LMFDB - Group of Dirichlet characters of modulus 243675

Show commands: PariGP / SageMath

sage: H = DirichletGroup(243675)

pari: g = idealstar(,243675,2)

Character group

sage: G.order() pari: g.no
Order	=	123120
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{18}\times C_{3420}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{243675}(36101,\cdot)$, $\chi_{243675}(77977,\cdot)$, $\chi_{243675}(129601,\cdot)$

First 32 of 123120 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$22$
$\chi_{243675}(1,\cdot)$	243675.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{243675}(2,\cdot)$	243675.beq	3420	yes	$-1$	$1$	$e\left(\frac{371}{3420}\right)$	$e\left(\frac{371}{1710}\right)$	$e\left(\frac{395}{684}\right)$	$e\left(\frac{371}{1140}\right)$	$e\left(\frac{1403}{1710}\right)$	$e\left(\frac{1219}{3420}\right)$	$e\left(\frac{391}{570}\right)$	$e\left(\frac{371}{855}\right)$	$e\left(\frac{493}{3420}\right)$	$e\left(\frac{353}{380}\right)$
$\chi_{243675}(4,\cdot)$	243675.bbx	1710	yes	$1$	$1$	$e\left(\frac{371}{1710}\right)$	$e\left(\frac{371}{855}\right)$	$e\left(\frac{53}{342}\right)$	$e\left(\frac{371}{570}\right)$	$e\left(\frac{548}{855}\right)$	$e\left(\frac{1219}{1710}\right)$	$e\left(\frac{106}{285}\right)$	$e\left(\frac{742}{855}\right)$	$e\left(\frac{493}{1710}\right)$	$e\left(\frac{163}{190}\right)$
$\chi_{243675}(7,\cdot)$	243675.yj	684	no	$-1$	$1$	$e\left(\frac{395}{684}\right)$	$e\left(\frac{53}{342}\right)$	$e\left(\frac{179}{684}\right)$	$e\left(\frac{167}{228}\right)$	$e\left(\frac{50}{171}\right)$	$e\left(\frac{109}{684}\right)$	$e\left(\frac{287}{342}\right)$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{161}{228}\right)$	$e\left(\frac{595}{684}\right)$
$\chi_{243675}(8,\cdot)$	243675.bac	1140	no	$-1$	$1$	$e\left(\frac{371}{1140}\right)$	$e\left(\frac{371}{570}\right)$	$e\left(\frac{167}{228}\right)$	$e\left(\frac{371}{380}\right)$	$e\left(\frac{263}{570}\right)$	$e\left(\frac{79}{1140}\right)$	$e\left(\frac{11}{190}\right)$	$e\left(\frac{86}{285}\right)$	$e\left(\frac{493}{1140}\right)$	$e\left(\frac{299}{380}\right)$
$\chi_{243675}(11,\cdot)$	243675.bcc	1710	yes	$-1$	$1$	$e\left(\frac{1403}{1710}\right)$	$e\left(\frac{548}{855}\right)$	$e\left(\frac{50}{171}\right)$	$e\left(\frac{263}{570}\right)$	$e\left(\frac{1043}{1710}\right)$	$e\left(\frac{86}{855}\right)$	$e\left(\frac{193}{1710}\right)$	$e\left(\frac{241}{855}\right)$	$e\left(\frac{121}{190}\right)$	$e\left(\frac{368}{855}\right)$
$\chi_{243675}(13,\cdot)$	243675.bev	3420	yes	$1$	$1$	$e\left(\frac{1219}{3420}\right)$	$e\left(\frac{1219}{1710}\right)$	$e\left(\frac{109}{684}\right)$	$e\left(\frac{79}{1140}\right)$	$e\left(\frac{86}{855}\right)$	$e\left(\frac{341}{3420}\right)$	$e\left(\frac{49}{95}\right)$	$e\left(\frac{364}{855}\right)$	$e\left(\frac{1457}{3420}\right)$	$e\left(\frac{521}{1140}\right)$
$\chi_{243675}(14,\cdot)$	243675.bdj	1710	yes	$1$	$1$	$e\left(\frac{391}{570}\right)$	$e\left(\frac{106}{285}\right)$	$e\left(\frac{287}{342}\right)$	$e\left(\frac{11}{190}\right)$	$e\left(\frac{193}{1710}\right)$	$e\left(\frac{49}{95}\right)$	$e\left(\frac{449}{855}\right)$	$e\left(\frac{212}{285}\right)$	$e\left(\frac{727}{855}\right)$	$e\left(\frac{683}{855}\right)$
$\chi_{243675}(16,\cdot)$	243675.zk	855	yes	$1$	$1$	$e\left(\frac{371}{855}\right)$	$e\left(\frac{742}{855}\right)$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{86}{285}\right)$	$e\left(\frac{241}{855}\right)$	$e\left(\frac{364}{855}\right)$	$e\left(\frac{212}{285}\right)$	$e\left(\frac{629}{855}\right)$	$e\left(\frac{493}{855}\right)$	$e\left(\frac{68}{95}\right)$
$\chi_{243675}(17,\cdot)$	243675.bdt	3420	no	$1$	$1$	$e\left(\frac{493}{3420}\right)$	$e\left(\frac{493}{1710}\right)$	$e\left(\frac{161}{228}\right)$	$e\left(\frac{493}{1140}\right)$	$e\left(\frac{121}{190}\right)$	$e\left(\frac{1457}{3420}\right)$	$e\left(\frac{727}{855}\right)$	$e\left(\frac{493}{855}\right)$	$e\left(\frac{1009}{3420}\right)$	$e\left(\frac{2671}{3420}\right)$
$\chi_{243675}(22,\cdot)$	243675.bdq	3420	yes	$1$	$1$	$e\left(\frac{353}{380}\right)$	$e\left(\frac{163}{190}\right)$	$e\left(\frac{595}{684}\right)$	$e\left(\frac{299}{380}\right)$	$e\left(\frac{368}{855}\right)$	$e\left(\frac{521}{1140}\right)$	$e\left(\frac{683}{855}\right)$	$e\left(\frac{68}{95}\right)$	$e\left(\frac{2671}{3420}\right)$	$e\left(\frac{1229}{3420}\right)$
$\chi_{243675}(23,\cdot)$	243675.beb	3420	yes	$1$	$1$	$e\left(\frac{2011}{3420}\right)$	$e\left(\frac{301}{1710}\right)$	$e\left(\frac{385}{684}\right)$	$e\left(\frac{871}{1140}\right)$	$e\left(\frac{493}{1710}\right)$	$e\left(\frac{2699}{3420}\right)$	$e\left(\frac{43}{285}\right)$	$e\left(\frac{301}{855}\right)$	$e\left(\frac{2723}{3420}\right)$	$e\left(\frac{333}{380}\right)$
$\chi_{243675}(26,\cdot)$	243675.or	114	no	$-1$	$1$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{22}{57}\right)$
$\chi_{243675}(28,\cdot)$	243675.rq	180	no	$-1$	$1$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{131}{180}\right)$
$\chi_{243675}(29,\cdot)$	243675.baj	1710	yes	$1$	$1$	$e\left(\frac{39}{190}\right)$	$e\left(\frac{39}{95}\right)$	$e\left(\frac{289}{342}\right)$	$e\left(\frac{117}{190}\right)$	$e\left(\frac{671}{1710}\right)$	$e\left(\frac{199}{285}\right)$	$e\left(\frac{43}{855}\right)$	$e\left(\frac{78}{95}\right)$	$e\left(\frac{314}{855}\right)$	$e\left(\frac{511}{855}\right)$
$\chi_{243675}(31,\cdot)$	243675.bcl	1710	yes	$-1$	$1$	$e\left(\frac{679}{1710}\right)$	$e\left(\frac{679}{855}\right)$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{109}{570}\right)$	$e\left(\frac{182}{855}\right)$	$e\left(\frac{1661}{1710}\right)$	$e\left(\frac{119}{1710}\right)$	$e\left(\frac{503}{855}\right)$	$e\left(\frac{9}{95}\right)$	$e\left(\frac{1043}{1710}\right)$
$\chi_{243675}(32,\cdot)$	243675.yb	684	no	$-1$	$1$	$e\left(\frac{371}{684}\right)$	$e\left(\frac{29}{342}\right)$	$e\left(\frac{607}{684}\right)$	$e\left(\frac{143}{228}\right)$	$e\left(\frac{35}{342}\right)$	$e\left(\frac{535}{684}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{29}{171}\right)$	$e\left(\frac{493}{684}\right)$	$e\left(\frac{49}{76}\right)$
$\chi_{243675}(34,\cdot)$	243675.bdl	1710	yes	$-1$	$1$	$e\left(\frac{24}{95}\right)$	$e\left(\frac{48}{95}\right)$	$e\left(\frac{97}{342}\right)$	$e\left(\frac{72}{95}\right)$	$e\left(\frac{391}{855}\right)$	$e\left(\frac{223}{285}\right)$	$e\left(\frac{917}{1710}\right)$	$e\left(\frac{1}{95}\right)$	$e\left(\frac{751}{1710}\right)$	$e\left(\frac{607}{855}\right)$
$\chi_{243675}(37,\cdot)$	243675.zz	1140	no	$1$	$1$	$e\left(\frac{1043}{1140}\right)$	$e\left(\frac{473}{570}\right)$	$e\left(\frac{73}{228}\right)$	$e\left(\frac{283}{380}\right)$	$e\left(\frac{272}{285}\right)$	$e\left(\frac{577}{1140}\right)$	$e\left(\frac{67}{285}\right)$	$e\left(\frac{188}{285}\right)$	$e\left(\frac{223}{380}\right)$	$e\left(\frac{991}{1140}\right)$
$\chi_{243675}(41,\cdot)$	243675.baq	1710	yes	$1$	$1$	$e\left(\frac{97}{285}\right)$	$e\left(\frac{194}{285}\right)$	$e\left(\frac{85}{171}\right)$	$e\left(\frac{2}{95}\right)$	$e\left(\frac{787}{1710}\right)$	$e\left(\frac{461}{570}\right)$	$e\left(\frac{716}{855}\right)$	$e\left(\frac{103}{285}\right)$	$e\left(\frac{71}{1710}\right)$	$e\left(\frac{1369}{1710}\right)$
$\chi_{243675}(43,\cdot)$	243675.yv	684	no	$-1$	$1$	$e\left(\frac{85}{684}\right)$	$e\left(\frac{85}{342}\right)$	$e\left(\frac{77}{684}\right)$	$e\left(\frac{85}{228}\right)$	$e\left(\frac{68}{171}\right)$	$e\left(\frac{35}{684}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{85}{171}\right)$	$e\left(\frac{305}{684}\right)$	$e\left(\frac{119}{228}\right)$
$\chi_{243675}(44,\cdot)$	243675.bda	1710	no	$-1$	$1$	$e\left(\frac{32}{855}\right)$	$e\left(\frac{64}{855}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{32}{285}\right)$	$e\left(\frac{143}{570}\right)$	$e\left(\frac{1391}{1710}\right)$	$e\left(\frac{829}{1710}\right)$	$e\left(\frac{128}{855}\right)$	$e\left(\frac{791}{855}\right)$	$e\left(\frac{493}{1710}\right)$
$\chi_{243675}(46,\cdot)$	243675.xb	570	no	$-1$	$1$	$e\left(\frac{397}{570}\right)$	$e\left(\frac{112}{285}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{17}{190}\right)$	$e\left(\frac{31}{285}\right)$	$e\left(\frac{83}{570}\right)$	$e\left(\frac{159}{190}\right)$	$e\left(\frac{224}{285}\right)$	$e\left(\frac{268}{285}\right)$	$e\left(\frac{153}{190}\right)$
$\chi_{243675}(47,\cdot)$	243675.bff	3420	yes	$1$	$1$	$e\left(\frac{359}{1140}\right)$	$e\left(\frac{359}{570}\right)$	$e\left(\frac{599}{684}\right)$	$e\left(\frac{359}{380}\right)$	$e\left(\frac{701}{1710}\right)$	$e\left(\frac{311}{1140}\right)$	$e\left(\frac{163}{855}\right)$	$e\left(\frac{74}{285}\right)$	$e\left(\frac{221}{3420}\right)$	$e\left(\frac{2479}{3420}\right)$
$\chi_{243675}(49,\cdot)$	243675.ud	342	no	$1$	$1$	$e\left(\frac{53}{342}\right)$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{179}{342}\right)$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{100}{171}\right)$	$e\left(\frac{109}{342}\right)$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{106}{171}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{253}{342}\right)$
$\chi_{243675}(52,\cdot)$	243675.bec	3420	yes	$1$	$1$	$e\left(\frac{1961}{3420}\right)$	$e\left(\frac{251}{1710}\right)$	$e\left(\frac{215}{684}\right)$	$e\left(\frac{821}{1140}\right)$	$e\left(\frac{634}{855}\right)$	$e\left(\frac{2779}{3420}\right)$	$e\left(\frac{253}{285}\right)$	$e\left(\frac{251}{855}\right)$	$e\left(\frac{2443}{3420}\right)$	$e\left(\frac{359}{1140}\right)$
$\chi_{243675}(53,\cdot)$	243675.bey	3420	no	$-1$	$1$	$e\left(\frac{317}{3420}\right)$	$e\left(\frac{317}{1710}\right)$	$e\left(\frac{35}{228}\right)$	$e\left(\frac{317}{1140}\right)$	$e\left(\frac{487}{570}\right)$	$e\left(\frac{1693}{3420}\right)$	$e\left(\frac{421}{1710}\right)$	$e\left(\frac{317}{855}\right)$	$e\left(\frac{3071}{3420}\right)$	$e\left(\frac{3239}{3420}\right)$
$\chi_{243675}(56,\cdot)$	243675.bbn	1710	yes	$1$	$1$	$e\left(\frac{772}{855}\right)$	$e\left(\frac{689}{855}\right)$	$e\left(\frac{170}{171}\right)$	$e\left(\frac{202}{285}\right)$	$e\left(\frac{1289}{1710}\right)$	$e\left(\frac{391}{1710}\right)$	$e\left(\frac{767}{855}\right)$	$e\left(\frac{523}{855}\right)$	$e\left(\frac{79}{570}\right)$	$e\left(\frac{1123}{1710}\right)$
$\chi_{243675}(58,\cdot)$	243675.beg	3420	yes	$-1$	$1$	$e\left(\frac{1073}{3420}\right)$	$e\left(\frac{1073}{1710}\right)$	$e\left(\frac{289}{684}\right)$	$e\left(\frac{1073}{1140}\right)$	$e\left(\frac{182}{855}\right)$	$e\left(\frac{187}{3420}\right)$	$e\left(\frac{1259}{1710}\right)$	$e\left(\frac{218}{855}\right)$	$e\left(\frac{583}{1140}\right)$	$e\left(\frac{1801}{3420}\right)$
$\chi_{243675}(59,\cdot)$	243675.bdj	1710	yes	$1$	$1$	$e\left(\frac{289}{570}\right)$	$e\left(\frac{4}{285}\right)$	$e\left(\frac{113}{342}\right)$	$e\left(\frac{99}{190}\right)$	$e\left(\frac{1357}{1710}\right)$	$e\left(\frac{61}{95}\right)$	$e\left(\frac{716}{855}\right)$	$e\left(\frac{8}{285}\right)$	$e\left(\frac{748}{855}\right)$	$e\left(\frac{257}{855}\right)$
$\chi_{243675}(61,\cdot)$	243675.zr	855	yes	$1$	$1$	$e\left(\frac{91}{95}\right)$	$e\left(\frac{87}{95}\right)$	$e\left(\frac{98}{171}\right)$	$e\left(\frac{83}{95}\right)$	$e\left(\frac{679}{855}\right)$	$e\left(\frac{232}{285}\right)$	$e\left(\frac{454}{855}\right)$	$e\left(\frac{79}{95}\right)$	$e\left(\frac{452}{855}\right)$	$e\left(\frac{643}{855}\right)$
$\chi_{243675}(62,\cdot)$	243675.qn	180	no	$1$	$1$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{1}{90}\right)$	$i$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{97}{180}\right)$

Click here to search among the remaining 123088 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	$243675$
Structure	\(C_{2}\times C_{18}\times C_{3420}\)
Order	$123120$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(22\)
\(\chi_{243675}(1,\cdot)\)	243675.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{243675}(2,\cdot)\)	243675.beq	3420	yes	\(-1\)	\(1\)	\(e\left(\frac{371}{3420}\right)\)	\(e\left(\frac{371}{1710}\right)\)	\(e\left(\frac{395}{684}\right)\)	\(e\left(\frac{371}{1140}\right)\)	\(e\left(\frac{1403}{1710}\right)\)	\(e\left(\frac{1219}{3420}\right)\)	\(e\left(\frac{391}{570}\right)\)	\(e\left(\frac{371}{855}\right)\)	\(e\left(\frac{493}{3420}\right)\)	\(e\left(\frac{353}{380}\right)\)
\(\chi_{243675}(4,\cdot)\)	243675.bbx	1710	yes	\(1\)	\(1\)	\(e\left(\frac{371}{1710}\right)\)	\(e\left(\frac{371}{855}\right)\)	\(e\left(\frac{53}{342}\right)\)	\(e\left(\frac{371}{570}\right)\)	\(e\left(\frac{548}{855}\right)\)	\(e\left(\frac{1219}{1710}\right)\)	\(e\left(\frac{106}{285}\right)\)	\(e\left(\frac{742}{855}\right)\)	\(e\left(\frac{493}{1710}\right)\)	\(e\left(\frac{163}{190}\right)\)
\(\chi_{243675}(7,\cdot)\)	243675.yj	684	no	\(-1\)	\(1\)	\(e\left(\frac{395}{684}\right)\)	\(e\left(\frac{53}{342}\right)\)	\(e\left(\frac{179}{684}\right)\)	\(e\left(\frac{167}{228}\right)\)	\(e\left(\frac{50}{171}\right)\)	\(e\left(\frac{109}{684}\right)\)	\(e\left(\frac{287}{342}\right)\)	\(e\left(\frac{53}{171}\right)\)	\(e\left(\frac{161}{228}\right)\)	\(e\left(\frac{595}{684}\right)\)
\(\chi_{243675}(8,\cdot)\)	243675.bac	1140	no	\(-1\)	\(1\)	\(e\left(\frac{371}{1140}\right)\)	\(e\left(\frac{371}{570}\right)\)	\(e\left(\frac{167}{228}\right)\)	\(e\left(\frac{371}{380}\right)\)	\(e\left(\frac{263}{570}\right)\)	\(e\left(\frac{79}{1140}\right)\)	\(e\left(\frac{11}{190}\right)\)	\(e\left(\frac{86}{285}\right)\)	\(e\left(\frac{493}{1140}\right)\)	\(e\left(\frac{299}{380}\right)\)
\(\chi_{243675}(11,\cdot)\)	243675.bcc	1710	yes	\(-1\)	\(1\)	\(e\left(\frac{1403}{1710}\right)\)	\(e\left(\frac{548}{855}\right)\)	\(e\left(\frac{50}{171}\right)\)	\(e\left(\frac{263}{570}\right)\)	\(e\left(\frac{1043}{1710}\right)\)	\(e\left(\frac{86}{855}\right)\)	\(e\left(\frac{193}{1710}\right)\)	\(e\left(\frac{241}{855}\right)\)	\(e\left(\frac{121}{190}\right)\)	\(e\left(\frac{368}{855}\right)\)
\(\chi_{243675}(13,\cdot)\)	243675.bev	3420	yes	\(1\)	\(1\)	\(e\left(\frac{1219}{3420}\right)\)	\(e\left(\frac{1219}{1710}\right)\)	\(e\left(\frac{109}{684}\right)\)	\(e\left(\frac{79}{1140}\right)\)	\(e\left(\frac{86}{855}\right)\)	\(e\left(\frac{341}{3420}\right)\)	\(e\left(\frac{49}{95}\right)\)	\(e\left(\frac{364}{855}\right)\)	\(e\left(\frac{1457}{3420}\right)\)	\(e\left(\frac{521}{1140}\right)\)
\(\chi_{243675}(14,\cdot)\)	243675.bdj	1710	yes	\(1\)	\(1\)	\(e\left(\frac{391}{570}\right)\)	\(e\left(\frac{106}{285}\right)\)	\(e\left(\frac{287}{342}\right)\)	\(e\left(\frac{11}{190}\right)\)	\(e\left(\frac{193}{1710}\right)\)	\(e\left(\frac{49}{95}\right)\)	\(e\left(\frac{449}{855}\right)\)	\(e\left(\frac{212}{285}\right)\)	\(e\left(\frac{727}{855}\right)\)	\(e\left(\frac{683}{855}\right)\)
\(\chi_{243675}(16,\cdot)\)	243675.zk	855	yes	\(1\)	\(1\)	\(e\left(\frac{371}{855}\right)\)	\(e\left(\frac{742}{855}\right)\)	\(e\left(\frac{53}{171}\right)\)	\(e\left(\frac{86}{285}\right)\)	\(e\left(\frac{241}{855}\right)\)	\(e\left(\frac{364}{855}\right)\)	\(e\left(\frac{212}{285}\right)\)	\(e\left(\frac{629}{855}\right)\)	\(e\left(\frac{493}{855}\right)\)	\(e\left(\frac{68}{95}\right)\)
\(\chi_{243675}(17,\cdot)\)	243675.bdt	3420	no	\(1\)	\(1\)	\(e\left(\frac{493}{3420}\right)\)	\(e\left(\frac{493}{1710}\right)\)	\(e\left(\frac{161}{228}\right)\)	\(e\left(\frac{493}{1140}\right)\)	\(e\left(\frac{121}{190}\right)\)	\(e\left(\frac{1457}{3420}\right)\)	\(e\left(\frac{727}{855}\right)\)	\(e\left(\frac{493}{855}\right)\)	\(e\left(\frac{1009}{3420}\right)\)	\(e\left(\frac{2671}{3420}\right)\)
\(\chi_{243675}(22,\cdot)\)	243675.bdq	3420	yes	\(1\)	\(1\)	\(e\left(\frac{353}{380}\right)\)	\(e\left(\frac{163}{190}\right)\)	\(e\left(\frac{595}{684}\right)\)	\(e\left(\frac{299}{380}\right)\)	\(e\left(\frac{368}{855}\right)\)	\(e\left(\frac{521}{1140}\right)\)	\(e\left(\frac{683}{855}\right)\)	\(e\left(\frac{68}{95}\right)\)	\(e\left(\frac{2671}{3420}\right)\)	\(e\left(\frac{1229}{3420}\right)\)
\(\chi_{243675}(23,\cdot)\)	243675.beb	3420	yes	\(1\)	\(1\)	\(e\left(\frac{2011}{3420}\right)\)	\(e\left(\frac{301}{1710}\right)\)	\(e\left(\frac{385}{684}\right)\)	\(e\left(\frac{871}{1140}\right)\)	\(e\left(\frac{493}{1710}\right)\)	\(e\left(\frac{2699}{3420}\right)\)	\(e\left(\frac{43}{285}\right)\)	\(e\left(\frac{301}{855}\right)\)	\(e\left(\frac{2723}{3420}\right)\)	\(e\left(\frac{333}{380}\right)\)
\(\chi_{243675}(26,\cdot)\)	243675.or	114	no	\(-1\)	\(1\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{22}{57}\right)\)
\(\chi_{243675}(28,\cdot)\)	243675.rq	180	no	\(-1\)	\(1\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{131}{180}\right)\)
\(\chi_{243675}(29,\cdot)\)	243675.baj	1710	yes	\(1\)	\(1\)	\(e\left(\frac{39}{190}\right)\)	\(e\left(\frac{39}{95}\right)\)	\(e\left(\frac{289}{342}\right)\)	\(e\left(\frac{117}{190}\right)\)	\(e\left(\frac{671}{1710}\right)\)	\(e\left(\frac{199}{285}\right)\)	\(e\left(\frac{43}{855}\right)\)	\(e\left(\frac{78}{95}\right)\)	\(e\left(\frac{314}{855}\right)\)	\(e\left(\frac{511}{855}\right)\)
\(\chi_{243675}(31,\cdot)\)	243675.bcl	1710	yes	\(-1\)	\(1\)	\(e\left(\frac{679}{1710}\right)\)	\(e\left(\frac{679}{855}\right)\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{109}{570}\right)\)	\(e\left(\frac{182}{855}\right)\)	\(e\left(\frac{1661}{1710}\right)\)	\(e\left(\frac{119}{1710}\right)\)	\(e\left(\frac{503}{855}\right)\)	\(e\left(\frac{9}{95}\right)\)	\(e\left(\frac{1043}{1710}\right)\)
\(\chi_{243675}(32,\cdot)\)	243675.yb	684	no	\(-1\)	\(1\)	\(e\left(\frac{371}{684}\right)\)	\(e\left(\frac{29}{342}\right)\)	\(e\left(\frac{607}{684}\right)\)	\(e\left(\frac{143}{228}\right)\)	\(e\left(\frac{35}{342}\right)\)	\(e\left(\frac{535}{684}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{29}{171}\right)\)	\(e\left(\frac{493}{684}\right)\)	\(e\left(\frac{49}{76}\right)\)
\(\chi_{243675}(34,\cdot)\)	243675.bdl	1710	yes	\(-1\)	\(1\)	\(e\left(\frac{24}{95}\right)\)	\(e\left(\frac{48}{95}\right)\)	\(e\left(\frac{97}{342}\right)\)	\(e\left(\frac{72}{95}\right)\)	\(e\left(\frac{391}{855}\right)\)	\(e\left(\frac{223}{285}\right)\)	\(e\left(\frac{917}{1710}\right)\)	\(e\left(\frac{1}{95}\right)\)	\(e\left(\frac{751}{1710}\right)\)	\(e\left(\frac{607}{855}\right)\)
\(\chi_{243675}(37,\cdot)\)	243675.zz	1140	no	\(1\)	\(1\)	\(e\left(\frac{1043}{1140}\right)\)	\(e\left(\frac{473}{570}\right)\)	\(e\left(\frac{73}{228}\right)\)	\(e\left(\frac{283}{380}\right)\)	\(e\left(\frac{272}{285}\right)\)	\(e\left(\frac{577}{1140}\right)\)	\(e\left(\frac{67}{285}\right)\)	\(e\left(\frac{188}{285}\right)\)	\(e\left(\frac{223}{380}\right)\)	\(e\left(\frac{991}{1140}\right)\)
\(\chi_{243675}(41,\cdot)\)	243675.baq	1710	yes	\(1\)	\(1\)	\(e\left(\frac{97}{285}\right)\)	\(e\left(\frac{194}{285}\right)\)	\(e\left(\frac{85}{171}\right)\)	\(e\left(\frac{2}{95}\right)\)	\(e\left(\frac{787}{1710}\right)\)	\(e\left(\frac{461}{570}\right)\)	\(e\left(\frac{716}{855}\right)\)	\(e\left(\frac{103}{285}\right)\)	\(e\left(\frac{71}{1710}\right)\)	\(e\left(\frac{1369}{1710}\right)\)
\(\chi_{243675}(43,\cdot)\)	243675.yv	684	no	\(-1\)	\(1\)	\(e\left(\frac{85}{684}\right)\)	\(e\left(\frac{85}{342}\right)\)	\(e\left(\frac{77}{684}\right)\)	\(e\left(\frac{85}{228}\right)\)	\(e\left(\frac{68}{171}\right)\)	\(e\left(\frac{35}{684}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{85}{171}\right)\)	\(e\left(\frac{305}{684}\right)\)	\(e\left(\frac{119}{228}\right)\)
\(\chi_{243675}(44,\cdot)\)	243675.bda	1710	no	\(-1\)	\(1\)	\(e\left(\frac{32}{855}\right)\)	\(e\left(\frac{64}{855}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{32}{285}\right)\)	\(e\left(\frac{143}{570}\right)\)	\(e\left(\frac{1391}{1710}\right)\)	\(e\left(\frac{829}{1710}\right)\)	\(e\left(\frac{128}{855}\right)\)	\(e\left(\frac{791}{855}\right)\)	\(e\left(\frac{493}{1710}\right)\)
\(\chi_{243675}(46,\cdot)\)	243675.xb	570	no	\(-1\)	\(1\)	\(e\left(\frac{397}{570}\right)\)	\(e\left(\frac{112}{285}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{17}{190}\right)\)	\(e\left(\frac{31}{285}\right)\)	\(e\left(\frac{83}{570}\right)\)	\(e\left(\frac{159}{190}\right)\)	\(e\left(\frac{224}{285}\right)\)	\(e\left(\frac{268}{285}\right)\)	\(e\left(\frac{153}{190}\right)\)
\(\chi_{243675}(47,\cdot)\)	243675.bff	3420	yes	\(1\)	\(1\)	\(e\left(\frac{359}{1140}\right)\)	\(e\left(\frac{359}{570}\right)\)	\(e\left(\frac{599}{684}\right)\)	\(e\left(\frac{359}{380}\right)\)	\(e\left(\frac{701}{1710}\right)\)	\(e\left(\frac{311}{1140}\right)\)	\(e\left(\frac{163}{855}\right)\)	\(e\left(\frac{74}{285}\right)\)	\(e\left(\frac{221}{3420}\right)\)	\(e\left(\frac{2479}{3420}\right)\)
\(\chi_{243675}(49,\cdot)\)	243675.ud	342	no	\(1\)	\(1\)	\(e\left(\frac{53}{342}\right)\)	\(e\left(\frac{53}{171}\right)\)	\(e\left(\frac{179}{342}\right)\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{100}{171}\right)\)	\(e\left(\frac{109}{342}\right)\)	\(e\left(\frac{116}{171}\right)\)	\(e\left(\frac{106}{171}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{253}{342}\right)\)
\(\chi_{243675}(52,\cdot)\)	243675.bec	3420	yes	\(1\)	\(1\)	\(e\left(\frac{1961}{3420}\right)\)	\(e\left(\frac{251}{1710}\right)\)	\(e\left(\frac{215}{684}\right)\)	\(e\left(\frac{821}{1140}\right)\)	\(e\left(\frac{634}{855}\right)\)	\(e\left(\frac{2779}{3420}\right)\)	\(e\left(\frac{253}{285}\right)\)	\(e\left(\frac{251}{855}\right)\)	\(e\left(\frac{2443}{3420}\right)\)	\(e\left(\frac{359}{1140}\right)\)
\(\chi_{243675}(53,\cdot)\)	243675.bey	3420	no	\(-1\)	\(1\)	\(e\left(\frac{317}{3420}\right)\)	\(e\left(\frac{317}{1710}\right)\)	\(e\left(\frac{35}{228}\right)\)	\(e\left(\frac{317}{1140}\right)\)	\(e\left(\frac{487}{570}\right)\)	\(e\left(\frac{1693}{3420}\right)\)	\(e\left(\frac{421}{1710}\right)\)	\(e\left(\frac{317}{855}\right)\)	\(e\left(\frac{3071}{3420}\right)\)	\(e\left(\frac{3239}{3420}\right)\)
\(\chi_{243675}(56,\cdot)\)	243675.bbn	1710	yes	\(1\)	\(1\)	\(e\left(\frac{772}{855}\right)\)	\(e\left(\frac{689}{855}\right)\)	\(e\left(\frac{170}{171}\right)\)	\(e\left(\frac{202}{285}\right)\)	\(e\left(\frac{1289}{1710}\right)\)	\(e\left(\frac{391}{1710}\right)\)	\(e\left(\frac{767}{855}\right)\)	\(e\left(\frac{523}{855}\right)\)	\(e\left(\frac{79}{570}\right)\)	\(e\left(\frac{1123}{1710}\right)\)
\(\chi_{243675}(58,\cdot)\)	243675.beg	3420	yes	\(-1\)	\(1\)	\(e\left(\frac{1073}{3420}\right)\)	\(e\left(\frac{1073}{1710}\right)\)	\(e\left(\frac{289}{684}\right)\)	\(e\left(\frac{1073}{1140}\right)\)	\(e\left(\frac{182}{855}\right)\)	\(e\left(\frac{187}{3420}\right)\)	\(e\left(\frac{1259}{1710}\right)\)	\(e\left(\frac{218}{855}\right)\)	\(e\left(\frac{583}{1140}\right)\)	\(e\left(\frac{1801}{3420}\right)\)
\(\chi_{243675}(59,\cdot)\)	243675.bdj	1710	yes	\(1\)	\(1\)	\(e\left(\frac{289}{570}\right)\)	\(e\left(\frac{4}{285}\right)\)	\(e\left(\frac{113}{342}\right)\)	\(e\left(\frac{99}{190}\right)\)	\(e\left(\frac{1357}{1710}\right)\)	\(e\left(\frac{61}{95}\right)\)	\(e\left(\frac{716}{855}\right)\)	\(e\left(\frac{8}{285}\right)\)	\(e\left(\frac{748}{855}\right)\)	\(e\left(\frac{257}{855}\right)\)
\(\chi_{243675}(61,\cdot)\)	243675.zr	855	yes	\(1\)	\(1\)	\(e\left(\frac{91}{95}\right)\)	\(e\left(\frac{87}{95}\right)\)	\(e\left(\frac{98}{171}\right)\)	\(e\left(\frac{83}{95}\right)\)	\(e\left(\frac{679}{855}\right)\)	\(e\left(\frac{232}{285}\right)\)	\(e\left(\frac{454}{855}\right)\)	\(e\left(\frac{79}{95}\right)\)	\(e\left(\frac{452}{855}\right)\)	\(e\left(\frac{643}{855}\right)\)
\(\chi_{243675}(62,\cdot)\)	243675.qn	180	no	\(1\)	\(1\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(i\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{97}{180}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 123120 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.