LMFDB - Dirichlet character orbit 2349.bn

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2349, base_ring=CyclotomicField(126)) M = H._module chi = DirichletCharacter(H, M([91,27])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(35,2349)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2349$
Conductor:	$783$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$126$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 783.bh	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{63})$
Fixed field:	Number field defined by a degree 126 polynomial (not computed)

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{2349}(35,\cdot)$	$-1$	$1$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{47}{63}\right)$
$\chi_{2349}(62,\cdot)$	$-1$	$1$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{53}{63}\right)$
$\chi_{2349}(71,\cdot)$	$-1$	$1$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{22}{63}\right)$
$\chi_{2349}(125,\cdot)$	$-1$	$1$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{34}{63}\right)$
$\chi_{2349}(179,\cdot)$	$-1$	$1$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{37}{63}\right)$
$\chi_{2349}(332,\cdot)$	$-1$	$1$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{50}{63}\right)$
$\chi_{2349}(341,\cdot)$	$-1$	$1$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{10}{63}\right)$
$\chi_{2349}(386,\cdot)$	$-1$	$1$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{62}{63}\right)$
$\chi_{2349}(440,\cdot)$	$-1$	$1$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{2}{63}\right)$
$\chi_{2349}(557,\cdot)$	$-1$	$1$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{40}{63}\right)$
$\chi_{2349}(584,\cdot)$	$-1$	$1$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{46}{63}\right)$
$\chi_{2349}(602,\cdot)$	$-1$	$1$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{38}{63}\right)$
$\chi_{2349}(818,\cdot)$	$-1$	$1$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{5}{63}\right)$
$\chi_{2349}(845,\cdot)$	$-1$	$1$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{11}{63}\right)$
$\chi_{2349}(854,\cdot)$	$-1$	$1$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{43}{63}\right)$
$\chi_{2349}(908,\cdot)$	$-1$	$1$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{55}{63}\right)$
$\chi_{2349}(962,\cdot)$	$-1$	$1$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{58}{63}\right)$
$\chi_{2349}(1115,\cdot)$	$-1$	$1$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{8}{63}\right)$
$\chi_{2349}(1124,\cdot)$	$-1$	$1$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{31}{63}\right)$
$\chi_{2349}(1169,\cdot)$	$-1$	$1$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{59}{126}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{20}{63}\right)$
$\chi_{2349}(1223,\cdot)$	$-1$	$1$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{23}{63}\right)$
$\chi_{2349}(1340,\cdot)$	$-1$	$1$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{61}{63}\right)$
$\chi_{2349}(1367,\cdot)$	$-1$	$1$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{4}{63}\right)$
$\chi_{2349}(1385,\cdot)$	$-1$	$1$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{59}{63}\right)$
$\chi_{2349}(1601,\cdot)$	$-1$	$1$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{26}{63}\right)$
$\chi_{2349}(1628,\cdot)$	$-1$	$1$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{32}{63}\right)$
$\chi_{2349}(1637,\cdot)$	$-1$	$1$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{1}{63}\right)$
$\chi_{2349}(1691,\cdot)$	$-1$	$1$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{13}{63}\right)$
$\chi_{2349}(1745,\cdot)$	$-1$	$1$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{16}{63}\right)$
$\chi_{2349}(1898,\cdot)$	$-1$	$1$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{29}{63}\right)$
$\chi_{2349}(1907,\cdot)$	$-1$	$1$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{52}{63}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{2349}(35,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)
\(\chi_{2349}(62,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)
\(\chi_{2349}(71,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)
\(\chi_{2349}(125,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)
\(\chi_{2349}(179,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)
\(\chi_{2349}(332,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)
\(\chi_{2349}(341,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)
\(\chi_{2349}(386,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)
\(\chi_{2349}(440,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{2}{63}\right)\)
\(\chi_{2349}(557,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)
\(\chi_{2349}(584,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)
\(\chi_{2349}(602,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)
\(\chi_{2349}(818,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)
\(\chi_{2349}(845,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)
\(\chi_{2349}(854,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)
\(\chi_{2349}(908,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)
\(\chi_{2349}(962,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)
\(\chi_{2349}(1115,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)
\(\chi_{2349}(1124,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)
\(\chi_{2349}(1169,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{59}{126}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)
\(\chi_{2349}(1223,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)
\(\chi_{2349}(1340,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)
\(\chi_{2349}(1367,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)
\(\chi_{2349}(1385,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)
\(\chi_{2349}(1601,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)
\(\chi_{2349}(1628,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)
\(\chi_{2349}(1637,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)
\(\chi_{2349}(1691,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)
\(\chi_{2349}(1745,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)
\(\chi_{2349}(1898,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)
\(\chi_{2349}(1907,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)

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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.bn
Modulus	$2349$
Conductor	$783$
Order	$126$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(2349\)
Conductor:	\(783\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(126\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 783.bh	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)