LMFDB - Dirichlet character orbit 2349.bj

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2349, base_ring=CyclotomicField(108)) M = H._module chi = DirichletCharacter(H, M([80,27])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(70,2349)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2349$
Conductor:	$2349$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$108$	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:	$\Q(\zeta_{108})$
Fixed field:	Number field defined by a degree 108 polynomial (not computed)

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{2349}(70,\cdot)$	$-1$	$1$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{26}{27}\right)$
$\chi_{2349}(133,\cdot)$	$-1$	$1$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{20}{27}\right)$
$\chi_{2349}(157,\cdot)$	$-1$	$1$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{19}{27}\right)$
$\chi_{2349}(220,\cdot)$	$-1$	$1$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{22}{27}\right)$
$\chi_{2349}(331,\cdot)$	$-1$	$1$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{5}{27}\right)$
$\chi_{2349}(394,\cdot)$	$-1$	$1$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{26}{27}\right)$
$\chi_{2349}(418,\cdot)$	$-1$	$1$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{16}{27}\right)$
$\chi_{2349}(481,\cdot)$	$-1$	$1$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{19}{27}\right)$
$\chi_{2349}(592,\cdot)$	$-1$	$1$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{11}{27}\right)$
$\chi_{2349}(655,\cdot)$	$-1$	$1$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{5}{27}\right)$
$\chi_{2349}(679,\cdot)$	$-1$	$1$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{13}{27}\right)$
$\chi_{2349}(742,\cdot)$	$-1$	$1$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{16}{27}\right)$
$\chi_{2349}(853,\cdot)$	$-1$	$1$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{17}{27}\right)$
$\chi_{2349}(916,\cdot)$	$-1$	$1$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{11}{27}\right)$
$\chi_{2349}(940,\cdot)$	$-1$	$1$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{10}{27}\right)$
$\chi_{2349}(1003,\cdot)$	$-1$	$1$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{13}{27}\right)$
$\chi_{2349}(1114,\cdot)$	$-1$	$1$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{23}{27}\right)$
$\chi_{2349}(1177,\cdot)$	$-1$	$1$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{17}{27}\right)$
$\chi_{2349}(1201,\cdot)$	$-1$	$1$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{7}{27}\right)$
$\chi_{2349}(1264,\cdot)$	$-1$	$1$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{10}{27}\right)$
$\chi_{2349}(1375,\cdot)$	$-1$	$1$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{2}{27}\right)$
$\chi_{2349}(1438,\cdot)$	$-1$	$1$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{23}{27}\right)$
$\chi_{2349}(1462,\cdot)$	$-1$	$1$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{4}{27}\right)$
$\chi_{2349}(1525,\cdot)$	$-1$	$1$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{7}{27}\right)$
$\chi_{2349}(1636,\cdot)$	$-1$	$1$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{8}{27}\right)$
$\chi_{2349}(1699,\cdot)$	$-1$	$1$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{2}{27}\right)$
$\chi_{2349}(1723,\cdot)$	$-1$	$1$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{1}{27}\right)$
$\chi_{2349}(1786,\cdot)$	$-1$	$1$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{4}{27}\right)$
$\chi_{2349}(1897,\cdot)$	$-1$	$1$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{14}{27}\right)$
$\chi_{2349}(1960,\cdot)$	$-1$	$1$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{8}{27}\right)$
$\chi_{2349}(1984,\cdot)$	$-1$	$1$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{25}{27}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{2349}(70,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{26}{27}\right)\)
\(\chi_{2349}(133,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{20}{27}\right)\)
\(\chi_{2349}(157,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{19}{27}\right)\)
\(\chi_{2349}(220,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{22}{27}\right)\)
\(\chi_{2349}(331,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{5}{27}\right)\)
\(\chi_{2349}(394,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{26}{27}\right)\)
\(\chi_{2349}(418,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{16}{27}\right)\)
\(\chi_{2349}(481,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{19}{27}\right)\)
\(\chi_{2349}(592,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{11}{27}\right)\)
\(\chi_{2349}(655,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{5}{27}\right)\)
\(\chi_{2349}(679,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{13}{27}\right)\)
\(\chi_{2349}(742,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{16}{27}\right)\)
\(\chi_{2349}(853,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{17}{27}\right)\)
\(\chi_{2349}(916,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{11}{27}\right)\)
\(\chi_{2349}(940,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{10}{27}\right)\)
\(\chi_{2349}(1003,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{13}{27}\right)\)
\(\chi_{2349}(1114,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{23}{27}\right)\)
\(\chi_{2349}(1177,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{17}{27}\right)\)
\(\chi_{2349}(1201,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{7}{27}\right)\)
\(\chi_{2349}(1264,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{10}{27}\right)\)
\(\chi_{2349}(1375,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{2}{27}\right)\)
\(\chi_{2349}(1438,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{23}{27}\right)\)
\(\chi_{2349}(1462,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{4}{27}\right)\)
\(\chi_{2349}(1525,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{7}{27}\right)\)
\(\chi_{2349}(1636,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{8}{27}\right)\)
\(\chi_{2349}(1699,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{2}{27}\right)\)
\(\chi_{2349}(1723,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{1}{27}\right)\)
\(\chi_{2349}(1786,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{4}{27}\right)\)
\(\chi_{2349}(1897,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{14}{27}\right)\)
\(\chi_{2349}(1960,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{8}{27}\right)\)
\(\chi_{2349}(1984,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{25}{27}\right)\)

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First 31 of 36 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	2349.bj
Modulus	$2349$
Conductor	$2349$
Order	$108$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(2349\)
Conductor:	\(2349\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(108\)	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)