LMFDB - Dirichlet character orbit 305760.fmx

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(305760, base_ring=CyclotomicField(168)) M = H._module chi = DirichletCharacter(H, M([84,105,84,0,160,98])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(11,305760)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$305760$
Conductor:	$61152$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$168$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 61152.bnl	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:	$\Q(\zeta_{168})$
Fixed field:	Number field defined by a degree 168 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{305760}(11,\cdot)$	$-1$	$1$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{305760}(3971,\cdot)$	$-1$	$1$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{155}{168}\right)$	$e\left(\frac{71}{84}\right)$
$\chi_{305760}(5891,\cdot)$	$-1$	$1$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{43}{168}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{305760}(8171,\cdot)$	$-1$	$1$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{127}{168}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{71}{168}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{168}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{305760}(21851,\cdot)$	$-1$	$1$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{305760}(25811,\cdot)$	$-1$	$1$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{47}{84}\right)$
$\chi_{305760}(27731,\cdot)$	$-1$	$1$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{149}{168}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{305760}(30011,\cdot)$	$-1$	$1$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{83}{168}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{65}{168}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{305760}(43691,\cdot)$	$-1$	$1$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{71}{168}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{127}{168}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{61}{168}\right)$	$e\left(\frac{61}{84}\right)$
$\chi_{305760}(47651,\cdot)$	$-1$	$1$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{305760}(49571,\cdot)$	$-1$	$1$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{19}{84}\right)$
$\chi_{305760}(51851,\cdot)$	$-1$	$1$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{95}{168}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{305760}(69491,\cdot)$	$-1$	$1$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{83}{84}\right)$
$\chi_{305760}(73691,\cdot)$	$-1$	$1$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{305760}(87371,\cdot)$	$-1$	$1$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{55}{168}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{37}{84}\right)$
$\chi_{305760}(91331,\cdot)$	$-1$	$1$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{65}{168}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{59}{84}\right)$
$\chi_{305760}(93251,\cdot)$	$-1$	$1$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{79}{84}\right)$
$\chi_{305760}(109211,\cdot)$	$-1$	$1$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{305760}(115091,\cdot)$	$-1$	$1$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{5}{168}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{61}{168}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{305760}(117371,\cdot)$	$-1$	$1$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{137}{168}\right)$	$e\left(\frac{53}{84}\right)$
$\chi_{305760}(131051,\cdot)$	$-1$	$1$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{95}{168}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{305760}(135011,\cdot)$	$-1$	$1$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{145}{168}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{305760}(136931,\cdot)$	$-1$	$1$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{137}{168}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{305760}(139211,\cdot)$	$-1$	$1$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{29}{84}\right)$
$\chi_{305760}(152891,\cdot)$	$-1$	$1$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{305760}(156851,\cdot)$	$-1$	$1$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{157}{168}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{71}{168}\right)$	$e\left(\frac{71}{84}\right)$
$\chi_{305760}(158771,\cdot)$	$-1$	$1$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{157}{168}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{127}{168}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{305760}(161051,\cdot)$	$-1$	$1$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{43}{168}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{155}{168}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{305760}(174731,\cdot)$	$-1$	$1$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{79}{168}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{157}{168}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{305760}(178691,\cdot)$	$-1$	$1$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{47}{84}\right)$
$\chi_{305760}(180611,\cdot)$	$-1$	$1$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{65}{168}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{31}{84}\right)$

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	\(-1\)	\(1\)	\(11\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{305760}(11,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{1}{84}\right)\)
\(\chi_{305760}(3971,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{155}{168}\right)\)	\(e\left(\frac{71}{84}\right)\)
\(\chi_{305760}(5891,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{43}{168}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{305760}(8171,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{127}{168}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{71}{168}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{168}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{305760}(21851,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{305760}(25811,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{47}{84}\right)\)
\(\chi_{305760}(27731,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{149}{168}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{305760}(30011,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{83}{168}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{65}{168}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{305760}(43691,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{71}{168}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{127}{168}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{61}{168}\right)\)	\(e\left(\frac{61}{84}\right)\)
\(\chi_{305760}(47651,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{305760}(49571,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{19}{84}\right)\)
\(\chi_{305760}(51851,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{41}{84}\right)\)
\(\chi_{305760}(69491,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{83}{84}\right)\)
\(\chi_{305760}(73691,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{17}{84}\right)\)
\(\chi_{305760}(87371,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{55}{168}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{37}{84}\right)\)
\(\chi_{305760}(91331,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{65}{168}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{59}{84}\right)\)
\(\chi_{305760}(93251,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{79}{84}\right)\)
\(\chi_{305760}(109211,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{305760}(115091,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{5}{168}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{61}{168}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{67}{84}\right)\)
\(\chi_{305760}(117371,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{137}{168}\right)\)	\(e\left(\frac{53}{84}\right)\)
\(\chi_{305760}(131051,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{305760}(135011,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{145}{168}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{305760}(136931,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{137}{168}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{55}{84}\right)\)
\(\chi_{305760}(139211,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{29}{84}\right)\)
\(\chi_{305760}(152891,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{1}{84}\right)\)
\(\chi_{305760}(156851,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{157}{168}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{71}{168}\right)\)	\(e\left(\frac{71}{84}\right)\)
\(\chi_{305760}(158771,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{157}{168}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{127}{168}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{305760}(161051,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{43}{168}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{155}{168}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{305760}(174731,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{79}{168}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{157}{168}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{305760}(178691,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{47}{84}\right)\)
\(\chi_{305760}(180611,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{65}{168}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{31}{84}\right)\)

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Basic properties

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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	305760.fmx
Modulus	$305760$
Conductor	$61152$
Order	$168$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(305760\)
Conductor:	\(61152\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(168\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 61152.bnl	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)