LMFDB - Dirichlet character orbit 1024.r

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1024, base_ring=CyclotomicField(256)) M = H._module chi = DirichletCharacter(H, M([128,163])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(3,1024)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1024$
Conductor:	$1024$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$256$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{256})$
Fixed field:	Number field defined by a degree 256 polynomial (not computed)

First 31 of 128 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{1024}(3,\cdot)$	$-1$	$1$	$e\left(\frac{73}{256}\right)$	$e\left(\frac{163}{256}\right)$	$e\left(\frac{15}{128}\right)$	$e\left(\frac{73}{128}\right)$	$e\left(\frac{31}{256}\right)$	$e\left(\frac{45}{256}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{165}{256}\right)$	$e\left(\frac{103}{256}\right)$
$\chi_{1024}(11,\cdot)$	$-1$	$1$	$e\left(\frac{31}{256}\right)$	$e\left(\frac{213}{256}\right)$	$e\left(\frac{73}{128}\right)$	$e\left(\frac{31}{128}\right)$	$e\left(\frac{185}{256}\right)$	$e\left(\frac{219}{256}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{35}{256}\right)$	$e\left(\frac{177}{256}\right)$
$\chi_{1024}(19,\cdot)$	$-1$	$1$	$e\left(\frac{165}{256}\right)$	$e\left(\frac{151}{256}\right)$	$e\left(\frac{83}{128}\right)$	$e\left(\frac{37}{128}\right)$	$e\left(\frac{35}{256}\right)$	$e\left(\frac{249}{256}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{145}{256}\right)$	$e\left(\frac{75}{256}\right)$
$\chi_{1024}(27,\cdot)$	$-1$	$1$	$e\left(\frac{219}{256}\right)$	$e\left(\frac{233}{256}\right)$	$e\left(\frac{45}{128}\right)$	$e\left(\frac{91}{128}\right)$	$e\left(\frac{93}{256}\right)$	$e\left(\frac{135}{256}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{239}{256}\right)$	$e\left(\frac{53}{256}\right)$
$\chi_{1024}(35,\cdot)$	$-1$	$1$	$e\left(\frac{193}{256}\right)$	$e\left(\frac{203}{256}\right)$	$e\left(\frac{87}{128}\right)$	$e\left(\frac{65}{128}\right)$	$e\left(\frac{103}{256}\right)$	$e\left(\frac{133}{256}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{61}{256}\right)$	$e\left(\frac{111}{256}\right)$
$\chi_{1024}(43,\cdot)$	$-1$	$1$	$e\left(\frac{87}{256}\right)$	$e\left(\frac{61}{256}\right)$	$e\left(\frac{81}{128}\right)$	$e\left(\frac{87}{128}\right)$	$e\left(\frac{65}{256}\right)$	$e\left(\frac{243}{256}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{123}{256}\right)$	$e\left(\frac{249}{256}\right)$
$\chi_{1024}(51,\cdot)$	$-1$	$1$	$e\left(\frac{157}{256}\right)$	$e\left(\frac{63}{256}\right)$	$e\left(\frac{27}{128}\right)$	$e\left(\frac{29}{128}\right)$	$e\left(\frac{235}{256}\right)$	$e\left(\frac{209}{256}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{169}{256}\right)$	$e\left(\frac{211}{256}\right)$
$\chi_{1024}(59,\cdot)$	$-1$	$1$	$e\left(\frac{147}{256}\right)$	$e\left(\frac{209}{256}\right)$	$e\left(\frac{53}{128}\right)$	$e\left(\frac{19}{128}\right)$	$e\left(\frac{101}{256}\right)$	$e\left(\frac{31}{256}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{199}{256}\right)$	$e\left(\frac{253}{256}\right)$
$\chi_{1024}(67,\cdot)$	$-1$	$1$	$e\left(\frac{57}{256}\right)$	$e\left(\frac{243}{256}\right)$	$e\left(\frac{31}{128}\right)$	$e\left(\frac{57}{128}\right)$	$e\left(\frac{175}{256}\right)$	$e\left(\frac{221}{256}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{213}{256}\right)$	$e\left(\frac{119}{256}\right)$
$\chi_{1024}(75,\cdot)$	$-1$	$1$	$e\left(\frac{143}{256}\right)$	$e\left(\frac{165}{256}\right)$	$e\left(\frac{89}{128}\right)$	$e\left(\frac{15}{128}\right)$	$e\left(\frac{201}{256}\right)$	$e\left(\frac{11}{256}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{211}{256}\right)$	$e\left(\frac{65}{256}\right)$
$\chi_{1024}(83,\cdot)$	$-1$	$1$	$e\left(\frac{149}{256}\right)$	$e\left(\frac{231}{256}\right)$	$e\left(\frac{99}{128}\right)$	$e\left(\frac{21}{128}\right)$	$e\left(\frac{179}{256}\right)$	$e\left(\frac{169}{256}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{193}{256}\right)$	$e\left(\frac{91}{256}\right)$
$\chi_{1024}(91,\cdot)$	$-1$	$1$	$e\left(\frac{75}{256}\right)$	$e\left(\frac{185}{256}\right)$	$e\left(\frac{61}{128}\right)$	$e\left(\frac{75}{128}\right)$	$e\left(\frac{109}{256}\right)$	$e\left(\frac{183}{256}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{159}{256}\right)$	$e\left(\frac{197}{256}\right)$
$\chi_{1024}(99,\cdot)$	$-1$	$1$	$e\left(\frac{177}{256}\right)$	$e\left(\frac{27}{256}\right)$	$e\left(\frac{103}{128}\right)$	$e\left(\frac{49}{128}\right)$	$e\left(\frac{247}{256}\right)$	$e\left(\frac{53}{256}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{109}{256}\right)$	$e\left(\frac{127}{256}\right)$
$\chi_{1024}(107,\cdot)$	$-1$	$1$	$e\left(\frac{199}{256}\right)$	$e\left(\frac{13}{256}\right)$	$e\left(\frac{97}{128}\right)$	$e\left(\frac{71}{128}\right)$	$e\left(\frac{81}{256}\right)$	$e\left(\frac{35}{256}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{43}{256}\right)$	$e\left(\frac{137}{256}\right)$
$\chi_{1024}(115,\cdot)$	$-1$	$1$	$e\left(\frac{141}{256}\right)$	$e\left(\frac{143}{256}\right)$	$e\left(\frac{43}{128}\right)$	$e\left(\frac{13}{128}\right)$	$e\left(\frac{123}{256}\right)$	$e\left(\frac{129}{256}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{217}{256}\right)$	$e\left(\frac{227}{256}\right)$
$\chi_{1024}(123,\cdot)$	$-1$	$1$	$e\left(\frac{3}{256}\right)$	$e\left(\frac{161}{256}\right)$	$e\left(\frac{69}{128}\right)$	$e\left(\frac{3}{128}\right)$	$e\left(\frac{117}{256}\right)$	$e\left(\frac{79}{256}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{119}{256}\right)$	$e\left(\frac{141}{256}\right)$
$\chi_{1024}(131,\cdot)$	$-1$	$1$	$e\left(\frac{41}{256}\right)$	$e\left(\frac{67}{256}\right)$	$e\left(\frac{47}{128}\right)$	$e\left(\frac{41}{128}\right)$	$e\left(\frac{63}{256}\right)$	$e\left(\frac{141}{256}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{5}{256}\right)$	$e\left(\frac{135}{256}\right)$
$\chi_{1024}(139,\cdot)$	$-1$	$1$	$e\left(\frac{255}{256}\right)$	$e\left(\frac{117}{256}\right)$	$e\left(\frac{105}{128}\right)$	$e\left(\frac{127}{128}\right)$	$e\left(\frac{217}{256}\right)$	$e\left(\frac{59}{256}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{131}{256}\right)$	$e\left(\frac{209}{256}\right)$
$\chi_{1024}(147,\cdot)$	$-1$	$1$	$e\left(\frac{133}{256}\right)$	$e\left(\frac{55}{256}\right)$	$e\left(\frac{115}{128}\right)$	$e\left(\frac{5}{128}\right)$	$e\left(\frac{67}{256}\right)$	$e\left(\frac{89}{256}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{241}{256}\right)$	$e\left(\frac{107}{256}\right)$
$\chi_{1024}(155,\cdot)$	$-1$	$1$	$e\left(\frac{187}{256}\right)$	$e\left(\frac{137}{256}\right)$	$e\left(\frac{77}{128}\right)$	$e\left(\frac{59}{128}\right)$	$e\left(\frac{125}{256}\right)$	$e\left(\frac{231}{256}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{79}{256}\right)$	$e\left(\frac{85}{256}\right)$
$\chi_{1024}(163,\cdot)$	$-1$	$1$	$e\left(\frac{161}{256}\right)$	$e\left(\frac{107}{256}\right)$	$e\left(\frac{119}{128}\right)$	$e\left(\frac{33}{128}\right)$	$e\left(\frac{135}{256}\right)$	$e\left(\frac{229}{256}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{157}{256}\right)$	$e\left(\frac{143}{256}\right)$
$\chi_{1024}(171,\cdot)$	$-1$	$1$	$e\left(\frac{55}{256}\right)$	$e\left(\frac{221}{256}\right)$	$e\left(\frac{113}{128}\right)$	$e\left(\frac{55}{128}\right)$	$e\left(\frac{97}{256}\right)$	$e\left(\frac{83}{256}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{219}{256}\right)$	$e\left(\frac{25}{256}\right)$
$\chi_{1024}(179,\cdot)$	$-1$	$1$	$e\left(\frac{125}{256}\right)$	$e\left(\frac{223}{256}\right)$	$e\left(\frac{59}{128}\right)$	$e\left(\frac{125}{128}\right)$	$e\left(\frac{11}{256}\right)$	$e\left(\frac{49}{256}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{9}{256}\right)$	$e\left(\frac{243}{256}\right)$
$\chi_{1024}(187,\cdot)$	$-1$	$1$	$e\left(\frac{115}{256}\right)$	$e\left(\frac{113}{256}\right)$	$e\left(\frac{85}{128}\right)$	$e\left(\frac{115}{128}\right)$	$e\left(\frac{133}{256}\right)$	$e\left(\frac{127}{256}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{39}{256}\right)$	$e\left(\frac{29}{256}\right)$
$\chi_{1024}(195,\cdot)$	$-1$	$1$	$e\left(\frac{25}{256}\right)$	$e\left(\frac{147}{256}\right)$	$e\left(\frac{63}{128}\right)$	$e\left(\frac{25}{128}\right)$	$e\left(\frac{207}{256}\right)$	$e\left(\frac{61}{256}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{53}{256}\right)$	$e\left(\frac{151}{256}\right)$
$\chi_{1024}(203,\cdot)$	$-1$	$1$	$e\left(\frac{111}{256}\right)$	$e\left(\frac{69}{256}\right)$	$e\left(\frac{121}{128}\right)$	$e\left(\frac{111}{128}\right)$	$e\left(\frac{233}{256}\right)$	$e\left(\frac{107}{256}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{51}{256}\right)$	$e\left(\frac{97}{256}\right)$
$\chi_{1024}(211,\cdot)$	$-1$	$1$	$e\left(\frac{117}{256}\right)$	$e\left(\frac{135}{256}\right)$	$e\left(\frac{3}{128}\right)$	$e\left(\frac{117}{128}\right)$	$e\left(\frac{211}{256}\right)$	$e\left(\frac{9}{256}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{33}{256}\right)$	$e\left(\frac{123}{256}\right)$
$\chi_{1024}(219,\cdot)$	$-1$	$1$	$e\left(\frac{43}{256}\right)$	$e\left(\frac{89}{256}\right)$	$e\left(\frac{93}{128}\right)$	$e\left(\frac{43}{128}\right)$	$e\left(\frac{141}{256}\right)$	$e\left(\frac{23}{256}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{255}{256}\right)$	$e\left(\frac{229}{256}\right)$
$\chi_{1024}(227,\cdot)$	$-1$	$1$	$e\left(\frac{145}{256}\right)$	$e\left(\frac{187}{256}\right)$	$e\left(\frac{7}{128}\right)$	$e\left(\frac{17}{128}\right)$	$e\left(\frac{23}{256}\right)$	$e\left(\frac{149}{256}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{205}{256}\right)$	$e\left(\frac{159}{256}\right)$
$\chi_{1024}(235,\cdot)$	$-1$	$1$	$e\left(\frac{167}{256}\right)$	$e\left(\frac{173}{256}\right)$	$e\left(\frac{1}{128}\right)$	$e\left(\frac{39}{128}\right)$	$e\left(\frac{113}{256}\right)$	$e\left(\frac{131}{256}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{139}{256}\right)$	$e\left(\frac{169}{256}\right)$
$\chi_{1024}(243,\cdot)$	$-1$	$1$	$e\left(\frac{109}{256}\right)$	$e\left(\frac{47}{256}\right)$	$e\left(\frac{75}{128}\right)$	$e\left(\frac{109}{128}\right)$	$e\left(\frac{155}{256}\right)$	$e\left(\frac{225}{256}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{57}{256}\right)$	$e\left(\frac{3}{256}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{1024}(3,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{256}\right)\)	\(e\left(\frac{163}{256}\right)\)	\(e\left(\frac{15}{128}\right)\)	\(e\left(\frac{73}{128}\right)\)	\(e\left(\frac{31}{256}\right)\)	\(e\left(\frac{45}{256}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{165}{256}\right)\)	\(e\left(\frac{103}{256}\right)\)
\(\chi_{1024}(11,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{256}\right)\)	\(e\left(\frac{213}{256}\right)\)	\(e\left(\frac{73}{128}\right)\)	\(e\left(\frac{31}{128}\right)\)	\(e\left(\frac{185}{256}\right)\)	\(e\left(\frac{219}{256}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{35}{256}\right)\)	\(e\left(\frac{177}{256}\right)\)
\(\chi_{1024}(19,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{165}{256}\right)\)	\(e\left(\frac{151}{256}\right)\)	\(e\left(\frac{83}{128}\right)\)	\(e\left(\frac{37}{128}\right)\)	\(e\left(\frac{35}{256}\right)\)	\(e\left(\frac{249}{256}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{145}{256}\right)\)	\(e\left(\frac{75}{256}\right)\)
\(\chi_{1024}(27,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{219}{256}\right)\)	\(e\left(\frac{233}{256}\right)\)	\(e\left(\frac{45}{128}\right)\)	\(e\left(\frac{91}{128}\right)\)	\(e\left(\frac{93}{256}\right)\)	\(e\left(\frac{135}{256}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{239}{256}\right)\)	\(e\left(\frac{53}{256}\right)\)
\(\chi_{1024}(35,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{193}{256}\right)\)	\(e\left(\frac{203}{256}\right)\)	\(e\left(\frac{87}{128}\right)\)	\(e\left(\frac{65}{128}\right)\)	\(e\left(\frac{103}{256}\right)\)	\(e\left(\frac{133}{256}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{61}{256}\right)\)	\(e\left(\frac{111}{256}\right)\)
\(\chi_{1024}(43,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{87}{256}\right)\)	\(e\left(\frac{61}{256}\right)\)	\(e\left(\frac{81}{128}\right)\)	\(e\left(\frac{87}{128}\right)\)	\(e\left(\frac{65}{256}\right)\)	\(e\left(\frac{243}{256}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{123}{256}\right)\)	\(e\left(\frac{249}{256}\right)\)
\(\chi_{1024}(51,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{157}{256}\right)\)	\(e\left(\frac{63}{256}\right)\)	\(e\left(\frac{27}{128}\right)\)	\(e\left(\frac{29}{128}\right)\)	\(e\left(\frac{235}{256}\right)\)	\(e\left(\frac{209}{256}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{169}{256}\right)\)	\(e\left(\frac{211}{256}\right)\)
\(\chi_{1024}(59,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{147}{256}\right)\)	\(e\left(\frac{209}{256}\right)\)	\(e\left(\frac{53}{128}\right)\)	\(e\left(\frac{19}{128}\right)\)	\(e\left(\frac{101}{256}\right)\)	\(e\left(\frac{31}{256}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{199}{256}\right)\)	\(e\left(\frac{253}{256}\right)\)
\(\chi_{1024}(67,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{256}\right)\)	\(e\left(\frac{243}{256}\right)\)	\(e\left(\frac{31}{128}\right)\)	\(e\left(\frac{57}{128}\right)\)	\(e\left(\frac{175}{256}\right)\)	\(e\left(\frac{221}{256}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{213}{256}\right)\)	\(e\left(\frac{119}{256}\right)\)
\(\chi_{1024}(75,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{143}{256}\right)\)	\(e\left(\frac{165}{256}\right)\)	\(e\left(\frac{89}{128}\right)\)	\(e\left(\frac{15}{128}\right)\)	\(e\left(\frac{201}{256}\right)\)	\(e\left(\frac{11}{256}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{211}{256}\right)\)	\(e\left(\frac{65}{256}\right)\)
\(\chi_{1024}(83,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{256}\right)\)	\(e\left(\frac{231}{256}\right)\)	\(e\left(\frac{99}{128}\right)\)	\(e\left(\frac{21}{128}\right)\)	\(e\left(\frac{179}{256}\right)\)	\(e\left(\frac{169}{256}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{193}{256}\right)\)	\(e\left(\frac{91}{256}\right)\)
\(\chi_{1024}(91,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{75}{256}\right)\)	\(e\left(\frac{185}{256}\right)\)	\(e\left(\frac{61}{128}\right)\)	\(e\left(\frac{75}{128}\right)\)	\(e\left(\frac{109}{256}\right)\)	\(e\left(\frac{183}{256}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{159}{256}\right)\)	\(e\left(\frac{197}{256}\right)\)
\(\chi_{1024}(99,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{177}{256}\right)\)	\(e\left(\frac{27}{256}\right)\)	\(e\left(\frac{103}{128}\right)\)	\(e\left(\frac{49}{128}\right)\)	\(e\left(\frac{247}{256}\right)\)	\(e\left(\frac{53}{256}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{109}{256}\right)\)	\(e\left(\frac{127}{256}\right)\)
\(\chi_{1024}(107,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{199}{256}\right)\)	\(e\left(\frac{13}{256}\right)\)	\(e\left(\frac{97}{128}\right)\)	\(e\left(\frac{71}{128}\right)\)	\(e\left(\frac{81}{256}\right)\)	\(e\left(\frac{35}{256}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{43}{256}\right)\)	\(e\left(\frac{137}{256}\right)\)
\(\chi_{1024}(115,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{141}{256}\right)\)	\(e\left(\frac{143}{256}\right)\)	\(e\left(\frac{43}{128}\right)\)	\(e\left(\frac{13}{128}\right)\)	\(e\left(\frac{123}{256}\right)\)	\(e\left(\frac{129}{256}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{217}{256}\right)\)	\(e\left(\frac{227}{256}\right)\)
\(\chi_{1024}(123,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{256}\right)\)	\(e\left(\frac{161}{256}\right)\)	\(e\left(\frac{69}{128}\right)\)	\(e\left(\frac{3}{128}\right)\)	\(e\left(\frac{117}{256}\right)\)	\(e\left(\frac{79}{256}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{119}{256}\right)\)	\(e\left(\frac{141}{256}\right)\)
\(\chi_{1024}(131,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{256}\right)\)	\(e\left(\frac{67}{256}\right)\)	\(e\left(\frac{47}{128}\right)\)	\(e\left(\frac{41}{128}\right)\)	\(e\left(\frac{63}{256}\right)\)	\(e\left(\frac{141}{256}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{5}{256}\right)\)	\(e\left(\frac{135}{256}\right)\)
\(\chi_{1024}(139,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{255}{256}\right)\)	\(e\left(\frac{117}{256}\right)\)	\(e\left(\frac{105}{128}\right)\)	\(e\left(\frac{127}{128}\right)\)	\(e\left(\frac{217}{256}\right)\)	\(e\left(\frac{59}{256}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{131}{256}\right)\)	\(e\left(\frac{209}{256}\right)\)
\(\chi_{1024}(147,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{256}\right)\)	\(e\left(\frac{55}{256}\right)\)	\(e\left(\frac{115}{128}\right)\)	\(e\left(\frac{5}{128}\right)\)	\(e\left(\frac{67}{256}\right)\)	\(e\left(\frac{89}{256}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{241}{256}\right)\)	\(e\left(\frac{107}{256}\right)\)
\(\chi_{1024}(155,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{187}{256}\right)\)	\(e\left(\frac{137}{256}\right)\)	\(e\left(\frac{77}{128}\right)\)	\(e\left(\frac{59}{128}\right)\)	\(e\left(\frac{125}{256}\right)\)	\(e\left(\frac{231}{256}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{79}{256}\right)\)	\(e\left(\frac{85}{256}\right)\)
\(\chi_{1024}(163,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{161}{256}\right)\)	\(e\left(\frac{107}{256}\right)\)	\(e\left(\frac{119}{128}\right)\)	\(e\left(\frac{33}{128}\right)\)	\(e\left(\frac{135}{256}\right)\)	\(e\left(\frac{229}{256}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{157}{256}\right)\)	\(e\left(\frac{143}{256}\right)\)
\(\chi_{1024}(171,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{256}\right)\)	\(e\left(\frac{221}{256}\right)\)	\(e\left(\frac{113}{128}\right)\)	\(e\left(\frac{55}{128}\right)\)	\(e\left(\frac{97}{256}\right)\)	\(e\left(\frac{83}{256}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{219}{256}\right)\)	\(e\left(\frac{25}{256}\right)\)
\(\chi_{1024}(179,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{125}{256}\right)\)	\(e\left(\frac{223}{256}\right)\)	\(e\left(\frac{59}{128}\right)\)	\(e\left(\frac{125}{128}\right)\)	\(e\left(\frac{11}{256}\right)\)	\(e\left(\frac{49}{256}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{9}{256}\right)\)	\(e\left(\frac{243}{256}\right)\)
\(\chi_{1024}(187,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{115}{256}\right)\)	\(e\left(\frac{113}{256}\right)\)	\(e\left(\frac{85}{128}\right)\)	\(e\left(\frac{115}{128}\right)\)	\(e\left(\frac{133}{256}\right)\)	\(e\left(\frac{127}{256}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{39}{256}\right)\)	\(e\left(\frac{29}{256}\right)\)
\(\chi_{1024}(195,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{256}\right)\)	\(e\left(\frac{147}{256}\right)\)	\(e\left(\frac{63}{128}\right)\)	\(e\left(\frac{25}{128}\right)\)	\(e\left(\frac{207}{256}\right)\)	\(e\left(\frac{61}{256}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{53}{256}\right)\)	\(e\left(\frac{151}{256}\right)\)
\(\chi_{1024}(203,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{111}{256}\right)\)	\(e\left(\frac{69}{256}\right)\)	\(e\left(\frac{121}{128}\right)\)	\(e\left(\frac{111}{128}\right)\)	\(e\left(\frac{233}{256}\right)\)	\(e\left(\frac{107}{256}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{51}{256}\right)\)	\(e\left(\frac{97}{256}\right)\)
\(\chi_{1024}(211,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{117}{256}\right)\)	\(e\left(\frac{135}{256}\right)\)	\(e\left(\frac{3}{128}\right)\)	\(e\left(\frac{117}{128}\right)\)	\(e\left(\frac{211}{256}\right)\)	\(e\left(\frac{9}{256}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{33}{256}\right)\)	\(e\left(\frac{123}{256}\right)\)
\(\chi_{1024}(219,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{256}\right)\)	\(e\left(\frac{89}{256}\right)\)	\(e\left(\frac{93}{128}\right)\)	\(e\left(\frac{43}{128}\right)\)	\(e\left(\frac{141}{256}\right)\)	\(e\left(\frac{23}{256}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{255}{256}\right)\)	\(e\left(\frac{229}{256}\right)\)
\(\chi_{1024}(227,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{145}{256}\right)\)	\(e\left(\frac{187}{256}\right)\)	\(e\left(\frac{7}{128}\right)\)	\(e\left(\frac{17}{128}\right)\)	\(e\left(\frac{23}{256}\right)\)	\(e\left(\frac{149}{256}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{205}{256}\right)\)	\(e\left(\frac{159}{256}\right)\)
\(\chi_{1024}(235,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{256}\right)\)	\(e\left(\frac{173}{256}\right)\)	\(e\left(\frac{1}{128}\right)\)	\(e\left(\frac{39}{128}\right)\)	\(e\left(\frac{113}{256}\right)\)	\(e\left(\frac{131}{256}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{139}{256}\right)\)	\(e\left(\frac{169}{256}\right)\)
\(\chi_{1024}(243,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{256}\right)\)	\(e\left(\frac{47}{256}\right)\)	\(e\left(\frac{75}{128}\right)\)	\(e\left(\frac{109}{128}\right)\)	\(e\left(\frac{155}{256}\right)\)	\(e\left(\frac{225}{256}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{57}{256}\right)\)	\(e\left(\frac{3}{256}\right)\)

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First 31 of 128 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	1024.r
Modulus	$1024$
Conductor	$1024$
Order	$256$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(1024\)
Conductor:	\(1024\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(256\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)