LMFDB - Dirichlet character orbit 736.bc

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(736, base_ring=CyclotomicField(88)) M = H._module chi = DirichletCharacter(H, M([0,11,4])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,736)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$736$
Conductor:	$736$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$88$	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:	$\Q(\zeta_{88})$
Fixed field:	Number field defined by a degree 88 polynomial

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{736}(5,\cdot)$	$-1$	$1$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{19}{88}\right)$
$\chi_{736}(21,\cdot)$	$-1$	$1$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{71}{88}\right)$
$\chi_{736}(37,\cdot)$	$-1$	$1$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{3}{88}\right)$
$\chi_{736}(53,\cdot)$	$-1$	$1$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{31}{88}\right)$
$\chi_{736}(61,\cdot)$	$-1$	$1$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{81}{88}\right)$
$\chi_{736}(109,\cdot)$	$-1$	$1$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{45}{88}\right)$
$\chi_{736}(125,\cdot)$	$-1$	$1$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{57}{88}\right)$
$\chi_{736}(149,\cdot)$	$-1$	$1$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{39}{88}\right)$
$\chi_{736}(157,\cdot)$	$-1$	$1$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{65}{88}\right)$
$\chi_{736}(181,\cdot)$	$-1$	$1$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{7}{88}\right)$
$\chi_{736}(189,\cdot)$	$-1$	$1$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{41}{88}\right)$
$\chi_{736}(205,\cdot)$	$-1$	$1$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{5}{88}\right)$
$\chi_{736}(221,\cdot)$	$-1$	$1$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{25}{88}\right)$
$\chi_{736}(237,\cdot)$	$-1$	$1$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{53}{88}\right)$
$\chi_{736}(245,\cdot)$	$-1$	$1$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{15}{88}\right)$
$\chi_{736}(293,\cdot)$	$-1$	$1$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{67}{88}\right)$
$\chi_{736}(309,\cdot)$	$-1$	$1$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{79}{88}\right)$
$\chi_{736}(333,\cdot)$	$-1$	$1$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{61}{88}\right)$
$\chi_{736}(341,\cdot)$	$-1$	$1$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{87}{88}\right)$
$\chi_{736}(365,\cdot)$	$-1$	$1$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{29}{88}\right)$
$\chi_{736}(373,\cdot)$	$-1$	$1$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{63}{88}\right)$
$\chi_{736}(389,\cdot)$	$-1$	$1$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{27}{88}\right)$
$\chi_{736}(405,\cdot)$	$-1$	$1$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{47}{88}\right)$
$\chi_{736}(421,\cdot)$	$-1$	$1$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{75}{88}\right)$
$\chi_{736}(429,\cdot)$	$-1$	$1$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{37}{88}\right)$
$\chi_{736}(477,\cdot)$	$-1$	$1$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{1}{88}\right)$
$\chi_{736}(493,\cdot)$	$-1$	$1$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{13}{88}\right)$
$\chi_{736}(517,\cdot)$	$-1$	$1$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{83}{88}\right)$
$\chi_{736}(525,\cdot)$	$-1$	$1$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{21}{88}\right)$
$\chi_{736}(549,\cdot)$	$-1$	$1$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{51}{88}\right)$
$\chi_{736}(557,\cdot)$	$-1$	$1$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{85}{88}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{736}(5,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{19}{88}\right)\)
\(\chi_{736}(21,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{71}{88}\right)\)
\(\chi_{736}(37,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{3}{88}\right)\)
\(\chi_{736}(53,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{31}{88}\right)\)
\(\chi_{736}(61,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{81}{88}\right)\)
\(\chi_{736}(109,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{45}{88}\right)\)
\(\chi_{736}(125,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{57}{88}\right)\)
\(\chi_{736}(149,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{39}{88}\right)\)
\(\chi_{736}(157,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{65}{88}\right)\)
\(\chi_{736}(181,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{7}{88}\right)\)
\(\chi_{736}(189,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{41}{88}\right)\)
\(\chi_{736}(205,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{5}{88}\right)\)
\(\chi_{736}(221,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{25}{88}\right)\)
\(\chi_{736}(237,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{53}{88}\right)\)
\(\chi_{736}(245,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{15}{88}\right)\)
\(\chi_{736}(293,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{67}{88}\right)\)
\(\chi_{736}(309,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{79}{88}\right)\)
\(\chi_{736}(333,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{61}{88}\right)\)
\(\chi_{736}(341,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{87}{88}\right)\)
\(\chi_{736}(365,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{29}{88}\right)\)
\(\chi_{736}(373,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{63}{88}\right)\)
\(\chi_{736}(389,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{27}{88}\right)\)
\(\chi_{736}(405,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{47}{88}\right)\)
\(\chi_{736}(421,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{75}{88}\right)\)
\(\chi_{736}(429,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{37}{88}\right)\)
\(\chi_{736}(477,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{1}{88}\right)\)
\(\chi_{736}(493,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{13}{88}\right)\)
\(\chi_{736}(517,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{83}{88}\right)\)
\(\chi_{736}(525,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{21}{88}\right)\)
\(\chi_{736}(549,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{51}{88}\right)\)
\(\chi_{736}(557,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{85}{88}\right)\)

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First 31 of 40 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	736.bc
Modulus	$736$
Conductor	$736$
Order	$88$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(736\)
Conductor:	\(736\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(88\)	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)