LMFDB - Dirichlet character orbit 512.m

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(512, base_ring=CyclotomicField(64)) M = H._module chi = DirichletCharacter(H, M([0,35])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(9, 512)) 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("512.9"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$512$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$256$	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:	no, induced from 256.m	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{512}(9,\cdot)$	$1$	$1$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{39}{64}\right)$
$\chi_{512}(25,\cdot)$	$1$	$1$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{45}{64}\right)$
$\chi_{512}(41,\cdot)$	$1$	$1$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{19}{64}\right)$
$\chi_{512}(57,\cdot)$	$1$	$1$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{25}{64}\right)$
$\chi_{512}(73,\cdot)$	$1$	$1$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{63}{64}\right)$
$\chi_{512}(89,\cdot)$	$1$	$1$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{5}{64}\right)$
$\chi_{512}(105,\cdot)$	$1$	$1$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{43}{64}\right)$
$\chi_{512}(121,\cdot)$	$1$	$1$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{49}{64}\right)$
$\chi_{512}(137,\cdot)$	$1$	$1$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{23}{64}\right)$
$\chi_{512}(153,\cdot)$	$1$	$1$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{29}{64}\right)$
$\chi_{512}(169,\cdot)$	$1$	$1$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{3}{64}\right)$
$\chi_{512}(185,\cdot)$	$1$	$1$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{9}{64}\right)$
$\chi_{512}(201,\cdot)$	$1$	$1$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{47}{64}\right)$
$\chi_{512}(217,\cdot)$	$1$	$1$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{53}{64}\right)$
$\chi_{512}(233,\cdot)$	$1$	$1$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{27}{64}\right)$
$\chi_{512}(249,\cdot)$	$1$	$1$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{33}{64}\right)$
$\chi_{512}(265,\cdot)$	$1$	$1$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{7}{64}\right)$
$\chi_{512}(281,\cdot)$	$1$	$1$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{13}{64}\right)$
$\chi_{512}(297,\cdot)$	$1$	$1$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{51}{64}\right)$
$\chi_{512}(313,\cdot)$	$1$	$1$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{57}{64}\right)$
$\chi_{512}(329,\cdot)$	$1$	$1$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{31}{64}\right)$
$\chi_{512}(345,\cdot)$	$1$	$1$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{37}{64}\right)$
$\chi_{512}(361,\cdot)$	$1$	$1$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{11}{64}\right)$
$\chi_{512}(377,\cdot)$	$1$	$1$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{17}{64}\right)$
$\chi_{512}(393,\cdot)$	$1$	$1$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{55}{64}\right)$
$\chi_{512}(409,\cdot)$	$1$	$1$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{61}{64}\right)$
$\chi_{512}(425,\cdot)$	$1$	$1$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{35}{64}\right)$
$\chi_{512}(441,\cdot)$	$1$	$1$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{41}{64}\right)$
$\chi_{512}(457,\cdot)$	$1$	$1$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{15}{64}\right)$
$\chi_{512}(473,\cdot)$	$1$	$1$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{21}{64}\right)$
$\chi_{512}(489,\cdot)$	$1$	$1$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{59}{64}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{512}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{39}{64}\right)\)
\(\chi_{512}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{45}{64}\right)\)
\(\chi_{512}(41,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)
\(\chi_{512}(57,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{25}{64}\right)\)
\(\chi_{512}(73,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{63}{64}\right)\)
\(\chi_{512}(89,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{5}{64}\right)\)
\(\chi_{512}(105,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{43}{64}\right)\)
\(\chi_{512}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)
\(\chi_{512}(137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{23}{64}\right)\)
\(\chi_{512}(153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{29}{64}\right)\)
\(\chi_{512}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)
\(\chi_{512}(185,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{9}{64}\right)\)
\(\chi_{512}(201,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{47}{64}\right)\)
\(\chi_{512}(217,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{53}{64}\right)\)
\(\chi_{512}(233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{27}{64}\right)\)
\(\chi_{512}(249,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{33}{64}\right)\)
\(\chi_{512}(265,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{7}{64}\right)\)
\(\chi_{512}(281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{13}{64}\right)\)
\(\chi_{512}(297,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{51}{64}\right)\)
\(\chi_{512}(313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)
\(\chi_{512}(329,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)
\(\chi_{512}(345,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{37}{64}\right)\)
\(\chi_{512}(361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{11}{64}\right)\)
\(\chi_{512}(377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{17}{64}\right)\)
\(\chi_{512}(393,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{55}{64}\right)\)
\(\chi_{512}(409,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)
\(\chi_{512}(425,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{35}{64}\right)\)
\(\chi_{512}(441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{41}{64}\right)\)
\(\chi_{512}(457,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{15}{64}\right)\)
\(\chi_{512}(473,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{21}{64}\right)\)
\(\chi_{512}(489,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{59}{64}\right)\)

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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	512.m
Modulus	$512$
Conductor	$256$
Order	$64$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(512\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(256\)	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:	no, induced from 256.m	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);