LMFDB - Dirichlet character orbit 7803.ca

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7803, base_ring=CyclotomicField(612)) M = H._module chi = DirichletCharacter(H, M([68,243])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(4,7803)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$7803$
Conductor:	$7803$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$612$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	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:	$\Q(\zeta_{612})$
Fixed field:	Number field defined by a degree 612 polynomial (not computed)

First 31 of 192 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{7803}(4,\cdot)$	$1$	$1$	$e\left(\frac{169}{306}\right)$	$e\left(\frac{16}{153}\right)$	$e\left(\frac{295}{612}\right)$	$e\left(\frac{197}{612}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{353}{612}\right)$	$e\left(\frac{109}{153}\right)$	$e\left(\frac{535}{612}\right)$	$e\left(\frac{32}{153}\right)$
$\chi_{7803}(13,\cdot)$	$1$	$1$	$e\left(\frac{109}{306}\right)$	$e\left(\frac{109}{153}\right)$	$e\left(\frac{145}{612}\right)$	$e\left(\frac{491}{612}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{121}{204}\right)$	$e\left(\frac{215}{612}\right)$	$e\left(\frac{121}{153}\right)$	$e\left(\frac{97}{612}\right)$	$e\left(\frac{65}{153}\right)$
$\chi_{7803}(106,\cdot)$	$1$	$1$	$e\left(\frac{53}{306}\right)$	$e\left(\frac{53}{153}\right)$	$e\left(\frac{107}{612}\right)$	$e\left(\frac{337}{612}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{71}{204}\right)$	$e\left(\frac{433}{612}\right)$	$e\left(\frac{122}{153}\right)$	$e\left(\frac{443}{612}\right)$	$e\left(\frac{106}{153}\right)$
$\chi_{7803}(115,\cdot)$	$1$	$1$	$e\left(\frac{191}{306}\right)$	$e\left(\frac{38}{153}\right)$	$e\left(\frac{605}{612}\right)$	$e\left(\frac{487}{612}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{125}{204}\right)$	$e\left(\frac{475}{612}\right)$	$e\left(\frac{125}{153}\right)$	$e\left(\frac{257}{612}\right)$	$e\left(\frac{76}{153}\right)$
$\chi_{7803}(157,\cdot)$	$1$	$1$	$e\left(\frac{301}{306}\right)$	$e\left(\frac{148}{153}\right)$	$e\left(\frac{319}{612}\right)$	$e\left(\frac{101}{612}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{103}{204}\right)$	$e\left(\frac{473}{612}\right)$	$e\left(\frac{52}{153}\right)$	$e\left(\frac{91}{612}\right)$	$e\left(\frac{143}{153}\right)$
$\chi_{7803}(166,\cdot)$	$1$	$1$	$e\left(\frac{79}{306}\right)$	$e\left(\frac{79}{153}\right)$	$e\left(\frac{529}{612}\right)$	$e\left(\frac{179}{612}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{25}{204}\right)$	$e\left(\frac{299}{612}\right)$	$e\left(\frac{127}{153}\right)$	$e\left(\frac{337}{612}\right)$	$e\left(\frac{5}{153}\right)$
$\chi_{7803}(259,\cdot)$	$1$	$1$	$e\left(\frac{185}{306}\right)$	$e\left(\frac{32}{153}\right)$	$e\left(\frac{131}{612}\right)$	$e\left(\frac{241}{612}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{167}{204}\right)$	$e\left(\frac{553}{612}\right)$	$e\left(\frac{65}{153}\right)$	$e\left(\frac{611}{612}\right)$	$e\left(\frac{64}{153}\right)$
$\chi_{7803}(268,\cdot)$	$1$	$1$	$e\left(\frac{161}{306}\right)$	$e\left(\frac{8}{153}\right)$	$e\left(\frac{377}{612}\right)$	$e\left(\frac{175}{612}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{29}{204}\right)$	$e\left(\frac{559}{612}\right)$	$e\left(\frac{131}{153}\right)$	$e\left(\frac{497}{612}\right)$	$e\left(\frac{16}{153}\right)$
$\chi_{7803}(310,\cdot)$	$1$	$1$	$e\left(\frac{127}{306}\right)$	$e\left(\frac{127}{153}\right)$	$e\left(\frac{343}{612}\right)$	$e\left(\frac{5}{612}\right)$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{199}{204}\right)$	$e\left(\frac{593}{612}\right)$	$e\left(\frac{148}{153}\right)$	$e\left(\frac{259}{612}\right)$	$e\left(\frac{101}{153}\right)$
$\chi_{7803}(319,\cdot)$	$1$	$1$	$e\left(\frac{49}{306}\right)$	$e\left(\frac{49}{153}\right)$	$e\left(\frac{301}{612}\right)$	$e\left(\frac{479}{612}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{133}{204}\right)$	$e\left(\frac{383}{612}\right)$	$e\left(\frac{133}{153}\right)$	$e\left(\frac{577}{612}\right)$	$e\left(\frac{98}{153}\right)$
$\chi_{7803}(412,\cdot)$	$1$	$1$	$e\left(\frac{11}{306}\right)$	$e\left(\frac{11}{153}\right)$	$e\left(\frac{155}{612}\right)$	$e\left(\frac{145}{612}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{61}{612}\right)$	$e\left(\frac{8}{153}\right)$	$e\left(\frac{167}{612}\right)$	$e\left(\frac{22}{153}\right)$
$\chi_{7803}(421,\cdot)$	$1$	$1$	$e\left(\frac{131}{306}\right)$	$e\left(\frac{131}{153}\right)$	$e\left(\frac{149}{612}\right)$	$e\left(\frac{475}{612}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{137}{204}\right)$	$e\left(\frac{31}{612}\right)$	$e\left(\frac{137}{153}\right)$	$e\left(\frac{125}{612}\right)$	$e\left(\frac{109}{153}\right)$
$\chi_{7803}(463,\cdot)$	$1$	$1$	$e\left(\frac{259}{306}\right)$	$e\left(\frac{106}{153}\right)$	$e\left(\frac{367}{612}\right)$	$e\left(\frac{521}{612}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{91}{204}\right)$	$e\left(\frac{101}{612}\right)$	$e\left(\frac{91}{153}\right)$	$e\left(\frac{427}{612}\right)$	$e\left(\frac{59}{153}\right)$
$\chi_{7803}(472,\cdot)$	$1$	$1$	$e\left(\frac{19}{306}\right)$	$e\left(\frac{19}{153}\right)$	$e\left(\frac{73}{612}\right)$	$e\left(\frac{167}{612}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{37}{204}\right)$	$e\left(\frac{467}{612}\right)$	$e\left(\frac{139}{153}\right)$	$e\left(\frac{205}{612}\right)$	$e\left(\frac{38}{153}\right)$
$\chi_{7803}(565,\cdot)$	$1$	$1$	$e\left(\frac{143}{306}\right)$	$e\left(\frac{143}{153}\right)$	$e\left(\frac{179}{612}\right)$	$e\left(\frac{49}{612}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{155}{204}\right)$	$e\left(\frac{181}{612}\right)$	$e\left(\frac{104}{153}\right)$	$e\left(\frac{335}{612}\right)$	$e\left(\frac{133}{153}\right)$
$\chi_{7803}(574,\cdot)$	$1$	$1$	$e\left(\frac{101}{306}\right)$	$e\left(\frac{101}{153}\right)$	$e\left(\frac{533}{612}\right)$	$e\left(\frac{163}{612}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{41}{204}\right)$	$e\left(\frac{115}{612}\right)$	$e\left(\frac{143}{153}\right)$	$e\left(\frac{365}{612}\right)$	$e\left(\frac{49}{153}\right)$
$\chi_{7803}(625,\cdot)$	$1$	$1$	$e\left(\frac{295}{306}\right)$	$e\left(\frac{142}{153}\right)$	$e\left(\frac{457}{612}\right)$	$e\left(\frac{467}{612}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{145}{204}\right)$	$e\left(\frac{551}{612}\right)$	$e\left(\frac{145}{153}\right)$	$e\left(\frac{445}{612}\right)$	$e\left(\frac{131}{153}\right)$
$\chi_{7803}(718,\cdot)$	$1$	$1$	$e\left(\frac{275}{306}\right)$	$e\left(\frac{122}{153}\right)$	$e\left(\frac{203}{612}\right)$	$e\left(\frac{565}{612}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{47}{204}\right)$	$e\left(\frac{301}{612}\right)$	$e\left(\frac{47}{153}\right)$	$e\left(\frac{503}{612}\right)$	$e\left(\frac{91}{153}\right)$
$\chi_{7803}(727,\cdot)$	$1$	$1$	$e\left(\frac{71}{306}\right)$	$e\left(\frac{71}{153}\right)$	$e\left(\frac{305}{612}\right)$	$e\left(\frac{463}{612}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{149}{204}\right)$	$e\left(\frac{199}{612}\right)$	$e\left(\frac{149}{153}\right)$	$e\left(\frac{605}{612}\right)$	$e\left(\frac{142}{153}\right)$
$\chi_{7803}(769,\cdot)$	$1$	$1$	$e\left(\frac{217}{306}\right)$	$e\left(\frac{64}{153}\right)$	$e\left(\frac{415}{612}\right)$	$e\left(\frac{329}{612}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{79}{204}\right)$	$e\left(\frac{341}{612}\right)$	$e\left(\frac{130}{153}\right)$	$e\left(\frac{151}{612}\right)$	$e\left(\frac{128}{153}\right)$
$\chi_{7803}(778,\cdot)$	$1$	$1$	$e\left(\frac{265}{306}\right)$	$e\left(\frac{112}{153}\right)$	$e\left(\frac{229}{612}\right)$	$e\left(\frac{155}{612}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{23}{612}\right)$	$e\left(\frac{151}{153}\right)$	$e\left(\frac{73}{612}\right)$	$e\left(\frac{71}{153}\right)$
$\chi_{7803}(871,\cdot)$	$1$	$1$	$e\left(\frac{101}{306}\right)$	$e\left(\frac{101}{153}\right)$	$e\left(\frac{227}{612}\right)$	$e\left(\frac{469}{612}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{143}{204}\right)$	$e\left(\frac{421}{612}\right)$	$e\left(\frac{143}{153}\right)$	$e\left(\frac{59}{612}\right)$	$e\left(\frac{49}{153}\right)$
$\chi_{7803}(880,\cdot)$	$1$	$1$	$e\left(\frac{41}{306}\right)$	$e\left(\frac{41}{153}\right)$	$e\left(\frac{77}{612}\right)$	$e\left(\frac{151}{612}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{283}{612}\right)$	$e\left(\frac{2}{153}\right)$	$e\left(\frac{233}{612}\right)$	$e\left(\frac{82}{153}\right)$
$\chi_{7803}(922,\cdot)$	$1$	$1$	$e\left(\frac{43}{306}\right)$	$e\left(\frac{43}{153}\right)$	$e\left(\frac{439}{612}\right)$	$e\left(\frac{233}{612}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{175}{204}\right)$	$e\left(\frac{461}{612}\right)$	$e\left(\frac{73}{153}\right)$	$e\left(\frac{319}{612}\right)$	$e\left(\frac{86}{153}\right)$
$\chi_{7803}(931,\cdot)$	$1$	$1$	$e\left(\frac{235}{306}\right)$	$e\left(\frac{82}{153}\right)$	$e\left(\frac{1}{612}\right)$	$e\left(\frac{455}{612}\right)$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{107}{612}\right)$	$e\left(\frac{4}{153}\right)$	$e\left(\frac{313}{612}\right)$	$e\left(\frac{11}{153}\right)$
$\chi_{7803}(1024,\cdot)$	$1$	$1$	$e\left(\frac{233}{306}\right)$	$e\left(\frac{80}{153}\right)$	$e\left(\frac{251}{612}\right)$	$e\left(\frac{373}{612}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{35}{204}\right)$	$e\left(\frac{541}{612}\right)$	$e\left(\frac{86}{153}\right)$	$e\left(\frac{227}{612}\right)$	$e\left(\frac{7}{153}\right)$
$\chi_{7803}(1033,\cdot)$	$1$	$1$	$e\left(\frac{11}{306}\right)$	$e\left(\frac{11}{153}\right)$	$e\left(\frac{461}{612}\right)$	$e\left(\frac{451}{612}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{161}{204}\right)$	$e\left(\frac{367}{612}\right)$	$e\left(\frac{8}{153}\right)$	$e\left(\frac{473}{612}\right)$	$e\left(\frac{22}{153}\right)$
$\chi_{7803}(1075,\cdot)$	$1$	$1$	$e\left(\frac{175}{306}\right)$	$e\left(\frac{22}{153}\right)$	$e\left(\frac{463}{612}\right)$	$e\left(\frac{137}{612}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{67}{204}\right)$	$e\left(\frac{581}{612}\right)$	$e\left(\frac{16}{153}\right)$	$e\left(\frac{487}{612}\right)$	$e\left(\frac{44}{153}\right)$
$\chi_{7803}(1084,\cdot)$	$1$	$1$	$e\left(\frac{205}{306}\right)$	$e\left(\frac{52}{153}\right)$	$e\left(\frac{385}{612}\right)$	$e\left(\frac{143}{612}\right)$	$e\left(\frac{1}{102}\right)$	$e\left(\frac{61}{204}\right)$	$e\left(\frac{191}{612}\right)$	$e\left(\frac{10}{153}\right)$	$e\left(\frac{553}{612}\right)$	$e\left(\frac{104}{153}\right)$
$\chi_{7803}(1177,\cdot)$	$1$	$1$	$e\left(\frac{59}{306}\right)$	$e\left(\frac{59}{153}\right)$	$e\left(\frac{275}{612}\right)$	$e\left(\frac{277}{612}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{131}{204}\right)$	$e\left(\frac{49}{612}\right)$	$e\left(\frac{29}{153}\right)$	$e\left(\frac{395}{612}\right)$	$e\left(\frac{118}{153}\right)$
$\chi_{7803}(1186,\cdot)$	$1$	$1$	$e\left(\frac{287}{306}\right)$	$e\left(\frac{134}{153}\right)$	$e\left(\frac{233}{612}\right)$	$e\left(\frac{139}{612}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{65}{204}\right)$	$e\left(\frac{451}{612}\right)$	$e\left(\frac{14}{153}\right)$	$e\left(\frac{101}{612}\right)$	$e\left(\frac{115}{153}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{7803}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{306}\right)\)	\(e\left(\frac{16}{153}\right)\)	\(e\left(\frac{295}{612}\right)\)	\(e\left(\frac{197}{612}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{353}{612}\right)\)	\(e\left(\frac{109}{153}\right)\)	\(e\left(\frac{535}{612}\right)\)	\(e\left(\frac{32}{153}\right)\)
\(\chi_{7803}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{306}\right)\)	\(e\left(\frac{109}{153}\right)\)	\(e\left(\frac{145}{612}\right)\)	\(e\left(\frac{491}{612}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{121}{204}\right)\)	\(e\left(\frac{215}{612}\right)\)	\(e\left(\frac{121}{153}\right)\)	\(e\left(\frac{97}{612}\right)\)	\(e\left(\frac{65}{153}\right)\)
\(\chi_{7803}(106,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{306}\right)\)	\(e\left(\frac{53}{153}\right)\)	\(e\left(\frac{107}{612}\right)\)	\(e\left(\frac{337}{612}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{71}{204}\right)\)	\(e\left(\frac{433}{612}\right)\)	\(e\left(\frac{122}{153}\right)\)	\(e\left(\frac{443}{612}\right)\)	\(e\left(\frac{106}{153}\right)\)
\(\chi_{7803}(115,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{306}\right)\)	\(e\left(\frac{38}{153}\right)\)	\(e\left(\frac{605}{612}\right)\)	\(e\left(\frac{487}{612}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{125}{204}\right)\)	\(e\left(\frac{475}{612}\right)\)	\(e\left(\frac{125}{153}\right)\)	\(e\left(\frac{257}{612}\right)\)	\(e\left(\frac{76}{153}\right)\)
\(\chi_{7803}(157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{301}{306}\right)\)	\(e\left(\frac{148}{153}\right)\)	\(e\left(\frac{319}{612}\right)\)	\(e\left(\frac{101}{612}\right)\)	\(e\left(\frac{97}{102}\right)\)	\(e\left(\frac{103}{204}\right)\)	\(e\left(\frac{473}{612}\right)\)	\(e\left(\frac{52}{153}\right)\)	\(e\left(\frac{91}{612}\right)\)	\(e\left(\frac{143}{153}\right)\)
\(\chi_{7803}(166,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{306}\right)\)	\(e\left(\frac{79}{153}\right)\)	\(e\left(\frac{529}{612}\right)\)	\(e\left(\frac{179}{612}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{25}{204}\right)\)	\(e\left(\frac{299}{612}\right)\)	\(e\left(\frac{127}{153}\right)\)	\(e\left(\frac{337}{612}\right)\)	\(e\left(\frac{5}{153}\right)\)
\(\chi_{7803}(259,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{185}{306}\right)\)	\(e\left(\frac{32}{153}\right)\)	\(e\left(\frac{131}{612}\right)\)	\(e\left(\frac{241}{612}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{167}{204}\right)\)	\(e\left(\frac{553}{612}\right)\)	\(e\left(\frac{65}{153}\right)\)	\(e\left(\frac{611}{612}\right)\)	\(e\left(\frac{64}{153}\right)\)
\(\chi_{7803}(268,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{306}\right)\)	\(e\left(\frac{8}{153}\right)\)	\(e\left(\frac{377}{612}\right)\)	\(e\left(\frac{175}{612}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{29}{204}\right)\)	\(e\left(\frac{559}{612}\right)\)	\(e\left(\frac{131}{153}\right)\)	\(e\left(\frac{497}{612}\right)\)	\(e\left(\frac{16}{153}\right)\)
\(\chi_{7803}(310,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{306}\right)\)	\(e\left(\frac{127}{153}\right)\)	\(e\left(\frac{343}{612}\right)\)	\(e\left(\frac{5}{612}\right)\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{199}{204}\right)\)	\(e\left(\frac{593}{612}\right)\)	\(e\left(\frac{148}{153}\right)\)	\(e\left(\frac{259}{612}\right)\)	\(e\left(\frac{101}{153}\right)\)
\(\chi_{7803}(319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{306}\right)\)	\(e\left(\frac{49}{153}\right)\)	\(e\left(\frac{301}{612}\right)\)	\(e\left(\frac{479}{612}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{133}{204}\right)\)	\(e\left(\frac{383}{612}\right)\)	\(e\left(\frac{133}{153}\right)\)	\(e\left(\frac{577}{612}\right)\)	\(e\left(\frac{98}{153}\right)\)
\(\chi_{7803}(412,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{306}\right)\)	\(e\left(\frac{11}{153}\right)\)	\(e\left(\frac{155}{612}\right)\)	\(e\left(\frac{145}{612}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{61}{612}\right)\)	\(e\left(\frac{8}{153}\right)\)	\(e\left(\frac{167}{612}\right)\)	\(e\left(\frac{22}{153}\right)\)
\(\chi_{7803}(421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{306}\right)\)	\(e\left(\frac{131}{153}\right)\)	\(e\left(\frac{149}{612}\right)\)	\(e\left(\frac{475}{612}\right)\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{137}{204}\right)\)	\(e\left(\frac{31}{612}\right)\)	\(e\left(\frac{137}{153}\right)\)	\(e\left(\frac{125}{612}\right)\)	\(e\left(\frac{109}{153}\right)\)
\(\chi_{7803}(463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{259}{306}\right)\)	\(e\left(\frac{106}{153}\right)\)	\(e\left(\frac{367}{612}\right)\)	\(e\left(\frac{521}{612}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{91}{204}\right)\)	\(e\left(\frac{101}{612}\right)\)	\(e\left(\frac{91}{153}\right)\)	\(e\left(\frac{427}{612}\right)\)	\(e\left(\frac{59}{153}\right)\)
\(\chi_{7803}(472,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{306}\right)\)	\(e\left(\frac{19}{153}\right)\)	\(e\left(\frac{73}{612}\right)\)	\(e\left(\frac{167}{612}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{37}{204}\right)\)	\(e\left(\frac{467}{612}\right)\)	\(e\left(\frac{139}{153}\right)\)	\(e\left(\frac{205}{612}\right)\)	\(e\left(\frac{38}{153}\right)\)
\(\chi_{7803}(565,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{306}\right)\)	\(e\left(\frac{143}{153}\right)\)	\(e\left(\frac{179}{612}\right)\)	\(e\left(\frac{49}{612}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{155}{204}\right)\)	\(e\left(\frac{181}{612}\right)\)	\(e\left(\frac{104}{153}\right)\)	\(e\left(\frac{335}{612}\right)\)	\(e\left(\frac{133}{153}\right)\)
\(\chi_{7803}(574,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{306}\right)\)	\(e\left(\frac{101}{153}\right)\)	\(e\left(\frac{533}{612}\right)\)	\(e\left(\frac{163}{612}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{41}{204}\right)\)	\(e\left(\frac{115}{612}\right)\)	\(e\left(\frac{143}{153}\right)\)	\(e\left(\frac{365}{612}\right)\)	\(e\left(\frac{49}{153}\right)\)
\(\chi_{7803}(625,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{295}{306}\right)\)	\(e\left(\frac{142}{153}\right)\)	\(e\left(\frac{457}{612}\right)\)	\(e\left(\frac{467}{612}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{145}{204}\right)\)	\(e\left(\frac{551}{612}\right)\)	\(e\left(\frac{145}{153}\right)\)	\(e\left(\frac{445}{612}\right)\)	\(e\left(\frac{131}{153}\right)\)
\(\chi_{7803}(718,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{275}{306}\right)\)	\(e\left(\frac{122}{153}\right)\)	\(e\left(\frac{203}{612}\right)\)	\(e\left(\frac{565}{612}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{47}{204}\right)\)	\(e\left(\frac{301}{612}\right)\)	\(e\left(\frac{47}{153}\right)\)	\(e\left(\frac{503}{612}\right)\)	\(e\left(\frac{91}{153}\right)\)
\(\chi_{7803}(727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{306}\right)\)	\(e\left(\frac{71}{153}\right)\)	\(e\left(\frac{305}{612}\right)\)	\(e\left(\frac{463}{612}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{149}{204}\right)\)	\(e\left(\frac{199}{612}\right)\)	\(e\left(\frac{149}{153}\right)\)	\(e\left(\frac{605}{612}\right)\)	\(e\left(\frac{142}{153}\right)\)
\(\chi_{7803}(769,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{217}{306}\right)\)	\(e\left(\frac{64}{153}\right)\)	\(e\left(\frac{415}{612}\right)\)	\(e\left(\frac{329}{612}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{79}{204}\right)\)	\(e\left(\frac{341}{612}\right)\)	\(e\left(\frac{130}{153}\right)\)	\(e\left(\frac{151}{612}\right)\)	\(e\left(\frac{128}{153}\right)\)
\(\chi_{7803}(778,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{265}{306}\right)\)	\(e\left(\frac{112}{153}\right)\)	\(e\left(\frac{229}{612}\right)\)	\(e\left(\frac{155}{612}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{23}{612}\right)\)	\(e\left(\frac{151}{153}\right)\)	\(e\left(\frac{73}{612}\right)\)	\(e\left(\frac{71}{153}\right)\)
\(\chi_{7803}(871,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{306}\right)\)	\(e\left(\frac{101}{153}\right)\)	\(e\left(\frac{227}{612}\right)\)	\(e\left(\frac{469}{612}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{143}{204}\right)\)	\(e\left(\frac{421}{612}\right)\)	\(e\left(\frac{143}{153}\right)\)	\(e\left(\frac{59}{612}\right)\)	\(e\left(\frac{49}{153}\right)\)
\(\chi_{7803}(880,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{306}\right)\)	\(e\left(\frac{41}{153}\right)\)	\(e\left(\frac{77}{612}\right)\)	\(e\left(\frac{151}{612}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{283}{612}\right)\)	\(e\left(\frac{2}{153}\right)\)	\(e\left(\frac{233}{612}\right)\)	\(e\left(\frac{82}{153}\right)\)
\(\chi_{7803}(922,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{306}\right)\)	\(e\left(\frac{43}{153}\right)\)	\(e\left(\frac{439}{612}\right)\)	\(e\left(\frac{233}{612}\right)\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{175}{204}\right)\)	\(e\left(\frac{461}{612}\right)\)	\(e\left(\frac{73}{153}\right)\)	\(e\left(\frac{319}{612}\right)\)	\(e\left(\frac{86}{153}\right)\)
\(\chi_{7803}(931,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{235}{306}\right)\)	\(e\left(\frac{82}{153}\right)\)	\(e\left(\frac{1}{612}\right)\)	\(e\left(\frac{455}{612}\right)\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{107}{612}\right)\)	\(e\left(\frac{4}{153}\right)\)	\(e\left(\frac{313}{612}\right)\)	\(e\left(\frac{11}{153}\right)\)
\(\chi_{7803}(1024,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{233}{306}\right)\)	\(e\left(\frac{80}{153}\right)\)	\(e\left(\frac{251}{612}\right)\)	\(e\left(\frac{373}{612}\right)\)	\(e\left(\frac{29}{102}\right)\)	\(e\left(\frac{35}{204}\right)\)	\(e\left(\frac{541}{612}\right)\)	\(e\left(\frac{86}{153}\right)\)	\(e\left(\frac{227}{612}\right)\)	\(e\left(\frac{7}{153}\right)\)
\(\chi_{7803}(1033,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{306}\right)\)	\(e\left(\frac{11}{153}\right)\)	\(e\left(\frac{461}{612}\right)\)	\(e\left(\frac{451}{612}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{161}{204}\right)\)	\(e\left(\frac{367}{612}\right)\)	\(e\left(\frac{8}{153}\right)\)	\(e\left(\frac{473}{612}\right)\)	\(e\left(\frac{22}{153}\right)\)
\(\chi_{7803}(1075,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{175}{306}\right)\)	\(e\left(\frac{22}{153}\right)\)	\(e\left(\frac{463}{612}\right)\)	\(e\left(\frac{137}{612}\right)\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{67}{204}\right)\)	\(e\left(\frac{581}{612}\right)\)	\(e\left(\frac{16}{153}\right)\)	\(e\left(\frac{487}{612}\right)\)	\(e\left(\frac{44}{153}\right)\)
\(\chi_{7803}(1084,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{205}{306}\right)\)	\(e\left(\frac{52}{153}\right)\)	\(e\left(\frac{385}{612}\right)\)	\(e\left(\frac{143}{612}\right)\)	\(e\left(\frac{1}{102}\right)\)	\(e\left(\frac{61}{204}\right)\)	\(e\left(\frac{191}{612}\right)\)	\(e\left(\frac{10}{153}\right)\)	\(e\left(\frac{553}{612}\right)\)	\(e\left(\frac{104}{153}\right)\)
\(\chi_{7803}(1177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{306}\right)\)	\(e\left(\frac{59}{153}\right)\)	\(e\left(\frac{275}{612}\right)\)	\(e\left(\frac{277}{612}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{131}{204}\right)\)	\(e\left(\frac{49}{612}\right)\)	\(e\left(\frac{29}{153}\right)\)	\(e\left(\frac{395}{612}\right)\)	\(e\left(\frac{118}{153}\right)\)
\(\chi_{7803}(1186,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{287}{306}\right)\)	\(e\left(\frac{134}{153}\right)\)	\(e\left(\frac{233}{612}\right)\)	\(e\left(\frac{139}{612}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{65}{204}\right)\)	\(e\left(\frac{451}{612}\right)\)	\(e\left(\frac{14}{153}\right)\)	\(e\left(\frac{101}{612}\right)\)	\(e\left(\frac{115}{153}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

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	7803.ca
Modulus	$7803$
Conductor	$7803$
Order	$612$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(7803\)
Conductor:	\(7803\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(612\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)