LMFDB - Dirichlet character orbit 8450.cx

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8450, base_ring=CyclotomicField(780)) M = H._module chi = DirichletCharacter(H, M([117,355])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(33,8450)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8450$
Conductor:	$4225$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$780$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4225.cw	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{780})$
Fixed field:	Number field defined by a degree 780 polynomial (not computed)

First 31 of 192 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{8450}(33,\cdot)$	$1$	$1$	$e\left(\frac{379}{780}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{379}{390}\right)$	$e\left(\frac{217}{780}\right)$	$e\left(\frac{311}{780}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{243}{260}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{119}{260}\right)$	$e\left(\frac{197}{390}\right)$
$\chi_{8450}(63,\cdot)$	$1$	$1$	$e\left(\frac{647}{780}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{257}{390}\right)$	$e\left(\frac{461}{780}\right)$	$e\left(\frac{463}{780}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{19}{260}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{127}{260}\right)$	$e\left(\frac{361}{390}\right)$
$\chi_{8450}(67,\cdot)$	$1$	$1$	$e\left(\frac{749}{780}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{359}{390}\right)$	$e\left(\frac{647}{780}\right)$	$e\left(\frac{61}{780}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{153}{260}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{229}{260}\right)$	$e\left(\frac{307}{390}\right)$
$\chi_{8450}(97,\cdot)$	$1$	$1$	$e\left(\frac{361}{780}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{361}{390}\right)$	$e\left(\frac{643}{780}\right)$	$e\left(\frac{749}{780}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{97}{260}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{101}{260}\right)$	$e\left(\frac{23}{390}\right)$
$\chi_{8450}(163,\cdot)$	$1$	$1$	$e\left(\frac{7}{780}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{7}{390}\right)$	$e\left(\frac{181}{780}\right)$	$e\left(\frac{263}{780}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{259}{260}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{260}\right)$	$e\left(\frac{371}{390}\right)$
$\chi_{8450}(197,\cdot)$	$1$	$1$	$e\left(\frac{461}{780}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{71}{390}\right)$	$e\left(\frac{443}{780}\right)$	$e\left(\frac{49}{780}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{157}{260}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{201}{260}\right)$	$e\left(\frac{253}{390}\right)$
$\chi_{8450}(227,\cdot)$	$1$	$1$	$e\left(\frac{733}{780}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{343}{390}\right)$	$e\left(\frac{679}{780}\right)$	$e\left(\frac{17}{780}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{81}{260}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{213}{260}\right)$	$e\left(\frac{239}{390}\right)$
$\chi_{8450}(323,\cdot)$	$1$	$1$	$e\left(\frac{443}{780}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{53}{390}\right)$	$e\left(\frac{89}{780}\right)$	$e\left(\frac{487}{780}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{11}{260}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{183}{260}\right)$	$e\left(\frac{79}{390}\right)$
$\chi_{8450}(327,\cdot)$	$1$	$1$	$e\left(\frac{173}{780}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{173}{390}\right)$	$e\left(\frac{239}{780}\right)$	$e\left(\frac{37}{780}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{161}{260}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{173}{260}\right)$	$e\left(\frac{199}{390}\right)$
$\chi_{8450}(423,\cdot)$	$1$	$1$	$e\left(\frac{43}{780}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{43}{390}\right)$	$e\left(\frac{109}{780}\right)$	$e\left(\frac{167}{780}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{31}{260}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{43}{260}\right)$	$e\left(\frac{329}{390}\right)$
$\chi_{8450}(453,\cdot)$	$1$	$1$	$e\left(\frac{731}{780}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{341}{390}\right)$	$e\left(\frac{293}{780}\right)$	$e\left(\frac{499}{780}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{7}{260}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{211}{260}\right)$	$e\left(\frac{133}{390}\right)$
$\chi_{8450}(487,\cdot)$	$1$	$1$	$e\left(\frac{697}{780}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{307}{390}\right)$	$e\left(\frac{751}{780}\right)$	$e\left(\frac{113}{780}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{49}{260}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{177}{260}\right)$	$e\left(\frac{281}{390}\right)$
$\chi_{8450}(553,\cdot)$	$1$	$1$	$e\left(\frac{451}{780}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{61}{390}\right)$	$e\left(\frac{73}{780}\right)$	$e\left(\frac{119}{780}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{47}{260}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{191}{260}\right)$	$e\left(\frac{113}{390}\right)$
$\chi_{8450}(583,\cdot)$	$1$	$1$	$e\left(\frac{239}{780}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{239}{390}\right)$	$e\left(\frac{497}{780}\right)$	$e\left(\frac{511}{780}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{3}{260}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{239}{260}\right)$	$e\left(\frac{187}{390}\right)$
$\chi_{8450}(617,\cdot)$	$1$	$1$	$e\left(\frac{289}{780}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{289}{390}\right)$	$e\left(\frac{7}{780}\right)$	$e\left(\frac{161}{780}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{33}{260}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{29}{260}\right)$	$e\left(\frac{107}{390}\right)$
$\chi_{8450}(683,\cdot)$	$1$	$1$	$e\left(\frac{79}{780}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{79}{390}\right)$	$e\left(\frac{37}{780}\right)$	$e\left(\frac{71}{780}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{63}{260}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{79}{260}\right)$	$e\left(\frac{287}{390}\right)$
$\chi_{8450}(713,\cdot)$	$1$	$1$	$e\left(\frac{527}{780}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{137}{390}\right)$	$e\left(\frac{701}{780}\right)$	$e\left(\frac{523}{780}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{259}{260}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{7}{260}\right)$	$e\left(\frac{241}{390}\right)$
$\chi_{8450}(717,\cdot)$	$1$	$1$	$e\left(\frac{89}{780}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{89}{390}\right)$	$e\left(\frac{407}{780}\right)$	$e\left(\frac{1}{780}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{173}{260}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{89}{260}\right)$	$e\left(\frac{37}{390}\right)$
$\chi_{8450}(747,\cdot)$	$1$	$1$	$e\left(\frac{661}{780}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{271}{390}\right)$	$e\left(\frac{43}{780}\right)$	$e\left(\frac{209}{780}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{17}{260}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{141}{260}\right)$	$e\left(\frac{323}{390}\right)$
$\chi_{8450}(813,\cdot)$	$1$	$1$	$e\left(\frac{487}{780}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{97}{390}\right)$	$e\left(\frac{1}{780}\right)$	$e\left(\frac{23}{780}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{79}{260}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{227}{260}\right)$	$e\left(\frac{71}{390}\right)$
$\chi_{8450}(847,\cdot)$	$1$	$1$	$e\left(\frac{581}{780}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{191}{390}\right)$	$e\left(\frac{203}{780}\right)$	$e\left(\frac{769}{780}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{177}{260}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{61}{260}\right)$	$e\left(\frac{373}{390}\right)$
$\chi_{8450}(877,\cdot)$	$1$	$1$	$e\left(\frac{253}{780}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{253}{390}\right)$	$e\left(\frac{79}{780}\right)$	$e\left(\frac{257}{780}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{260}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{253}{260}\right)$	$e\left(\frac{149}{390}\right)$
$\chi_{8450}(973,\cdot)$	$1$	$1$	$e\left(\frac{323}{780}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{323}{390}\right)$	$e\left(\frac{329}{780}\right)$	$e\left(\frac{547}{780}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{251}{260}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{63}{260}\right)$	$e\left(\frac{349}{390}\right)$
$\chi_{8450}(977,\cdot)$	$1$	$1$	$e\left(\frac{293}{780}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{293}{390}\right)$	$e\left(\frac{779}{780}\right)$	$e\left(\frac{757}{780}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{181}{260}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{33}{260}\right)$	$e\left(\frac{319}{390}\right)$
$\chi_{8450}(1073,\cdot)$	$1$	$1$	$e\left(\frac{523}{780}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{133}{390}\right)$	$e\left(\frac{709}{780}\right)$	$e\left(\frac{707}{780}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{111}{260}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{3}{260}\right)$	$e\left(\frac{29}{390}\right)$
$\chi_{8450}(1137,\cdot)$	$1$	$1$	$e\left(\frac{217}{780}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{217}{390}\right)$	$e\left(\frac{151}{780}\right)$	$e\left(\frac{353}{780}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{229}{260}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{217}{260}\right)$	$e\left(\frac{191}{390}\right)$
$\chi_{8450}(1203,\cdot)$	$1$	$1$	$e\left(\frac{151}{780}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{151}{390}\right)$	$e\left(\frac{673}{780}\right)$	$e\left(\frac{659}{780}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{127}{260}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{151}{260}\right)$	$e\left(\frac{203}{390}\right)$
$\chi_{8450}(1233,\cdot)$	$1$	$1$	$e\left(\frac{119}{780}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{119}{390}\right)$	$e\left(\frac{737}{780}\right)$	$e\left(\frac{571}{780}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{243}{260}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{119}{260}\right)$	$e\left(\frac{67}{390}\right)$
$\chi_{8450}(1237,\cdot)$	$1$	$1$	$e\left(\frac{497}{780}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{107}{390}\right)$	$e\left(\frac{371}{780}\right)$	$e\left(\frac{733}{780}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{189}{260}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{237}{260}\right)$	$e\left(\frac{211}{390}\right)$
$\chi_{8450}(1267,\cdot)$	$1$	$1$	$e\left(\frac{589}{780}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{199}{390}\right)$	$e\left(\frac{187}{780}\right)$	$e\left(\frac{401}{780}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{213}{260}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{69}{260}\right)$	$e\left(\frac{17}{390}\right)$
$\chi_{8450}(1363,\cdot)$	$1$	$1$	$e\left(\frac{407}{780}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{17}{390}\right)$	$e\left(\frac{161}{780}\right)$	$e\left(\frac{583}{780}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{239}{260}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{147}{260}\right)$	$e\left(\frac{121}{390}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{8450}(33,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{379}{780}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{379}{390}\right)\)	\(e\left(\frac{217}{780}\right)\)	\(e\left(\frac{311}{780}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{243}{260}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{119}{260}\right)\)	\(e\left(\frac{197}{390}\right)\)
\(\chi_{8450}(63,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{647}{780}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{257}{390}\right)\)	\(e\left(\frac{461}{780}\right)\)	\(e\left(\frac{463}{780}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{19}{260}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{127}{260}\right)\)	\(e\left(\frac{361}{390}\right)\)
\(\chi_{8450}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{749}{780}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{359}{390}\right)\)	\(e\left(\frac{647}{780}\right)\)	\(e\left(\frac{61}{780}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{153}{260}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{229}{260}\right)\)	\(e\left(\frac{307}{390}\right)\)
\(\chi_{8450}(97,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{361}{780}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{361}{390}\right)\)	\(e\left(\frac{643}{780}\right)\)	\(e\left(\frac{749}{780}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{97}{260}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{101}{260}\right)\)	\(e\left(\frac{23}{390}\right)\)
\(\chi_{8450}(163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{780}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{7}{390}\right)\)	\(e\left(\frac{181}{780}\right)\)	\(e\left(\frac{263}{780}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{259}{260}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{260}\right)\)	\(e\left(\frac{371}{390}\right)\)
\(\chi_{8450}(197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{461}{780}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{71}{390}\right)\)	\(e\left(\frac{443}{780}\right)\)	\(e\left(\frac{49}{780}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{157}{260}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{201}{260}\right)\)	\(e\left(\frac{253}{390}\right)\)
\(\chi_{8450}(227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{733}{780}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{343}{390}\right)\)	\(e\left(\frac{679}{780}\right)\)	\(e\left(\frac{17}{780}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{81}{260}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{213}{260}\right)\)	\(e\left(\frac{239}{390}\right)\)
\(\chi_{8450}(323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{443}{780}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{53}{390}\right)\)	\(e\left(\frac{89}{780}\right)\)	\(e\left(\frac{487}{780}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{11}{260}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{183}{260}\right)\)	\(e\left(\frac{79}{390}\right)\)
\(\chi_{8450}(327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{780}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{173}{390}\right)\)	\(e\left(\frac{239}{780}\right)\)	\(e\left(\frac{37}{780}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{161}{260}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{173}{260}\right)\)	\(e\left(\frac{199}{390}\right)\)
\(\chi_{8450}(423,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{780}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{43}{390}\right)\)	\(e\left(\frac{109}{780}\right)\)	\(e\left(\frac{167}{780}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{31}{260}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{43}{260}\right)\)	\(e\left(\frac{329}{390}\right)\)
\(\chi_{8450}(453,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{731}{780}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{341}{390}\right)\)	\(e\left(\frac{293}{780}\right)\)	\(e\left(\frac{499}{780}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{7}{260}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{211}{260}\right)\)	\(e\left(\frac{133}{390}\right)\)
\(\chi_{8450}(487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{697}{780}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{307}{390}\right)\)	\(e\left(\frac{751}{780}\right)\)	\(e\left(\frac{113}{780}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{49}{260}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{177}{260}\right)\)	\(e\left(\frac{281}{390}\right)\)
\(\chi_{8450}(553,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{451}{780}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{61}{390}\right)\)	\(e\left(\frac{73}{780}\right)\)	\(e\left(\frac{119}{780}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{47}{260}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{191}{260}\right)\)	\(e\left(\frac{113}{390}\right)\)
\(\chi_{8450}(583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{780}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{239}{390}\right)\)	\(e\left(\frac{497}{780}\right)\)	\(e\left(\frac{511}{780}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{3}{260}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{239}{260}\right)\)	\(e\left(\frac{187}{390}\right)\)
\(\chi_{8450}(617,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{289}{780}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{289}{390}\right)\)	\(e\left(\frac{7}{780}\right)\)	\(e\left(\frac{161}{780}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{33}{260}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{29}{260}\right)\)	\(e\left(\frac{107}{390}\right)\)
\(\chi_{8450}(683,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{780}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{79}{390}\right)\)	\(e\left(\frac{37}{780}\right)\)	\(e\left(\frac{71}{780}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{63}{260}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{79}{260}\right)\)	\(e\left(\frac{287}{390}\right)\)
\(\chi_{8450}(713,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{527}{780}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{137}{390}\right)\)	\(e\left(\frac{701}{780}\right)\)	\(e\left(\frac{523}{780}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{259}{260}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{7}{260}\right)\)	\(e\left(\frac{241}{390}\right)\)
\(\chi_{8450}(717,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{780}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{89}{390}\right)\)	\(e\left(\frac{407}{780}\right)\)	\(e\left(\frac{1}{780}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{173}{260}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{89}{260}\right)\)	\(e\left(\frac{37}{390}\right)\)
\(\chi_{8450}(747,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{661}{780}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{271}{390}\right)\)	\(e\left(\frac{43}{780}\right)\)	\(e\left(\frac{209}{780}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{17}{260}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{141}{260}\right)\)	\(e\left(\frac{323}{390}\right)\)
\(\chi_{8450}(813,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{487}{780}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{97}{390}\right)\)	\(e\left(\frac{1}{780}\right)\)	\(e\left(\frac{23}{780}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{79}{260}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{227}{260}\right)\)	\(e\left(\frac{71}{390}\right)\)
\(\chi_{8450}(847,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{581}{780}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{191}{390}\right)\)	\(e\left(\frac{203}{780}\right)\)	\(e\left(\frac{769}{780}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{177}{260}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{61}{260}\right)\)	\(e\left(\frac{373}{390}\right)\)
\(\chi_{8450}(877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{253}{780}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{253}{390}\right)\)	\(e\left(\frac{79}{780}\right)\)	\(e\left(\frac{257}{780}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{260}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{253}{260}\right)\)	\(e\left(\frac{149}{390}\right)\)
\(\chi_{8450}(973,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{323}{780}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{323}{390}\right)\)	\(e\left(\frac{329}{780}\right)\)	\(e\left(\frac{547}{780}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{251}{260}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{63}{260}\right)\)	\(e\left(\frac{349}{390}\right)\)
\(\chi_{8450}(977,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{293}{780}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{293}{390}\right)\)	\(e\left(\frac{779}{780}\right)\)	\(e\left(\frac{757}{780}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{181}{260}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{33}{260}\right)\)	\(e\left(\frac{319}{390}\right)\)
\(\chi_{8450}(1073,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{523}{780}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{133}{390}\right)\)	\(e\left(\frac{709}{780}\right)\)	\(e\left(\frac{707}{780}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{111}{260}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{3}{260}\right)\)	\(e\left(\frac{29}{390}\right)\)
\(\chi_{8450}(1137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{217}{780}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{217}{390}\right)\)	\(e\left(\frac{151}{780}\right)\)	\(e\left(\frac{353}{780}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{229}{260}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{217}{260}\right)\)	\(e\left(\frac{191}{390}\right)\)
\(\chi_{8450}(1203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{780}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{151}{390}\right)\)	\(e\left(\frac{673}{780}\right)\)	\(e\left(\frac{659}{780}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{127}{260}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{151}{260}\right)\)	\(e\left(\frac{203}{390}\right)\)
\(\chi_{8450}(1233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{780}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{119}{390}\right)\)	\(e\left(\frac{737}{780}\right)\)	\(e\left(\frac{571}{780}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{243}{260}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{119}{260}\right)\)	\(e\left(\frac{67}{390}\right)\)
\(\chi_{8450}(1237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{497}{780}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{107}{390}\right)\)	\(e\left(\frac{371}{780}\right)\)	\(e\left(\frac{733}{780}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{189}{260}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{237}{260}\right)\)	\(e\left(\frac{211}{390}\right)\)
\(\chi_{8450}(1267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{589}{780}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{199}{390}\right)\)	\(e\left(\frac{187}{780}\right)\)	\(e\left(\frac{401}{780}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{213}{260}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{69}{260}\right)\)	\(e\left(\frac{17}{390}\right)\)
\(\chi_{8450}(1363,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{407}{780}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{17}{390}\right)\)	\(e\left(\frac{161}{780}\right)\)	\(e\left(\frac{583}{780}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{239}{260}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{147}{260}\right)\)	\(e\left(\frac{121}{390}\right)\)

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First 31 of 192 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	8450.cx
Modulus	$8450$
Conductor	$4225$
Order	$780$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8450\)
Conductor:	\(4225\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(780\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4225.cw	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)