LMFDB - Dirichlet character orbit 4336.dn

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4336, base_ring=CyclotomicField(270)) M = H._module chi = DirichletCharacter(H, M([135,0,17])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(15, 4336)) 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("4336.15"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$4336$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1084$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$270$	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 1084.bf	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{135})$
Fixed field:	Number field defined by a degree 270 polynomial (not computed)

First 31 of 72 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{4336}(15,\cdot)$	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{119}{270}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{131}{270}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{77}{135}\right)$	$e\left(\frac{29}{135}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{83}{270}\right)$
$\chi_{4336}(95,\cdot)$	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{173}{270}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{77}{270}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{104}{135}\right)$	$e\left(\frac{83}{135}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{191}{270}\right)$
$\chi_{4336}(143,\cdot)$	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{121}{270}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{199}{270}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{118}{135}\right)$	$e\left(\frac{76}{135}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{157}{270}\right)$
$\chi_{4336}(159,\cdot)$	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{41}{270}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{179}{270}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{98}{135}\right)$	$e\left(\frac{86}{135}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{167}{270}\right)$
$\chi_{4336}(255,\cdot)$	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{127}{270}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{133}{270}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{106}{135}\right)$	$e\left(\frac{82}{135}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{109}{270}\right)$
$\chi_{4336}(319,\cdot)$	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{1}{270}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{169}{270}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{88}{135}\right)$	$e\left(\frac{91}{135}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{37}{270}\right)$
$\chi_{4336}(367,\cdot)$	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{269}{270}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{101}{270}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{47}{135}\right)$	$e\left(\frac{44}{135}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{233}{270}\right)$
$\chi_{4336}(479,\cdot)$	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{67}{270}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{253}{270}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{91}{135}\right)$	$e\left(\frac{22}{135}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{49}{270}\right)$
$\chi_{4336}(639,\cdot)$	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{97}{270}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{193}{270}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{31}{135}\right)$	$e\left(\frac{52}{135}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{79}{270}\right)$
$\chi_{4336}(703,\cdot)$	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{19}{270}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{241}{270}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{52}{135}\right)$	$e\left(\frac{109}{135}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{163}{270}\right)$
$\chi_{4336}(735,\cdot)$	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{217}{270}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{223}{270}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{61}{135}\right)$	$e\left(\frac{37}{135}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{199}{270}\right)$
$\chi_{4336}(751,\cdot)$	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{109}{270}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{61}{270}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{135}\right)$	$e\left(\frac{64}{135}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{253}{270}\right)$
$\chi_{4336}(799,\cdot)$	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{47}{270}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{113}{270}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{86}{135}\right)$	$e\left(\frac{92}{135}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{119}{270}\right)$
$\chi_{4336}(879,\cdot)$	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{53}{270}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{47}{270}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{74}{135}\right)$	$e\left(\frac{98}{135}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{71}{270}\right)$
$\chi_{4336}(1023,\cdot)$	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{31}{270}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{109}{270}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{28}{135}\right)$	$e\left(\frac{121}{135}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{67}{270}\right)$
$\chi_{4336}(1039,\cdot)$	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{263}{270}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{167}{270}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{59}{135}\right)$	$e\left(\frac{38}{135}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{270}\right)$
$\chi_{4336}(1135,\cdot)$	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{17}{270}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{173}{270}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{135}\right)$	$e\left(\frac{62}{135}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{89}{270}\right)$
$\chi_{4336}(1231,\cdot)$	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{107}{270}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{263}{270}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{101}{135}\right)$	$e\left(\frac{17}{135}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{179}{270}\right)$
$\chi_{4336}(1407,\cdot)$	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{71}{270}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{119}{270}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{38}{135}\right)$	$e\left(\frac{116}{135}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{197}{270}\right)$
$\chi_{4336}(1471,\cdot)$	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{221}{270}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{89}{270}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{8}{135}\right)$	$e\left(\frac{131}{135}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{77}{270}\right)$
$\chi_{4336}(1615,\cdot)$	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{181}{270}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{79}{270}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{133}{135}\right)$	$e\left(\frac{1}{135}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{217}{270}\right)$
$\chi_{4336}(1647,\cdot)$	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{193}{270}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{217}{270}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{109}{135}\right)$	$e\left(\frac{13}{135}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{121}{270}\right)$
$\chi_{4336}(1727,\cdot)$	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{251}{270}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{29}{270}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{83}{135}\right)$	$e\left(\frac{26}{135}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{107}{270}\right)$
$\chi_{4336}(1759,\cdot)$	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{247}{270}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{163}{270}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{135}\right)$	$e\left(\frac{67}{135}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{229}{270}\right)$
$\chi_{4336}(1775,\cdot)$	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{29}{270}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{41}{270}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{122}{135}\right)$	$e\left(\frac{74}{135}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{263}{270}\right)$
$\chi_{4336}(1823,\cdot)$	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{89}{270}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{191}{270}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{2}{135}\right)$	$e\left(\frac{134}{135}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{53}{270}\right)$
$\chi_{4336}(1903,\cdot)$	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{7}{270}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{103}{270}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{76}{135}\right)$	$e\left(\frac{97}{135}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{259}{270}\right)$
$\chi_{4336}(1935,\cdot)$	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{61}{270}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{49}{270}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{103}{135}\right)$	$e\left(\frac{16}{135}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{97}{270}\right)$
$\chi_{4336}(2015,\cdot)$	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{161}{270}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{209}{270}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{128}{135}\right)$	$e\left(\frac{71}{135}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{17}{270}\right)$
$\chi_{4336}(2047,\cdot)$	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{227}{270}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{270}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{131}{135}\right)$	$e\left(\frac{2}{135}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{270}\right)$
$\chi_{4336}(2079,\cdot)$	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{257}{270}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{233}{270}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{71}{135}\right)$	$e\left(\frac{32}{135}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{59}{270}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{4336}(15,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{119}{270}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{131}{270}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{77}{135}\right)\)	\(e\left(\frac{29}{135}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{83}{270}\right)\)
\(\chi_{4336}(95,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{173}{270}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{77}{270}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{104}{135}\right)\)	\(e\left(\frac{83}{135}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{191}{270}\right)\)
\(\chi_{4336}(143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{121}{270}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{199}{270}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{118}{135}\right)\)	\(e\left(\frac{76}{135}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{157}{270}\right)\)
\(\chi_{4336}(159,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{41}{270}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{179}{270}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{98}{135}\right)\)	\(e\left(\frac{86}{135}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{167}{270}\right)\)
\(\chi_{4336}(255,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{127}{270}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{133}{270}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{106}{135}\right)\)	\(e\left(\frac{82}{135}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{109}{270}\right)\)
\(\chi_{4336}(319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{1}{270}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{169}{270}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{88}{135}\right)\)	\(e\left(\frac{91}{135}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{37}{270}\right)\)
\(\chi_{4336}(367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{269}{270}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{101}{270}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{47}{135}\right)\)	\(e\left(\frac{44}{135}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{233}{270}\right)\)
\(\chi_{4336}(479,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{67}{270}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{253}{270}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{91}{135}\right)\)	\(e\left(\frac{22}{135}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{49}{270}\right)\)
\(\chi_{4336}(639,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{97}{270}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{193}{270}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{31}{135}\right)\)	\(e\left(\frac{52}{135}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{79}{270}\right)\)
\(\chi_{4336}(703,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{19}{270}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{241}{270}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{52}{135}\right)\)	\(e\left(\frac{109}{135}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{163}{270}\right)\)
\(\chi_{4336}(735,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{217}{270}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{223}{270}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{61}{135}\right)\)	\(e\left(\frac{37}{135}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{199}{270}\right)\)
\(\chi_{4336}(751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{109}{270}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{61}{270}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{135}\right)\)	\(e\left(\frac{64}{135}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{253}{270}\right)\)
\(\chi_{4336}(799,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{47}{270}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{113}{270}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{86}{135}\right)\)	\(e\left(\frac{92}{135}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{119}{270}\right)\)
\(\chi_{4336}(879,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{53}{270}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{47}{270}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{74}{135}\right)\)	\(e\left(\frac{98}{135}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{71}{270}\right)\)
\(\chi_{4336}(1023,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{31}{270}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{109}{270}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{28}{135}\right)\)	\(e\left(\frac{121}{135}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{67}{270}\right)\)
\(\chi_{4336}(1039,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{263}{270}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{167}{270}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{59}{135}\right)\)	\(e\left(\frac{38}{135}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{270}\right)\)
\(\chi_{4336}(1135,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{17}{270}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{173}{270}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{11}{135}\right)\)	\(e\left(\frac{62}{135}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{89}{270}\right)\)
\(\chi_{4336}(1231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{107}{270}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{263}{270}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{101}{135}\right)\)	\(e\left(\frac{17}{135}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{179}{270}\right)\)
\(\chi_{4336}(1407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{71}{270}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{119}{270}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{38}{135}\right)\)	\(e\left(\frac{116}{135}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{197}{270}\right)\)
\(\chi_{4336}(1471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{221}{270}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{89}{270}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{8}{135}\right)\)	\(e\left(\frac{131}{135}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{77}{270}\right)\)
\(\chi_{4336}(1615,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{181}{270}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{79}{270}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{133}{135}\right)\)	\(e\left(\frac{1}{135}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{217}{270}\right)\)
\(\chi_{4336}(1647,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{193}{270}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{217}{270}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{109}{135}\right)\)	\(e\left(\frac{13}{135}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{121}{270}\right)\)
\(\chi_{4336}(1727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{251}{270}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{29}{270}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{83}{135}\right)\)	\(e\left(\frac{26}{135}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{107}{270}\right)\)
\(\chi_{4336}(1759,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{247}{270}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{163}{270}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{135}\right)\)	\(e\left(\frac{67}{135}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{229}{270}\right)\)
\(\chi_{4336}(1775,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{29}{270}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{41}{270}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{122}{135}\right)\)	\(e\left(\frac{74}{135}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{263}{270}\right)\)
\(\chi_{4336}(1823,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{89}{270}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{191}{270}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{2}{135}\right)\)	\(e\left(\frac{134}{135}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{53}{270}\right)\)
\(\chi_{4336}(1903,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{7}{270}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{103}{270}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{76}{135}\right)\)	\(e\left(\frac{97}{135}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{259}{270}\right)\)
\(\chi_{4336}(1935,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{61}{270}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{49}{270}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{103}{135}\right)\)	\(e\left(\frac{16}{135}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{97}{270}\right)\)
\(\chi_{4336}(2015,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{161}{270}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{209}{270}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{128}{135}\right)\)	\(e\left(\frac{71}{135}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{17}{270}\right)\)
\(\chi_{4336}(2047,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{227}{270}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{270}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{131}{135}\right)\)	\(e\left(\frac{2}{135}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{29}{270}\right)\)
\(\chi_{4336}(2079,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{257}{270}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{233}{270}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{71}{135}\right)\)	\(e\left(\frac{32}{135}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{59}{270}\right)\)

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First 31 of 72 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	4336.dn
Modulus	$4336$
Conductor	$1084$
Order	$270$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(4336\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1084\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(270\)	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 1084.bf	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);