LMFDB - Dirichlet character orbit 10439.qu

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10439, base_ring=CyclotomicField(360)) M = H._module chi = DirichletCharacter(H, M([72,30,35])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(15, 10439)) 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("10439.15"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$10439$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$10439$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$360$	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:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{360})$
Fixed field:	Number field defined by a degree 360 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{10439}(15,\cdot)$	$1$	$1$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{233}{360}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{10439}(20,\cdot)$	$1$	$1$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{319}{360}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{10439}(59,\cdot)$	$1$	$1$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{43}{360}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{10439}(141,\cdot)$	$1$	$1$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{59}{360}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{10439}(279,\cdot)$	$1$	$1$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{313}{360}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{10439}(306,\cdot)$	$1$	$1$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{79}{360}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{10439}(345,\cdot)$	$1$	$1$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{283}{360}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{10439}(466,\cdot)$	$1$	$1$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{263}{360}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{10439}(522,\cdot)$	$1$	$1$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{41}{360}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{10439}(544,\cdot)$	$1$	$1$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{251}{360}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{10439}(696,\cdot)$	$1$	$1$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{127}{360}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{10439}(938,\cdot)$	$1$	$1$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{77}{360}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{10439}(1137,\cdot)$	$1$	$1$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{73}{360}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{10439}(1246,\cdot)$	$1$	$1$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{167}{360}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{10439}(1345,\cdot)$	$1$	$1$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{37}{360}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{10439}(1358,\cdot)$	$1$	$1$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{121}{360}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{10439}(1445,\cdot)$	$1$	$1$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{53}{360}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{10439}(1567,\cdot)$	$1$	$1$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{91}{360}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{10439}(1653,\cdot)$	$1$	$1$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{137}{360}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{10439}(1918,\cdot)$	$1$	$1$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{103}{360}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{10439}(2039,\cdot)$	$1$	$1$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{203}{360}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{10439}(2073,\cdot)$	$1$	$1$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{301}{360}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{10439}(2203,\cdot)$	$1$	$1$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{277}{360}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{10439}(2204,\cdot)$	$1$	$1$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{223}{360}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{10439}(2594,\cdot)$	$1$	$1$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{199}{360}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{10439}(2654,\cdot)$	$1$	$1$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{317}{360}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{10439}(2819,\cdot)$	$1$	$1$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{227}{360}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{10439}(2836,\cdot)$	$1$	$1$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{149}{360}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{10439}(3144,\cdot)$	$1$	$1$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{239}{360}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{10439}(3243,\cdot)$	$1$	$1$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{109}{360}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{10439}(3369,\cdot)$	$1$	$1$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{257}{360}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{36}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{10439}(15,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{233}{360}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{10439}(20,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{319}{360}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{10439}(59,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{43}{360}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{10439}(141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{59}{360}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{10439}(279,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{313}{360}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{10439}(306,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{79}{360}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{10439}(345,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{283}{360}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{10439}(466,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{263}{360}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{10439}(522,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{41}{360}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{10439}(544,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{251}{360}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{10439}(696,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{127}{360}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{10439}(938,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{77}{360}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{10439}(1137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{73}{360}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{10439}(1246,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{167}{360}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{10439}(1345,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{37}{360}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{10439}(1358,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{121}{360}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{10439}(1445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{53}{360}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{10439}(1567,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{91}{360}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{10439}(1653,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{137}{360}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{35}{36}\right)\)
\(\chi_{10439}(1918,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{103}{360}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{10439}(2039,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{203}{360}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{10439}(2073,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{301}{360}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{10439}(2203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{277}{360}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{10439}(2204,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{223}{360}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{10439}(2594,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{199}{360}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{10439}(2654,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{317}{360}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{35}{36}\right)\)
\(\chi_{10439}(2819,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{227}{360}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{10439}(2836,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{149}{360}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{10439}(3144,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{239}{360}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{10439}(3243,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{109}{360}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{10439}(3369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{257}{360}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{36}\right)\)

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First 31 of 96 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	10439.qu
Modulus	$10439$
Conductor	$10439$
Order	$360$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(10439\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(10439\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(360\)	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:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);