LMFDB - Dirichlet character orbit 2704.cy

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2704, base_ring=CyclotomicField(156)) M = H._module chi = DirichletCharacter(H, M([78,39,103])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(11,2704)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2704$
Conductor:	$2704$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$156$	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:	$\Q(\zeta_{156})$
Fixed field:	Number field defined by a degree 156 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{2704}(11,\cdot)$	$1$	$1$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2704}(59,\cdot)$	$1$	$1$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2704}(67,\cdot)$	$1$	$1$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2704}(219,\cdot)$	$1$	$1$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2704}(227,\cdot)$	$1$	$1$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2704}(267,\cdot)$	$1$	$1$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2704}(275,\cdot)$	$1$	$1$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2704}(435,\cdot)$	$1$	$1$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2704}(475,\cdot)$	$1$	$1$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2704}(483,\cdot)$	$1$	$1$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2704}(635,\cdot)$	$1$	$1$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2704}(643,\cdot)$	$1$	$1$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2704}(683,\cdot)$	$1$	$1$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2704}(691,\cdot)$	$1$	$1$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2704}(843,\cdot)$	$1$	$1$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2704}(851,\cdot)$	$1$	$1$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2704}(891,\cdot)$	$1$	$1$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2704}(899,\cdot)$	$1$	$1$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2704}(1051,\cdot)$	$1$	$1$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2704}(1059,\cdot)$	$1$	$1$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2704}(1099,\cdot)$	$1$	$1$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2704}(1107,\cdot)$	$1$	$1$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2704}(1259,\cdot)$	$1$	$1$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2704}(1267,\cdot)$	$1$	$1$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2704}(1307,\cdot)$	$1$	$1$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2704}(1315,\cdot)$	$1$	$1$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2704}(1467,\cdot)$	$1$	$1$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2704}(1475,\cdot)$	$1$	$1$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2704}(1515,\cdot)$	$1$	$1$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2704}(1523,\cdot)$	$1$	$1$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2704}(1675,\cdot)$	$1$	$1$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{5}{6}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{2704}(11,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2704}(59,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2704}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2704}(219,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2704}(227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2704}(267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2704}(275,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2704}(435,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2704}(475,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2704}(483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2704}(635,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2704}(643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2704}(683,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2704}(691,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2704}(843,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2704}(851,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2704}(891,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2704}(899,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2704}(1051,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2704}(1059,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2704}(1099,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2704}(1107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2704}(1259,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2704}(1267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2704}(1307,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2704}(1315,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2704}(1467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2704}(1475,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2704}(1515,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2704}(1523,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2704}(1675,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{5}{6}\right)\)

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First 31 of 48 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	2704.cy
Modulus	$2704$
Conductor	$2704$
Order	$156$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(2704\)
Conductor:	\(2704\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(156\)	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)