LMFDB - Dirichlet character orbit 7803.cd

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7803, base_ring=CyclotomicField(816)) M = H._module chi = DirichletCharacter(H, M([680,393])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(44,7803)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$7803$
Conductor:	$2601$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$816$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2601.bn	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{816})$
Fixed field:	Number field defined by a degree 816 polynomial (not computed)

First 31 of 256 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{7803}(44,\cdot)$	$1$	$1$	$e\left(\frac{139}{408}\right)$	$e\left(\frac{139}{204}\right)$	$e\left(\frac{373}{816}\right)$	$e\left(\frac{803}{816}\right)$	$e\left(\frac{3}{136}\right)$	$e\left(\frac{217}{272}\right)$	$e\left(\frac{743}{816}\right)$	$e\left(\frac{13}{204}\right)$	$e\left(\frac{265}{816}\right)$	$e\left(\frac{37}{102}\right)$
$\chi_{7803}(62,\cdot)$	$1$	$1$	$e\left(\frac{71}{408}\right)$	$e\left(\frac{71}{204}\right)$	$e\left(\frac{305}{816}\right)$	$e\left(\frac{55}{816}\right)$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{149}{272}\right)$	$e\left(\frac{811}{816}\right)$	$e\left(\frac{149}{204}\right)$	$e\left(\frac{197}{816}\right)$	$e\left(\frac{71}{102}\right)$
$\chi_{7803}(71,\cdot)$	$1$	$1$	$e\left(\frac{145}{408}\right)$	$e\left(\frac{145}{204}\right)$	$e\left(\frac{439}{816}\right)$	$e\left(\frac{641}{816}\right)$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{243}{272}\right)$	$e\left(\frac{461}{816}\right)$	$e\left(\frac{175}{204}\right)$	$e\left(\frac{115}{816}\right)$	$e\left(\frac{43}{102}\right)$
$\chi_{7803}(116,\cdot)$	$1$	$1$	$e\left(\frac{377}{408}\right)$	$e\left(\frac{173}{204}\right)$	$e\left(\frac{815}{816}\right)$	$e\left(\frac{361}{816}\right)$	$e\left(\frac{105}{136}\right)$	$e\left(\frac{251}{272}\right)$	$e\left(\frac{709}{816}\right)$	$e\left(\frac{47}{204}\right)$	$e\left(\frac{299}{816}\right)$	$e\left(\frac{71}{102}\right)$
$\chi_{7803}(125,\cdot)$	$1$	$1$	$e\left(\frac{295}{408}\right)$	$e\left(\frac{91}{204}\right)$	$e\left(\frac{457}{816}\right)$	$e\left(\frac{671}{816}\right)$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{77}{272}\right)$	$e\left(\frac{755}{816}\right)$	$e\left(\frac{145}{204}\right)$	$e\left(\frac{445}{816}\right)$	$e\left(\frac{91}{102}\right)$
$\chi_{7803}(143,\cdot)$	$1$	$1$	$e\left(\frac{59}{408}\right)$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{173}{816}\right)$	$e\left(\frac{379}{816}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{97}{272}\right)$	$e\left(\frac{559}{816}\right)$	$e\left(\frac{29}{204}\right)$	$e\left(\frac{497}{816}\right)$	$e\left(\frac{59}{102}\right)$
$\chi_{7803}(197,\cdot)$	$1$	$1$	$e\left(\frac{155}{408}\right)$	$e\left(\frac{155}{204}\right)$	$e\left(\frac{5}{816}\right)$	$e\left(\frac{643}{816}\right)$	$e\left(\frac{19}{136}\right)$	$e\left(\frac{105}{272}\right)$	$e\left(\frac{535}{816}\right)$	$e\left(\frac{173}{204}\right)$	$e\left(\frac{137}{816}\right)$	$e\left(\frac{53}{102}\right)$
$\chi_{7803}(233,\cdot)$	$1$	$1$	$e\left(\frac{109}{408}\right)$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{43}{816}\right)$	$e\left(\frac{797}{816}\right)$	$e\left(\frac{109}{136}\right)$	$e\left(\frac{87}{272}\right)$	$e\left(\frac{521}{816}\right)$	$e\left(\frac{19}{204}\right)$	$e\left(\frac{199}{816}\right)$	$e\left(\frac{7}{102}\right)$
$\chi_{7803}(260,\cdot)$	$1$	$1$	$e\left(\frac{61}{408}\right)$	$e\left(\frac{61}{204}\right)$	$e\left(\frac{739}{816}\right)$	$e\left(\frac{53}{816}\right)$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{15}{272}\right)$	$e\left(\frac{737}{816}\right)$	$e\left(\frac{151}{204}\right)$	$e\left(\frac{175}{816}\right)$	$e\left(\frac{61}{102}\right)$
$\chi_{7803}(278,\cdot)$	$1$	$1$	$e\left(\frac{95}{408}\right)$	$e\left(\frac{95}{204}\right)$	$e\left(\frac{569}{816}\right)$	$e\left(\frac{223}{816}\right)$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{253}{272}\right)$	$e\left(\frac{499}{816}\right)$	$e\left(\frac{185}{204}\right)$	$e\left(\frac{413}{816}\right)$	$e\left(\frac{95}{102}\right)$
$\chi_{7803}(368,\cdot)$	$1$	$1$	$e\left(\frac{199}{408}\right)$	$e\left(\frac{199}{204}\right)$	$e\left(\frac{625}{816}\right)$	$e\left(\frac{407}{816}\right)$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{69}{272}\right)$	$e\left(\frac{779}{816}\right)$	$e\left(\frac{1}{204}\right)$	$e\left(\frac{805}{816}\right)$	$e\left(\frac{97}{102}\right)$
$\chi_{7803}(386,\cdot)$	$1$	$1$	$e\left(\frac{77}{408}\right)$	$e\left(\frac{77}{204}\right)$	$e\left(\frac{779}{816}\right)$	$e\left(\frac{301}{816}\right)$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{39}{272}\right)$	$e\left(\frac{121}{816}\right)$	$e\left(\frac{107}{204}\right)$	$e\left(\frac{455}{816}\right)$	$e\left(\frac{77}{102}\right)$
$\chi_{7803}(413,\cdot)$	$1$	$1$	$e\left(\frac{365}{408}\right)$	$e\left(\frac{161}{204}\right)$	$e\left(\frac{275}{816}\right)$	$e\left(\frac{277}{816}\right)$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{63}{272}\right)$	$e\left(\frac{49}{816}\right)$	$e\left(\frac{131}{204}\right)$	$e\left(\frac{191}{816}\right)$	$e\left(\frac{59}{102}\right)$
$\chi_{7803}(422,\cdot)$	$1$	$1$	$e\left(\frac{361}{408}\right)$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{367}{816}\right)$	$e\left(\frac{521}{816}\right)$	$e\left(\frac{89}{136}\right)$	$e\left(\frac{91}{272}\right)$	$e\left(\frac{101}{816}\right)$	$e\left(\frac{91}{204}\right)$	$e\left(\frac{427}{816}\right)$	$e\left(\frac{55}{102}\right)$
$\chi_{7803}(449,\cdot)$	$1$	$1$	$e\left(\frac{163}{408}\right)$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{637}{816}\right)$	$e\left(\frac{155}{816}\right)$	$e\left(\frac{27}{136}\right)$	$e\left(\frac{49}{272}\right)$	$e\left(\frac{431}{816}\right)$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{481}{816}\right)$	$e\left(\frac{61}{102}\right)$
$\chi_{7803}(521,\cdot)$	$1$	$1$	$e\left(\frac{263}{408}\right)$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{785}{816}\right)$	$e\left(\frac{583}{816}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{165}{272}\right)$	$e\left(\frac{763}{816}\right)$	$e\left(\frac{29}{204}\right)$	$e\left(\frac{293}{816}\right)$	$e\left(\frac{59}{102}\right)$
$\chi_{7803}(530,\cdot)$	$1$	$1$	$e\left(\frac{169}{408}\right)$	$e\left(\frac{169}{204}\right)$	$e\left(\frac{295}{816}\right)$	$e\left(\frac{401}{816}\right)$	$e\left(\frac{33}{136}\right)$	$e\left(\frac{211}{272}\right)$	$e\left(\frac{557}{816}\right)$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{739}{816}\right)$	$e\left(\frac{67}{102}\right)$
$\chi_{7803}(575,\cdot)$	$1$	$1$	$e\left(\frac{353}{408}\right)$	$e\left(\frac{149}{204}\right)$	$e\left(\frac{143}{816}\right)$	$e\left(\frac{601}{816}\right)$	$e\left(\frac{81}{136}\right)$	$e\left(\frac{11}{272}\right)$	$e\left(\frac{613}{816}\right)$	$e\left(\frac{11}{204}\right)$	$e\left(\frac{491}{816}\right)$	$e\left(\frac{47}{102}\right)$
$\chi_{7803}(584,\cdot)$	$1$	$1$	$e\left(\frac{103}{408}\right)$	$e\left(\frac{103}{204}\right)$	$e\left(\frac{793}{816}\right)$	$e\left(\frac{143}{816}\right)$	$e\left(\frac{103}{136}\right)$	$e\left(\frac{61}{272}\right)$	$e\left(\frac{803}{816}\right)$	$e\left(\frac{61}{204}\right)$	$e\left(\frac{349}{816}\right)$	$e\left(\frac{1}{102}\right)$
$\chi_{7803}(602,\cdot)$	$1$	$1$	$e\left(\frac{11}{408}\right)$	$e\left(\frac{11}{204}\right)$	$e\left(\frac{461}{816}\right)$	$e\left(\frac{43}{816}\right)$	$e\left(\frac{11}{136}\right)$	$e\left(\frac{161}{272}\right)$	$e\left(\frac{367}{816}\right)$	$e\left(\frac{161}{204}\right)$	$e\left(\frac{65}{816}\right)$	$e\left(\frac{11}{102}\right)$
$\chi_{7803}(656,\cdot)$	$1$	$1$	$e\left(\frac{203}{408}\right)$	$e\left(\frac{203}{204}\right)$	$e\left(\frac{533}{816}\right)$	$e\left(\frac{163}{816}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{41}{272}\right)$	$e\left(\frac{727}{816}\right)$	$e\left(\frac{41}{204}\right)$	$e\left(\frac{569}{816}\right)$	$e\left(\frac{101}{102}\right)$
$\chi_{7803}(683,\cdot)$	$1$	$1$	$e\left(\frac{41}{408}\right)$	$e\left(\frac{41}{204}\right)$	$e\left(\frac{791}{816}\right)$	$e\left(\frac{49}{816}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{19}{272}\right)$	$e\left(\frac{589}{816}\right)$	$e\left(\frac{155}{204}\right)$	$e\left(\frac{131}{816}\right)$	$e\left(\frac{41}{102}\right)$
$\chi_{7803}(692,\cdot)$	$1$	$1$	$e\left(\frac{13}{408}\right)$	$e\left(\frac{13}{204}\right)$	$e\left(\frac{619}{816}\right)$	$e\left(\frac{125}{816}\right)$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{215}{272}\right)$	$e\left(\frac{137}{816}\right)$	$e\left(\frac{79}{204}\right)$	$e\left(\frac{151}{816}\right)$	$e\left(\frac{13}{102}\right)$
$\chi_{7803}(719,\cdot)$	$1$	$1$	$e\left(\frac{157}{408}\right)$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{163}{816}\right)$	$e\left(\frac{725}{816}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{159}{272}\right)$	$e\left(\frac{305}{816}\right)$	$e\left(\frac{91}{204}\right)$	$e\left(\frac{223}{816}\right)$	$e\left(\frac{55}{102}\right)$
$\chi_{7803}(737,\cdot)$	$1$	$1$	$e\left(\frac{311}{408}\right)$	$e\left(\frac{107}{204}\right)$	$e\left(\frac{89}{816}\right)$	$e\left(\frac{511}{816}\right)$	$e\left(\frac{39}{136}\right)$	$e\left(\frac{237}{272}\right)$	$e\left(\frac{547}{816}\right)$	$e\left(\frac{101}{204}\right)$	$e\left(\frac{317}{816}\right)$	$e\left(\frac{5}{102}\right)$
$\chi_{7803}(845,\cdot)$	$1$	$1$	$e\left(\frac{389}{408}\right)$	$e\left(\frac{185}{204}\right)$	$e\left(\frac{539}{816}\right)$	$e\left(\frac{445}{816}\right)$	$e\left(\frac{117}{136}\right)$	$e\left(\frac{167}{272}\right)$	$e\left(\frac{553}{816}\right)$	$e\left(\frac{167}{204}\right)$	$e\left(\frac{407}{816}\right)$	$e\left(\frac{83}{102}\right)$
$\chi_{7803}(872,\cdot)$	$1$	$1$	$e\left(\frac{53}{408}\right)$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{515}{816}\right)$	$e\left(\frac{133}{816}\right)$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{207}{272}\right)$	$e\left(\frac{433}{816}\right)$	$e\left(\frac{71}{204}\right)$	$e\left(\frac{239}{816}\right)$	$e\left(\frac{53}{102}\right)$
$\chi_{7803}(881,\cdot)$	$1$	$1$	$e\left(\frac{337}{408}\right)$	$e\left(\frac{133}{204}\right)$	$e\left(\frac{511}{816}\right)$	$e\left(\frac{761}{816}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{123}{272}\right)$	$e\left(\frac{5}{816}\right)$	$e\left(\frac{55}{204}\right)$	$e\left(\frac{619}{816}\right)$	$e\left(\frac{31}{102}\right)$
$\chi_{7803}(908,\cdot)$	$1$	$1$	$e\left(\frac{115}{408}\right)$	$e\left(\frac{115}{204}\right)$	$e\left(\frac{109}{816}\right)$	$e\left(\frac{635}{816}\right)$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{113}{272}\right)$	$e\left(\frac{239}{816}\right)$	$e\left(\frac{181}{204}\right)$	$e\left(\frac{49}{816}\right)$	$e\left(\frac{13}{102}\right)$
$\chi_{7803}(962,\cdot)$	$1$	$1$	$e\left(\frac{235}{408}\right)$	$e\left(\frac{31}{204}\right)$	$e\left(\frac{613}{816}\right)$	$e\left(\frac{659}{816}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{89}{272}\right)$	$e\left(\frac{311}{816}\right)$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{313}{816}\right)$	$e\left(\frac{31}{102}\right)$
$\chi_{7803}(980,\cdot)$	$1$	$1$	$e\left(\frac{47}{408}\right)$	$e\left(\frac{47}{204}\right)$	$e\left(\frac{449}{816}\right)$	$e\left(\frac{295}{816}\right)$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{181}{272}\right)$	$e\left(\frac{715}{816}\right)$	$e\left(\frac{113}{204}\right)$	$e\left(\frac{389}{816}\right)$	$e\left(\frac{47}{102}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{7803}(44,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{408}\right)\)	\(e\left(\frac{139}{204}\right)\)	\(e\left(\frac{373}{816}\right)\)	\(e\left(\frac{803}{816}\right)\)	\(e\left(\frac{3}{136}\right)\)	\(e\left(\frac{217}{272}\right)\)	\(e\left(\frac{743}{816}\right)\)	\(e\left(\frac{13}{204}\right)\)	\(e\left(\frac{265}{816}\right)\)	\(e\left(\frac{37}{102}\right)\)
\(\chi_{7803}(62,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{408}\right)\)	\(e\left(\frac{71}{204}\right)\)	\(e\left(\frac{305}{816}\right)\)	\(e\left(\frac{55}{816}\right)\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{149}{272}\right)\)	\(e\left(\frac{811}{816}\right)\)	\(e\left(\frac{149}{204}\right)\)	\(e\left(\frac{197}{816}\right)\)	\(e\left(\frac{71}{102}\right)\)
\(\chi_{7803}(71,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{408}\right)\)	\(e\left(\frac{145}{204}\right)\)	\(e\left(\frac{439}{816}\right)\)	\(e\left(\frac{641}{816}\right)\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{243}{272}\right)\)	\(e\left(\frac{461}{816}\right)\)	\(e\left(\frac{175}{204}\right)\)	\(e\left(\frac{115}{816}\right)\)	\(e\left(\frac{43}{102}\right)\)
\(\chi_{7803}(116,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{377}{408}\right)\)	\(e\left(\frac{173}{204}\right)\)	\(e\left(\frac{815}{816}\right)\)	\(e\left(\frac{361}{816}\right)\)	\(e\left(\frac{105}{136}\right)\)	\(e\left(\frac{251}{272}\right)\)	\(e\left(\frac{709}{816}\right)\)	\(e\left(\frac{47}{204}\right)\)	\(e\left(\frac{299}{816}\right)\)	\(e\left(\frac{71}{102}\right)\)
\(\chi_{7803}(125,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{295}{408}\right)\)	\(e\left(\frac{91}{204}\right)\)	\(e\left(\frac{457}{816}\right)\)	\(e\left(\frac{671}{816}\right)\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{77}{272}\right)\)	\(e\left(\frac{755}{816}\right)\)	\(e\left(\frac{145}{204}\right)\)	\(e\left(\frac{445}{816}\right)\)	\(e\left(\frac{91}{102}\right)\)
\(\chi_{7803}(143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{408}\right)\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{173}{816}\right)\)	\(e\left(\frac{379}{816}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{97}{272}\right)\)	\(e\left(\frac{559}{816}\right)\)	\(e\left(\frac{29}{204}\right)\)	\(e\left(\frac{497}{816}\right)\)	\(e\left(\frac{59}{102}\right)\)
\(\chi_{7803}(197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{155}{408}\right)\)	\(e\left(\frac{155}{204}\right)\)	\(e\left(\frac{5}{816}\right)\)	\(e\left(\frac{643}{816}\right)\)	\(e\left(\frac{19}{136}\right)\)	\(e\left(\frac{105}{272}\right)\)	\(e\left(\frac{535}{816}\right)\)	\(e\left(\frac{173}{204}\right)\)	\(e\left(\frac{137}{816}\right)\)	\(e\left(\frac{53}{102}\right)\)
\(\chi_{7803}(233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{408}\right)\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{43}{816}\right)\)	\(e\left(\frac{797}{816}\right)\)	\(e\left(\frac{109}{136}\right)\)	\(e\left(\frac{87}{272}\right)\)	\(e\left(\frac{521}{816}\right)\)	\(e\left(\frac{19}{204}\right)\)	\(e\left(\frac{199}{816}\right)\)	\(e\left(\frac{7}{102}\right)\)
\(\chi_{7803}(260,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{408}\right)\)	\(e\left(\frac{61}{204}\right)\)	\(e\left(\frac{739}{816}\right)\)	\(e\left(\frac{53}{816}\right)\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{15}{272}\right)\)	\(e\left(\frac{737}{816}\right)\)	\(e\left(\frac{151}{204}\right)\)	\(e\left(\frac{175}{816}\right)\)	\(e\left(\frac{61}{102}\right)\)
\(\chi_{7803}(278,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{408}\right)\)	\(e\left(\frac{95}{204}\right)\)	\(e\left(\frac{569}{816}\right)\)	\(e\left(\frac{223}{816}\right)\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{253}{272}\right)\)	\(e\left(\frac{499}{816}\right)\)	\(e\left(\frac{185}{204}\right)\)	\(e\left(\frac{413}{816}\right)\)	\(e\left(\frac{95}{102}\right)\)
\(\chi_{7803}(368,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{408}\right)\)	\(e\left(\frac{199}{204}\right)\)	\(e\left(\frac{625}{816}\right)\)	\(e\left(\frac{407}{816}\right)\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{69}{272}\right)\)	\(e\left(\frac{779}{816}\right)\)	\(e\left(\frac{1}{204}\right)\)	\(e\left(\frac{805}{816}\right)\)	\(e\left(\frac{97}{102}\right)\)
\(\chi_{7803}(386,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{408}\right)\)	\(e\left(\frac{77}{204}\right)\)	\(e\left(\frac{779}{816}\right)\)	\(e\left(\frac{301}{816}\right)\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{39}{272}\right)\)	\(e\left(\frac{121}{816}\right)\)	\(e\left(\frac{107}{204}\right)\)	\(e\left(\frac{455}{816}\right)\)	\(e\left(\frac{77}{102}\right)\)
\(\chi_{7803}(413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{365}{408}\right)\)	\(e\left(\frac{161}{204}\right)\)	\(e\left(\frac{275}{816}\right)\)	\(e\left(\frac{277}{816}\right)\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{63}{272}\right)\)	\(e\left(\frac{49}{816}\right)\)	\(e\left(\frac{131}{204}\right)\)	\(e\left(\frac{191}{816}\right)\)	\(e\left(\frac{59}{102}\right)\)
\(\chi_{7803}(422,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{361}{408}\right)\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{367}{816}\right)\)	\(e\left(\frac{521}{816}\right)\)	\(e\left(\frac{89}{136}\right)\)	\(e\left(\frac{91}{272}\right)\)	\(e\left(\frac{101}{816}\right)\)	\(e\left(\frac{91}{204}\right)\)	\(e\left(\frac{427}{816}\right)\)	\(e\left(\frac{55}{102}\right)\)
\(\chi_{7803}(449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{408}\right)\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{637}{816}\right)\)	\(e\left(\frac{155}{816}\right)\)	\(e\left(\frac{27}{136}\right)\)	\(e\left(\frac{49}{272}\right)\)	\(e\left(\frac{431}{816}\right)\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{481}{816}\right)\)	\(e\left(\frac{61}{102}\right)\)
\(\chi_{7803}(521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{263}{408}\right)\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{785}{816}\right)\)	\(e\left(\frac{583}{816}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{165}{272}\right)\)	\(e\left(\frac{763}{816}\right)\)	\(e\left(\frac{29}{204}\right)\)	\(e\left(\frac{293}{816}\right)\)	\(e\left(\frac{59}{102}\right)\)
\(\chi_{7803}(530,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{408}\right)\)	\(e\left(\frac{169}{204}\right)\)	\(e\left(\frac{295}{816}\right)\)	\(e\left(\frac{401}{816}\right)\)	\(e\left(\frac{33}{136}\right)\)	\(e\left(\frac{211}{272}\right)\)	\(e\left(\frac{557}{816}\right)\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{739}{816}\right)\)	\(e\left(\frac{67}{102}\right)\)
\(\chi_{7803}(575,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{353}{408}\right)\)	\(e\left(\frac{149}{204}\right)\)	\(e\left(\frac{143}{816}\right)\)	\(e\left(\frac{601}{816}\right)\)	\(e\left(\frac{81}{136}\right)\)	\(e\left(\frac{11}{272}\right)\)	\(e\left(\frac{613}{816}\right)\)	\(e\left(\frac{11}{204}\right)\)	\(e\left(\frac{491}{816}\right)\)	\(e\left(\frac{47}{102}\right)\)
\(\chi_{7803}(584,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{408}\right)\)	\(e\left(\frac{103}{204}\right)\)	\(e\left(\frac{793}{816}\right)\)	\(e\left(\frac{143}{816}\right)\)	\(e\left(\frac{103}{136}\right)\)	\(e\left(\frac{61}{272}\right)\)	\(e\left(\frac{803}{816}\right)\)	\(e\left(\frac{61}{204}\right)\)	\(e\left(\frac{349}{816}\right)\)	\(e\left(\frac{1}{102}\right)\)
\(\chi_{7803}(602,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{408}\right)\)	\(e\left(\frac{11}{204}\right)\)	\(e\left(\frac{461}{816}\right)\)	\(e\left(\frac{43}{816}\right)\)	\(e\left(\frac{11}{136}\right)\)	\(e\left(\frac{161}{272}\right)\)	\(e\left(\frac{367}{816}\right)\)	\(e\left(\frac{161}{204}\right)\)	\(e\left(\frac{65}{816}\right)\)	\(e\left(\frac{11}{102}\right)\)
\(\chi_{7803}(656,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{408}\right)\)	\(e\left(\frac{203}{204}\right)\)	\(e\left(\frac{533}{816}\right)\)	\(e\left(\frac{163}{816}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{41}{272}\right)\)	\(e\left(\frac{727}{816}\right)\)	\(e\left(\frac{41}{204}\right)\)	\(e\left(\frac{569}{816}\right)\)	\(e\left(\frac{101}{102}\right)\)
\(\chi_{7803}(683,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{408}\right)\)	\(e\left(\frac{41}{204}\right)\)	\(e\left(\frac{791}{816}\right)\)	\(e\left(\frac{49}{816}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{19}{272}\right)\)	\(e\left(\frac{589}{816}\right)\)	\(e\left(\frac{155}{204}\right)\)	\(e\left(\frac{131}{816}\right)\)	\(e\left(\frac{41}{102}\right)\)
\(\chi_{7803}(692,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{408}\right)\)	\(e\left(\frac{13}{204}\right)\)	\(e\left(\frac{619}{816}\right)\)	\(e\left(\frac{125}{816}\right)\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{215}{272}\right)\)	\(e\left(\frac{137}{816}\right)\)	\(e\left(\frac{79}{204}\right)\)	\(e\left(\frac{151}{816}\right)\)	\(e\left(\frac{13}{102}\right)\)
\(\chi_{7803}(719,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{408}\right)\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{163}{816}\right)\)	\(e\left(\frac{725}{816}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{159}{272}\right)\)	\(e\left(\frac{305}{816}\right)\)	\(e\left(\frac{91}{204}\right)\)	\(e\left(\frac{223}{816}\right)\)	\(e\left(\frac{55}{102}\right)\)
\(\chi_{7803}(737,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{311}{408}\right)\)	\(e\left(\frac{107}{204}\right)\)	\(e\left(\frac{89}{816}\right)\)	\(e\left(\frac{511}{816}\right)\)	\(e\left(\frac{39}{136}\right)\)	\(e\left(\frac{237}{272}\right)\)	\(e\left(\frac{547}{816}\right)\)	\(e\left(\frac{101}{204}\right)\)	\(e\left(\frac{317}{816}\right)\)	\(e\left(\frac{5}{102}\right)\)
\(\chi_{7803}(845,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{389}{408}\right)\)	\(e\left(\frac{185}{204}\right)\)	\(e\left(\frac{539}{816}\right)\)	\(e\left(\frac{445}{816}\right)\)	\(e\left(\frac{117}{136}\right)\)	\(e\left(\frac{167}{272}\right)\)	\(e\left(\frac{553}{816}\right)\)	\(e\left(\frac{167}{204}\right)\)	\(e\left(\frac{407}{816}\right)\)	\(e\left(\frac{83}{102}\right)\)
\(\chi_{7803}(872,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{408}\right)\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{515}{816}\right)\)	\(e\left(\frac{133}{816}\right)\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{207}{272}\right)\)	\(e\left(\frac{433}{816}\right)\)	\(e\left(\frac{71}{204}\right)\)	\(e\left(\frac{239}{816}\right)\)	\(e\left(\frac{53}{102}\right)\)
\(\chi_{7803}(881,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{337}{408}\right)\)	\(e\left(\frac{133}{204}\right)\)	\(e\left(\frac{511}{816}\right)\)	\(e\left(\frac{761}{816}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{123}{272}\right)\)	\(e\left(\frac{5}{816}\right)\)	\(e\left(\frac{55}{204}\right)\)	\(e\left(\frac{619}{816}\right)\)	\(e\left(\frac{31}{102}\right)\)
\(\chi_{7803}(908,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{408}\right)\)	\(e\left(\frac{115}{204}\right)\)	\(e\left(\frac{109}{816}\right)\)	\(e\left(\frac{635}{816}\right)\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{113}{272}\right)\)	\(e\left(\frac{239}{816}\right)\)	\(e\left(\frac{181}{204}\right)\)	\(e\left(\frac{49}{816}\right)\)	\(e\left(\frac{13}{102}\right)\)
\(\chi_{7803}(962,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{235}{408}\right)\)	\(e\left(\frac{31}{204}\right)\)	\(e\left(\frac{613}{816}\right)\)	\(e\left(\frac{659}{816}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{89}{272}\right)\)	\(e\left(\frac{311}{816}\right)\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{313}{816}\right)\)	\(e\left(\frac{31}{102}\right)\)
\(\chi_{7803}(980,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{408}\right)\)	\(e\left(\frac{47}{204}\right)\)	\(e\left(\frac{449}{816}\right)\)	\(e\left(\frac{295}{816}\right)\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{181}{272}\right)\)	\(e\left(\frac{715}{816}\right)\)	\(e\left(\frac{113}{204}\right)\)	\(e\left(\frac{389}{816}\right)\)	\(e\left(\frac{47}{102}\right)\)

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First 31 of 256 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.cd
Modulus	$7803$
Conductor	$2601$
Order	$816$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(7803\)
Conductor:	\(2601\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(816\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2601.bn	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)