LMFDB - Dirichlet character orbit 228672.bjo

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228672, base_ring=CyclotomicField(396)) M = H._module chi = DirichletCharacter(H, M([198,297,66,376])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(47, 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("228672.47"); 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:	$57168$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$396$	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 57168.wa	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:	$\Q(\zeta_{396})$	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 396 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 120 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{228672}(47,\cdot)$	$1$	$1$	$e\left(\frac{211}{396}\right)$	$e\left(\frac{5}{99}\right)$	$e\left(\frac{137}{396}\right)$	$e\left(\frac{191}{396}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{113}{396}\right)$	$e\left(\frac{85}{198}\right)$	$e\left(\frac{13}{198}\right)$	$e\left(\frac{365}{396}\right)$	$e\left(\frac{31}{66}\right)$
$\chi_{228672}(3791,\cdot)$	$1$	$1$	$e\left(\frac{73}{396}\right)$	$e\left(\frac{89}{99}\right)$	$e\left(\frac{23}{396}\right)$	$e\left(\frac{113}{396}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{71}{396}\right)$	$e\left(\frac{127}{198}\right)$	$e\left(\frac{73}{198}\right)$	$e\left(\frac{359}{396}\right)$	$e\left(\frac{37}{66}\right)$
$\chi_{228672}(4559,\cdot)$	$1$	$1$	$e\left(\frac{221}{396}\right)$	$e\left(\frac{85}{99}\right)$	$e\left(\frac{151}{396}\right)$	$e\left(\frac{277}{396}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{139}{396}\right)$	$e\left(\frac{59}{198}\right)$	$e\left(\frac{23}{198}\right)$	$e\left(\frac{67}{396}\right)$	$e\left(\frac{65}{66}\right)$
$\chi_{228672}(6671,\cdot)$	$1$	$1$	$e\left(\frac{361}{396}\right)$	$e\left(\frac{17}{99}\right)$	$e\left(\frac{347}{396}\right)$	$e\left(\frac{293}{396}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{107}{396}\right)$	$e\left(\frac{91}{198}\right)$	$e\left(\frac{163}{198}\right)$	$e\left(\frac{251}{396}\right)$	$e\left(\frac{13}{66}\right)$
$\chi_{228672}(7439,\cdot)$	$1$	$1$	$e\left(\frac{5}{396}\right)$	$e\left(\frac{40}{99}\right)$	$e\left(\frac{7}{396}\right)$	$e\left(\frac{241}{396}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{211}{396}\right)$	$e\left(\frac{185}{198}\right)$	$e\left(\frac{5}{198}\right)$	$e\left(\frac{247}{396}\right)$	$e\left(\frac{17}{66}\right)$
$\chi_{228672}(9263,\cdot)$	$1$	$1$	$e\left(\frac{247}{396}\right)$	$e\left(\frac{95}{99}\right)$	$e\left(\frac{29}{396}\right)$	$e\left(\frac{263}{396}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{365}{396}\right)$	$e\left(\frac{31}{198}\right)$	$e\left(\frac{49}{198}\right)$	$e\left(\frac{5}{396}\right)$	$e\left(\frac{61}{66}\right)$
$\chi_{228672}(10319,\cdot)$	$1$	$1$	$e\left(\frac{149}{396}\right)$	$e\left(\frac{4}{99}\right)$	$e\left(\frac{367}{396}\right)$	$e\left(\frac{133}{396}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{31}{396}\right)$	$e\left(\frac{167}{198}\right)$	$e\left(\frac{149}{198}\right)$	$e\left(\frac{391}{396}\right)$	$e\left(\frac{5}{66}\right)$
$\chi_{228672}(10895,\cdot)$	$1$	$1$	$e\left(\frac{89}{396}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{283}{396}\right)$	$e\left(\frac{13}{396}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{271}{396}\right)$	$e\left(\frac{125}{198}\right)$	$e\left(\frac{89}{198}\right)$	$e\left(\frac{199}{396}\right)$	$e\left(\frac{65}{66}\right)$
$\chi_{228672}(11183,\cdot)$	$1$	$1$	$e\left(\frac{335}{396}\right)$	$e\left(\frac{7}{99}\right)$	$e\left(\frac{73}{396}\right)$	$e\left(\frac{307}{396}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{277}{396}\right)$	$e\left(\frac{119}{198}\right)$	$e\left(\frac{137}{198}\right)$	$e\left(\frac{313}{396}\right)$	$e\left(\frac{17}{66}\right)$
$\chi_{228672}(15215,\cdot)$	$1$	$1$	$e\left(\frac{227}{396}\right)$	$e\left(\frac{34}{99}\right)$	$e\left(\frac{1}{396}\right)$	$e\left(\frac{91}{396}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{313}{396}\right)$	$e\left(\frac{83}{198}\right)$	$e\left(\frac{29}{198}\right)$	$e\left(\frac{205}{396}\right)$	$e\left(\frac{59}{66}\right)$
$\chi_{228672}(16367,\cdot)$	$1$	$1$	$e\left(\frac{179}{396}\right)$	$e\left(\frac{46}{99}\right)$	$e\left(\frac{13}{396}\right)$	$e\left(\frac{391}{396}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{109}{396}\right)$	$e\left(\frac{89}{198}\right)$	$e\left(\frac{179}{198}\right)$	$e\left(\frac{289}{396}\right)$	$e\left(\frac{41}{66}\right)$
$\chi_{228672}(18671,\cdot)$	$1$	$1$	$e\left(\frac{239}{396}\right)$	$e\left(\frac{31}{99}\right)$	$e\left(\frac{97}{396}\right)$	$e\left(\frac{115}{396}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{265}{396}\right)$	$e\left(\frac{131}{198}\right)$	$e\left(\frac{41}{198}\right)$	$e\left(\frac{85}{396}\right)$	$e\left(\frac{47}{66}\right)$
$\chi_{228672}(19631,\cdot)$	$1$	$1$	$e\left(\frac{43}{396}\right)$	$e\left(\frac{47}{99}\right)$	$e\left(\frac{377}{396}\right)$	$e\left(\frac{251}{396}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{389}{396}\right)$	$e\left(\frac{7}{198}\right)$	$e\left(\frac{43}{198}\right)$	$e\left(\frac{65}{396}\right)$	$e\left(\frac{1}{66}\right)$
$\chi_{228672}(19919,\cdot)$	$1$	$1$	$e\left(\frac{25}{396}\right)$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{35}{396}\right)$	$e\left(\frac{17}{396}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{263}{396}\right)$	$e\left(\frac{133}{198}\right)$	$e\left(\frac{25}{198}\right)$	$e\left(\frac{47}{396}\right)$	$e\left(\frac{19}{66}\right)$
$\chi_{228672}(20207,\cdot)$	$1$	$1$	$e\left(\frac{367}{396}\right)$	$e\left(\frac{65}{99}\right)$	$e\left(\frac{197}{396}\right)$	$e\left(\frac{107}{396}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{281}{396}\right)$	$e\left(\frac{115}{198}\right)$	$e\left(\frac{169}{198}\right)$	$e\left(\frac{389}{396}\right)$	$e\left(\frac{7}{66}\right)$
$\chi_{228672}(21647,\cdot)$	$1$	$1$	$e\left(\frac{301}{396}\right)$	$e\left(\frac{32}{99}\right)$	$e\left(\frac{263}{396}\right)$	$e\left(\frac{173}{396}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{347}{396}\right)$	$e\left(\frac{49}{198}\right)$	$e\left(\frac{103}{198}\right)$	$e\left(\frac{59}{396}\right)$	$e\left(\frac{7}{66}\right)$
$\chi_{228672}(22511,\cdot)$	$1$	$1$	$e\left(\frac{127}{396}\right)$	$e\left(\frac{26}{99}\right)$	$e\left(\frac{257}{396}\right)$	$e\left(\frac{23}{396}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{53}{396}\right)$	$e\left(\frac{145}{198}\right)$	$e\left(\frac{127}{198}\right)$	$e\left(\frac{17}{396}\right)$	$e\left(\frac{49}{66}\right)$
$\chi_{228672}(24527,\cdot)$	$1$	$1$	$e\left(\frac{205}{396}\right)$	$e\left(\frac{56}{99}\right)$	$e\left(\frac{287}{396}\right)$	$e\left(\frac{377}{396}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{335}{396}\right)$	$e\left(\frac{61}{198}\right)$	$e\left(\frac{7}{198}\right)$	$e\left(\frac{227}{396}\right)$	$e\left(\frac{37}{66}\right)$
$\chi_{228672}(24719,\cdot)$	$1$	$1$	$e\left(\frac{281}{396}\right)$	$e\left(\frac{70}{99}\right)$	$e\left(\frac{235}{396}\right)$	$e\left(\frac{1}{396}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{295}{396}\right)$	$e\left(\frac{101}{198}\right)$	$e\left(\frac{83}{198}\right)$	$e\left(\frac{259}{396}\right)$	$e\left(\frac{5}{66}\right)$
$\chi_{228672}(29135,\cdot)$	$1$	$1$	$e\left(\frac{349}{396}\right)$	$e\left(\frac{20}{99}\right)$	$e\left(\frac{251}{396}\right)$	$e\left(\frac{269}{396}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{155}{396}\right)$	$e\left(\frac{43}{198}\right)$	$e\left(\frac{151}{198}\right)$	$e\left(\frac{371}{396}\right)$	$e\left(\frac{25}{66}\right)$
$\chi_{228672}(30191,\cdot)$	$1$	$1$	$e\left(\frac{95}{396}\right)$	$e\left(\frac{67}{99}\right)$	$e\left(\frac{133}{396}\right)$	$e\left(\frac{223}{396}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{49}{396}\right)$	$e\left(\frac{149}{198}\right)$	$e\left(\frac{95}{198}\right)$	$e\left(\frac{337}{396}\right)$	$e\left(\frac{59}{66}\right)$
$\chi_{228672}(31727,\cdot)$	$1$	$1$	$e\left(\frac{355}{396}\right)$	$e\left(\frac{68}{99}\right)$	$e\left(\frac{101}{396}\right)$	$e\left(\frac{83}{396}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{329}{396}\right)$	$e\left(\frac{67}{198}\right)$	$e\left(\frac{157}{198}\right)$	$e\left(\frac{113}{396}\right)$	$e\left(\frac{19}{66}\right)$
$\chi_{228672}(33359,\cdot)$	$1$	$1$	$e\left(\frac{305}{396}\right)$	$e\left(\frac{64}{99}\right)$	$e\left(\frac{31}{396}\right)$	$e\left(\frac{49}{396}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{199}{396}\right)$	$e\left(\frac{197}{198}\right)$	$e\left(\frac{107}{198}\right)$	$e\left(\frac{19}{396}\right)$	$e\left(\frac{47}{66}\right)$
$\chi_{228672}(34223,\cdot)$	$1$	$1$	$e\left(\frac{299}{396}\right)$	$e\left(\frac{16}{99}\right)$	$e\left(\frac{181}{396}\right)$	$e\left(\frac{235}{396}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{25}{396}\right)$	$e\left(\frac{173}{198}\right)$	$e\left(\frac{101}{198}\right)$	$e\left(\frac{277}{396}\right)$	$e\left(\frac{53}{66}\right)$
$\chi_{228672}(37391,\cdot)$	$1$	$1$	$e\left(\frac{389}{396}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{307}{396}\right)$	$e\left(\frac{217}{396}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{259}{396}\right)$	$e\left(\frac{137}{198}\right)$	$e\left(\frac{191}{198}\right)$	$e\left(\frac{367}{396}\right)$	$e\left(\frac{29}{66}\right)$
$\chi_{228672}(38063,\cdot)$	$1$	$1$	$e\left(\frac{295}{396}\right)$	$e\left(\frac{83}{99}\right)$	$e\left(\frac{17}{396}\right)$	$e\left(\frac{359}{396}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{173}{396}\right)$	$e\left(\frac{25}{198}\right)$	$e\left(\frac{97}{198}\right)$	$e\left(\frac{317}{396}\right)$	$e\left(\frac{13}{66}\right)$
$\chi_{228672}(40847,\cdot)$	$1$	$1$	$e\left(\frac{197}{396}\right)$	$e\left(\frac{91}{99}\right)$	$e\left(\frac{355}{396}\right)$	$e\left(\frac{229}{396}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{235}{396}\right)$	$e\left(\frac{161}{198}\right)$	$e\left(\frac{197}{198}\right)$	$e\left(\frac{307}{396}\right)$	$e\left(\frac{23}{66}\right)$
$\chi_{228672}(41231,\cdot)$	$1$	$1$	$e\left(\frac{145}{396}\right)$	$e\left(\frac{71}{99}\right)$	$e\left(\frac{203}{396}\right)$	$e\left(\frac{257}{396}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{179}{396}\right)$	$e\left(\frac{19}{198}\right)$	$e\left(\frac{145}{198}\right)$	$e\left(\frac{35}{396}\right)$	$e\left(\frac{31}{66}\right)$
$\chi_{228672}(41711,\cdot)$	$1$	$1$	$e\left(\frac{311}{396}\right)$	$e\left(\frac{13}{99}\right)$	$e\left(\frac{277}{396}\right)$	$e\left(\frac{259}{396}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{373}{396}\right)$	$e\left(\frac{23}{198}\right)$	$e\left(\frac{113}{198}\right)$	$e\left(\frac{157}{396}\right)$	$e\left(\frac{41}{66}\right)$
$\chi_{228672}(41807,\cdot)$	$1$	$1$	$e\left(\frac{373}{396}\right)$	$e\left(\frac{14}{99}\right)$	$e\left(\frac{47}{396}\right)$	$e\left(\frac{317}{396}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{59}{396}\right)$	$e\left(\frac{139}{198}\right)$	$e\left(\frac{175}{198}\right)$	$e\left(\frac{131}{396}\right)$	$e\left(\frac{1}{66}\right)$
$\chi_{228672}(46127,\cdot)$	$1$	$1$	$e\left(\frac{19}{396}\right)$	$e\left(\frac{53}{99}\right)$	$e\left(\frac{185}{396}\right)$	$e\left(\frac{203}{396}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{89}{396}\right)$	$e\left(\frac{109}{198}\right)$	$e\left(\frac{19}{198}\right)$	$e\left(\frac{305}{396}\right)$	$e\left(\frac{25}{66}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Character	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{228672}(47,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{211}{396}\right)\)	\(e\left(\frac{5}{99}\right)\)	\(e\left(\frac{137}{396}\right)\)	\(e\left(\frac{191}{396}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{113}{396}\right)\)	\(e\left(\frac{85}{198}\right)\)	\(e\left(\frac{13}{198}\right)\)	\(e\left(\frac{365}{396}\right)\)	\(e\left(\frac{31}{66}\right)\)
\(\chi_{228672}(3791,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{396}\right)\)	\(e\left(\frac{89}{99}\right)\)	\(e\left(\frac{23}{396}\right)\)	\(e\left(\frac{113}{396}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{71}{396}\right)\)	\(e\left(\frac{127}{198}\right)\)	\(e\left(\frac{73}{198}\right)\)	\(e\left(\frac{359}{396}\right)\)	\(e\left(\frac{37}{66}\right)\)
\(\chi_{228672}(4559,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{221}{396}\right)\)	\(e\left(\frac{85}{99}\right)\)	\(e\left(\frac{151}{396}\right)\)	\(e\left(\frac{277}{396}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{139}{396}\right)\)	\(e\left(\frac{59}{198}\right)\)	\(e\left(\frac{23}{198}\right)\)	\(e\left(\frac{67}{396}\right)\)	\(e\left(\frac{65}{66}\right)\)
\(\chi_{228672}(6671,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{361}{396}\right)\)	\(e\left(\frac{17}{99}\right)\)	\(e\left(\frac{347}{396}\right)\)	\(e\left(\frac{293}{396}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{107}{396}\right)\)	\(e\left(\frac{91}{198}\right)\)	\(e\left(\frac{163}{198}\right)\)	\(e\left(\frac{251}{396}\right)\)	\(e\left(\frac{13}{66}\right)\)
\(\chi_{228672}(7439,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{396}\right)\)	\(e\left(\frac{40}{99}\right)\)	\(e\left(\frac{7}{396}\right)\)	\(e\left(\frac{241}{396}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{211}{396}\right)\)	\(e\left(\frac{185}{198}\right)\)	\(e\left(\frac{5}{198}\right)\)	\(e\left(\frac{247}{396}\right)\)	\(e\left(\frac{17}{66}\right)\)
\(\chi_{228672}(9263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{247}{396}\right)\)	\(e\left(\frac{95}{99}\right)\)	\(e\left(\frac{29}{396}\right)\)	\(e\left(\frac{263}{396}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{365}{396}\right)\)	\(e\left(\frac{31}{198}\right)\)	\(e\left(\frac{49}{198}\right)\)	\(e\left(\frac{5}{396}\right)\)	\(e\left(\frac{61}{66}\right)\)
\(\chi_{228672}(10319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{396}\right)\)	\(e\left(\frac{4}{99}\right)\)	\(e\left(\frac{367}{396}\right)\)	\(e\left(\frac{133}{396}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{31}{396}\right)\)	\(e\left(\frac{167}{198}\right)\)	\(e\left(\frac{149}{198}\right)\)	\(e\left(\frac{391}{396}\right)\)	\(e\left(\frac{5}{66}\right)\)
\(\chi_{228672}(10895,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{396}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{283}{396}\right)\)	\(e\left(\frac{13}{396}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{271}{396}\right)\)	\(e\left(\frac{125}{198}\right)\)	\(e\left(\frac{89}{198}\right)\)	\(e\left(\frac{199}{396}\right)\)	\(e\left(\frac{65}{66}\right)\)
\(\chi_{228672}(11183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{335}{396}\right)\)	\(e\left(\frac{7}{99}\right)\)	\(e\left(\frac{73}{396}\right)\)	\(e\left(\frac{307}{396}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{277}{396}\right)\)	\(e\left(\frac{119}{198}\right)\)	\(e\left(\frac{137}{198}\right)\)	\(e\left(\frac{313}{396}\right)\)	\(e\left(\frac{17}{66}\right)\)
\(\chi_{228672}(15215,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{396}\right)\)	\(e\left(\frac{34}{99}\right)\)	\(e\left(\frac{1}{396}\right)\)	\(e\left(\frac{91}{396}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{313}{396}\right)\)	\(e\left(\frac{83}{198}\right)\)	\(e\left(\frac{29}{198}\right)\)	\(e\left(\frac{205}{396}\right)\)	\(e\left(\frac{59}{66}\right)\)
\(\chi_{228672}(16367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{396}\right)\)	\(e\left(\frac{46}{99}\right)\)	\(e\left(\frac{13}{396}\right)\)	\(e\left(\frac{391}{396}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{109}{396}\right)\)	\(e\left(\frac{89}{198}\right)\)	\(e\left(\frac{179}{198}\right)\)	\(e\left(\frac{289}{396}\right)\)	\(e\left(\frac{41}{66}\right)\)
\(\chi_{228672}(18671,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{396}\right)\)	\(e\left(\frac{31}{99}\right)\)	\(e\left(\frac{97}{396}\right)\)	\(e\left(\frac{115}{396}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{265}{396}\right)\)	\(e\left(\frac{131}{198}\right)\)	\(e\left(\frac{41}{198}\right)\)	\(e\left(\frac{85}{396}\right)\)	\(e\left(\frac{47}{66}\right)\)
\(\chi_{228672}(19631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{396}\right)\)	\(e\left(\frac{47}{99}\right)\)	\(e\left(\frac{377}{396}\right)\)	\(e\left(\frac{251}{396}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{389}{396}\right)\)	\(e\left(\frac{7}{198}\right)\)	\(e\left(\frac{43}{198}\right)\)	\(e\left(\frac{65}{396}\right)\)	\(e\left(\frac{1}{66}\right)\)
\(\chi_{228672}(19919,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{396}\right)\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{35}{396}\right)\)	\(e\left(\frac{17}{396}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{263}{396}\right)\)	\(e\left(\frac{133}{198}\right)\)	\(e\left(\frac{25}{198}\right)\)	\(e\left(\frac{47}{396}\right)\)	\(e\left(\frac{19}{66}\right)\)
\(\chi_{228672}(20207,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{367}{396}\right)\)	\(e\left(\frac{65}{99}\right)\)	\(e\left(\frac{197}{396}\right)\)	\(e\left(\frac{107}{396}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{281}{396}\right)\)	\(e\left(\frac{115}{198}\right)\)	\(e\left(\frac{169}{198}\right)\)	\(e\left(\frac{389}{396}\right)\)	\(e\left(\frac{7}{66}\right)\)
\(\chi_{228672}(21647,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{301}{396}\right)\)	\(e\left(\frac{32}{99}\right)\)	\(e\left(\frac{263}{396}\right)\)	\(e\left(\frac{173}{396}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{347}{396}\right)\)	\(e\left(\frac{49}{198}\right)\)	\(e\left(\frac{103}{198}\right)\)	\(e\left(\frac{59}{396}\right)\)	\(e\left(\frac{7}{66}\right)\)
\(\chi_{228672}(22511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{396}\right)\)	\(e\left(\frac{26}{99}\right)\)	\(e\left(\frac{257}{396}\right)\)	\(e\left(\frac{23}{396}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{53}{396}\right)\)	\(e\left(\frac{145}{198}\right)\)	\(e\left(\frac{127}{198}\right)\)	\(e\left(\frac{17}{396}\right)\)	\(e\left(\frac{49}{66}\right)\)
\(\chi_{228672}(24527,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{205}{396}\right)\)	\(e\left(\frac{56}{99}\right)\)	\(e\left(\frac{287}{396}\right)\)	\(e\left(\frac{377}{396}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{335}{396}\right)\)	\(e\left(\frac{61}{198}\right)\)	\(e\left(\frac{7}{198}\right)\)	\(e\left(\frac{227}{396}\right)\)	\(e\left(\frac{37}{66}\right)\)
\(\chi_{228672}(24719,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{281}{396}\right)\)	\(e\left(\frac{70}{99}\right)\)	\(e\left(\frac{235}{396}\right)\)	\(e\left(\frac{1}{396}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{295}{396}\right)\)	\(e\left(\frac{101}{198}\right)\)	\(e\left(\frac{83}{198}\right)\)	\(e\left(\frac{259}{396}\right)\)	\(e\left(\frac{5}{66}\right)\)
\(\chi_{228672}(29135,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{349}{396}\right)\)	\(e\left(\frac{20}{99}\right)\)	\(e\left(\frac{251}{396}\right)\)	\(e\left(\frac{269}{396}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{155}{396}\right)\)	\(e\left(\frac{43}{198}\right)\)	\(e\left(\frac{151}{198}\right)\)	\(e\left(\frac{371}{396}\right)\)	\(e\left(\frac{25}{66}\right)\)
\(\chi_{228672}(30191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{396}\right)\)	\(e\left(\frac{67}{99}\right)\)	\(e\left(\frac{133}{396}\right)\)	\(e\left(\frac{223}{396}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{49}{396}\right)\)	\(e\left(\frac{149}{198}\right)\)	\(e\left(\frac{95}{198}\right)\)	\(e\left(\frac{337}{396}\right)\)	\(e\left(\frac{59}{66}\right)\)
\(\chi_{228672}(31727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{355}{396}\right)\)	\(e\left(\frac{68}{99}\right)\)	\(e\left(\frac{101}{396}\right)\)	\(e\left(\frac{83}{396}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{329}{396}\right)\)	\(e\left(\frac{67}{198}\right)\)	\(e\left(\frac{157}{198}\right)\)	\(e\left(\frac{113}{396}\right)\)	\(e\left(\frac{19}{66}\right)\)
\(\chi_{228672}(33359,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{305}{396}\right)\)	\(e\left(\frac{64}{99}\right)\)	\(e\left(\frac{31}{396}\right)\)	\(e\left(\frac{49}{396}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{199}{396}\right)\)	\(e\left(\frac{197}{198}\right)\)	\(e\left(\frac{107}{198}\right)\)	\(e\left(\frac{19}{396}\right)\)	\(e\left(\frac{47}{66}\right)\)
\(\chi_{228672}(34223,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{299}{396}\right)\)	\(e\left(\frac{16}{99}\right)\)	\(e\left(\frac{181}{396}\right)\)	\(e\left(\frac{235}{396}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{25}{396}\right)\)	\(e\left(\frac{173}{198}\right)\)	\(e\left(\frac{101}{198}\right)\)	\(e\left(\frac{277}{396}\right)\)	\(e\left(\frac{53}{66}\right)\)
\(\chi_{228672}(37391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{389}{396}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{307}{396}\right)\)	\(e\left(\frac{217}{396}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{259}{396}\right)\)	\(e\left(\frac{137}{198}\right)\)	\(e\left(\frac{191}{198}\right)\)	\(e\left(\frac{367}{396}\right)\)	\(e\left(\frac{29}{66}\right)\)
\(\chi_{228672}(38063,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{295}{396}\right)\)	\(e\left(\frac{83}{99}\right)\)	\(e\left(\frac{17}{396}\right)\)	\(e\left(\frac{359}{396}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{173}{396}\right)\)	\(e\left(\frac{25}{198}\right)\)	\(e\left(\frac{97}{198}\right)\)	\(e\left(\frac{317}{396}\right)\)	\(e\left(\frac{13}{66}\right)\)
\(\chi_{228672}(40847,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{396}\right)\)	\(e\left(\frac{91}{99}\right)\)	\(e\left(\frac{355}{396}\right)\)	\(e\left(\frac{229}{396}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{235}{396}\right)\)	\(e\left(\frac{161}{198}\right)\)	\(e\left(\frac{197}{198}\right)\)	\(e\left(\frac{307}{396}\right)\)	\(e\left(\frac{23}{66}\right)\)
\(\chi_{228672}(41231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{396}\right)\)	\(e\left(\frac{71}{99}\right)\)	\(e\left(\frac{203}{396}\right)\)	\(e\left(\frac{257}{396}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{179}{396}\right)\)	\(e\left(\frac{19}{198}\right)\)	\(e\left(\frac{145}{198}\right)\)	\(e\left(\frac{35}{396}\right)\)	\(e\left(\frac{31}{66}\right)\)
\(\chi_{228672}(41711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{311}{396}\right)\)	\(e\left(\frac{13}{99}\right)\)	\(e\left(\frac{277}{396}\right)\)	\(e\left(\frac{259}{396}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{373}{396}\right)\)	\(e\left(\frac{23}{198}\right)\)	\(e\left(\frac{113}{198}\right)\)	\(e\left(\frac{157}{396}\right)\)	\(e\left(\frac{41}{66}\right)\)
\(\chi_{228672}(41807,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{373}{396}\right)\)	\(e\left(\frac{14}{99}\right)\)	\(e\left(\frac{47}{396}\right)\)	\(e\left(\frac{317}{396}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{59}{396}\right)\)	\(e\left(\frac{139}{198}\right)\)	\(e\left(\frac{175}{198}\right)\)	\(e\left(\frac{131}{396}\right)\)	\(e\left(\frac{1}{66}\right)\)
\(\chi_{228672}(46127,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{396}\right)\)	\(e\left(\frac{53}{99}\right)\)	\(e\left(\frac{185}{396}\right)\)	\(e\left(\frac{203}{396}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{89}{396}\right)\)	\(e\left(\frac{109}{198}\right)\)	\(e\left(\frac{19}{198}\right)\)	\(e\left(\frac{305}{396}\right)\)	\(e\left(\frac{25}{66}\right)\)

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First 31 of 120 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.bjo
Modulus	$228672$
Conductor	$57168$
Order	$396$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(228672\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(57168\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(396\)	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 57168.wa	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);