LMFDB - Dirichlet character orbit 8450.ct

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8450, base_ring=CyclotomicField(390)) M = H._module chi = DirichletCharacter(H, M([234,125])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(121,8450)) 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:	$390$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4225.cu	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:	$\Q(\zeta_{195})$
Fixed field:	Number field defined by a degree 390 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{8450}(121,\cdot)$	$1$	$1$	$e\left(\frac{184}{195}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{173}{195}\right)$	$e\left(\frac{239}{390}\right)$	$e\left(\frac{116}{195}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{31}{130}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{54}{65}\right)$	$e\left(\frac{4}{195}\right)$
$\chi_{8450}(231,\cdot)$	$1$	$1$	$e\left(\frac{56}{195}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{112}{195}\right)$	$e\left(\frac{361}{390}\right)$	$e\left(\frac{154}{195}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{49}{130}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{56}{65}\right)$	$e\left(\frac{86}{195}\right)$
$\chi_{8450}(381,\cdot)$	$1$	$1$	$e\left(\frac{151}{195}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{107}{195}\right)$	$e\left(\frac{371}{390}\right)$	$e\left(\frac{74}{195}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{21}{65}\right)$	$e\left(\frac{16}{195}\right)$
$\chi_{8450}(491,\cdot)$	$1$	$1$	$e\left(\frac{113}{195}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{31}{195}\right)$	$e\left(\frac{133}{390}\right)$	$e\left(\frac{67}{195}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{107}{130}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{48}{65}\right)$	$e\left(\frac{83}{195}\right)$
$\chi_{8450}(511,\cdot)$	$1$	$1$	$e\left(\frac{37}{195}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{74}{195}\right)$	$e\left(\frac{47}{390}\right)$	$e\left(\frac{53}{195}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{37}{65}\right)$	$e\left(\frac{22}{195}\right)$
$\chi_{8450}(621,\cdot)$	$1$	$1$	$e\left(\frac{44}{195}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{88}{195}\right)$	$e\left(\frac{19}{390}\right)$	$e\left(\frac{121}{195}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{71}{130}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{44}{65}\right)$	$e\left(\frac{179}{195}\right)$
$\chi_{8450}(641,\cdot)$	$1$	$1$	$e\left(\frac{118}{195}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{41}{195}\right)$	$e\left(\frac{113}{390}\right)$	$e\left(\frac{32}{195}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{87}{130}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{28}{195}\right)$
$\chi_{8450}(771,\cdot)$	$1$	$1$	$e\left(\frac{4}{195}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{8}{195}\right)$	$e\left(\frac{179}{390}\right)$	$e\left(\frac{11}{195}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{101}{130}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{34}{195}\right)$
$\chi_{8450}(881,\cdot)$	$1$	$1$	$e\left(\frac{101}{195}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{7}{195}\right)$	$e\left(\frac{181}{390}\right)$	$e\left(\frac{34}{195}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{129}{130}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{36}{65}\right)$	$e\left(\frac{176}{195}\right)$
$\chi_{8450}(1011,\cdot)$	$1$	$1$	$e\left(\frac{32}{195}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{64}{195}\right)$	$e\left(\frac{67}{390}\right)$	$e\left(\frac{88}{195}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{93}{130}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{77}{195}\right)$
$\chi_{8450}(1031,\cdot)$	$1$	$1$	$e\left(\frac{166}{195}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{137}{195}\right)$	$e\left(\frac{311}{390}\right)$	$e\left(\frac{164}{195}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{129}{130}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{36}{65}\right)$	$e\left(\frac{46}{195}\right)$
$\chi_{8450}(1141,\cdot)$	$1$	$1$	$e\left(\frac{158}{195}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{121}{195}\right)$	$e\left(\frac{343}{390}\right)$	$e\left(\frac{142}{195}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{57}{130}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{173}{195}\right)$
$\chi_{8450}(1271,\cdot)$	$1$	$1$	$e\left(\frac{89}{195}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{178}{195}\right)$	$e\left(\frac{229}{390}\right)$	$e\left(\frac{1}{195}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{21}{130}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{24}{65}\right)$	$e\left(\frac{74}{195}\right)$
$\chi_{8450}(1291,\cdot)$	$1$	$1$	$e\left(\frac{133}{195}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{71}{195}\right)$	$e\left(\frac{53}{390}\right)$	$e\left(\frac{122}{195}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{65}\right)$	$e\left(\frac{58}{195}\right)$
$\chi_{8450}(1421,\cdot)$	$1$	$1$	$e\left(\frac{19}{195}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{38}{195}\right)$	$e\left(\frac{119}{390}\right)$	$e\left(\frac{101}{195}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{41}{130}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{65}\right)$	$e\left(\frac{64}{195}\right)$
$\chi_{8450}(1531,\cdot)$	$1$	$1$	$e\left(\frac{146}{195}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{97}{195}\right)$	$e\left(\frac{1}{390}\right)$	$e\left(\frac{109}{195}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{79}{130}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{16}{65}\right)$	$e\left(\frac{71}{195}\right)$
$\chi_{8450}(1661,\cdot)$	$1$	$1$	$e\left(\frac{77}{195}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{154}{195}\right)$	$e\left(\frac{277}{390}\right)$	$e\left(\frac{163}{195}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{12}{65}\right)$	$e\left(\frac{167}{195}\right)$
$\chi_{8450}(1681,\cdot)$	$1$	$1$	$e\left(\frac{181}{195}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{167}{195}\right)$	$e\left(\frac{251}{390}\right)$	$e\left(\frac{59}{195}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{69}{130}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{51}{65}\right)$	$e\left(\frac{76}{195}\right)$
$\chi_{8450}(1791,\cdot)$	$1$	$1$	$e\left(\frac{8}{195}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{16}{195}\right)$	$e\left(\frac{163}{390}\right)$	$e\left(\frac{22}{195}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{130}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{8}{65}\right)$	$e\left(\frac{68}{195}\right)$
$\chi_{8450}(1811,\cdot)$	$1$	$1$	$e\left(\frac{67}{195}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{134}{195}\right)$	$e\left(\frac{317}{390}\right)$	$e\left(\frac{38}{195}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{83}{130}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{65}\right)$	$e\left(\frac{82}{195}\right)$
$\chi_{8450}(1921,\cdot)$	$1$	$1$	$e\left(\frac{134}{195}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{73}{195}\right)$	$e\left(\frac{49}{390}\right)$	$e\left(\frac{76}{195}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{101}{130}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{164}{195}\right)$
$\chi_{8450}(1941,\cdot)$	$1$	$1$	$e\left(\frac{148}{195}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{101}{195}\right)$	$e\left(\frac{383}{390}\right)$	$e\left(\frac{17}{195}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{97}{130}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{18}{65}\right)$	$e\left(\frac{88}{195}\right)$
$\chi_{8450}(2071,\cdot)$	$1$	$1$	$e\left(\frac{34}{195}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{68}{195}\right)$	$e\left(\frac{59}{390}\right)$	$e\left(\frac{191}{195}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{111}{130}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{34}{65}\right)$	$e\left(\frac{94}{195}\right)$
$\chi_{8450}(2181,\cdot)$	$1$	$1$	$e\left(\frac{191}{195}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{187}{195}\right)$	$e\left(\frac{211}{390}\right)$	$e\left(\frac{184}{195}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{29}{130}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{161}{195}\right)$
$\chi_{8450}(2311,\cdot)$	$1$	$1$	$e\left(\frac{122}{195}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{49}{195}\right)$	$e\left(\frac{97}{390}\right)$	$e\left(\frac{43}{195}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{123}{130}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{57}{65}\right)$	$e\left(\frac{62}{195}\right)$
$\chi_{8450}(2331,\cdot)$	$1$	$1$	$e\left(\frac{1}{195}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{2}{195}\right)$	$e\left(\frac{191}{390}\right)$	$e\left(\frac{149}{195}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{9}{130}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{65}\right)$	$e\left(\frac{106}{195}\right)$
$\chi_{8450}(2441,\cdot)$	$1$	$1$	$e\left(\frac{53}{195}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{106}{195}\right)$	$e\left(\frac{373}{390}\right)$	$e\left(\frac{97}{195}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{87}{130}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{158}{195}\right)$
$\chi_{8450}(2461,\cdot)$	$1$	$1$	$e\left(\frac{82}{195}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{164}{195}\right)$	$e\left(\frac{257}{390}\right)$	$e\left(\frac{128}{195}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{130}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{17}{65}\right)$	$e\left(\frac{112}{195}\right)$
$\chi_{8450}(2571,\cdot)$	$1$	$1$	$e\left(\frac{179}{195}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{163}{195}\right)$	$e\left(\frac{259}{390}\right)$	$e\left(\frac{151}{195}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{51}{130}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{59}{195}\right)$
$\chi_{8450}(2591,\cdot)$	$1$	$1$	$e\left(\frac{163}{195}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{131}{195}\right)$	$e\left(\frac{323}{390}\right)$	$e\left(\frac{107}{195}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{37}{130}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{118}{195}\right)$
$\chi_{8450}(2721,\cdot)$	$1$	$1$	$e\left(\frac{49}{195}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{98}{195}\right)$	$e\left(\frac{389}{390}\right)$	$e\left(\frac{86}{195}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{51}{130}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{124}{195}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{8450}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{184}{195}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{173}{195}\right)\)	\(e\left(\frac{239}{390}\right)\)	\(e\left(\frac{116}{195}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{31}{130}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{54}{65}\right)\)	\(e\left(\frac{4}{195}\right)\)
\(\chi_{8450}(231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{56}{195}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{112}{195}\right)\)	\(e\left(\frac{361}{390}\right)\)	\(e\left(\frac{154}{195}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{49}{130}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{56}{65}\right)\)	\(e\left(\frac{86}{195}\right)\)
\(\chi_{8450}(381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{195}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{107}{195}\right)\)	\(e\left(\frac{371}{390}\right)\)	\(e\left(\frac{74}{195}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{21}{65}\right)\)	\(e\left(\frac{16}{195}\right)\)
\(\chi_{8450}(491,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{195}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{31}{195}\right)\)	\(e\left(\frac{133}{390}\right)\)	\(e\left(\frac{67}{195}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{107}{130}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{48}{65}\right)\)	\(e\left(\frac{83}{195}\right)\)
\(\chi_{8450}(511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{195}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{74}{195}\right)\)	\(e\left(\frac{47}{390}\right)\)	\(e\left(\frac{53}{195}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{37}{65}\right)\)	\(e\left(\frac{22}{195}\right)\)
\(\chi_{8450}(621,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{195}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{88}{195}\right)\)	\(e\left(\frac{19}{390}\right)\)	\(e\left(\frac{121}{195}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{71}{130}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{44}{65}\right)\)	\(e\left(\frac{179}{195}\right)\)
\(\chi_{8450}(641,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{118}{195}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{41}{195}\right)\)	\(e\left(\frac{113}{390}\right)\)	\(e\left(\frac{32}{195}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{87}{130}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{28}{195}\right)\)
\(\chi_{8450}(771,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{195}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{8}{195}\right)\)	\(e\left(\frac{179}{390}\right)\)	\(e\left(\frac{11}{195}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{101}{130}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{34}{195}\right)\)
\(\chi_{8450}(881,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{195}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{7}{195}\right)\)	\(e\left(\frac{181}{390}\right)\)	\(e\left(\frac{34}{195}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{129}{130}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{36}{65}\right)\)	\(e\left(\frac{176}{195}\right)\)
\(\chi_{8450}(1011,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{195}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{64}{195}\right)\)	\(e\left(\frac{67}{390}\right)\)	\(e\left(\frac{88}{195}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{93}{130}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{77}{195}\right)\)
\(\chi_{8450}(1031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{166}{195}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{137}{195}\right)\)	\(e\left(\frac{311}{390}\right)\)	\(e\left(\frac{164}{195}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{129}{130}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{36}{65}\right)\)	\(e\left(\frac{46}{195}\right)\)
\(\chi_{8450}(1141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{158}{195}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{121}{195}\right)\)	\(e\left(\frac{343}{390}\right)\)	\(e\left(\frac{142}{195}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{57}{130}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{173}{195}\right)\)
\(\chi_{8450}(1271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{195}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{178}{195}\right)\)	\(e\left(\frac{229}{390}\right)\)	\(e\left(\frac{1}{195}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{21}{130}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{24}{65}\right)\)	\(e\left(\frac{74}{195}\right)\)
\(\chi_{8450}(1291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{195}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{71}{195}\right)\)	\(e\left(\frac{53}{390}\right)\)	\(e\left(\frac{122}{195}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{65}\right)\)	\(e\left(\frac{58}{195}\right)\)
\(\chi_{8450}(1421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{195}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{38}{195}\right)\)	\(e\left(\frac{119}{390}\right)\)	\(e\left(\frac{101}{195}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{41}{130}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{65}\right)\)	\(e\left(\frac{64}{195}\right)\)
\(\chi_{8450}(1531,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{146}{195}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{97}{195}\right)\)	\(e\left(\frac{1}{390}\right)\)	\(e\left(\frac{109}{195}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{79}{130}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{16}{65}\right)\)	\(e\left(\frac{71}{195}\right)\)
\(\chi_{8450}(1661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{195}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{154}{195}\right)\)	\(e\left(\frac{277}{390}\right)\)	\(e\left(\frac{163}{195}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{12}{65}\right)\)	\(e\left(\frac{167}{195}\right)\)
\(\chi_{8450}(1681,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{195}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{167}{195}\right)\)	\(e\left(\frac{251}{390}\right)\)	\(e\left(\frac{59}{195}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{69}{130}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{51}{65}\right)\)	\(e\left(\frac{76}{195}\right)\)
\(\chi_{8450}(1791,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{195}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{16}{195}\right)\)	\(e\left(\frac{163}{390}\right)\)	\(e\left(\frac{22}{195}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{130}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{8}{65}\right)\)	\(e\left(\frac{68}{195}\right)\)
\(\chi_{8450}(1811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{195}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{134}{195}\right)\)	\(e\left(\frac{317}{390}\right)\)	\(e\left(\frac{38}{195}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{83}{130}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{65}\right)\)	\(e\left(\frac{82}{195}\right)\)
\(\chi_{8450}(1921,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{134}{195}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{73}{195}\right)\)	\(e\left(\frac{49}{390}\right)\)	\(e\left(\frac{76}{195}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{101}{130}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{164}{195}\right)\)
\(\chi_{8450}(1941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{148}{195}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{101}{195}\right)\)	\(e\left(\frac{383}{390}\right)\)	\(e\left(\frac{17}{195}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{97}{130}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{18}{65}\right)\)	\(e\left(\frac{88}{195}\right)\)
\(\chi_{8450}(2071,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{195}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{68}{195}\right)\)	\(e\left(\frac{59}{390}\right)\)	\(e\left(\frac{191}{195}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{111}{130}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{34}{65}\right)\)	\(e\left(\frac{94}{195}\right)\)
\(\chi_{8450}(2181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{195}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{187}{195}\right)\)	\(e\left(\frac{211}{390}\right)\)	\(e\left(\frac{184}{195}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{29}{130}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{161}{195}\right)\)
\(\chi_{8450}(2311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{122}{195}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{49}{195}\right)\)	\(e\left(\frac{97}{390}\right)\)	\(e\left(\frac{43}{195}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{123}{130}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{57}{65}\right)\)	\(e\left(\frac{62}{195}\right)\)
\(\chi_{8450}(2331,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{195}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{2}{195}\right)\)	\(e\left(\frac{191}{390}\right)\)	\(e\left(\frac{149}{195}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{9}{130}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{65}\right)\)	\(e\left(\frac{106}{195}\right)\)
\(\chi_{8450}(2441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{195}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{106}{195}\right)\)	\(e\left(\frac{373}{390}\right)\)	\(e\left(\frac{97}{195}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{87}{130}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{158}{195}\right)\)
\(\chi_{8450}(2461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{195}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{164}{195}\right)\)	\(e\left(\frac{257}{390}\right)\)	\(e\left(\frac{128}{195}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{130}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{17}{65}\right)\)	\(e\left(\frac{112}{195}\right)\)
\(\chi_{8450}(2571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{195}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{163}{195}\right)\)	\(e\left(\frac{259}{390}\right)\)	\(e\left(\frac{151}{195}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{51}{130}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{59}{195}\right)\)
\(\chi_{8450}(2591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{195}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{131}{195}\right)\)	\(e\left(\frac{323}{390}\right)\)	\(e\left(\frac{107}{195}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{37}{130}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{118}{195}\right)\)
\(\chi_{8450}(2721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{195}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{98}{195}\right)\)	\(e\left(\frac{389}{390}\right)\)	\(e\left(\frac{86}{195}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{51}{130}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{124}{195}\right)\)

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First 31 of 96 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.ct
Modulus	$8450$
Conductor	$4225$
Order	$390$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8450\)
Conductor:	\(4225\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(390\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4225.cu	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)