LMFDB - Dirichlet character orbit 768.z

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(768, base_ring=CyclotomicField(64)) M = H._module chi = DirichletCharacter(H, M([0,47,0])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(13,768)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$768$
Conductor:	$256$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$64$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 256.m	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{64})$
Fixed field:	Number field defined by a degree 64 polynomial

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{768}(13,\cdot)$	$1$	$1$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{768}(37,\cdot)$	$1$	$1$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{768}(61,\cdot)$	$1$	$1$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{768}(85,\cdot)$	$1$	$1$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{768}(109,\cdot)$	$1$	$1$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{768}(133,\cdot)$	$1$	$1$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{768}(157,\cdot)$	$1$	$1$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{768}(181,\cdot)$	$1$	$1$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{768}(205,\cdot)$	$1$	$1$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{768}(229,\cdot)$	$1$	$1$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{768}(253,\cdot)$	$1$	$1$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{768}(277,\cdot)$	$1$	$1$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{768}(301,\cdot)$	$1$	$1$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{768}(325,\cdot)$	$1$	$1$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{768}(349,\cdot)$	$1$	$1$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{768}(373,\cdot)$	$1$	$1$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{768}(397,\cdot)$	$1$	$1$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{768}(421,\cdot)$	$1$	$1$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{768}(445,\cdot)$	$1$	$1$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{768}(469,\cdot)$	$1$	$1$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{768}(493,\cdot)$	$1$	$1$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{768}(517,\cdot)$	$1$	$1$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{768}(541,\cdot)$	$1$	$1$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{768}(565,\cdot)$	$1$	$1$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{768}(589,\cdot)$	$1$	$1$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{768}(613,\cdot)$	$1$	$1$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{768}(637,\cdot)$	$1$	$1$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{768}(661,\cdot)$	$1$	$1$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{768}(685,\cdot)$	$1$	$1$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{768}(709,\cdot)$	$1$	$1$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{768}(733,\cdot)$	$1$	$1$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{3}{8}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{768}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{768}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{768}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{768}(85,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{768}(109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{768}(133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{768}(157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{768}(181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{768}(205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{768}(229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{768}(253,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{768}(277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{768}(301,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{768}(325,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{768}(349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{768}(373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{768}(397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{768}(421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{768}(445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{768}(469,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{768}(493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{768}(517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{768}(541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{768}(565,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{768}(589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{768}(613,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{768}(637,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{768}(661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{768}(685,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{768}(709,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{768}(733,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)

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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	768.z
Modulus	$768$
Conductor	$256$
Order	$64$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(768\)
Conductor:	\(256\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(64\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 256.m	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)