LMFDB - Dirichlet character orbit 34727.oz

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(34727, base_ring=CyclotomicField(440)) M = H._module chi = DirichletCharacter(H, M([220,356,11])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(6, 34727)) 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("34727.6"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$34727$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$34727$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$440$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{440})$
Fixed field:	Number field defined by a degree 440 polynomial (not computed)

First 31 of 160 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$12$	$13$
$\chi_{34727}(6,\cdot)$	$-1$	$1$	$e\left(\frac{101}{220}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{437}{440}\right)$	$e\left(\frac{437}{440}\right)$
$\chi_{34727}(216,\cdot)$	$-1$	$1$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{431}{440}\right)$	$e\left(\frac{431}{440}\right)$
$\chi_{34727}(272,\cdot)$	$-1$	$1$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{149}{440}\right)$	$e\left(\frac{149}{440}\right)$
$\chi_{34727}(321,\cdot)$	$-1$	$1$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{383}{440}\right)$	$e\left(\frac{383}{440}\right)$
$\chi_{34727}(552,\cdot)$	$-1$	$1$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{133}{440}\right)$	$e\left(\frac{133}{440}\right)$
$\chi_{34727}(755,\cdot)$	$-1$	$1$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{301}{440}\right)$	$e\left(\frac{301}{440}\right)$
$\chi_{34727}(930,\cdot)$	$-1$	$1$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{287}{440}\right)$	$e\left(\frac{287}{440}\right)$
$\chi_{34727}(1119,\cdot)$	$-1$	$1$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{39}{440}\right)$	$e\left(\frac{39}{440}\right)$
$\chi_{34727}(1161,\cdot)$	$-1$	$1$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{387}{440}\right)$	$e\left(\frac{387}{440}\right)$
$\chi_{34727}(1910,\cdot)$	$-1$	$1$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{321}{440}\right)$	$e\left(\frac{321}{440}\right)$
$\chi_{34727}(2085,\cdot)$	$-1$	$1$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{17}{440}\right)$	$e\left(\frac{17}{440}\right)$
$\chi_{34727}(2120,\cdot)$	$-1$	$1$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{101}{220}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{419}{440}\right)$	$e\left(\frac{419}{440}\right)$
$\chi_{34727}(2400,\cdot)$	$-1$	$1$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{113}{440}\right)$	$e\left(\frac{113}{440}\right)$
$\chi_{34727}(2449,\cdot)$	$-1$	$1$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{411}{440}\right)$	$e\left(\frac{411}{440}\right)$
$\chi_{34727}(2631,\cdot)$	$-1$	$1$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{83}{440}\right)$	$e\left(\frac{83}{440}\right)$
$\chi_{34727}(2967,\cdot)$	$-1$	$1$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{89}{440}\right)$	$e\left(\frac{89}{440}\right)$
$\chi_{34727}(3163,\cdot)$	$-1$	$1$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{117}{440}\right)$	$e\left(\frac{117}{440}\right)$
$\chi_{34727}(3373,\cdot)$	$-1$	$1$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{31}{440}\right)$	$e\left(\frac{31}{440}\right)$
$\chi_{34727}(3429,\cdot)$	$-1$	$1$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{349}{440}\right)$	$e\left(\frac{349}{440}\right)$
$\chi_{34727}(3478,\cdot)$	$-1$	$1$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{303}{440}\right)$	$e\left(\frac{303}{440}\right)$
$\chi_{34727}(3709,\cdot)$	$-1$	$1$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{53}{440}\right)$	$e\left(\frac{53}{440}\right)$
$\chi_{34727}(4276,\cdot)$	$-1$	$1$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{181}{220}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{239}{440}\right)$	$e\left(\frac{239}{440}\right)$
$\chi_{34727}(4318,\cdot)$	$-1$	$1$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{67}{440}\right)$	$e\left(\frac{67}{440}\right)$
$\chi_{34727}(5067,\cdot)$	$-1$	$1$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{361}{440}\right)$	$e\left(\frac{361}{440}\right)$
$\chi_{34727}(5242,\cdot)$	$-1$	$1$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{137}{440}\right)$	$e\left(\frac{137}{440}\right)$
$\chi_{34727}(5277,\cdot)$	$-1$	$1$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{181}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{179}{440}\right)$	$e\left(\frac{179}{440}\right)$
$\chi_{34727}(5788,\cdot)$	$-1$	$1$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{3}{440}\right)$	$e\left(\frac{3}{440}\right)$
$\chi_{34727}(6124,\cdot)$	$-1$	$1$	$e\left(\frac{97}{220}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{289}{440}\right)$	$e\left(\frac{289}{440}\right)$
$\chi_{34727}(6320,\cdot)$	$-1$	$1$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{237}{440}\right)$	$e\left(\frac{237}{440}\right)$
$\chi_{34727}(6530,\cdot)$	$-1$	$1$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{71}{440}\right)$	$e\left(\frac{71}{440}\right)$
$\chi_{34727}(6586,\cdot)$	$-1$	$1$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{109}{440}\right)$	$e\left(\frac{109}{440}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(12\)	\(13\)
\(\chi_{34727}(6,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{220}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{437}{440}\right)\)	\(e\left(\frac{437}{440}\right)\)
\(\chi_{34727}(216,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{431}{440}\right)\)	\(e\left(\frac{431}{440}\right)\)
\(\chi_{34727}(272,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{111}{220}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{149}{440}\right)\)	\(e\left(\frac{149}{440}\right)\)
\(\chi_{34727}(321,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{383}{440}\right)\)	\(e\left(\frac{383}{440}\right)\)
\(\chi_{34727}(552,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{133}{440}\right)\)	\(e\left(\frac{133}{440}\right)\)
\(\chi_{34727}(755,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{301}{440}\right)\)	\(e\left(\frac{301}{440}\right)\)
\(\chi_{34727}(930,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{287}{440}\right)\)	\(e\left(\frac{287}{440}\right)\)
\(\chi_{34727}(1119,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{39}{440}\right)\)	\(e\left(\frac{39}{440}\right)\)
\(\chi_{34727}(1161,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{387}{440}\right)\)	\(e\left(\frac{387}{440}\right)\)
\(\chi_{34727}(1910,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{321}{440}\right)\)	\(e\left(\frac{321}{440}\right)\)
\(\chi_{34727}(2085,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{17}{440}\right)\)	\(e\left(\frac{17}{440}\right)\)
\(\chi_{34727}(2120,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{101}{220}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{419}{440}\right)\)	\(e\left(\frac{419}{440}\right)\)
\(\chi_{34727}(2400,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{113}{440}\right)\)	\(e\left(\frac{113}{440}\right)\)
\(\chi_{34727}(2449,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{411}{440}\right)\)	\(e\left(\frac{411}{440}\right)\)
\(\chi_{34727}(2631,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{83}{440}\right)\)	\(e\left(\frac{83}{440}\right)\)
\(\chi_{34727}(2967,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{89}{440}\right)\)	\(e\left(\frac{89}{440}\right)\)
\(\chi_{34727}(3163,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{117}{440}\right)\)	\(e\left(\frac{117}{440}\right)\)
\(\chi_{34727}(3373,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{31}{440}\right)\)	\(e\left(\frac{31}{440}\right)\)
\(\chi_{34727}(3429,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{349}{440}\right)\)	\(e\left(\frac{349}{440}\right)\)
\(\chi_{34727}(3478,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{303}{440}\right)\)	\(e\left(\frac{303}{440}\right)\)
\(\chi_{34727}(3709,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{53}{440}\right)\)	\(e\left(\frac{53}{440}\right)\)
\(\chi_{34727}(4276,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{181}{220}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{239}{440}\right)\)	\(e\left(\frac{239}{440}\right)\)
\(\chi_{34727}(4318,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{67}{440}\right)\)	\(e\left(\frac{67}{440}\right)\)
\(\chi_{34727}(5067,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{361}{440}\right)\)	\(e\left(\frac{361}{440}\right)\)
\(\chi_{34727}(5242,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{137}{440}\right)\)	\(e\left(\frac{137}{440}\right)\)
\(\chi_{34727}(5277,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{181}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{179}{440}\right)\)	\(e\left(\frac{179}{440}\right)\)
\(\chi_{34727}(5788,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{3}{440}\right)\)	\(e\left(\frac{3}{440}\right)\)
\(\chi_{34727}(6124,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{220}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{289}{440}\right)\)	\(e\left(\frac{289}{440}\right)\)
\(\chi_{34727}(6320,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{237}{440}\right)\)	\(e\left(\frac{237}{440}\right)\)
\(\chi_{34727}(6530,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{89}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{71}{440}\right)\)	\(e\left(\frac{71}{440}\right)\)
\(\chi_{34727}(6586,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{109}{440}\right)\)	\(e\left(\frac{109}{440}\right)\)

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Basic properties

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First 31 of 160 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	34727.oz
Modulus	$34727$
Conductor	$34727$
Order	$440$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(34727\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(34727\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(440\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);