LMFDB - Dirichlet character orbit 10400.pm

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10400, base_ring=CyclotomicField(120)) M = H._module chi = DirichletCharacter(H, M([0,15,102,10])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(197, 10400)) 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("10400.197"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$10400$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$10400$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$120$	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:	$\Q(\zeta_{120})$	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 120 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{10400}(197,\cdot)$	$1$	$1$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{49}{120}\right)$
$\chi_{10400}(813,\cdot)$	$1$	$1$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{23}{120}\right)$
$\chi_{10400}(973,\cdot)$	$1$	$1$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{120}\right)$
$\chi_{10400}(1237,\cdot)$	$1$	$1$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{13}{120}\right)$
$\chi_{10400}(1397,\cdot)$	$1$	$1$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{29}{120}\right)$
$\chi_{10400}(1853,\cdot)$	$1$	$1$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{59}{120}\right)$
$\chi_{10400}(2013,\cdot)$	$1$	$1$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{43}{120}\right)$
$\chi_{10400}(2277,\cdot)$	$1$	$1$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{97}{120}\right)$
$\chi_{10400}(2437,\cdot)$	$1$	$1$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{113}{120}\right)$
$\chi_{10400}(3053,\cdot)$	$1$	$1$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{79}{120}\right)$
$\chi_{10400}(3317,\cdot)$	$1$	$1$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{61}{120}\right)$
$\chi_{10400}(3477,\cdot)$	$1$	$1$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{77}{120}\right)$
$\chi_{10400}(3933,\cdot)$	$1$	$1$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{11}{120}\right)$
$\chi_{10400}(4517,\cdot)$	$1$	$1$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{41}{120}\right)$
$\chi_{10400}(4973,\cdot)$	$1$	$1$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{47}{120}\right)$
$\chi_{10400}(5133,\cdot)$	$1$	$1$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{31}{120}\right)$
$\chi_{10400}(5397,\cdot)$	$1$	$1$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{109}{120}\right)$
$\chi_{10400}(6013,\cdot)$	$1$	$1$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{83}{120}\right)$
$\chi_{10400}(6173,\cdot)$	$1$	$1$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{67}{120}\right)$
$\chi_{10400}(6437,\cdot)$	$1$	$1$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{73}{120}\right)$
$\chi_{10400}(6597,\cdot)$	$1$	$1$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{89}{120}\right)$
$\chi_{10400}(7053,\cdot)$	$1$	$1$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{119}{120}\right)$
$\chi_{10400}(7213,\cdot)$	$1$	$1$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{103}{120}\right)$
$\chi_{10400}(7477,\cdot)$	$1$	$1$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{37}{120}\right)$
$\chi_{10400}(7637,\cdot)$	$1$	$1$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{53}{120}\right)$
$\chi_{10400}(8253,\cdot)$	$1$	$1$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{19}{120}\right)$
$\chi_{10400}(8517,\cdot)$	$1$	$1$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{120}\right)$
$\chi_{10400}(8677,\cdot)$	$1$	$1$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{17}{120}\right)$
$\chi_{10400}(9133,\cdot)$	$1$	$1$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{71}{120}\right)$
$\chi_{10400}(9717,\cdot)$	$1$	$1$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{101}{120}\right)$
$\chi_{10400}(10173,\cdot)$	$1$	$1$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{107}{120}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{10400}(197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{49}{120}\right)\)
\(\chi_{10400}(813,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{23}{120}\right)\)
\(\chi_{10400}(973,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{120}\right)\)
\(\chi_{10400}(1237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{13}{120}\right)\)
\(\chi_{10400}(1397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{29}{120}\right)\)
\(\chi_{10400}(1853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{59}{120}\right)\)
\(\chi_{10400}(2013,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{43}{120}\right)\)
\(\chi_{10400}(2277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{97}{120}\right)\)
\(\chi_{10400}(2437,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{113}{120}\right)\)
\(\chi_{10400}(3053,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{79}{120}\right)\)
\(\chi_{10400}(3317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{61}{120}\right)\)
\(\chi_{10400}(3477,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{77}{120}\right)\)
\(\chi_{10400}(3933,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{11}{120}\right)\)
\(\chi_{10400}(4517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{41}{120}\right)\)
\(\chi_{10400}(4973,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{47}{120}\right)\)
\(\chi_{10400}(5133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{31}{120}\right)\)
\(\chi_{10400}(5397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{109}{120}\right)\)
\(\chi_{10400}(6013,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{83}{120}\right)\)
\(\chi_{10400}(6173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{67}{120}\right)\)
\(\chi_{10400}(6437,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{73}{120}\right)\)
\(\chi_{10400}(6597,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{89}{120}\right)\)
\(\chi_{10400}(7053,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{119}{120}\right)\)
\(\chi_{10400}(7213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{103}{120}\right)\)
\(\chi_{10400}(7477,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{37}{120}\right)\)
\(\chi_{10400}(7637,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{53}{120}\right)\)
\(\chi_{10400}(8253,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{19}{120}\right)\)
\(\chi_{10400}(8517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{120}\right)\)
\(\chi_{10400}(8677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{17}{120}\right)\)
\(\chi_{10400}(9133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{71}{120}\right)\)
\(\chi_{10400}(9717,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{101}{120}\right)\)
\(\chi_{10400}(10173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{107}{120}\right)\)

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First 31 of 32 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	10400.pm
Modulus	$10400$
Conductor	$10400$
Order	$120$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(10400\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(10400\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(120\)	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);