LMFDB - Dirichlet character orbit 508288.op

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(508288, base_ring=CyclotomicField(480)) M = H._module chi = DirichletCharacter(H, M([0,255,384,400])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(69,508288)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$508288$
Conductor:	$26752$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$480$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 26752.kg	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:	$\Q(\zeta_{480})$
Fixed field:	Number field defined by a degree 480 polynomial (not computed)

First 31 of 128 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$21$	$23$	$25$
$\chi_{508288}(69,\cdot)$	$-1$	$1$	$e\left(\frac{397}{480}\right)$	$e\left(\frac{31}{480}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{449}{480}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{31}{240}\right)$
$\chi_{508288}(2957,\cdot)$	$-1$	$1$	$e\left(\frac{19}{480}\right)$	$e\left(\frac{97}{480}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{19}{240}\right)$	$e\left(\frac{383}{480}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{97}{240}\right)$
$\chi_{508288}(5845,\cdot)$	$-1$	$1$	$e\left(\frac{73}{480}\right)$	$e\left(\frac{19}{480}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{73}{240}\right)$	$e\left(\frac{461}{480}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{19}{240}\right)$
$\chi_{508288}(8957,\cdot)$	$-1$	$1$	$e\left(\frac{407}{480}\right)$	$e\left(\frac{461}{480}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{19}{480}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{221}{240}\right)$
$\chi_{508288}(11621,\cdot)$	$-1$	$1$	$e\left(\frac{421}{480}\right)$	$e\left(\frac{103}{480}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{377}{480}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{103}{240}\right)$
$\chi_{508288}(11845,\cdot)$	$-1$	$1$	$e\left(\frac{269}{480}\right)$	$e\left(\frac{287}{480}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{193}{480}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{47}{240}\right)$
$\chi_{508288}(14733,\cdot)$	$-1$	$1$	$e\left(\frac{83}{480}\right)$	$e\left(\frac{449}{480}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{31}{480}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{209}{240}\right)$
$\chi_{508288}(20509,\cdot)$	$-1$	$1$	$e\left(\frac{431}{480}\right)$	$e\left(\frac{53}{480}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{427}{480}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{53}{240}\right)$
$\chi_{508288}(31837,\cdot)$	$-1$	$1$	$e\left(\frac{127}{480}\right)$	$e\left(\frac{421}{480}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{59}{480}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{181}{240}\right)$
$\chi_{508288}(34725,\cdot)$	$-1$	$1$	$e\left(\frac{469}{480}\right)$	$e\left(\frac{247}{480}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{233}{480}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{7}{240}\right)$
$\chi_{508288}(37613,\cdot)$	$-1$	$1$	$e\left(\frac{283}{480}\right)$	$e\left(\frac{409}{480}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{71}{480}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{169}{240}\right)$
$\chi_{508288}(40725,\cdot)$	$-1$	$1$	$e\left(\frac{377}{480}\right)$	$e\left(\frac{131}{480}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{137}{240}\right)$	$e\left(\frac{349}{480}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{131}{240}\right)$
$\chi_{508288}(43389,\cdot)$	$-1$	$1$	$e\left(\frac{151}{480}\right)$	$e\left(\frac{13}{480}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{467}{480}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{13}{240}\right)$
$\chi_{508288}(43613,\cdot)$	$-1$	$1$	$e\left(\frac{479}{480}\right)$	$e\left(\frac{197}{480}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{283}{480}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{197}{240}\right)$
$\chi_{508288}(46501,\cdot)$	$-1$	$1$	$e\left(\frac{53}{480}\right)$	$e\left(\frac{119}{480}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{53}{240}\right)$	$e\left(\frac{361}{480}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{119}{240}\right)$
$\chi_{508288}(52277,\cdot)$	$-1$	$1$	$e\left(\frac{401}{480}\right)$	$e\left(\frac{203}{480}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{161}{240}\right)$	$e\left(\frac{277}{480}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{203}{240}\right)$
$\chi_{508288}(63605,\cdot)$	$-1$	$1$	$e\left(\frac{97}{480}\right)$	$e\left(\frac{91}{480}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{97}{240}\right)$	$e\left(\frac{389}{480}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{91}{240}\right)$
$\chi_{508288}(66493,\cdot)$	$-1$	$1$	$e\left(\frac{199}{480}\right)$	$e\left(\frac{157}{480}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{199}{240}\right)$	$e\left(\frac{323}{480}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{157}{240}\right)$
$\chi_{508288}(69381,\cdot)$	$-1$	$1$	$e\left(\frac{253}{480}\right)$	$e\left(\frac{79}{480}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{13}{240}\right)$	$e\left(\frac{401}{480}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{79}{240}\right)$
$\chi_{508288}(72493,\cdot)$	$-1$	$1$	$e\left(\frac{107}{480}\right)$	$e\left(\frac{41}{480}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{107}{240}\right)$	$e\left(\frac{439}{480}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{41}{240}\right)$
$\chi_{508288}(75157,\cdot)$	$-1$	$1$	$e\left(\frac{121}{480}\right)$	$e\left(\frac{163}{480}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{317}{480}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{163}{240}\right)$
$\chi_{508288}(75381,\cdot)$	$-1$	$1$	$e\left(\frac{449}{480}\right)$	$e\left(\frac{347}{480}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{133}{480}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{107}{240}\right)$
$\chi_{508288}(78269,\cdot)$	$-1$	$1$	$e\left(\frac{263}{480}\right)$	$e\left(\frac{29}{480}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{451}{480}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{29}{240}\right)$
$\chi_{508288}(84045,\cdot)$	$-1$	$1$	$e\left(\frac{131}{480}\right)$	$e\left(\frac{113}{480}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{367}{480}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{113}{240}\right)$
$\chi_{508288}(95373,\cdot)$	$-1$	$1$	$e\left(\frac{307}{480}\right)$	$e\left(\frac{1}{480}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{479}{480}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{1}{240}\right)$
$\chi_{508288}(98261,\cdot)$	$-1$	$1$	$e\left(\frac{169}{480}\right)$	$e\left(\frac{307}{480}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{169}{240}\right)$	$e\left(\frac{173}{480}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{67}{240}\right)$
$\chi_{508288}(101149,\cdot)$	$-1$	$1$	$e\left(\frac{463}{480}\right)$	$e\left(\frac{469}{480}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{11}{480}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{229}{240}\right)$
$\chi_{508288}(104261,\cdot)$	$-1$	$1$	$e\left(\frac{77}{480}\right)$	$e\left(\frac{191}{480}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{289}{480}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{191}{240}\right)$
$\chi_{508288}(106925,\cdot)$	$-1$	$1$	$e\left(\frac{331}{480}\right)$	$e\left(\frac{73}{480}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{407}{480}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{73}{240}\right)$
$\chi_{508288}(107149,\cdot)$	$-1$	$1$	$e\left(\frac{179}{480}\right)$	$e\left(\frac{257}{480}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{179}{240}\right)$	$e\left(\frac{223}{480}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{17}{240}\right)$
$\chi_{508288}(110037,\cdot)$	$-1$	$1$	$e\left(\frac{233}{480}\right)$	$e\left(\frac{179}{480}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{233}{240}\right)$	$e\left(\frac{301}{480}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{179}{240}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\(\chi_{508288}(69,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{397}{480}\right)\)	\(e\left(\frac{31}{480}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{449}{480}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{31}{240}\right)\)
\(\chi_{508288}(2957,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{480}\right)\)	\(e\left(\frac{97}{480}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{19}{240}\right)\)	\(e\left(\frac{383}{480}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{97}{240}\right)\)
\(\chi_{508288}(5845,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{480}\right)\)	\(e\left(\frac{19}{480}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{73}{240}\right)\)	\(e\left(\frac{461}{480}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{19}{240}\right)\)
\(\chi_{508288}(8957,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{407}{480}\right)\)	\(e\left(\frac{461}{480}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{19}{480}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{221}{240}\right)\)
\(\chi_{508288}(11621,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{421}{480}\right)\)	\(e\left(\frac{103}{480}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{377}{480}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{103}{240}\right)\)
\(\chi_{508288}(11845,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{269}{480}\right)\)	\(e\left(\frac{287}{480}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{193}{480}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{47}{240}\right)\)
\(\chi_{508288}(14733,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{480}\right)\)	\(e\left(\frac{449}{480}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{83}{240}\right)\)	\(e\left(\frac{31}{480}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{209}{240}\right)\)
\(\chi_{508288}(20509,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{431}{480}\right)\)	\(e\left(\frac{53}{480}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{191}{240}\right)\)	\(e\left(\frac{427}{480}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{53}{240}\right)\)
\(\chi_{508288}(31837,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{480}\right)\)	\(e\left(\frac{421}{480}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{59}{480}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{181}{240}\right)\)
\(\chi_{508288}(34725,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{469}{480}\right)\)	\(e\left(\frac{247}{480}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{233}{480}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{7}{240}\right)\)
\(\chi_{508288}(37613,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{283}{480}\right)\)	\(e\left(\frac{409}{480}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{43}{240}\right)\)	\(e\left(\frac{71}{480}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{169}{240}\right)\)
\(\chi_{508288}(40725,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{377}{480}\right)\)	\(e\left(\frac{131}{480}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{137}{240}\right)\)	\(e\left(\frac{349}{480}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{131}{240}\right)\)
\(\chi_{508288}(43389,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{151}{480}\right)\)	\(e\left(\frac{13}{480}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{467}{480}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{13}{240}\right)\)
\(\chi_{508288}(43613,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{479}{480}\right)\)	\(e\left(\frac{197}{480}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{283}{480}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{197}{240}\right)\)
\(\chi_{508288}(46501,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{480}\right)\)	\(e\left(\frac{119}{480}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{53}{240}\right)\)	\(e\left(\frac{361}{480}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{119}{240}\right)\)
\(\chi_{508288}(52277,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{401}{480}\right)\)	\(e\left(\frac{203}{480}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{161}{240}\right)\)	\(e\left(\frac{277}{480}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{203}{240}\right)\)
\(\chi_{508288}(63605,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{480}\right)\)	\(e\left(\frac{91}{480}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{389}{480}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{91}{240}\right)\)
\(\chi_{508288}(66493,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{199}{480}\right)\)	\(e\left(\frac{157}{480}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{199}{240}\right)\)	\(e\left(\frac{323}{480}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{157}{240}\right)\)
\(\chi_{508288}(69381,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{253}{480}\right)\)	\(e\left(\frac{79}{480}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{13}{240}\right)\)	\(e\left(\frac{401}{480}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{79}{240}\right)\)
\(\chi_{508288}(72493,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{107}{480}\right)\)	\(e\left(\frac{41}{480}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{107}{240}\right)\)	\(e\left(\frac{439}{480}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{41}{240}\right)\)
\(\chi_{508288}(75157,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{480}\right)\)	\(e\left(\frac{163}{480}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{317}{480}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{163}{240}\right)\)
\(\chi_{508288}(75381,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{449}{480}\right)\)	\(e\left(\frac{347}{480}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{133}{480}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{107}{240}\right)\)
\(\chi_{508288}(78269,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{263}{480}\right)\)	\(e\left(\frac{29}{480}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{451}{480}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{29}{240}\right)\)
\(\chi_{508288}(84045,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{480}\right)\)	\(e\left(\frac{113}{480}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{367}{480}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{113}{240}\right)\)
\(\chi_{508288}(95373,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{307}{480}\right)\)	\(e\left(\frac{1}{480}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{479}{480}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{1}{240}\right)\)
\(\chi_{508288}(98261,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{169}{480}\right)\)	\(e\left(\frac{307}{480}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{169}{240}\right)\)	\(e\left(\frac{173}{480}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{67}{240}\right)\)
\(\chi_{508288}(101149,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{463}{480}\right)\)	\(e\left(\frac{469}{480}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{11}{480}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{229}{240}\right)\)
\(\chi_{508288}(104261,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{480}\right)\)	\(e\left(\frac{191}{480}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{289}{480}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{191}{240}\right)\)
\(\chi_{508288}(106925,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{331}{480}\right)\)	\(e\left(\frac{73}{480}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{407}{480}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{73}{240}\right)\)
\(\chi_{508288}(107149,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{179}{480}\right)\)	\(e\left(\frac{257}{480}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{179}{240}\right)\)	\(e\left(\frac{223}{480}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{17}{240}\right)\)
\(\chi_{508288}(110037,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{233}{480}\right)\)	\(e\left(\frac{179}{480}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{233}{240}\right)\)	\(e\left(\frac{301}{480}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{179}{240}\right)\)

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First 31 of 128 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	508288.op
Modulus	$508288$
Conductor	$26752$
Order	$480$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(508288\)
Conductor:	\(26752\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(480\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 26752.kg	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)