LMFDB - Dirichlet character orbit 305760.eel

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(305760, base_ring=CyclotomicField(84)) M = H._module chi = DirichletCharacter(H, M([0,63,42,0,30,7])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(41,305760)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$305760$
Conductor:	$30576$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$84$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 30576.ben	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:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{305760}(41,\cdot)$	$-1$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{43}{84}\right)$	$i$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{305760}(5081,\cdot)$	$-1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{37}{84}\right)$	$-i$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{305760}(16841,\cdot)$	$-1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{23}{84}\right)$	$i$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{305760}(31961,\cdot)$	$-1$	$1$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{84}\right)$	$-i$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{5}{28}\right)$
$\chi_{305760}(43721,\cdot)$	$-1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{19}{84}\right)$	$i$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{305760}(48761,\cdot)$	$-1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{84}\right)$	$-i$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{305760}(60521,\cdot)$	$-1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{83}{84}\right)$	$i$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{305760}(75641,\cdot)$	$-1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{65}{84}\right)$	$-i$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{305760}(87401,\cdot)$	$-1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{79}{84}\right)$	$i$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{305760}(92441,\cdot)$	$-1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{73}{84}\right)$	$-i$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{305760}(104201,\cdot)$	$-1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{59}{84}\right)$	$i$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{305760}(119321,\cdot)$	$-1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{41}{84}\right)$	$-i$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{305760}(131081,\cdot)$	$-1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{55}{84}\right)$	$i$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{305760}(163001,\cdot)$	$-1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{17}{84}\right)$	$-i$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{305760}(174761,\cdot)$	$-1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{31}{84}\right)$	$i$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{305760}(179801,\cdot)$	$-1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{25}{84}\right)$	$-i$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{305760}(191561,\cdot)$	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{84}\right)$	$i$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{305760}(223481,\cdot)$	$-1$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{84}\right)$	$-i$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{305760}(235241,\cdot)$	$-1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{71}{84}\right)$	$i$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{305760}(250361,\cdot)$	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{53}{84}\right)$	$-i$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{305760}(262121,\cdot)$	$-1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{67}{84}\right)$	$i$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{305760}(267161,\cdot)$	$-1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{61}{84}\right)$	$-i$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{5}{28}\right)$
$\chi_{305760}(278921,\cdot)$	$-1$	$1$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{47}{84}\right)$	$i$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{305760}(294041,\cdot)$	$-1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{29}{84}\right)$	$-i$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{1}{28}\right)$

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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	\(-1\)	\(1\)	\(11\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{305760}(41,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(i\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{305760}(5081,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(-i\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{305760}(16841,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(i\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{305760}(31961,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(-i\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{305760}(43721,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(i\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{305760}(48761,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(-i\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{305760}(60521,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(i\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{305760}(75641,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(-i\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{305760}(87401,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(i\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{305760}(92441,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(-i\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{305760}(104201,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(i\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{305760}(119321,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(-i\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{305760}(131081,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(i\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{305760}(163001,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(-i\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{305760}(174761,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(i\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{305760}(179801,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(-i\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{305760}(191561,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(i\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{305760}(223481,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(-i\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{305760}(235241,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(i\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{305760}(250361,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(-i\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{305760}(262121,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(i\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{305760}(267161,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(-i\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{305760}(278921,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(i\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{305760}(294041,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(-i\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)

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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	305760.eel
Modulus	$305760$
Conductor	$30576$
Order	$84$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(305760\)
Conductor:	\(30576\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(84\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 30576.ben	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)