LMFDB - Dirichlet character orbit 228672.bra

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228672, base_ring=CyclotomicField(1584)) M = H._module chi = DirichletCharacter(H, M([792,891,0,136])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(91, 228672)) 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("228672.91"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$228672$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$25408$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$1584$	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 25408.id	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:	$\Q(\zeta_{1584})$	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 1584 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 480 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{228672}(91,\cdot)$	$-1$	$1$	$e\left(\frac{1027}{1584}\right)$	$e\left(\frac{295}{792}\right)$	$e\left(\frac{527}{1584}\right)$	$e\left(\frac{173}{1584}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{677}{1584}\right)$	$e\left(\frac{49}{792}\right)$	$e\left(\frac{235}{792}\right)$	$e\left(\frac{521}{1584}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{228672}(307,\cdot)$	$-1$	$1$	$e\left(\frac{1541}{1584}\right)$	$e\left(\frac{401}{792}\right)$	$e\left(\frac{217}{1584}\right)$	$e\left(\frac{1003}{1584}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{931}{1584}\right)$	$e\left(\frac{719}{792}\right)$	$e\left(\frac{749}{792}\right)$	$e\left(\frac{1519}{1584}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{228672}(667,\cdot)$	$-1$	$1$	$e\left(\frac{883}{1584}\right)$	$e\left(\frac{367}{792}\right)$	$e\left(\frac{959}{1584}\right)$	$e\left(\frac{1469}{1584}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{1253}{1584}\right)$	$e\left(\frac{265}{792}\right)$	$e\left(\frac{91}{792}\right)$	$e\left(\frac{377}{1584}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{228672}(1099,\cdot)$	$-1$	$1$	$e\left(\frac{887}{1584}\right)$	$e\left(\frac{35}{792}\right)$	$e\left(\frac{1123}{1584}\right)$	$e\left(\frac{1081}{1584}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{577}{1584}\right)$	$e\left(\frac{677}{792}\right)$	$e\left(\frac{95}{792}\right)$	$e\left(\frac{1525}{1584}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{228672}(1459,\cdot)$	$-1$	$1$	$e\left(\frac{149}{1584}\right)$	$e\left(\frac{305}{792}\right)$	$e\left(\frac{169}{1584}\right)$	$e\left(\frac{1387}{1584}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{163}{1584}\right)$	$e\left(\frac{695}{792}\right)$	$e\left(\frac{149}{792}\right)$	$e\left(\frac{1183}{1584}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{228672}(1675,\cdot)$	$-1$	$1$	$e\left(\frac{391}{1584}\right)$	$e\left(\frac{19}{792}\right)$	$e\left(\frac{1379}{1584}\right)$	$e\left(\frac{89}{1584}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{449}{1584}\right)$	$e\left(\frac{277}{792}\right)$	$e\left(\frac{391}{792}\right)$	$e\left(\frac{149}{1584}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{228672}(2611,\cdot)$	$-1$	$1$	$e\left(\frac{901}{1584}\right)$	$e\left(\frac{457}{792}\right)$	$e\left(\frac{905}{1584}\right)$	$e\left(\frac{1307}{1584}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{1379}{1584}\right)$	$e\left(\frac{535}{792}\right)$	$e\left(\frac{109}{792}\right)$	$e\left(\frac{1583}{1584}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{228672}(2827,\cdot)$	$-1$	$1$	$e\left(\frac{359}{1584}\right)$	$e\left(\frac{299}{792}\right)$	$e\left(\frac{67}{1584}\right)$	$e\left(\frac{25}{1584}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{1105}{1584}\right)$	$e\left(\frac{149}{792}\right)$	$e\left(\frac{359}{792}\right)$	$e\left(\frac{469}{1584}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{228672}(3547,\cdot)$	$-1$	$1$	$e\left(\frac{1475}{1584}\right)$	$e\left(\frac{335}{792}\right)$	$e\left(\frac{1471}{1584}\right)$	$e\left(\frac{1069}{1584}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{997}{1584}\right)$	$e\left(\frac{257}{792}\right)$	$e\left(\frac{683}{792}\right)$	$e\left(\frac{793}{1584}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{228672}(3691,\cdot)$	$-1$	$1$	$e\left(\frac{79}{1584}\right)$	$e\left(\frac{571}{792}\right)$	$e\left(\frac{1259}{1584}\right)$	$e\left(\frac{257}{1584}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{905}{1584}\right)$	$e\left(\frac{613}{792}\right)$	$e\left(\frac{79}{792}\right)$	$e\left(\frac{893}{1584}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{228672}(4267,\cdot)$	$-1$	$1$	$e\left(\frac{863}{1584}\right)$	$e\left(\frac{443}{792}\right)$	$e\left(\frac{139}{1584}\right)$	$e\left(\frac{241}{1584}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{1465}{1584}\right)$	$e\left(\frac{581}{792}\right)$	$e\left(\frac{71}{792}\right)$	$e\left(\frac{973}{1584}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{228672}(4411,\cdot)$	$-1$	$1$	$e\left(\frac{1019}{1584}\right)$	$e\left(\frac{167}{792}\right)$	$e\left(\frac{199}{1584}\right)$	$e\left(\frac{949}{1584}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{445}{1584}\right)$	$e\left(\frac{17}{792}\right)$	$e\left(\frac{227}{792}\right)$	$e\left(\frac{1393}{1584}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{228672}(4483,\cdot)$	$-1$	$1$	$e\left(\frac{1409}{1584}\right)$	$e\left(\frac{269}{792}\right)$	$e\left(\frac{1141}{1584}\right)$	$e\left(\frac{1135}{1584}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{1063}{1584}\right)$	$e\left(\frac{587}{792}\right)$	$e\left(\frac{617}{792}\right)$	$e\left(\frac{67}{1584}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{228672}(4555,\cdot)$	$-1$	$1$	$e\left(\frac{775}{1584}\right)$	$e\left(\frac{619}{792}\right)$	$e\left(\frac{1283}{1584}\right)$	$e\left(\frac{857}{1584}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{497}{1584}\right)$	$e\left(\frac{229}{792}\right)$	$e\left(\frac{775}{792}\right)$	$e\left(\frac{1061}{1584}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{228672}(5203,\cdot)$	$-1$	$1$	$e\left(\frac{541}{1584}\right)$	$e\left(\frac{241}{792}\right)$	$e\left(\frac{401}{1584}\right)$	$e\left(\frac{1379}{1584}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{443}{1584}\right)$	$e\left(\frac{679}{792}\right)$	$e\left(\frac{541}{792}\right)$	$e\left(\frac{1223}{1584}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{228672}(5491,\cdot)$	$-1$	$1$	$e\left(\frac{581}{1584}\right)$	$e\left(\frac{89}{792}\right)$	$e\left(\frac{457}{1584}\right)$	$e\left(\frac{667}{1584}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{19}{1584}\right)$	$e\left(\frac{47}{792}\right)$	$e\left(\frac{581}{792}\right)$	$e\left(\frac{31}{1584}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{228672}(5779,\cdot)$	$-1$	$1$	$e\left(\frac{1181}{1584}\right)$	$e\left(\frac{185}{792}\right)$	$e\left(\frac{1297}{1584}\right)$	$e\left(\frac{1075}{1584}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{1579}{1584}\right)$	$e\left(\frac{71}{792}\right)$	$e\left(\frac{389}{792}\right)$	$e\left(\frac{1159}{1584}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{228672}(5995,\cdot)$	$-1$	$1$	$e\left(\frac{1039}{1584}\right)$	$e\left(\frac{91}{792}\right)$	$e\left(\frac{1019}{1584}\right)$	$e\left(\frac{593}{1584}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{233}{1584}\right)$	$e\left(\frac{493}{792}\right)$	$e\left(\frac{247}{792}\right)$	$e\left(\frac{797}{1584}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{228672}(6283,\cdot)$	$-1$	$1$	$e\left(\frac{1255}{1584}\right)$	$e\left(\frac{379}{792}\right)$	$e\left(\frac{371}{1584}\right)$	$e\left(\frac{233}{1584}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{161}{1584}\right)$	$e\left(\frac{565}{792}\right)$	$e\left(\frac{463}{792}\right)$	$e\left(\frac{1013}{1584}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{228672}(6355,\cdot)$	$-1$	$1$	$e\left(\frac{1421}{1584}\right)$	$e\left(\frac{65}{792}\right)$	$e\left(\frac{49}{1584}\right)$	$e\left(\frac{1555}{1584}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{619}{1584}\right)$	$e\left(\frac{239}{792}\right)$	$e\left(\frac{629}{792}\right)$	$e\left(\frac{343}{1584}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{228672}(6571,\cdot)$	$-1$	$1$	$e\left(\frac{1327}{1584}\right)$	$e\left(\frac{739}{792}\right)$	$e\left(\frac{155}{1584}\right)$	$e\left(\frac{1169}{1584}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{665}{1584}\right)$	$e\left(\frac{61}{792}\right)$	$e\left(\frac{535}{792}\right)$	$e\left(\frac{1085}{1584}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{228672}(7579,\cdot)$	$-1$	$1$	$e\left(\frac{1123}{1584}\right)$	$e\left(\frac{247}{792}\right)$	$e\left(\frac{1295}{1584}\right)$	$e\left(\frac{365}{1584}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{293}{1584}\right)$	$e\left(\frac{433}{792}\right)$	$e\left(\frac{331}{792}\right)$	$e\left(\frac{1145}{1584}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{228672}(7867,\cdot)$	$-1$	$1$	$e\left(\frac{203}{1584}\right)$	$e\left(\frac{575}{792}\right)$	$e\left(\frac{7}{1584}\right)$	$e\left(\frac{901}{1584}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{541}{1584}\right)$	$e\left(\frac{713}{792}\right)$	$e\left(\frac{203}{792}\right)$	$e\left(\frac{49}{1584}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{228672}(8659,\cdot)$	$-1$	$1$	$e\left(\frac{637}{1584}\right)$	$e\left(\frac{193}{792}\right)$	$e\left(\frac{1169}{1584}\right)$	$e\left(\frac{1571}{1584}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{59}{1584}\right)$	$e\left(\frac{271}{792}\right)$	$e\left(\frac{637}{792}\right)$	$e\left(\frac{263}{1584}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{228672}(9235,\cdot)$	$-1$	$1$	$e\left(\frac{845}{1584}\right)$	$e\left(\frac{353}{792}\right)$	$e\left(\frac{193}{1584}\right)$	$e\left(\frac{403}{1584}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{1339}{1584}\right)$	$e\left(\frac{311}{792}\right)$	$e\left(\frac{53}{792}\right)$	$e\left(\frac{1351}{1584}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{228672}(10027,\cdot)$	$-1$	$1$	$e\left(\frac{1487}{1584}\right)$	$e\left(\frac{131}{792}\right)$	$e\left(\frac{379}{1584}\right)$	$e\left(\frac{1489}{1584}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{553}{1584}\right)$	$e\left(\frac{701}{792}\right)$	$e\left(\frac{695}{792}\right)$	$e\left(\frac{1069}{1584}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{228672}(11035,\cdot)$	$-1$	$1$	$e\left(\frac{1427}{1584}\right)$	$e\left(\frac{359}{792}\right)$	$e\left(\frac{1087}{1584}\right)$	$e\left(\frac{973}{1584}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{1189}{1584}\right)$	$e\left(\frac{65}{792}\right)$	$e\left(\frac{635}{792}\right)$	$e\left(\frac{1273}{1584}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{228672}(11107,\cdot)$	$-1$	$1$	$e\left(\frac{169}{1584}\right)$	$e\left(\frac{229}{792}\right)$	$e\left(\frac{989}{1584}\right)$	$e\left(\frac{1031}{1584}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{1535}{1584}\right)$	$e\left(\frac{379}{792}\right)$	$e\left(\frac{169}{792}\right)$	$e\left(\frac{587}{1584}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{228672}(11899,\cdot)$	$-1$	$1$	$e\left(\frac{1451}{1584}\right)$	$e\left(\frac{743}{792}\right)$	$e\left(\frac{487}{1584}\right)$	$e\left(\frac{229}{1584}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{301}{1584}\right)$	$e\left(\frac{161}{792}\right)$	$e\left(\frac{659}{792}\right)$	$e\left(\frac{241}{1584}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{228672}(12115,\cdot)$	$-1$	$1$	$e\left(\frac{125}{1584}\right)$	$e\left(\frac{713}{792}\right)$	$e\left(\frac{769}{1584}\right)$	$e\left(\frac{547}{1584}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{1051}{1584}\right)$	$e\left(\frac{599}{792}\right)$	$e\left(\frac{125}{792}\right)$	$e\left(\frac{631}{1584}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{228672}(12835,\cdot)$	$-1$	$1$	$e\left(\frac{1513}{1584}\right)$	$e\left(\frac{349}{792}\right)$	$e\left(\frac{653}{1584}\right)$	$e\left(\frac{551}{1584}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{911}{1584}\right)$	$e\left(\frac{211}{792}\right)$	$e\left(\frac{721}{792}\right)$	$e\left(\frac{1403}{1584}\right)$	$e\left(\frac{8}{11}\right)$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{228672}(91,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1027}{1584}\right)\)	\(e\left(\frac{295}{792}\right)\)	\(e\left(\frac{527}{1584}\right)\)	\(e\left(\frac{173}{1584}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{677}{1584}\right)\)	\(e\left(\frac{49}{792}\right)\)	\(e\left(\frac{235}{792}\right)\)	\(e\left(\frac{521}{1584}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{228672}(307,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1541}{1584}\right)\)	\(e\left(\frac{401}{792}\right)\)	\(e\left(\frac{217}{1584}\right)\)	\(e\left(\frac{1003}{1584}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{931}{1584}\right)\)	\(e\left(\frac{719}{792}\right)\)	\(e\left(\frac{749}{792}\right)\)	\(e\left(\frac{1519}{1584}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{228672}(667,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{883}{1584}\right)\)	\(e\left(\frac{367}{792}\right)\)	\(e\left(\frac{959}{1584}\right)\)	\(e\left(\frac{1469}{1584}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{1253}{1584}\right)\)	\(e\left(\frac{265}{792}\right)\)	\(e\left(\frac{91}{792}\right)\)	\(e\left(\frac{377}{1584}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{228672}(1099,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{887}{1584}\right)\)	\(e\left(\frac{35}{792}\right)\)	\(e\left(\frac{1123}{1584}\right)\)	\(e\left(\frac{1081}{1584}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{577}{1584}\right)\)	\(e\left(\frac{677}{792}\right)\)	\(e\left(\frac{95}{792}\right)\)	\(e\left(\frac{1525}{1584}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{228672}(1459,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{1584}\right)\)	\(e\left(\frac{305}{792}\right)\)	\(e\left(\frac{169}{1584}\right)\)	\(e\left(\frac{1387}{1584}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{163}{1584}\right)\)	\(e\left(\frac{695}{792}\right)\)	\(e\left(\frac{149}{792}\right)\)	\(e\left(\frac{1183}{1584}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{228672}(1675,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{391}{1584}\right)\)	\(e\left(\frac{19}{792}\right)\)	\(e\left(\frac{1379}{1584}\right)\)	\(e\left(\frac{89}{1584}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{449}{1584}\right)\)	\(e\left(\frac{277}{792}\right)\)	\(e\left(\frac{391}{792}\right)\)	\(e\left(\frac{149}{1584}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{228672}(2611,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{901}{1584}\right)\)	\(e\left(\frac{457}{792}\right)\)	\(e\left(\frac{905}{1584}\right)\)	\(e\left(\frac{1307}{1584}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{1379}{1584}\right)\)	\(e\left(\frac{535}{792}\right)\)	\(e\left(\frac{109}{792}\right)\)	\(e\left(\frac{1583}{1584}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{228672}(2827,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{359}{1584}\right)\)	\(e\left(\frac{299}{792}\right)\)	\(e\left(\frac{67}{1584}\right)\)	\(e\left(\frac{25}{1584}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{1105}{1584}\right)\)	\(e\left(\frac{149}{792}\right)\)	\(e\left(\frac{359}{792}\right)\)	\(e\left(\frac{469}{1584}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{228672}(3547,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1475}{1584}\right)\)	\(e\left(\frac{335}{792}\right)\)	\(e\left(\frac{1471}{1584}\right)\)	\(e\left(\frac{1069}{1584}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{997}{1584}\right)\)	\(e\left(\frac{257}{792}\right)\)	\(e\left(\frac{683}{792}\right)\)	\(e\left(\frac{793}{1584}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{228672}(3691,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{1584}\right)\)	\(e\left(\frac{571}{792}\right)\)	\(e\left(\frac{1259}{1584}\right)\)	\(e\left(\frac{257}{1584}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{905}{1584}\right)\)	\(e\left(\frac{613}{792}\right)\)	\(e\left(\frac{79}{792}\right)\)	\(e\left(\frac{893}{1584}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{228672}(4267,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{863}{1584}\right)\)	\(e\left(\frac{443}{792}\right)\)	\(e\left(\frac{139}{1584}\right)\)	\(e\left(\frac{241}{1584}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{1465}{1584}\right)\)	\(e\left(\frac{581}{792}\right)\)	\(e\left(\frac{71}{792}\right)\)	\(e\left(\frac{973}{1584}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{228672}(4411,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1019}{1584}\right)\)	\(e\left(\frac{167}{792}\right)\)	\(e\left(\frac{199}{1584}\right)\)	\(e\left(\frac{949}{1584}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{445}{1584}\right)\)	\(e\left(\frac{17}{792}\right)\)	\(e\left(\frac{227}{792}\right)\)	\(e\left(\frac{1393}{1584}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{228672}(4483,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1409}{1584}\right)\)	\(e\left(\frac{269}{792}\right)\)	\(e\left(\frac{1141}{1584}\right)\)	\(e\left(\frac{1135}{1584}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{1063}{1584}\right)\)	\(e\left(\frac{587}{792}\right)\)	\(e\left(\frac{617}{792}\right)\)	\(e\left(\frac{67}{1584}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{228672}(4555,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{775}{1584}\right)\)	\(e\left(\frac{619}{792}\right)\)	\(e\left(\frac{1283}{1584}\right)\)	\(e\left(\frac{857}{1584}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{497}{1584}\right)\)	\(e\left(\frac{229}{792}\right)\)	\(e\left(\frac{775}{792}\right)\)	\(e\left(\frac{1061}{1584}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{228672}(5203,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{541}{1584}\right)\)	\(e\left(\frac{241}{792}\right)\)	\(e\left(\frac{401}{1584}\right)\)	\(e\left(\frac{1379}{1584}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{443}{1584}\right)\)	\(e\left(\frac{679}{792}\right)\)	\(e\left(\frac{541}{792}\right)\)	\(e\left(\frac{1223}{1584}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{228672}(5491,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{581}{1584}\right)\)	\(e\left(\frac{89}{792}\right)\)	\(e\left(\frac{457}{1584}\right)\)	\(e\left(\frac{667}{1584}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{19}{1584}\right)\)	\(e\left(\frac{47}{792}\right)\)	\(e\left(\frac{581}{792}\right)\)	\(e\left(\frac{31}{1584}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{228672}(5779,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1181}{1584}\right)\)	\(e\left(\frac{185}{792}\right)\)	\(e\left(\frac{1297}{1584}\right)\)	\(e\left(\frac{1075}{1584}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{1579}{1584}\right)\)	\(e\left(\frac{71}{792}\right)\)	\(e\left(\frac{389}{792}\right)\)	\(e\left(\frac{1159}{1584}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{228672}(5995,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1039}{1584}\right)\)	\(e\left(\frac{91}{792}\right)\)	\(e\left(\frac{1019}{1584}\right)\)	\(e\left(\frac{593}{1584}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{233}{1584}\right)\)	\(e\left(\frac{493}{792}\right)\)	\(e\left(\frac{247}{792}\right)\)	\(e\left(\frac{797}{1584}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{228672}(6283,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1255}{1584}\right)\)	\(e\left(\frac{379}{792}\right)\)	\(e\left(\frac{371}{1584}\right)\)	\(e\left(\frac{233}{1584}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{161}{1584}\right)\)	\(e\left(\frac{565}{792}\right)\)	\(e\left(\frac{463}{792}\right)\)	\(e\left(\frac{1013}{1584}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{228672}(6355,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1421}{1584}\right)\)	\(e\left(\frac{65}{792}\right)\)	\(e\left(\frac{49}{1584}\right)\)	\(e\left(\frac{1555}{1584}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{619}{1584}\right)\)	\(e\left(\frac{239}{792}\right)\)	\(e\left(\frac{629}{792}\right)\)	\(e\left(\frac{343}{1584}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{228672}(6571,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1327}{1584}\right)\)	\(e\left(\frac{739}{792}\right)\)	\(e\left(\frac{155}{1584}\right)\)	\(e\left(\frac{1169}{1584}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{665}{1584}\right)\)	\(e\left(\frac{61}{792}\right)\)	\(e\left(\frac{535}{792}\right)\)	\(e\left(\frac{1085}{1584}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{228672}(7579,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1123}{1584}\right)\)	\(e\left(\frac{247}{792}\right)\)	\(e\left(\frac{1295}{1584}\right)\)	\(e\left(\frac{365}{1584}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{293}{1584}\right)\)	\(e\left(\frac{433}{792}\right)\)	\(e\left(\frac{331}{792}\right)\)	\(e\left(\frac{1145}{1584}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{228672}(7867,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{203}{1584}\right)\)	\(e\left(\frac{575}{792}\right)\)	\(e\left(\frac{7}{1584}\right)\)	\(e\left(\frac{901}{1584}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{541}{1584}\right)\)	\(e\left(\frac{713}{792}\right)\)	\(e\left(\frac{203}{792}\right)\)	\(e\left(\frac{49}{1584}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{228672}(8659,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{637}{1584}\right)\)	\(e\left(\frac{193}{792}\right)\)	\(e\left(\frac{1169}{1584}\right)\)	\(e\left(\frac{1571}{1584}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{59}{1584}\right)\)	\(e\left(\frac{271}{792}\right)\)	\(e\left(\frac{637}{792}\right)\)	\(e\left(\frac{263}{1584}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{228672}(9235,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{845}{1584}\right)\)	\(e\left(\frac{353}{792}\right)\)	\(e\left(\frac{193}{1584}\right)\)	\(e\left(\frac{403}{1584}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{1339}{1584}\right)\)	\(e\left(\frac{311}{792}\right)\)	\(e\left(\frac{53}{792}\right)\)	\(e\left(\frac{1351}{1584}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{228672}(10027,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1487}{1584}\right)\)	\(e\left(\frac{131}{792}\right)\)	\(e\left(\frac{379}{1584}\right)\)	\(e\left(\frac{1489}{1584}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{553}{1584}\right)\)	\(e\left(\frac{701}{792}\right)\)	\(e\left(\frac{695}{792}\right)\)	\(e\left(\frac{1069}{1584}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{228672}(11035,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1427}{1584}\right)\)	\(e\left(\frac{359}{792}\right)\)	\(e\left(\frac{1087}{1584}\right)\)	\(e\left(\frac{973}{1584}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{1189}{1584}\right)\)	\(e\left(\frac{65}{792}\right)\)	\(e\left(\frac{635}{792}\right)\)	\(e\left(\frac{1273}{1584}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{228672}(11107,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{169}{1584}\right)\)	\(e\left(\frac{229}{792}\right)\)	\(e\left(\frac{989}{1584}\right)\)	\(e\left(\frac{1031}{1584}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{1535}{1584}\right)\)	\(e\left(\frac{379}{792}\right)\)	\(e\left(\frac{169}{792}\right)\)	\(e\left(\frac{587}{1584}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{228672}(11899,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1451}{1584}\right)\)	\(e\left(\frac{743}{792}\right)\)	\(e\left(\frac{487}{1584}\right)\)	\(e\left(\frac{229}{1584}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{301}{1584}\right)\)	\(e\left(\frac{161}{792}\right)\)	\(e\left(\frac{659}{792}\right)\)	\(e\left(\frac{241}{1584}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{228672}(12115,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{125}{1584}\right)\)	\(e\left(\frac{713}{792}\right)\)	\(e\left(\frac{769}{1584}\right)\)	\(e\left(\frac{547}{1584}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{1051}{1584}\right)\)	\(e\left(\frac{599}{792}\right)\)	\(e\left(\frac{125}{792}\right)\)	\(e\left(\frac{631}{1584}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{228672}(12835,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1513}{1584}\right)\)	\(e\left(\frac{349}{792}\right)\)	\(e\left(\frac{653}{1584}\right)\)	\(e\left(\frac{551}{1584}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{911}{1584}\right)\)	\(e\left(\frac{211}{792}\right)\)	\(e\left(\frac{721}{792}\right)\)	\(e\left(\frac{1403}{1584}\right)\)	\(e\left(\frac{8}{11}\right)\)

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First 31 of 480 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	228672.bra
Modulus	$228672$
Conductor	$25408$
Order	$1584$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(228672\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(25408\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(1584\)	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 25408.id	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);