LMFDB - Dirichlet character orbit 416000.brt

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416000, base_ring=CyclotomicField(2400)) M = H._module chi = DirichletCharacter(H, M([0,225,336,1600])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(9, 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("416000.9"); 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:	$208000$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$2400$	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:	no, induced from 208000.blp	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{2400})$	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 2400 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 640 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{416000}(9,\cdot)$	$1$	$1$	$e\left(\frac{2227}{2400}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{1027}{1200}\right)$	$e\left(\frac{661}{2400}\right)$	$e\left(\frac{107}{600}\right)$	$e\left(\frac{23}{2400}\right)$	$e\left(\frac{79}{800}\right)$	$e\left(\frac{383}{1200}\right)$	$e\left(\frac{627}{800}\right)$	$e\left(\frac{2107}{2400}\right)$
$\chi_{416000}(809,\cdot)$	$1$	$1$	$e\left(\frac{1487}{2400}\right)$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{287}{1200}\right)$	$e\left(\frac{1241}{2400}\right)$	$e\left(\frac{367}{600}\right)$	$e\left(\frac{163}{2400}\right)$	$e\left(\frac{699}{800}\right)$	$e\left(\frac{523}{1200}\right)$	$e\left(\frac{687}{800}\right)$	$e\left(\frac{1367}{2400}\right)$
$\chi_{416000}(2089,\cdot)$	$1$	$1$	$e\left(\frac{463}{2400}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{463}{1200}\right)$	$e\left(\frac{409}{2400}\right)$	$e\left(\frac{383}{600}\right)$	$e\left(\frac{1187}{2400}\right)$	$e\left(\frac{251}{800}\right)$	$e\left(\frac{827}{1200}\right)$	$e\left(\frac{463}{800}\right)$	$e\left(\frac{1783}{2400}\right)$
$\chi_{416000}(2889,\cdot)$	$1$	$1$	$e\left(\frac{2123}{2400}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{923}{1200}\right)$	$e\left(\frac{989}{2400}\right)$	$e\left(\frac{43}{600}\right)$	$e\left(\frac{1327}{2400}\right)$	$e\left(\frac{71}{800}\right)$	$e\left(\frac{967}{1200}\right)$	$e\left(\frac{523}{800}\right)$	$e\left(\frac{1043}{2400}\right)$
$\chi_{416000}(3129,\cdot)$	$1$	$1$	$e\left(\frac{1261}{2400}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{61}{1200}\right)$	$e\left(\frac{523}{2400}\right)$	$e\left(\frac{101}{600}\right)$	$e\left(\frac{1289}{2400}\right)$	$e\left(\frac{497}{800}\right)$	$e\left(\frac{1169}{1200}\right)$	$e\left(\frac{461}{800}\right)$	$e\left(\frac{901}{2400}\right)$
$\chi_{416000}(3929,\cdot)$	$1$	$1$	$e\left(\frac{521}{2400}\right)$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{521}{1200}\right)$	$e\left(\frac{1103}{2400}\right)$	$e\left(\frac{361}{600}\right)$	$e\left(\frac{1429}{2400}\right)$	$e\left(\frac{317}{800}\right)$	$e\left(\frac{109}{1200}\right)$	$e\left(\frac{521}{800}\right)$	$e\left(\frac{161}{2400}\right)$
$\chi_{416000}(4169,\cdot)$	$1$	$1$	$e\left(\frac{1579}{2400}\right)$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{379}{1200}\right)$	$e\left(\frac{1597}{2400}\right)$	$e\left(\frac{539}{600}\right)$	$e\left(\frac{1871}{2400}\right)$	$e\left(\frac{583}{800}\right)$	$e\left(\frac{791}{1200}\right)$	$e\left(\frac{779}{800}\right)$	$e\left(\frac{1939}{2400}\right)$
$\chi_{416000}(4969,\cdot)$	$1$	$1$	$e\left(\frac{839}{2400}\right)$	$e\left(\frac{37}{240}\right)$	$e\left(\frac{839}{1200}\right)$	$e\left(\frac{2177}{2400}\right)$	$e\left(\frac{199}{600}\right)$	$e\left(\frac{2011}{2400}\right)$	$e\left(\frac{403}{800}\right)$	$e\left(\frac{931}{1200}\right)$	$e\left(\frac{39}{800}\right)$	$e\left(\frac{1199}{2400}\right)$
$\chi_{416000}(5209,\cdot)$	$1$	$1$	$e\left(\frac{1417}{2400}\right)$	$e\left(\frac{11}{240}\right)$	$e\left(\frac{217}{1200}\right)$	$e\left(\frac{1231}{2400}\right)$	$e\left(\frac{497}{600}\right)$	$e\left(\frac{533}{2400}\right)$	$e\left(\frac{509}{800}\right)$	$e\left(\frac{893}{1200}\right)$	$e\left(\frac{617}{800}\right)$	$e\left(\frac{97}{2400}\right)$
$\chi_{416000}(6009,\cdot)$	$1$	$1$	$e\left(\frac{677}{2400}\right)$	$e\left(\frac{31}{240}\right)$	$e\left(\frac{677}{1200}\right)$	$e\left(\frac{1811}{2400}\right)$	$e\left(\frac{157}{600}\right)$	$e\left(\frac{673}{2400}\right)$	$e\left(\frac{329}{800}\right)$	$e\left(\frac{1033}{1200}\right)$	$e\left(\frac{677}{800}\right)$	$e\left(\frac{1757}{2400}\right)$
$\chi_{416000}(7289,\cdot)$	$1$	$1$	$e\left(\frac{2053}{2400}\right)$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{853}{1200}\right)$	$e\left(\frac{979}{2400}\right)$	$e\left(\frac{173}{600}\right)$	$e\left(\frac{1697}{2400}\right)$	$e\left(\frac{681}{800}\right)$	$e\left(\frac{137}{1200}\right)$	$e\left(\frac{453}{800}\right)$	$e\left(\frac{2173}{2400}\right)$
$\chi_{416000}(8089,\cdot)$	$1$	$1$	$e\left(\frac{1313}{2400}\right)$	$e\left(\frac{19}{240}\right)$	$e\left(\frac{113}{1200}\right)$	$e\left(\frac{1559}{2400}\right)$	$e\left(\frac{433}{600}\right)$	$e\left(\frac{1837}{2400}\right)$	$e\left(\frac{501}{800}\right)$	$e\left(\frac{277}{1200}\right)$	$e\left(\frac{513}{800}\right)$	$e\left(\frac{1433}{2400}\right)$
$\chi_{416000}(8329,\cdot)$	$1$	$1$	$e\left(\frac{451}{2400}\right)$	$e\left(\frac{233}{240}\right)$	$e\left(\frac{451}{1200}\right)$	$e\left(\frac{1093}{2400}\right)$	$e\left(\frac{491}{600}\right)$	$e\left(\frac{1799}{2400}\right)$	$e\left(\frac{127}{800}\right)$	$e\left(\frac{479}{1200}\right)$	$e\left(\frac{451}{800}\right)$	$e\left(\frac{1291}{2400}\right)$
$\chi_{416000}(9129,\cdot)$	$1$	$1$	$e\left(\frac{2111}{2400}\right)$	$e\left(\frac{13}{240}\right)$	$e\left(\frac{911}{1200}\right)$	$e\left(\frac{1673}{2400}\right)$	$e\left(\frac{151}{600}\right)$	$e\left(\frac{1939}{2400}\right)$	$e\left(\frac{747}{800}\right)$	$e\left(\frac{619}{1200}\right)$	$e\left(\frac{511}{800}\right)$	$e\left(\frac{551}{2400}\right)$
$\chi_{416000}(9369,\cdot)$	$1$	$1$	$e\left(\frac{769}{2400}\right)$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{769}{1200}\right)$	$e\left(\frac{2167}{2400}\right)$	$e\left(\frac{329}{600}\right)$	$e\left(\frac{2381}{2400}\right)$	$e\left(\frac{213}{800}\right)$	$e\left(\frac{101}{1200}\right)$	$e\left(\frac{769}{800}\right)$	$e\left(\frac{2329}{2400}\right)$
$\chi_{416000}(10169,\cdot)$	$1$	$1$	$e\left(\frac{29}{2400}\right)$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{29}{1200}\right)$	$e\left(\frac{347}{2400}\right)$	$e\left(\frac{589}{600}\right)$	$e\left(\frac{121}{2400}\right)$	$e\left(\frac{33}{800}\right)$	$e\left(\frac{241}{1200}\right)$	$e\left(\frac{29}{800}\right)$	$e\left(\frac{1589}{2400}\right)$
$\chi_{416000}(10409,\cdot)$	$1$	$1$	$e\left(\frac{607}{2400}\right)$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{607}{1200}\right)$	$e\left(\frac{1801}{2400}\right)$	$e\left(\frac{287}{600}\right)$	$e\left(\frac{1043}{2400}\right)$	$e\left(\frac{139}{800}\right)$	$e\left(\frac{203}{1200}\right)$	$e\left(\frac{607}{800}\right)$	$e\left(\frac{487}{2400}\right)$
$\chi_{416000}(11209,\cdot)$	$1$	$1$	$e\left(\frac{2267}{2400}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{1067}{1200}\right)$	$e\left(\frac{2381}{2400}\right)$	$e\left(\frac{547}{600}\right)$	$e\left(\frac{1183}{2400}\right)$	$e\left(\frac{759}{800}\right)$	$e\left(\frac{343}{1200}\right)$	$e\left(\frac{667}{800}\right)$	$e\left(\frac{2147}{2400}\right)$
$\chi_{416000}(12489,\cdot)$	$1$	$1$	$e\left(\frac{1243}{2400}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{43}{1200}\right)$	$e\left(\frac{1549}{2400}\right)$	$e\left(\frac{563}{600}\right)$	$e\left(\frac{2207}{2400}\right)$	$e\left(\frac{311}{800}\right)$	$e\left(\frac{647}{1200}\right)$	$e\left(\frac{443}{800}\right)$	$e\left(\frac{163}{2400}\right)$
$\chi_{416000}(13289,\cdot)$	$1$	$1$	$e\left(\frac{503}{2400}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{503}{1200}\right)$	$e\left(\frac{2129}{2400}\right)$	$e\left(\frac{223}{600}\right)$	$e\left(\frac{2347}{2400}\right)$	$e\left(\frac{131}{800}\right)$	$e\left(\frac{787}{1200}\right)$	$e\left(\frac{503}{800}\right)$	$e\left(\frac{1823}{2400}\right)$
$\chi_{416000}(13529,\cdot)$	$1$	$1$	$e\left(\frac{2041}{2400}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{841}{1200}\right)$	$e\left(\frac{1663}{2400}\right)$	$e\left(\frac{281}{600}\right)$	$e\left(\frac{2309}{2400}\right)$	$e\left(\frac{557}{800}\right)$	$e\left(\frac{989}{1200}\right)$	$e\left(\frac{441}{800}\right)$	$e\left(\frac{1681}{2400}\right)$
$\chi_{416000}(14329,\cdot)$	$1$	$1$	$e\left(\frac{1301}{2400}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{101}{1200}\right)$	$e\left(\frac{2243}{2400}\right)$	$e\left(\frac{541}{600}\right)$	$e\left(\frac{49}{2400}\right)$	$e\left(\frac{377}{800}\right)$	$e\left(\frac{1129}{1200}\right)$	$e\left(\frac{501}{800}\right)$	$e\left(\frac{941}{2400}\right)$
$\chi_{416000}(14569,\cdot)$	$1$	$1$	$e\left(\frac{2359}{2400}\right)$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{1159}{1200}\right)$	$e\left(\frac{337}{2400}\right)$	$e\left(\frac{119}{600}\right)$	$e\left(\frac{491}{2400}\right)$	$e\left(\frac{643}{800}\right)$	$e\left(\frac{611}{1200}\right)$	$e\left(\frac{759}{800}\right)$	$e\left(\frac{319}{2400}\right)$
$\chi_{416000}(15369,\cdot)$	$1$	$1$	$e\left(\frac{1619}{2400}\right)$	$e\left(\frac{217}{240}\right)$	$e\left(\frac{419}{1200}\right)$	$e\left(\frac{917}{2400}\right)$	$e\left(\frac{379}{600}\right)$	$e\left(\frac{631}{2400}\right)$	$e\left(\frac{463}{800}\right)$	$e\left(\frac{751}{1200}\right)$	$e\left(\frac{19}{800}\right)$	$e\left(\frac{1979}{2400}\right)$
$\chi_{416000}(15609,\cdot)$	$1$	$1$	$e\left(\frac{2197}{2400}\right)$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{997}{1200}\right)$	$e\left(\frac{2371}{2400}\right)$	$e\left(\frac{77}{600}\right)$	$e\left(\frac{1553}{2400}\right)$	$e\left(\frac{569}{800}\right)$	$e\left(\frac{713}{1200}\right)$	$e\left(\frac{597}{800}\right)$	$e\left(\frac{877}{2400}\right)$
$\chi_{416000}(16409,\cdot)$	$1$	$1$	$e\left(\frac{1457}{2400}\right)$	$e\left(\frac{211}{240}\right)$	$e\left(\frac{257}{1200}\right)$	$e\left(\frac{551}{2400}\right)$	$e\left(\frac{337}{600}\right)$	$e\left(\frac{1693}{2400}\right)$	$e\left(\frac{389}{800}\right)$	$e\left(\frac{853}{1200}\right)$	$e\left(\frac{657}{800}\right)$	$e\left(\frac{137}{2400}\right)$
$\chi_{416000}(17689,\cdot)$	$1$	$1$	$e\left(\frac{433}{2400}\right)$	$e\left(\frac{179}{240}\right)$	$e\left(\frac{433}{1200}\right)$	$e\left(\frac{2119}{2400}\right)$	$e\left(\frac{353}{600}\right)$	$e\left(\frac{317}{2400}\right)$	$e\left(\frac{741}{800}\right)$	$e\left(\frac{1157}{1200}\right)$	$e\left(\frac{433}{800}\right)$	$e\left(\frac{553}{2400}\right)$
$\chi_{416000}(18489,\cdot)$	$1$	$1$	$e\left(\frac{2093}{2400}\right)$	$e\left(\frac{199}{240}\right)$	$e\left(\frac{893}{1200}\right)$	$e\left(\frac{299}{2400}\right)$	$e\left(\frac{13}{600}\right)$	$e\left(\frac{457}{2400}\right)$	$e\left(\frac{561}{800}\right)$	$e\left(\frac{97}{1200}\right)$	$e\left(\frac{493}{800}\right)$	$e\left(\frac{2213}{2400}\right)$
$\chi_{416000}(18729,\cdot)$	$1$	$1$	$e\left(\frac{1231}{2400}\right)$	$e\left(\frac{173}{240}\right)$	$e\left(\frac{31}{1200}\right)$	$e\left(\frac{2233}{2400}\right)$	$e\left(\frac{71}{600}\right)$	$e\left(\frac{419}{2400}\right)$	$e\left(\frac{187}{800}\right)$	$e\left(\frac{299}{1200}\right)$	$e\left(\frac{431}{800}\right)$	$e\left(\frac{2071}{2400}\right)$
$\chi_{416000}(19529,\cdot)$	$1$	$1$	$e\left(\frac{491}{2400}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{491}{1200}\right)$	$e\left(\frac{413}{2400}\right)$	$e\left(\frac{331}{600}\right)$	$e\left(\frac{559}{2400}\right)$	$e\left(\frac{7}{800}\right)$	$e\left(\frac{439}{1200}\right)$	$e\left(\frac{491}{800}\right)$	$e\left(\frac{1331}{2400}\right)$
$\chi_{416000}(19769,\cdot)$	$1$	$1$	$e\left(\frac{1549}{2400}\right)$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{349}{1200}\right)$	$e\left(\frac{907}{2400}\right)$	$e\left(\frac{509}{600}\right)$	$e\left(\frac{1001}{2400}\right)$	$e\left(\frac{273}{800}\right)$	$e\left(\frac{1121}{1200}\right)$	$e\left(\frac{749}{800}\right)$	$e\left(\frac{709}{2400}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{416000}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2227}{2400}\right)\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{1027}{1200}\right)\)	\(e\left(\frac{661}{2400}\right)\)	\(e\left(\frac{107}{600}\right)\)	\(e\left(\frac{23}{2400}\right)\)	\(e\left(\frac{79}{800}\right)\)	\(e\left(\frac{383}{1200}\right)\)	\(e\left(\frac{627}{800}\right)\)	\(e\left(\frac{2107}{2400}\right)\)
\(\chi_{416000}(809,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1487}{2400}\right)\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{287}{1200}\right)\)	\(e\left(\frac{1241}{2400}\right)\)	\(e\left(\frac{367}{600}\right)\)	\(e\left(\frac{163}{2400}\right)\)	\(e\left(\frac{699}{800}\right)\)	\(e\left(\frac{523}{1200}\right)\)	\(e\left(\frac{687}{800}\right)\)	\(e\left(\frac{1367}{2400}\right)\)
\(\chi_{416000}(2089,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{463}{2400}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{463}{1200}\right)\)	\(e\left(\frac{409}{2400}\right)\)	\(e\left(\frac{383}{600}\right)\)	\(e\left(\frac{1187}{2400}\right)\)	\(e\left(\frac{251}{800}\right)\)	\(e\left(\frac{827}{1200}\right)\)	\(e\left(\frac{463}{800}\right)\)	\(e\left(\frac{1783}{2400}\right)\)
\(\chi_{416000}(2889,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2123}{2400}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{923}{1200}\right)\)	\(e\left(\frac{989}{2400}\right)\)	\(e\left(\frac{43}{600}\right)\)	\(e\left(\frac{1327}{2400}\right)\)	\(e\left(\frac{71}{800}\right)\)	\(e\left(\frac{967}{1200}\right)\)	\(e\left(\frac{523}{800}\right)\)	\(e\left(\frac{1043}{2400}\right)\)
\(\chi_{416000}(3129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1261}{2400}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{61}{1200}\right)\)	\(e\left(\frac{523}{2400}\right)\)	\(e\left(\frac{101}{600}\right)\)	\(e\left(\frac{1289}{2400}\right)\)	\(e\left(\frac{497}{800}\right)\)	\(e\left(\frac{1169}{1200}\right)\)	\(e\left(\frac{461}{800}\right)\)	\(e\left(\frac{901}{2400}\right)\)
\(\chi_{416000}(3929,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{521}{2400}\right)\)	\(e\left(\frac{43}{240}\right)\)	\(e\left(\frac{521}{1200}\right)\)	\(e\left(\frac{1103}{2400}\right)\)	\(e\left(\frac{361}{600}\right)\)	\(e\left(\frac{1429}{2400}\right)\)	\(e\left(\frac{317}{800}\right)\)	\(e\left(\frac{109}{1200}\right)\)	\(e\left(\frac{521}{800}\right)\)	\(e\left(\frac{161}{2400}\right)\)
\(\chi_{416000}(4169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1579}{2400}\right)\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{379}{1200}\right)\)	\(e\left(\frac{1597}{2400}\right)\)	\(e\left(\frac{539}{600}\right)\)	\(e\left(\frac{1871}{2400}\right)\)	\(e\left(\frac{583}{800}\right)\)	\(e\left(\frac{791}{1200}\right)\)	\(e\left(\frac{779}{800}\right)\)	\(e\left(\frac{1939}{2400}\right)\)
\(\chi_{416000}(4969,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{839}{2400}\right)\)	\(e\left(\frac{37}{240}\right)\)	\(e\left(\frac{839}{1200}\right)\)	\(e\left(\frac{2177}{2400}\right)\)	\(e\left(\frac{199}{600}\right)\)	\(e\left(\frac{2011}{2400}\right)\)	\(e\left(\frac{403}{800}\right)\)	\(e\left(\frac{931}{1200}\right)\)	\(e\left(\frac{39}{800}\right)\)	\(e\left(\frac{1199}{2400}\right)\)
\(\chi_{416000}(5209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1417}{2400}\right)\)	\(e\left(\frac{11}{240}\right)\)	\(e\left(\frac{217}{1200}\right)\)	\(e\left(\frac{1231}{2400}\right)\)	\(e\left(\frac{497}{600}\right)\)	\(e\left(\frac{533}{2400}\right)\)	\(e\left(\frac{509}{800}\right)\)	\(e\left(\frac{893}{1200}\right)\)	\(e\left(\frac{617}{800}\right)\)	\(e\left(\frac{97}{2400}\right)\)
\(\chi_{416000}(6009,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{677}{2400}\right)\)	\(e\left(\frac{31}{240}\right)\)	\(e\left(\frac{677}{1200}\right)\)	\(e\left(\frac{1811}{2400}\right)\)	\(e\left(\frac{157}{600}\right)\)	\(e\left(\frac{673}{2400}\right)\)	\(e\left(\frac{329}{800}\right)\)	\(e\left(\frac{1033}{1200}\right)\)	\(e\left(\frac{677}{800}\right)\)	\(e\left(\frac{1757}{2400}\right)\)
\(\chi_{416000}(7289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2053}{2400}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{853}{1200}\right)\)	\(e\left(\frac{979}{2400}\right)\)	\(e\left(\frac{173}{600}\right)\)	\(e\left(\frac{1697}{2400}\right)\)	\(e\left(\frac{681}{800}\right)\)	\(e\left(\frac{137}{1200}\right)\)	\(e\left(\frac{453}{800}\right)\)	\(e\left(\frac{2173}{2400}\right)\)
\(\chi_{416000}(8089,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1313}{2400}\right)\)	\(e\left(\frac{19}{240}\right)\)	\(e\left(\frac{113}{1200}\right)\)	\(e\left(\frac{1559}{2400}\right)\)	\(e\left(\frac{433}{600}\right)\)	\(e\left(\frac{1837}{2400}\right)\)	\(e\left(\frac{501}{800}\right)\)	\(e\left(\frac{277}{1200}\right)\)	\(e\left(\frac{513}{800}\right)\)	\(e\left(\frac{1433}{2400}\right)\)
\(\chi_{416000}(8329,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{451}{2400}\right)\)	\(e\left(\frac{233}{240}\right)\)	\(e\left(\frac{451}{1200}\right)\)	\(e\left(\frac{1093}{2400}\right)\)	\(e\left(\frac{491}{600}\right)\)	\(e\left(\frac{1799}{2400}\right)\)	\(e\left(\frac{127}{800}\right)\)	\(e\left(\frac{479}{1200}\right)\)	\(e\left(\frac{451}{800}\right)\)	\(e\left(\frac{1291}{2400}\right)\)
\(\chi_{416000}(9129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2111}{2400}\right)\)	\(e\left(\frac{13}{240}\right)\)	\(e\left(\frac{911}{1200}\right)\)	\(e\left(\frac{1673}{2400}\right)\)	\(e\left(\frac{151}{600}\right)\)	\(e\left(\frac{1939}{2400}\right)\)	\(e\left(\frac{747}{800}\right)\)	\(e\left(\frac{619}{1200}\right)\)	\(e\left(\frac{511}{800}\right)\)	\(e\left(\frac{551}{2400}\right)\)
\(\chi_{416000}(9369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{769}{2400}\right)\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{769}{1200}\right)\)	\(e\left(\frac{2167}{2400}\right)\)	\(e\left(\frac{329}{600}\right)\)	\(e\left(\frac{2381}{2400}\right)\)	\(e\left(\frac{213}{800}\right)\)	\(e\left(\frac{101}{1200}\right)\)	\(e\left(\frac{769}{800}\right)\)	\(e\left(\frac{2329}{2400}\right)\)
\(\chi_{416000}(10169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{2400}\right)\)	\(e\left(\frac{7}{240}\right)\)	\(e\left(\frac{29}{1200}\right)\)	\(e\left(\frac{347}{2400}\right)\)	\(e\left(\frac{589}{600}\right)\)	\(e\left(\frac{121}{2400}\right)\)	\(e\left(\frac{33}{800}\right)\)	\(e\left(\frac{241}{1200}\right)\)	\(e\left(\frac{29}{800}\right)\)	\(e\left(\frac{1589}{2400}\right)\)
\(\chi_{416000}(10409,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{607}{2400}\right)\)	\(e\left(\frac{221}{240}\right)\)	\(e\left(\frac{607}{1200}\right)\)	\(e\left(\frac{1801}{2400}\right)\)	\(e\left(\frac{287}{600}\right)\)	\(e\left(\frac{1043}{2400}\right)\)	\(e\left(\frac{139}{800}\right)\)	\(e\left(\frac{203}{1200}\right)\)	\(e\left(\frac{607}{800}\right)\)	\(e\left(\frac{487}{2400}\right)\)
\(\chi_{416000}(11209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2267}{2400}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{1067}{1200}\right)\)	\(e\left(\frac{2381}{2400}\right)\)	\(e\left(\frac{547}{600}\right)\)	\(e\left(\frac{1183}{2400}\right)\)	\(e\left(\frac{759}{800}\right)\)	\(e\left(\frac{343}{1200}\right)\)	\(e\left(\frac{667}{800}\right)\)	\(e\left(\frac{2147}{2400}\right)\)
\(\chi_{416000}(12489,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1243}{2400}\right)\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{43}{1200}\right)\)	\(e\left(\frac{1549}{2400}\right)\)	\(e\left(\frac{563}{600}\right)\)	\(e\left(\frac{2207}{2400}\right)\)	\(e\left(\frac{311}{800}\right)\)	\(e\left(\frac{647}{1200}\right)\)	\(e\left(\frac{443}{800}\right)\)	\(e\left(\frac{163}{2400}\right)\)
\(\chi_{416000}(13289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{503}{2400}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{503}{1200}\right)\)	\(e\left(\frac{2129}{2400}\right)\)	\(e\left(\frac{223}{600}\right)\)	\(e\left(\frac{2347}{2400}\right)\)	\(e\left(\frac{131}{800}\right)\)	\(e\left(\frac{787}{1200}\right)\)	\(e\left(\frac{503}{800}\right)\)	\(e\left(\frac{1823}{2400}\right)\)
\(\chi_{416000}(13529,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2041}{2400}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{841}{1200}\right)\)	\(e\left(\frac{1663}{2400}\right)\)	\(e\left(\frac{281}{600}\right)\)	\(e\left(\frac{2309}{2400}\right)\)	\(e\left(\frac{557}{800}\right)\)	\(e\left(\frac{989}{1200}\right)\)	\(e\left(\frac{441}{800}\right)\)	\(e\left(\frac{1681}{2400}\right)\)
\(\chi_{416000}(14329,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1301}{2400}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{101}{1200}\right)\)	\(e\left(\frac{2243}{2400}\right)\)	\(e\left(\frac{541}{600}\right)\)	\(e\left(\frac{49}{2400}\right)\)	\(e\left(\frac{377}{800}\right)\)	\(e\left(\frac{1129}{1200}\right)\)	\(e\left(\frac{501}{800}\right)\)	\(e\left(\frac{941}{2400}\right)\)
\(\chi_{416000}(14569,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2359}{2400}\right)\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{1159}{1200}\right)\)	\(e\left(\frac{337}{2400}\right)\)	\(e\left(\frac{119}{600}\right)\)	\(e\left(\frac{491}{2400}\right)\)	\(e\left(\frac{643}{800}\right)\)	\(e\left(\frac{611}{1200}\right)\)	\(e\left(\frac{759}{800}\right)\)	\(e\left(\frac{319}{2400}\right)\)
\(\chi_{416000}(15369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1619}{2400}\right)\)	\(e\left(\frac{217}{240}\right)\)	\(e\left(\frac{419}{1200}\right)\)	\(e\left(\frac{917}{2400}\right)\)	\(e\left(\frac{379}{600}\right)\)	\(e\left(\frac{631}{2400}\right)\)	\(e\left(\frac{463}{800}\right)\)	\(e\left(\frac{751}{1200}\right)\)	\(e\left(\frac{19}{800}\right)\)	\(e\left(\frac{1979}{2400}\right)\)
\(\chi_{416000}(15609,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2197}{2400}\right)\)	\(e\left(\frac{191}{240}\right)\)	\(e\left(\frac{997}{1200}\right)\)	\(e\left(\frac{2371}{2400}\right)\)	\(e\left(\frac{77}{600}\right)\)	\(e\left(\frac{1553}{2400}\right)\)	\(e\left(\frac{569}{800}\right)\)	\(e\left(\frac{713}{1200}\right)\)	\(e\left(\frac{597}{800}\right)\)	\(e\left(\frac{877}{2400}\right)\)
\(\chi_{416000}(16409,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1457}{2400}\right)\)	\(e\left(\frac{211}{240}\right)\)	\(e\left(\frac{257}{1200}\right)\)	\(e\left(\frac{551}{2400}\right)\)	\(e\left(\frac{337}{600}\right)\)	\(e\left(\frac{1693}{2400}\right)\)	\(e\left(\frac{389}{800}\right)\)	\(e\left(\frac{853}{1200}\right)\)	\(e\left(\frac{657}{800}\right)\)	\(e\left(\frac{137}{2400}\right)\)
\(\chi_{416000}(17689,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{433}{2400}\right)\)	\(e\left(\frac{179}{240}\right)\)	\(e\left(\frac{433}{1200}\right)\)	\(e\left(\frac{2119}{2400}\right)\)	\(e\left(\frac{353}{600}\right)\)	\(e\left(\frac{317}{2400}\right)\)	\(e\left(\frac{741}{800}\right)\)	\(e\left(\frac{1157}{1200}\right)\)	\(e\left(\frac{433}{800}\right)\)	\(e\left(\frac{553}{2400}\right)\)
\(\chi_{416000}(18489,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2093}{2400}\right)\)	\(e\left(\frac{199}{240}\right)\)	\(e\left(\frac{893}{1200}\right)\)	\(e\left(\frac{299}{2400}\right)\)	\(e\left(\frac{13}{600}\right)\)	\(e\left(\frac{457}{2400}\right)\)	\(e\left(\frac{561}{800}\right)\)	\(e\left(\frac{97}{1200}\right)\)	\(e\left(\frac{493}{800}\right)\)	\(e\left(\frac{2213}{2400}\right)\)
\(\chi_{416000}(18729,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1231}{2400}\right)\)	\(e\left(\frac{173}{240}\right)\)	\(e\left(\frac{31}{1200}\right)\)	\(e\left(\frac{2233}{2400}\right)\)	\(e\left(\frac{71}{600}\right)\)	\(e\left(\frac{419}{2400}\right)\)	\(e\left(\frac{187}{800}\right)\)	\(e\left(\frac{299}{1200}\right)\)	\(e\left(\frac{431}{800}\right)\)	\(e\left(\frac{2071}{2400}\right)\)
\(\chi_{416000}(19529,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{491}{2400}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{491}{1200}\right)\)	\(e\left(\frac{413}{2400}\right)\)	\(e\left(\frac{331}{600}\right)\)	\(e\left(\frac{559}{2400}\right)\)	\(e\left(\frac{7}{800}\right)\)	\(e\left(\frac{439}{1200}\right)\)	\(e\left(\frac{491}{800}\right)\)	\(e\left(\frac{1331}{2400}\right)\)
\(\chi_{416000}(19769,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1549}{2400}\right)\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{349}{1200}\right)\)	\(e\left(\frac{907}{2400}\right)\)	\(e\left(\frac{509}{600}\right)\)	\(e\left(\frac{1001}{2400}\right)\)	\(e\left(\frac{273}{800}\right)\)	\(e\left(\frac{1121}{1200}\right)\)	\(e\left(\frac{749}{800}\right)\)	\(e\left(\frac{709}{2400}\right)\)

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Basic properties

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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.brt
Modulus	$416000$
Conductor	$208000$
Order	$2400$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(416000\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(208000\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(2400\)	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:	no, induced from 208000.blp	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);