LMFDB - Dirichlet character orbit 1600.cn

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1600, base_ring=CyclotomicField(80)) M = H._module chi = DirichletCharacter(H, M([0,75,76])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(13,1600)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1600$
Conductor:	$1600$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$80$	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:	$\Q(\zeta_{80})$
Fixed field:	Number field defined by a degree 80 polynomial

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{1600}(13,\cdot)$	$-1$	$1$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{31}{80}\right)$
$\chi_{1600}(37,\cdot)$	$-1$	$1$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{41}{80}\right)$
$\chi_{1600}(117,\cdot)$	$-1$	$1$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{37}{80}\right)$
$\chi_{1600}(173,\cdot)$	$-1$	$1$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{39}{80}\right)$
$\chi_{1600}(197,\cdot)$	$-1$	$1$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{33}{80}\right)$
$\chi_{1600}(253,\cdot)$	$-1$	$1$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{3}{80}\right)$
$\chi_{1600}(277,\cdot)$	$-1$	$1$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{29}{80}\right)$
$\chi_{1600}(333,\cdot)$	$-1$	$1$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{47}{80}\right)$
$\chi_{1600}(413,\cdot)$	$-1$	$1$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{11}{80}\right)$
$\chi_{1600}(437,\cdot)$	$-1$	$1$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{21}{80}\right)$
$\chi_{1600}(517,\cdot)$	$-1$	$1$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{17}{80}\right)$
$\chi_{1600}(573,\cdot)$	$-1$	$1$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{19}{80}\right)$
$\chi_{1600}(597,\cdot)$	$-1$	$1$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{13}{80}\right)$
$\chi_{1600}(653,\cdot)$	$-1$	$1$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{63}{80}\right)$
$\chi_{1600}(677,\cdot)$	$-1$	$1$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{9}{80}\right)$
$\chi_{1600}(733,\cdot)$	$-1$	$1$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{27}{80}\right)$
$\chi_{1600}(813,\cdot)$	$-1$	$1$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{71}{80}\right)$
$\chi_{1600}(837,\cdot)$	$-1$	$1$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{1}{80}\right)$
$\chi_{1600}(917,\cdot)$	$-1$	$1$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{77}{80}\right)$
$\chi_{1600}(973,\cdot)$	$-1$	$1$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{79}{80}\right)$
$\chi_{1600}(997,\cdot)$	$-1$	$1$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{73}{80}\right)$
$\chi_{1600}(1053,\cdot)$	$-1$	$1$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{43}{80}\right)$
$\chi_{1600}(1077,\cdot)$	$-1$	$1$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{69}{80}\right)$
$\chi_{1600}(1133,\cdot)$	$-1$	$1$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{7}{80}\right)$
$\chi_{1600}(1213,\cdot)$	$-1$	$1$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{51}{80}\right)$
$\chi_{1600}(1237,\cdot)$	$-1$	$1$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{61}{80}\right)$
$\chi_{1600}(1317,\cdot)$	$-1$	$1$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{57}{80}\right)$
$\chi_{1600}(1373,\cdot)$	$-1$	$1$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{59}{80}\right)$
$\chi_{1600}(1397,\cdot)$	$-1$	$1$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{53}{80}\right)$
$\chi_{1600}(1453,\cdot)$	$-1$	$1$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{23}{80}\right)$
$\chi_{1600}(1477,\cdot)$	$-1$	$1$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{49}{80}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{1600}(13,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)
\(\chi_{1600}(37,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)
\(\chi_{1600}(117,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)
\(\chi_{1600}(173,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)
\(\chi_{1600}(197,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)
\(\chi_{1600}(253,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)
\(\chi_{1600}(277,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)
\(\chi_{1600}(333,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)
\(\chi_{1600}(413,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)
\(\chi_{1600}(437,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{21}{80}\right)\)
\(\chi_{1600}(517,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)
\(\chi_{1600}(573,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)
\(\chi_{1600}(597,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)
\(\chi_{1600}(653,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)
\(\chi_{1600}(677,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)
\(\chi_{1600}(733,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)
\(\chi_{1600}(813,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)
\(\chi_{1600}(837,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)
\(\chi_{1600}(917,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)
\(\chi_{1600}(973,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)
\(\chi_{1600}(997,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)
\(\chi_{1600}(1053,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)
\(\chi_{1600}(1077,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)
\(\chi_{1600}(1133,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{7}{80}\right)\)
\(\chi_{1600}(1213,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)
\(\chi_{1600}(1237,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)
\(\chi_{1600}(1317,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)
\(\chi_{1600}(1373,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)
\(\chi_{1600}(1397,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)
\(\chi_{1600}(1453,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)
\(\chi_{1600}(1477,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)

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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	1600.cn
Modulus	$1600$
Conductor	$1600$
Order	$80$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(1600\)
Conductor:	\(1600\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(80\)	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)