LMFDB - Group of Dirichlet characters of modulus 327184

Show commands: PariGP / SageMath

sage: H = DirichletGroup(327184)

pari: g = idealstar(,327184,2)

Character group

sage: G.order() pari: g.no
Order	=	137280
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{8580}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{327184}(286287,\cdot)$, $\chi_{327184}(81797,\cdot)$, $\chi_{327184}(132497,\cdot)$, $\chi_{327184}(174241,\cdot)$

First 32 of 137280 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$5$	$7$	$9$	$15$	$17$	$19$	$21$	$23$	$25$
$\chi_{327184}(1,\cdot)$	327184.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{327184}(3,\cdot)$	327184.to	780	no	$-1$	$1$	$e\left(\frac{557}{780}\right)$	$e\left(\frac{27}{260}\right)$	$e\left(\frac{127}{195}\right)$	$e\left(\frac{167}{390}\right)$	$e\left(\frac{319}{390}\right)$	$e\left(\frac{49}{195}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{27}{130}\right)$
$\chi_{327184}(5,\cdot)$	327184.wl	2860	yes	$-1$	$1$	$e\left(\frac{27}{260}\right)$	$e\left(\frac{394}{715}\right)$	$e\left(\frac{1093}{2860}\right)$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{1873}{2860}\right)$	$e\left(\frac{553}{1430}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{139}{286}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{73}{715}\right)$
$\chi_{327184}(7,\cdot)$	327184.xv	8580	no	$-1$	$1$	$e\left(\frac{127}{195}\right)$	$e\left(\frac{1093}{2860}\right)$	$e\left(\frac{2887}{8580}\right)$	$e\left(\frac{59}{195}\right)$	$e\left(\frac{287}{8580}\right)$	$e\left(\frac{556}{2145}\right)$	$e\left(\frac{571}{660}\right)$	$e\left(\frac{565}{572}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{1093}{1430}\right)$
$\chi_{327184}(9,\cdot)$	327184.qy	390	no	$1$	$1$	$e\left(\frac{167}{390}\right)$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{59}{195}\right)$	$e\left(\frac{167}{195}\right)$	$e\left(\frac{124}{195}\right)$	$e\left(\frac{98}{195}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{27}{65}\right)$
$\chi_{327184}(15,\cdot)$	327184.yn	8580	no	$1$	$1$	$e\left(\frac{319}{390}\right)$	$e\left(\frac{1873}{2860}\right)$	$e\left(\frac{287}{8580}\right)$	$e\left(\frac{124}{195}\right)$	$e\left(\frac{4057}{8580}\right)$	$e\left(\frac{2737}{4290}\right)$	$e\left(\frac{101}{660}\right)$	$e\left(\frac{487}{572}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{443}{1430}\right)$
$\chi_{327184}(17,\cdot)$	327184.xi	4290	no	$-1$	$1$	$e\left(\frac{49}{195}\right)$	$e\left(\frac{553}{1430}\right)$	$e\left(\frac{556}{2145}\right)$	$e\left(\frac{98}{195}\right)$	$e\left(\frac{2737}{4290}\right)$	$e\left(\frac{2009}{4290}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{73}{143}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{553}{715}\right)$
$\chi_{327184}(19,\cdot)$	327184.sj	660	no	$-1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{571}{660}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{101}{660}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{37}{55}\right)$
$\chi_{327184}(21,\cdot)$	327184.ro	572	yes	$1$	$1$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{139}{286}\right)$	$e\left(\frac{565}{572}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{487}{572}\right)$	$e\left(\frac{73}{143}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{101}{286}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{139}{143}\right)$
$\chi_{327184}(23,\cdot)$	327184.jm	66	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{327184}(25,\cdot)$	327184.uu	1430	no	$1$	$1$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{73}{715}\right)$	$e\left(\frac{1093}{1430}\right)$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{443}{1430}\right)$	$e\left(\frac{553}{715}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{139}{143}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{146}{715}\right)$
$\chi_{327184}(27,\cdot)$	327184.pc	260	no	$-1$	$1$	$e\left(\frac{37}{260}\right)$	$e\left(\frac{81}{260}\right)$	$e\left(\frac{62}{65}\right)$	$e\left(\frac{37}{130}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{5}{52}\right)$	$1$	$e\left(\frac{81}{130}\right)$
$\chi_{327184}(29,\cdot)$	327184.yg	8580	yes	$-1$	$1$	$e\left(\frac{503}{780}\right)$	$e\left(\frac{1413}{2860}\right)$	$e\left(\frac{38}{2145}\right)$	$e\left(\frac{113}{390}\right)$	$e\left(\frac{298}{2145}\right)$	$e\left(\frac{37}{4290}\right)$	$e\left(\frac{491}{660}\right)$	$e\left(\frac{379}{572}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{1413}{1430}\right)$
$\chi_{327184}(31,\cdot)$	327184.wh	2860	no	$1$	$1$	$e\left(\frac{129}{130}\right)$	$e\left(\frac{189}{2860}\right)$	$e\left(\frac{1077}{2860}\right)$	$e\left(\frac{64}{65}\right)$	$e\left(\frac{167}{2860}\right)$	$e\left(\frac{1377}{1430}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{211}{572}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{189}{1430}\right)$
$\chi_{327184}(35,\cdot)$	327184.yb	8580	yes	$1$	$1$	$e\left(\frac{589}{780}\right)$	$e\left(\frac{2669}{2860}\right)$	$e\left(\frac{3083}{4290}\right)$	$e\left(\frac{199}{390}\right)$	$e\left(\frac{2953}{4290}\right)$	$e\left(\frac{2771}{4290}\right)$	$e\left(\frac{133}{660}\right)$	$e\left(\frac{271}{572}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{1239}{1430}\right)$
$\chi_{327184}(37,\cdot)$	327184.yi	8580	yes	$-1$	$1$	$e\left(\frac{293}{780}\right)$	$e\left(\frac{309}{1430}\right)$	$e\left(\frac{6377}{8580}\right)$	$e\left(\frac{293}{390}\right)$	$e\left(\frac{5077}{8580}\right)$	$e\left(\frac{127}{4290}\right)$	$e\left(\frac{59}{165}\right)$	$e\left(\frac{17}{143}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{309}{715}\right)$
$\chi_{327184}(41,\cdot)$	327184.yo	8580	no	$1$	$1$	$e\left(\frac{181}{390}\right)$	$e\left(\frac{2507}{2860}\right)$	$e\left(\frac{6563}{8580}\right)$	$e\left(\frac{181}{195}\right)$	$e\left(\frac{2923}{8580}\right)$	$e\left(\frac{1709}{2145}\right)$	$e\left(\frac{179}{660}\right)$	$e\left(\frac{131}{572}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{1077}{1430}\right)$
$\chi_{327184}(43,\cdot)$	327184.vp	1716	yes	$1$	$1$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{61}{572}\right)$	$e\left(\frac{116}{429}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{142}{429}\right)$	$e\left(\frac{271}{858}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{283}{572}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{61}{286}\right)$
$\chi_{327184}(45,\cdot)$	327184.vn	1716	yes	$-1$	$1$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{217}{286}\right)$	$e\left(\frac{1175}{1716}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{499}{1716}\right)$	$e\left(\frac{763}{858}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{31}{143}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{74}{143}\right)$
$\chi_{327184}(47,\cdot)$	327184.wh	2860	no	$1$	$1$	$e\left(\frac{127}{130}\right)$	$e\left(\frac{1607}{2860}\right)$	$e\left(\frac{2711}{2860}\right)$	$e\left(\frac{62}{65}\right)$	$e\left(\frac{1541}{2860}\right)$	$e\left(\frac{881}{1430}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{529}{572}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{177}{1430}\right)$
$\chi_{327184}(49,\cdot)$	327184.xh	4290	no	$1$	$1$	$e\left(\frac{59}{195}\right)$	$e\left(\frac{1093}{1430}\right)$	$e\left(\frac{2887}{4290}\right)$	$e\left(\frac{118}{195}\right)$	$e\left(\frac{287}{4290}\right)$	$e\left(\frac{1112}{2145}\right)$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{279}{286}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{378}{715}\right)$
$\chi_{327184}(51,\cdot)$	327184.wn	2860	yes	$1$	$1$	$e\left(\frac{251}{260}\right)$	$e\left(\frac{1403}{2860}\right)$	$e\left(\frac{651}{715}\right)$	$e\left(\frac{121}{130}\right)$	$e\left(\frac{326}{715}\right)$	$e\left(\frac{1029}{1430}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{501}{572}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1403}{1430}\right)$
$\chi_{327184}(53,\cdot)$	327184.ws	2860	yes	$1$	$1$	$e\left(\frac{243}{260}\right)$	$e\left(\frac{1379}{2860}\right)$	$e\left(\frac{791}{1430}\right)$	$e\left(\frac{113}{130}\right)$	$e\left(\frac{298}{715}\right)$	$e\left(\frac{376}{715}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{279}{572}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1379}{1430}\right)$
$\chi_{327184}(57,\cdot)$	327184.wg	2860	no	$1$	$1$	$e\left(\frac{69}{130}\right)$	$e\left(\frac{1259}{2860}\right)$	$e\left(\frac{1477}{2860}\right)$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{2777}{2860}\right)$	$e\left(\frac{41}{715}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{27}{572}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{1259}{1430}\right)$
$\chi_{327184}(59,\cdot)$	327184.yj	8580	yes	$1$	$1$	$e\left(\frac{523}{780}\right)$	$e\left(\frac{1139}{1430}\right)$	$e\left(\frac{367}{8580}\right)$	$e\left(\frac{133}{390}\right)$	$e\left(\frac{4007}{8580}\right)$	$e\left(\frac{47}{4290}\right)$	$e\left(\frac{323}{330}\right)$	$e\left(\frac{102}{143}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{424}{715}\right)$
$\chi_{327184}(61,\cdot)$	327184.yg	8580	yes	$-1$	$1$	$e\left(\frac{571}{780}\right)$	$e\left(\frac{441}{2860}\right)$	$e\left(\frac{991}{2145}\right)$	$e\left(\frac{181}{390}\right)$	$e\left(\frac{1901}{2145}\right)$	$e\left(\frac{2489}{4290}\right)$	$e\left(\frac{547}{660}\right)$	$e\left(\frac{111}{572}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{441}{1430}\right)$
$\chi_{327184}(63,\cdot)$	327184.yp	8580	no	$-1$	$1$	$e\left(\frac{31}{390}\right)$	$e\left(\frac{1687}{2860}\right)$	$e\left(\frac{5483}{8580}\right)$	$e\left(\frac{31}{195}\right)$	$e\left(\frac{5743}{8580}\right)$	$e\left(\frac{1634}{2145}\right)$	$e\left(\frac{329}{660}\right)$	$e\left(\frac{411}{572}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{257}{1430}\right)$
$\chi_{327184}(67,\cdot)$	327184.vm	1716	yes	$1$	$1$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{45}{286}\right)$	$e\left(\frac{1273}{1716}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{545}{1716}\right)$	$e\left(\frac{149}{858}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{129}{143}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{45}{143}\right)$
$\chi_{327184}(69,\cdot)$	327184.ye	8580	yes	$1$	$1$	$e\left(\frac{37}{780}\right)$	$e\left(\frac{557}{2860}\right)$	$e\left(\frac{1657}{2145}\right)$	$e\left(\frac{37}{390}\right)$	$e\left(\frac{1039}{4290}\right)$	$e\left(\frac{214}{2145}\right)$	$e\left(\frac{529}{660}\right)$	$e\left(\frac{469}{572}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{557}{1430}\right)$
$\chi_{327184}(71,\cdot)$	327184.xt	8580	no	$1$	$1$	$e\left(\frac{19}{195}\right)$	$e\left(\frac{1831}{2860}\right)$	$e\left(\frac{3859}{8580}\right)$	$e\left(\frac{38}{195}\right)$	$e\left(\frac{6329}{8580}\right)$	$e\left(\frac{389}{4290}\right)$	$e\left(\frac{7}{660}\right)$	$e\left(\frac{313}{572}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{401}{1430}\right)$
$\chi_{327184}(73,\cdot)$	327184.wg	2860	no	$1$	$1$	$e\left(\frac{83}{130}\right)$	$e\left(\frac{953}{2860}\right)$	$e\left(\frac{959}{2860}\right)$	$e\left(\frac{18}{65}\right)$	$e\left(\frac{2779}{2860}\right)$	$e\left(\frac{152}{715}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{557}{572}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{953}{1430}\right)$
$\chi_{327184}(75,\cdot)$	327184.yd	8580	yes	$-1$	$1$	$e\left(\frac{719}{780}\right)$	$e\left(\frac{589}{2860}\right)$	$e\left(\frac{1783}{4290}\right)$	$e\left(\frac{329}{390}\right)$	$e\left(\frac{274}{2145}\right)$	$e\left(\frac{53}{2145}\right)$	$e\left(\frac{323}{660}\right)$	$e\left(\frac{193}{572}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{589}{1430}\right)$

Click here to search among the remaining 137248 characters.

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 $\F_{q}$

Modulus	$327184$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{8580}\)
Order	$137280$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)	\(25\)
\(\chi_{327184}(1,\cdot)\)	327184.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{327184}(3,\cdot)\)	327184.to	780	no	\(-1\)	\(1\)	\(e\left(\frac{557}{780}\right)\)	\(e\left(\frac{27}{260}\right)\)	\(e\left(\frac{127}{195}\right)\)	\(e\left(\frac{167}{390}\right)\)	\(e\left(\frac{319}{390}\right)\)	\(e\left(\frac{49}{195}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{27}{130}\right)\)
\(\chi_{327184}(5,\cdot)\)	327184.wl	2860	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{260}\right)\)	\(e\left(\frac{394}{715}\right)\)	\(e\left(\frac{1093}{2860}\right)\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{1873}{2860}\right)\)	\(e\left(\frac{553}{1430}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{139}{286}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{73}{715}\right)\)
\(\chi_{327184}(7,\cdot)\)	327184.xv	8580	no	\(-1\)	\(1\)	\(e\left(\frac{127}{195}\right)\)	\(e\left(\frac{1093}{2860}\right)\)	\(e\left(\frac{2887}{8580}\right)\)	\(e\left(\frac{59}{195}\right)\)	\(e\left(\frac{287}{8580}\right)\)	\(e\left(\frac{556}{2145}\right)\)	\(e\left(\frac{571}{660}\right)\)	\(e\left(\frac{565}{572}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{1093}{1430}\right)\)
\(\chi_{327184}(9,\cdot)\)	327184.qy	390	no	\(1\)	\(1\)	\(e\left(\frac{167}{390}\right)\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{59}{195}\right)\)	\(e\left(\frac{167}{195}\right)\)	\(e\left(\frac{124}{195}\right)\)	\(e\left(\frac{98}{195}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{27}{65}\right)\)
\(\chi_{327184}(15,\cdot)\)	327184.yn	8580	no	\(1\)	\(1\)	\(e\left(\frac{319}{390}\right)\)	\(e\left(\frac{1873}{2860}\right)\)	\(e\left(\frac{287}{8580}\right)\)	\(e\left(\frac{124}{195}\right)\)	\(e\left(\frac{4057}{8580}\right)\)	\(e\left(\frac{2737}{4290}\right)\)	\(e\left(\frac{101}{660}\right)\)	\(e\left(\frac{487}{572}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{443}{1430}\right)\)
\(\chi_{327184}(17,\cdot)\)	327184.xi	4290	no	\(-1\)	\(1\)	\(e\left(\frac{49}{195}\right)\)	\(e\left(\frac{553}{1430}\right)\)	\(e\left(\frac{556}{2145}\right)\)	\(e\left(\frac{98}{195}\right)\)	\(e\left(\frac{2737}{4290}\right)\)	\(e\left(\frac{2009}{4290}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{73}{143}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{553}{715}\right)\)
\(\chi_{327184}(19,\cdot)\)	327184.sj	660	no	\(-1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{571}{660}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{101}{660}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{37}{55}\right)\)
\(\chi_{327184}(21,\cdot)\)	327184.ro	572	yes	\(1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{139}{286}\right)\)	\(e\left(\frac{565}{572}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{487}{572}\right)\)	\(e\left(\frac{73}{143}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{101}{286}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{139}{143}\right)\)
\(\chi_{327184}(23,\cdot)\)	327184.jm	66	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{327184}(25,\cdot)\)	327184.uu	1430	no	\(1\)	\(1\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{73}{715}\right)\)	\(e\left(\frac{1093}{1430}\right)\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{443}{1430}\right)\)	\(e\left(\frac{553}{715}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{139}{143}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{146}{715}\right)\)
\(\chi_{327184}(27,\cdot)\)	327184.pc	260	no	\(-1\)	\(1\)	\(e\left(\frac{37}{260}\right)\)	\(e\left(\frac{81}{260}\right)\)	\(e\left(\frac{62}{65}\right)\)	\(e\left(\frac{37}{130}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(1\)	\(e\left(\frac{81}{130}\right)\)
\(\chi_{327184}(29,\cdot)\)	327184.yg	8580	yes	\(-1\)	\(1\)	\(e\left(\frac{503}{780}\right)\)	\(e\left(\frac{1413}{2860}\right)\)	\(e\left(\frac{38}{2145}\right)\)	\(e\left(\frac{113}{390}\right)\)	\(e\left(\frac{298}{2145}\right)\)	\(e\left(\frac{37}{4290}\right)\)	\(e\left(\frac{491}{660}\right)\)	\(e\left(\frac{379}{572}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{1413}{1430}\right)\)
\(\chi_{327184}(31,\cdot)\)	327184.wh	2860	no	\(1\)	\(1\)	\(e\left(\frac{129}{130}\right)\)	\(e\left(\frac{189}{2860}\right)\)	\(e\left(\frac{1077}{2860}\right)\)	\(e\left(\frac{64}{65}\right)\)	\(e\left(\frac{167}{2860}\right)\)	\(e\left(\frac{1377}{1430}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{211}{572}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{189}{1430}\right)\)
\(\chi_{327184}(35,\cdot)\)	327184.yb	8580	yes	\(1\)	\(1\)	\(e\left(\frac{589}{780}\right)\)	\(e\left(\frac{2669}{2860}\right)\)	\(e\left(\frac{3083}{4290}\right)\)	\(e\left(\frac{199}{390}\right)\)	\(e\left(\frac{2953}{4290}\right)\)	\(e\left(\frac{2771}{4290}\right)\)	\(e\left(\frac{133}{660}\right)\)	\(e\left(\frac{271}{572}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{1239}{1430}\right)\)
\(\chi_{327184}(37,\cdot)\)	327184.yi	8580	yes	\(-1\)	\(1\)	\(e\left(\frac{293}{780}\right)\)	\(e\left(\frac{309}{1430}\right)\)	\(e\left(\frac{6377}{8580}\right)\)	\(e\left(\frac{293}{390}\right)\)	\(e\left(\frac{5077}{8580}\right)\)	\(e\left(\frac{127}{4290}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{17}{143}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{309}{715}\right)\)
\(\chi_{327184}(41,\cdot)\)	327184.yo	8580	no	\(1\)	\(1\)	\(e\left(\frac{181}{390}\right)\)	\(e\left(\frac{2507}{2860}\right)\)	\(e\left(\frac{6563}{8580}\right)\)	\(e\left(\frac{181}{195}\right)\)	\(e\left(\frac{2923}{8580}\right)\)	\(e\left(\frac{1709}{2145}\right)\)	\(e\left(\frac{179}{660}\right)\)	\(e\left(\frac{131}{572}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{1077}{1430}\right)\)
\(\chi_{327184}(43,\cdot)\)	327184.vp	1716	yes	\(1\)	\(1\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{61}{572}\right)\)	\(e\left(\frac{116}{429}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{142}{429}\right)\)	\(e\left(\frac{271}{858}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{283}{572}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{61}{286}\right)\)
\(\chi_{327184}(45,\cdot)\)	327184.vn	1716	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{217}{286}\right)\)	\(e\left(\frac{1175}{1716}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{499}{1716}\right)\)	\(e\left(\frac{763}{858}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{31}{143}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{74}{143}\right)\)
\(\chi_{327184}(47,\cdot)\)	327184.wh	2860	no	\(1\)	\(1\)	\(e\left(\frac{127}{130}\right)\)	\(e\left(\frac{1607}{2860}\right)\)	\(e\left(\frac{2711}{2860}\right)\)	\(e\left(\frac{62}{65}\right)\)	\(e\left(\frac{1541}{2860}\right)\)	\(e\left(\frac{881}{1430}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{529}{572}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{177}{1430}\right)\)
\(\chi_{327184}(49,\cdot)\)	327184.xh	4290	no	\(1\)	\(1\)	\(e\left(\frac{59}{195}\right)\)	\(e\left(\frac{1093}{1430}\right)\)	\(e\left(\frac{2887}{4290}\right)\)	\(e\left(\frac{118}{195}\right)\)	\(e\left(\frac{287}{4290}\right)\)	\(e\left(\frac{1112}{2145}\right)\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{279}{286}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{378}{715}\right)\)
\(\chi_{327184}(51,\cdot)\)	327184.wn	2860	yes	\(1\)	\(1\)	\(e\left(\frac{251}{260}\right)\)	\(e\left(\frac{1403}{2860}\right)\)	\(e\left(\frac{651}{715}\right)\)	\(e\left(\frac{121}{130}\right)\)	\(e\left(\frac{326}{715}\right)\)	\(e\left(\frac{1029}{1430}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{501}{572}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1403}{1430}\right)\)
\(\chi_{327184}(53,\cdot)\)	327184.ws	2860	yes	\(1\)	\(1\)	\(e\left(\frac{243}{260}\right)\)	\(e\left(\frac{1379}{2860}\right)\)	\(e\left(\frac{791}{1430}\right)\)	\(e\left(\frac{113}{130}\right)\)	\(e\left(\frac{298}{715}\right)\)	\(e\left(\frac{376}{715}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{279}{572}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1379}{1430}\right)\)
\(\chi_{327184}(57,\cdot)\)	327184.wg	2860	no	\(1\)	\(1\)	\(e\left(\frac{69}{130}\right)\)	\(e\left(\frac{1259}{2860}\right)\)	\(e\left(\frac{1477}{2860}\right)\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{2777}{2860}\right)\)	\(e\left(\frac{41}{715}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{27}{572}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{1259}{1430}\right)\)
\(\chi_{327184}(59,\cdot)\)	327184.yj	8580	yes	\(1\)	\(1\)	\(e\left(\frac{523}{780}\right)\)	\(e\left(\frac{1139}{1430}\right)\)	\(e\left(\frac{367}{8580}\right)\)	\(e\left(\frac{133}{390}\right)\)	\(e\left(\frac{4007}{8580}\right)\)	\(e\left(\frac{47}{4290}\right)\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{102}{143}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{424}{715}\right)\)
\(\chi_{327184}(61,\cdot)\)	327184.yg	8580	yes	\(-1\)	\(1\)	\(e\left(\frac{571}{780}\right)\)	\(e\left(\frac{441}{2860}\right)\)	\(e\left(\frac{991}{2145}\right)\)	\(e\left(\frac{181}{390}\right)\)	\(e\left(\frac{1901}{2145}\right)\)	\(e\left(\frac{2489}{4290}\right)\)	\(e\left(\frac{547}{660}\right)\)	\(e\left(\frac{111}{572}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{441}{1430}\right)\)
\(\chi_{327184}(63,\cdot)\)	327184.yp	8580	no	\(-1\)	\(1\)	\(e\left(\frac{31}{390}\right)\)	\(e\left(\frac{1687}{2860}\right)\)	\(e\left(\frac{5483}{8580}\right)\)	\(e\left(\frac{31}{195}\right)\)	\(e\left(\frac{5743}{8580}\right)\)	\(e\left(\frac{1634}{2145}\right)\)	\(e\left(\frac{329}{660}\right)\)	\(e\left(\frac{411}{572}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{257}{1430}\right)\)
\(\chi_{327184}(67,\cdot)\)	327184.vm	1716	yes	\(1\)	\(1\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{45}{286}\right)\)	\(e\left(\frac{1273}{1716}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{545}{1716}\right)\)	\(e\left(\frac{149}{858}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{129}{143}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{45}{143}\right)\)
\(\chi_{327184}(69,\cdot)\)	327184.ye	8580	yes	\(1\)	\(1\)	\(e\left(\frac{37}{780}\right)\)	\(e\left(\frac{557}{2860}\right)\)	\(e\left(\frac{1657}{2145}\right)\)	\(e\left(\frac{37}{390}\right)\)	\(e\left(\frac{1039}{4290}\right)\)	\(e\left(\frac{214}{2145}\right)\)	\(e\left(\frac{529}{660}\right)\)	\(e\left(\frac{469}{572}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{557}{1430}\right)\)
\(\chi_{327184}(71,\cdot)\)	327184.xt	8580	no	\(1\)	\(1\)	\(e\left(\frac{19}{195}\right)\)	\(e\left(\frac{1831}{2860}\right)\)	\(e\left(\frac{3859}{8580}\right)\)	\(e\left(\frac{38}{195}\right)\)	\(e\left(\frac{6329}{8580}\right)\)	\(e\left(\frac{389}{4290}\right)\)	\(e\left(\frac{7}{660}\right)\)	\(e\left(\frac{313}{572}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{401}{1430}\right)\)
\(\chi_{327184}(73,\cdot)\)	327184.wg	2860	no	\(1\)	\(1\)	\(e\left(\frac{83}{130}\right)\)	\(e\left(\frac{953}{2860}\right)\)	\(e\left(\frac{959}{2860}\right)\)	\(e\left(\frac{18}{65}\right)\)	\(e\left(\frac{2779}{2860}\right)\)	\(e\left(\frac{152}{715}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{557}{572}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{953}{1430}\right)\)
\(\chi_{327184}(75,\cdot)\)	327184.yd	8580	yes	\(-1\)	\(1\)	\(e\left(\frac{719}{780}\right)\)	\(e\left(\frac{589}{2860}\right)\)	\(e\left(\frac{1783}{4290}\right)\)	\(e\left(\frac{329}{390}\right)\)	\(e\left(\frac{274}{2145}\right)\)	\(e\left(\frac{53}{2145}\right)\)	\(e\left(\frac{323}{660}\right)\)	\(e\left(\frac{193}{572}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{589}{1430}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 137280 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.