LMFDB - Dirichlet character orbit 736.bf

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(736, base_ring=CyclotomicField(88)) M = H._module chi = DirichletCharacter(H, M([0,77,56])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(13,736)) 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:	even	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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{736}(13,\cdot)$	$1$	$1$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{57}{88}\right)$
$\chi_{736}(29,\cdot)$	$1$	$1$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{45}{88}\right)$
$\chi_{736}(77,\cdot)$	$1$	$1$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{81}{88}\right)$
$\chi_{736}(85,\cdot)$	$1$	$1$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{75}{88}\right)$
$\chi_{736}(101,\cdot)$	$1$	$1$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{47}{88}\right)$
$\chi_{736}(117,\cdot)$	$1$	$1$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{27}{88}\right)$
$\chi_{736}(133,\cdot)$	$1$	$1$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{63}{88}\right)$
$\chi_{736}(141,\cdot)$	$1$	$1$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{73}{88}\right)$
$\chi_{736}(165,\cdot)$	$1$	$1$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{87}{88}\right)$
$\chi_{736}(173,\cdot)$	$1$	$1$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{17}{88}\right)$
$\chi_{736}(197,\cdot)$	$1$	$1$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{79}{88}\right)$
$\chi_{736}(213,\cdot)$	$1$	$1$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{67}{88}\right)$
$\chi_{736}(261,\cdot)$	$1$	$1$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{15}{88}\right)$
$\chi_{736}(269,\cdot)$	$1$	$1$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{9}{88}\right)$
$\chi_{736}(285,\cdot)$	$1$	$1$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{69}{88}\right)$
$\chi_{736}(301,\cdot)$	$1$	$1$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{49}{88}\right)$
$\chi_{736}(317,\cdot)$	$1$	$1$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{85}{88}\right)$
$\chi_{736}(325,\cdot)$	$1$	$1$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{7}{88}\right)$
$\chi_{736}(349,\cdot)$	$1$	$1$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{21}{88}\right)$
$\chi_{736}(357,\cdot)$	$1$	$1$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{39}{88}\right)$
$\chi_{736}(381,\cdot)$	$1$	$1$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{13}{88}\right)$
$\chi_{736}(397,\cdot)$	$1$	$1$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{1}{88}\right)$
$\chi_{736}(445,\cdot)$	$1$	$1$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{37}{88}\right)$
$\chi_{736}(453,\cdot)$	$1$	$1$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{31}{88}\right)$
$\chi_{736}(469,\cdot)$	$1$	$1$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{3}{88}\right)$
$\chi_{736}(485,\cdot)$	$1$	$1$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{71}{88}\right)$
$\chi_{736}(501,\cdot)$	$1$	$1$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{19}{88}\right)$
$\chi_{736}(509,\cdot)$	$1$	$1$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{29}{88}\right)$
$\chi_{736}(533,\cdot)$	$1$	$1$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{43}{88}\right)$
$\chi_{736}(541,\cdot)$	$1$	$1$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{61}{88}\right)$
$\chi_{736}(565,\cdot)$	$1$	$1$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{35}{88}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{736}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{57}{88}\right)\)
\(\chi_{736}(29,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{45}{88}\right)\)
\(\chi_{736}(77,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{81}{88}\right)\)
\(\chi_{736}(85,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{75}{88}\right)\)
\(\chi_{736}(101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{47}{88}\right)\)
\(\chi_{736}(117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{27}{88}\right)\)
\(\chi_{736}(133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{63}{88}\right)\)
\(\chi_{736}(141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{73}{88}\right)\)
\(\chi_{736}(165,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{87}{88}\right)\)
\(\chi_{736}(173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{17}{88}\right)\)
\(\chi_{736}(197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{79}{88}\right)\)
\(\chi_{736}(213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{67}{88}\right)\)
\(\chi_{736}(261,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{15}{88}\right)\)
\(\chi_{736}(269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{9}{88}\right)\)
\(\chi_{736}(285,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{69}{88}\right)\)
\(\chi_{736}(301,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{49}{88}\right)\)
\(\chi_{736}(317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{85}{88}\right)\)
\(\chi_{736}(325,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{7}{88}\right)\)
\(\chi_{736}(349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{21}{88}\right)\)
\(\chi_{736}(357,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{39}{88}\right)\)
\(\chi_{736}(381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{13}{88}\right)\)
\(\chi_{736}(397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{1}{88}\right)\)
\(\chi_{736}(445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{37}{88}\right)\)
\(\chi_{736}(453,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{31}{88}\right)\)
\(\chi_{736}(469,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{3}{88}\right)\)
\(\chi_{736}(485,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{71}{88}\right)\)
\(\chi_{736}(501,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{19}{88}\right)\)
\(\chi_{736}(509,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{29}{88}\right)\)
\(\chi_{736}(533,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{43}{88}\right)\)
\(\chi_{736}(541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{61}{88}\right)\)
\(\chi_{736}(565,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{35}{88}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

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.bf
Modulus	$736$
Conductor	$736$
Order	$88$
Real	no
Primitive	yes
Minimal	yes
Parity	even

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:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)