LMFDB - Dirichlet character orbit 3840.dr

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3840, base_ring=CyclotomicField(64)) M = H._module chi = DirichletCharacter(H, M([0,5,32,48])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(53, 3840)) 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("3840.53"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$3840$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$3840$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$64$	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:	$\Q(\zeta_{64})$	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 64 polynomial	comment:Fixed field sage:chi.fixed_field()

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{3840}(53,\cdot)$	$1$	$1$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{11}{32}\right)$
$\chi_{3840}(77,\cdot)$	$1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{17}{32}\right)$
$\chi_{3840}(293,\cdot)$	$1$	$1$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{23}{32}\right)$
$\chi_{3840}(317,\cdot)$	$1$	$1$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{29}{32}\right)$
$\chi_{3840}(533,\cdot)$	$1$	$1$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{3}{32}\right)$
$\chi_{3840}(557,\cdot)$	$1$	$1$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{9}{32}\right)$
$\chi_{3840}(773,\cdot)$	$1$	$1$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{15}{32}\right)$
$\chi_{3840}(797,\cdot)$	$1$	$1$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{21}{32}\right)$
$\chi_{3840}(1013,\cdot)$	$1$	$1$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{27}{32}\right)$
$\chi_{3840}(1037,\cdot)$	$1$	$1$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{1}{32}\right)$
$\chi_{3840}(1253,\cdot)$	$1$	$1$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{7}{32}\right)$
$\chi_{3840}(1277,\cdot)$	$1$	$1$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{13}{32}\right)$
$\chi_{3840}(1493,\cdot)$	$1$	$1$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{19}{32}\right)$
$\chi_{3840}(1517,\cdot)$	$1$	$1$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{25}{32}\right)$
$\chi_{3840}(1733,\cdot)$	$1$	$1$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{31}{32}\right)$
$\chi_{3840}(1757,\cdot)$	$1$	$1$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{5}{32}\right)$
$\chi_{3840}(1973,\cdot)$	$1$	$1$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{11}{32}\right)$
$\chi_{3840}(1997,\cdot)$	$1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{17}{32}\right)$
$\chi_{3840}(2213,\cdot)$	$1$	$1$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{23}{32}\right)$
$\chi_{3840}(2237,\cdot)$	$1$	$1$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{29}{32}\right)$
$\chi_{3840}(2453,\cdot)$	$1$	$1$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{3}{32}\right)$
$\chi_{3840}(2477,\cdot)$	$1$	$1$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{9}{32}\right)$
$\chi_{3840}(2693,\cdot)$	$1$	$1$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{15}{32}\right)$
$\chi_{3840}(2717,\cdot)$	$1$	$1$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{21}{32}\right)$
$\chi_{3840}(2933,\cdot)$	$1$	$1$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{27}{32}\right)$
$\chi_{3840}(2957,\cdot)$	$1$	$1$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{1}{32}\right)$
$\chi_{3840}(3173,\cdot)$	$1$	$1$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{7}{32}\right)$
$\chi_{3840}(3197,\cdot)$	$1$	$1$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{13}{32}\right)$
$\chi_{3840}(3413,\cdot)$	$1$	$1$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{19}{32}\right)$
$\chi_{3840}(3437,\cdot)$	$1$	$1$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{25}{32}\right)$
$\chi_{3840}(3653,\cdot)$	$1$	$1$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{31}{32}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{3840}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)
\(\chi_{3840}(77,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)
\(\chi_{3840}(293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)
\(\chi_{3840}(317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)
\(\chi_{3840}(533,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)
\(\chi_{3840}(557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)
\(\chi_{3840}(773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)
\(\chi_{3840}(797,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)
\(\chi_{3840}(1013,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)
\(\chi_{3840}(1037,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)
\(\chi_{3840}(1253,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)
\(\chi_{3840}(1277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)
\(\chi_{3840}(1493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)
\(\chi_{3840}(1517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)
\(\chi_{3840}(1733,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)
\(\chi_{3840}(1757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)
\(\chi_{3840}(1973,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)
\(\chi_{3840}(1997,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)
\(\chi_{3840}(2213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)
\(\chi_{3840}(2237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)
\(\chi_{3840}(2453,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)
\(\chi_{3840}(2477,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)
\(\chi_{3840}(2693,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)
\(\chi_{3840}(2717,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)
\(\chi_{3840}(2933,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)
\(\chi_{3840}(2957,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)
\(\chi_{3840}(3173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)
\(\chi_{3840}(3197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)
\(\chi_{3840}(3413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)
\(\chi_{3840}(3437,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)
\(\chi_{3840}(3653,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)

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Basic properties

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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	3840.dr
Modulus	$3840$
Conductor	$3840$
Order	$64$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(3840\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(3840\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(64\)	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);