LMFDB - Dirichlet character orbit 20800.uq

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(20800, base_ring=CyclotomicField(240)) M = H._module chi = DirichletCharacter(H, M([120,45,84,80])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(3, 20800)) 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("20800.3"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$20800$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$20800$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$240$	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:	$\Q(\zeta_{240})$	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 240 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 64 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{20800}(3,\cdot)$	$1$	$1$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{23}{240}\right)$
$\chi_{20800}(347,\cdot)$	$1$	$1$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{139}{240}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{133}{240}\right)$
$\chi_{20800}(1147,\cdot)$	$1$	$1$	$e\left(\frac{233}{240}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{179}{240}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{217}{240}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{173}{240}\right)$
$\chi_{20800}(1283,\cdot)$	$1$	$1$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{7}{240}\right)$
$\chi_{20800}(1387,\cdot)$	$1$	$1$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{103}{240}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{149}{240}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{121}{240}\right)$
$\chi_{20800}(2083,\cdot)$	$1$	$1$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{161}{240}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{47}{240}\right)$
$\chi_{20800}(2187,\cdot)$	$1$	$1$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{109}{240}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{161}{240}\right)$
$\chi_{20800}(2323,\cdot)$	$1$	$1$	$e\left(\frac{79}{240}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{37}{240}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{139}{240}\right)$
$\chi_{20800}(2427,\cdot)$	$1$	$1$	$e\left(\frac{169}{240}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{109}{240}\right)$
$\chi_{20800}(3123,\cdot)$	$1$	$1$	$e\left(\frac{119}{240}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{179}{240}\right)$
$\chi_{20800}(3227,\cdot)$	$1$	$1$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{107}{240}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{149}{240}\right)$
$\chi_{20800}(3363,\cdot)$	$1$	$1$	$e\left(\frac{211}{240}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{179}{240}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{31}{240}\right)$
$\chi_{20800}(3467,\cdot)$	$1$	$1$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{31}{240}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{173}{240}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{97}{240}\right)$
$\chi_{20800}(4163,\cdot)$	$1$	$1$	$e\left(\frac{11}{240}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{233}{240}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{139}{240}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{71}{240}\right)$
$\chi_{20800}(4267,\cdot)$	$1$	$1$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{71}{240}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{133}{240}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{137}{240}\right)$
$\chi_{20800}(4403,\cdot)$	$1$	$1$	$e\left(\frac{103}{240}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{109}{240}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{163}{240}\right)$
$\chi_{20800}(5203,\cdot)$	$1$	$1$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{149}{240}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{203}{240}\right)$
$\chi_{20800}(5547,\cdot)$	$1$	$1$	$e\left(\frac{133}{240}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{199}{240}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{73}{240}\right)$
$\chi_{20800}(6347,\cdot)$	$1$	$1$	$e\left(\frac{173}{240}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{113}{240}\right)$
$\chi_{20800}(6483,\cdot)$	$1$	$1$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{187}{240}\right)$
$\chi_{20800}(6587,\cdot)$	$1$	$1$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{61}{240}\right)$
$\chi_{20800}(7283,\cdot)$	$1$	$1$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{103}{240}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{227}{240}\right)$
$\chi_{20800}(7387,\cdot)$	$1$	$1$	$e\left(\frac{161}{240}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{101}{240}\right)$
$\chi_{20800}(7523,\cdot)$	$1$	$1$	$e\left(\frac{19}{240}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{97}{240}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{79}{240}\right)$
$\chi_{20800}(7627,\cdot)$	$1$	$1$	$e\left(\frac{109}{240}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{49}{240}\right)$
$\chi_{20800}(8323,\cdot)$	$1$	$1$	$e\left(\frac{59}{240}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{137}{240}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{119}{240}\right)$
$\chi_{20800}(8427,\cdot)$	$1$	$1$	$e\left(\frac{149}{240}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{89}{240}\right)$
$\chi_{20800}(8563,\cdot)$	$1$	$1$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{13}{240}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{119}{240}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{211}{240}\right)$
$\chi_{20800}(8667,\cdot)$	$1$	$1$	$e\left(\frac{97}{240}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{37}{240}\right)$
$\chi_{20800}(9363,\cdot)$	$1$	$1$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{53}{240}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{79}{240}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{11}{240}\right)$
$\chi_{20800}(9467,\cdot)$	$1$	$1$	$e\left(\frac{137}{240}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{73}{240}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{77}{240}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{20800}(3,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{23}{240}\right)\)
\(\chi_{20800}(347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{139}{240}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{133}{240}\right)\)
\(\chi_{20800}(1147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{233}{240}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{179}{240}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{217}{240}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{173}{240}\right)\)
\(\chi_{20800}(1283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{7}{240}\right)\)
\(\chi_{20800}(1387,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{103}{240}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{149}{240}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{121}{240}\right)\)
\(\chi_{20800}(2083,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{161}{240}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{163}{240}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{47}{240}\right)\)
\(\chi_{20800}(2187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{221}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{109}{240}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{161}{240}\right)\)
\(\chi_{20800}(2323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{37}{240}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{191}{240}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{139}{240}\right)\)
\(\chi_{20800}(2427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{240}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{109}{240}\right)\)
\(\chi_{20800}(3123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{179}{240}\right)\)
\(\chi_{20800}(3227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{107}{240}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{149}{240}\right)\)
\(\chi_{20800}(3363,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{211}{240}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{179}{240}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{31}{240}\right)\)
\(\chi_{20800}(3467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{31}{240}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{173}{240}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{97}{240}\right)\)
\(\chi_{20800}(4163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{233}{240}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{139}{240}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{71}{240}\right)\)
\(\chi_{20800}(4267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{71}{240}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{133}{240}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{137}{240}\right)\)
\(\chi_{20800}(4403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{109}{240}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{163}{240}\right)\)
\(\chi_{20800}(5203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{149}{240}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{203}{240}\right)\)
\(\chi_{20800}(5547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{199}{240}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{73}{240}\right)\)
\(\chi_{20800}(6347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{113}{240}\right)\)
\(\chi_{20800}(6483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{187}{240}\right)\)
\(\chi_{20800}(6587,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{163}{240}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{61}{240}\right)\)
\(\chi_{20800}(7283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{221}{240}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{103}{240}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{227}{240}\right)\)
\(\chi_{20800}(7387,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{240}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{101}{240}\right)\)
\(\chi_{20800}(7523,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{240}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{79}{240}\right)\)
\(\chi_{20800}(7627,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{221}{240}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{49}{240}\right)\)
\(\chi_{20800}(8323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{137}{240}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{119}{240}\right)\)
\(\chi_{20800}(8427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{89}{240}\right)\)
\(\chi_{20800}(8563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{13}{240}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{119}{240}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{211}{240}\right)\)
\(\chi_{20800}(8667,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{113}{240}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{37}{240}\right)\)
\(\chi_{20800}(9363,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{53}{240}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{79}{240}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{11}{240}\right)\)
\(\chi_{20800}(9467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{240}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{73}{240}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{77}{240}\right)\)

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First 31 of 64 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	20800.uq
Modulus	$20800$
Conductor	$20800$
Order	$240$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(20800\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(20800\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(240\)	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);