LMFDB - Dirichlet character orbit 8450.cw

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8450, base_ring=CyclotomicField(780)) M = H._module chi = DirichletCharacter(H, M([624,515])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(11,8450)) 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.cx	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:	$\Q(\zeta_{780})$
Fixed field:	Number field defined by a degree 780 polynomial (not computed)

First 31 of 192 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{8450}(11,\cdot)$	$-1$	$1$	$e\left(\frac{92}{195}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{184}{195}\right)$	$e\left(\frac{629}{780}\right)$	$e\left(\frac{311}{390}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{31}{260}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{2}{195}\right)$
$\chi_{8450}(41,\cdot)$	$-1$	$1$	$e\left(\frac{188}{195}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{181}{195}\right)$	$e\left(\frac{251}{780}\right)$	$e\left(\frac{59}{390}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{69}{260}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{58}{65}\right)$	$e\left(\frac{38}{195}\right)$
$\chi_{8450}(71,\cdot)$	$-1$	$1$	$e\left(\frac{19}{195}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{38}{195}\right)$	$e\left(\frac{43}{780}\right)$	$e\left(\frac{7}{390}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{17}{260}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{19}{65}\right)$	$e\left(\frac{64}{195}\right)$
$\chi_{8450}(111,\cdot)$	$-1$	$1$	$e\left(\frac{37}{195}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{74}{195}\right)$	$e\left(\frac{289}{780}\right)$	$e\left(\frac{301}{390}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{211}{260}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{37}{65}\right)$	$e\left(\frac{22}{195}\right)$
$\chi_{8450}(141,\cdot)$	$-1$	$1$	$e\left(\frac{8}{195}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{16}{195}\right)$	$e\left(\frac{521}{780}\right)$	$e\left(\frac{239}{390}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{79}{260}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{8}{65}\right)$	$e\left(\frac{68}{195}\right)$
$\chi_{8450}(171,\cdot)$	$-1$	$1$	$e\left(\frac{194}{195}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{193}{195}\right)$	$e\left(\frac{203}{780}\right)$	$e\left(\frac{287}{390}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{177}{260}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{64}{65}\right)$	$e\left(\frac{89}{195}\right)$
$\chi_{8450}(241,\cdot)$	$-1$	$1$	$e\left(\frac{178}{195}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{161}{195}\right)$	$e\left(\frac{721}{780}\right)$	$e\left(\frac{199}{390}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{19}{260}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{48}{65}\right)$	$e\left(\frac{148}{195}\right)$
$\chi_{8450}(271,\cdot)$	$-1$	$1$	$e\left(\frac{119}{195}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{43}{195}\right)$	$e\left(\frac{413}{780}\right)$	$e\left(\frac{167}{390}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{127}{260}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{54}{65}\right)$	$e\left(\frac{134}{195}\right)$
$\chi_{8450}(331,\cdot)$	$-1$	$1$	$e\left(\frac{166}{195}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{137}{195}\right)$	$e\left(\frac{427}{780}\right)$	$e\left(\frac{133}{390}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{193}{260}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{36}{65}\right)$	$e\left(\frac{46}{195}\right)$
$\chi_{8450}(371,\cdot)$	$-1$	$1$	$e\left(\frac{124}{195}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{53}{195}\right)$	$e\left(\frac{373}{780}\right)$	$e\left(\frac{97}{390}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{87}{260}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{79}{195}\right)$
$\chi_{8450}(431,\cdot)$	$-1$	$1$	$e\left(\frac{11}{195}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{22}{195}\right)$	$e\left(\frac{107}{780}\right)$	$e\left(\frac{353}{390}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{133}{260}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{65}\right)$	$e\left(\frac{191}{195}\right)$
$\chi_{8450}(461,\cdot)$	$-1$	$1$	$e\left(\frac{142}{195}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{89}{195}\right)$	$e\left(\frac{619}{780}\right)$	$e\left(\frac{1}{390}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{21}{260}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{12}{65}\right)$	$e\left(\frac{37}{195}\right)$
$\chi_{8450}(531,\cdot)$	$-1$	$1$	$e\left(\frac{146}{195}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{97}{195}\right)$	$e\left(\frac{197}{780}\right)$	$e\left(\frac{23}{390}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{223}{260}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{16}{65}\right)$	$e\left(\frac{71}{195}\right)$
$\chi_{8450}(561,\cdot)$	$-1$	$1$	$e\left(\frac{17}{195}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{34}{195}\right)$	$e\left(\frac{59}{780}\right)$	$e\left(\frac{191}{390}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{241}{260}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{65}\right)$	$e\left(\frac{47}{195}\right)$
$\chi_{8450}(591,\cdot)$	$-1$	$1$	$e\left(\frac{118}{195}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{41}{195}\right)$	$e\left(\frac{31}{780}\right)$	$e\left(\frac{259}{390}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{109}{260}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{28}{195}\right)$
$\chi_{8450}(631,\cdot)$	$-1$	$1$	$e\left(\frac{16}{195}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{32}{195}\right)$	$e\left(\frac{457}{780}\right)$	$e\left(\frac{283}{390}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{223}{260}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{16}{65}\right)$	$e\left(\frac{136}{195}\right)$
$\chi_{8450}(661,\cdot)$	$-1$	$1$	$e\left(\frac{62}{195}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{124}{195}\right)$	$e\left(\frac{89}{780}\right)$	$e\left(\frac{341}{390}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{260}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{62}{65}\right)$	$e\left(\frac{137}{195}\right)$
$\chi_{8450}(691,\cdot)$	$-1$	$1$	$e\left(\frac{23}{195}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{46}{195}\right)$	$e\left(\frac{11}{780}\right)$	$e\left(\frac{29}{390}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{89}{260}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{23}{65}\right)$	$e\left(\frac{98}{195}\right)$
$\chi_{8450}(721,\cdot)$	$-1$	$1$	$e\left(\frac{94}{195}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{188}{195}\right)$	$e\left(\frac{223}{780}\right)$	$e\left(\frac{127}{390}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{197}{260}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{65}\right)$	$e\left(\frac{19}{195}\right)$
$\chi_{8450}(761,\cdot)$	$-1$	$1$	$e\left(\frac{157}{195}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{119}{195}\right)$	$e\left(\frac{109}{780}\right)$	$e\left(\frac{181}{390}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{31}{260}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{67}{195}\right)$
$\chi_{8450}(791,\cdot)$	$-1$	$1$	$e\left(\frac{173}{195}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{151}{195}\right)$	$e\left(\frac{761}{780}\right)$	$e\left(\frac{269}{390}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{59}{260}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{43}{65}\right)$	$e\left(\frac{8}{195}\right)$
$\chi_{8450}(821,\cdot)$	$-1$	$1$	$e\left(\frac{29}{195}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{58}{195}\right)$	$e\left(\frac{743}{780}\right)$	$e\left(\frac{257}{390}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{197}{260}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{29}{65}\right)$	$e\left(\frac{149}{195}\right)$
$\chi_{8450}(891,\cdot)$	$-1$	$1$	$e\left(\frac{103}{195}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{11}{195}\right)$	$e\left(\frac{541}{780}\right)$	$e\left(\frac{79}{390}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{99}{260}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{38}{65}\right)$	$e\left(\frac{193}{195}\right)$
$\chi_{8450}(921,\cdot)$	$-1$	$1$	$e\left(\frac{89}{195}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{178}{195}\right)$	$e\left(\frac{653}{780}\right)$	$e\left(\frac{197}{390}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{107}{260}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{24}{65}\right)$	$e\left(\frac{74}{195}\right)$
$\chi_{8450}(981,\cdot)$	$-1$	$1$	$e\left(\frac{46}{195}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{92}{195}\right)$	$e\left(\frac{607}{780}\right)$	$e\left(\frac{253}{390}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{113}{260}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{46}{65}\right)$	$e\left(\frac{1}{195}\right)$
$\chi_{8450}(1021,\cdot)$	$-1$	$1$	$e\left(\frac{49}{195}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{98}{195}\right)$	$e\left(\frac{193}{780}\right)$	$e\left(\frac{367}{390}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{167}{260}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{124}{195}\right)$
$\chi_{8450}(1081,\cdot)$	$-1$	$1$	$e\left(\frac{41}{195}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{82}{195}\right)$	$e\left(\frac{647}{780}\right)$	$e\left(\frac{323}{390}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{153}{260}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{56}{195}\right)$
$\chi_{8450}(1111,\cdot)$	$-1$	$1$	$e\left(\frac{22}{195}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{44}{195}\right)$	$e\left(\frac{19}{780}\right)$	$e\left(\frac{121}{390}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{201}{260}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{22}{65}\right)$	$e\left(\frac{187}{195}\right)$
$\chi_{8450}(1181,\cdot)$	$-1$	$1$	$e\left(\frac{116}{195}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{37}{195}\right)$	$e\left(\frac{437}{780}\right)$	$e\left(\frac{53}{390}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{203}{260}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{51}{65}\right)$	$e\left(\frac{11}{195}\right)$
$\chi_{8450}(1211,\cdot)$	$-1$	$1$	$e\left(\frac{47}{195}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{94}{195}\right)$	$e\left(\frac{599}{780}\right)$	$e\left(\frac{161}{390}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{260}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{47}{65}\right)$	$e\left(\frac{107}{195}\right)$
$\chi_{8450}(1241,\cdot)$	$-1$	$1$	$e\left(\frac{193}{195}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{191}{195}\right)$	$e\left(\frac{211}{780}\right)$	$e\left(\frac{379}{390}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{29}{260}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{63}{65}\right)$	$e\left(\frac{178}{195}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{8450}(11,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{92}{195}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{184}{195}\right)\)	\(e\left(\frac{629}{780}\right)\)	\(e\left(\frac{311}{390}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{31}{260}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{2}{195}\right)\)
\(\chi_{8450}(41,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{188}{195}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{181}{195}\right)\)	\(e\left(\frac{251}{780}\right)\)	\(e\left(\frac{59}{390}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{69}{260}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{58}{65}\right)\)	\(e\left(\frac{38}{195}\right)\)
\(\chi_{8450}(71,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{195}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{38}{195}\right)\)	\(e\left(\frac{43}{780}\right)\)	\(e\left(\frac{7}{390}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{17}{260}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{19}{65}\right)\)	\(e\left(\frac{64}{195}\right)\)
\(\chi_{8450}(111,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{195}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{74}{195}\right)\)	\(e\left(\frac{289}{780}\right)\)	\(e\left(\frac{301}{390}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{211}{260}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{37}{65}\right)\)	\(e\left(\frac{22}{195}\right)\)
\(\chi_{8450}(141,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{195}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{16}{195}\right)\)	\(e\left(\frac{521}{780}\right)\)	\(e\left(\frac{239}{390}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{79}{260}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{8}{65}\right)\)	\(e\left(\frac{68}{195}\right)\)
\(\chi_{8450}(171,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{194}{195}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{193}{195}\right)\)	\(e\left(\frac{203}{780}\right)\)	\(e\left(\frac{287}{390}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{177}{260}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{64}{65}\right)\)	\(e\left(\frac{89}{195}\right)\)
\(\chi_{8450}(241,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{178}{195}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{161}{195}\right)\)	\(e\left(\frac{721}{780}\right)\)	\(e\left(\frac{199}{390}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{19}{260}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{48}{65}\right)\)	\(e\left(\frac{148}{195}\right)\)
\(\chi_{8450}(271,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{195}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{43}{195}\right)\)	\(e\left(\frac{413}{780}\right)\)	\(e\left(\frac{167}{390}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{127}{260}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{54}{65}\right)\)	\(e\left(\frac{134}{195}\right)\)
\(\chi_{8450}(331,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{166}{195}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{137}{195}\right)\)	\(e\left(\frac{427}{780}\right)\)	\(e\left(\frac{133}{390}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{193}{260}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{36}{65}\right)\)	\(e\left(\frac{46}{195}\right)\)
\(\chi_{8450}(371,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{124}{195}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{53}{195}\right)\)	\(e\left(\frac{373}{780}\right)\)	\(e\left(\frac{97}{390}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{87}{260}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{79}{195}\right)\)
\(\chi_{8450}(431,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{195}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{22}{195}\right)\)	\(e\left(\frac{107}{780}\right)\)	\(e\left(\frac{353}{390}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{133}{260}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{65}\right)\)	\(e\left(\frac{191}{195}\right)\)
\(\chi_{8450}(461,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{142}{195}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{89}{195}\right)\)	\(e\left(\frac{619}{780}\right)\)	\(e\left(\frac{1}{390}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{21}{260}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{12}{65}\right)\)	\(e\left(\frac{37}{195}\right)\)
\(\chi_{8450}(531,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{146}{195}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{97}{195}\right)\)	\(e\left(\frac{197}{780}\right)\)	\(e\left(\frac{23}{390}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{223}{260}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{16}{65}\right)\)	\(e\left(\frac{71}{195}\right)\)
\(\chi_{8450}(561,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{195}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{34}{195}\right)\)	\(e\left(\frac{59}{780}\right)\)	\(e\left(\frac{191}{390}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{241}{260}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{65}\right)\)	\(e\left(\frac{47}{195}\right)\)
\(\chi_{8450}(591,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{118}{195}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{41}{195}\right)\)	\(e\left(\frac{31}{780}\right)\)	\(e\left(\frac{259}{390}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{109}{260}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{28}{195}\right)\)
\(\chi_{8450}(631,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{16}{195}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{32}{195}\right)\)	\(e\left(\frac{457}{780}\right)\)	\(e\left(\frac{283}{390}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{223}{260}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{16}{65}\right)\)	\(e\left(\frac{136}{195}\right)\)
\(\chi_{8450}(661,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{62}{195}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{124}{195}\right)\)	\(e\left(\frac{89}{780}\right)\)	\(e\left(\frac{341}{390}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{11}{260}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{62}{65}\right)\)	\(e\left(\frac{137}{195}\right)\)
\(\chi_{8450}(691,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{195}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{46}{195}\right)\)	\(e\left(\frac{11}{780}\right)\)	\(e\left(\frac{29}{390}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{89}{260}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{23}{65}\right)\)	\(e\left(\frac{98}{195}\right)\)
\(\chi_{8450}(721,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{94}{195}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{188}{195}\right)\)	\(e\left(\frac{223}{780}\right)\)	\(e\left(\frac{127}{390}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{197}{260}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{29}{65}\right)\)	\(e\left(\frac{19}{195}\right)\)
\(\chi_{8450}(761,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{157}{195}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{119}{195}\right)\)	\(e\left(\frac{109}{780}\right)\)	\(e\left(\frac{181}{390}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{31}{260}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{67}{195}\right)\)
\(\chi_{8450}(791,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{173}{195}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{151}{195}\right)\)	\(e\left(\frac{761}{780}\right)\)	\(e\left(\frac{269}{390}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{59}{260}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{43}{65}\right)\)	\(e\left(\frac{8}{195}\right)\)
\(\chi_{8450}(821,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{195}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{58}{195}\right)\)	\(e\left(\frac{743}{780}\right)\)	\(e\left(\frac{257}{390}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{197}{260}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{29}{65}\right)\)	\(e\left(\frac{149}{195}\right)\)
\(\chi_{8450}(891,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{195}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{11}{195}\right)\)	\(e\left(\frac{541}{780}\right)\)	\(e\left(\frac{79}{390}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{99}{260}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{38}{65}\right)\)	\(e\left(\frac{193}{195}\right)\)
\(\chi_{8450}(921,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{195}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{178}{195}\right)\)	\(e\left(\frac{653}{780}\right)\)	\(e\left(\frac{197}{390}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{107}{260}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{24}{65}\right)\)	\(e\left(\frac{74}{195}\right)\)
\(\chi_{8450}(981,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{46}{195}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{92}{195}\right)\)	\(e\left(\frac{607}{780}\right)\)	\(e\left(\frac{253}{390}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{113}{260}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{46}{65}\right)\)	\(e\left(\frac{1}{195}\right)\)
\(\chi_{8450}(1021,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{195}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{98}{195}\right)\)	\(e\left(\frac{193}{780}\right)\)	\(e\left(\frac{367}{390}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{167}{260}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{124}{195}\right)\)
\(\chi_{8450}(1081,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{195}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{82}{195}\right)\)	\(e\left(\frac{647}{780}\right)\)	\(e\left(\frac{323}{390}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{153}{260}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{56}{195}\right)\)
\(\chi_{8450}(1111,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{22}{195}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{44}{195}\right)\)	\(e\left(\frac{19}{780}\right)\)	\(e\left(\frac{121}{390}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{201}{260}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{22}{65}\right)\)	\(e\left(\frac{187}{195}\right)\)
\(\chi_{8450}(1181,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{116}{195}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{37}{195}\right)\)	\(e\left(\frac{437}{780}\right)\)	\(e\left(\frac{53}{390}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{203}{260}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{51}{65}\right)\)	\(e\left(\frac{11}{195}\right)\)
\(\chi_{8450}(1211,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{195}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{94}{195}\right)\)	\(e\left(\frac{599}{780}\right)\)	\(e\left(\frac{161}{390}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{260}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{47}{65}\right)\)	\(e\left(\frac{107}{195}\right)\)
\(\chi_{8450}(1241,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{193}{195}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{191}{195}\right)\)	\(e\left(\frac{211}{780}\right)\)	\(e\left(\frac{379}{390}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{29}{260}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{63}{65}\right)\)	\(e\left(\frac{178}{195}\right)\)

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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.cw
Modulus	$8450$
Conductor	$4225$
Order	$780$
Real	no
Primitive	no
Minimal	yes
Parity	odd

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.cx	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)