\chi_{416000}(19547,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{739}{1600}\right)\)	\(e\left(\frac{97}{160}\right)\)	\(e\left(\frac{739}{800}\right)\)	\(e\left(\frac{1077}{1600}\right)\)	\(e\left(\frac{99}{400}\right)\)	\(e\left(\frac{1111}{1600}\right)\)	\(e\left(\frac{109}{1600}\right)\)	\(e\left(\frac{431}{800}\right)\)	\(e\left(\frac{617}{1600}\right)\)	\(e\left(\frac{1099}{1600}\right)\)

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First 31 of 640 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	416000.brd
Modulus	$416000$
Conductor	$416000$
Order	$1600$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(416000\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(416000\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(1600\)	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);