LMFDB - Group of Dirichlet characters of modulus 344760

Show commands: PariGP / SageMath

sage: H = DirichletGroup(344760)

pari: g = idealstar(,344760,2)

Character group

sage: G.order() pari: g.no
Order	=	79872
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{4}\times C_{624}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{344760}(86191,\cdot)$, $\chi_{344760}(172381,\cdot)$, $\chi_{344760}(229841,\cdot)$, $\chi_{344760}(206857,\cdot)$, $\chi_{344760}(316201,\cdot)$, $\chi_{344760}(304201,\cdot)$

First 32 of 79872 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	$-1$	$1$	$7$	$11$	$19$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{344760}(1,\cdot)$	344760.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{344760}(7,\cdot)$	344760.dde	624	no	$1$	$1$	$e\left(\frac{439}{624}\right)$	$e\left(\frac{599}{624}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{545}{624}\right)$	$e\left(\frac{19}{208}\right)$	$e\left(\frac{317}{624}\right)$	$e\left(\frac{539}{624}\right)$	$e\left(\frac{95}{312}\right)$	$e\left(\frac{37}{52}\right)$
$\chi_{344760}(11,\cdot)$	344760.dfr	624	no	$1$	$1$	$e\left(\frac{599}{624}\right)$	$e\left(\frac{355}{624}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{61}{624}\right)$	$e\left(\frac{63}{208}\right)$	$e\left(\frac{397}{624}\right)$	$e\left(\frac{271}{624}\right)$	$e\left(\frac{133}{312}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{344760}(19,\cdot)$	344760.bgj	24	no	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{12}\right)$	$-i$
$\chi_{344760}(23,\cdot)$	344760.brs	48	no	$1$	$1$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{7}{24}\right)$	$1$
$\chi_{344760}(29,\cdot)$	344760.dco	624	yes	$1$	$1$	$e\left(\frac{545}{624}\right)$	$e\left(\frac{61}{624}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{511}{624}\right)$	$e\left(\frac{145}{208}\right)$	$e\left(\frac{331}{624}\right)$	$e\left(\frac{145}{624}\right)$	$e\left(\frac{283}{312}\right)$	$e\left(\frac{21}{52}\right)$
$\chi_{344760}(31,\cdot)$	344760.crw	208	no	$-1$	$1$	$e\left(\frac{19}{208}\right)$	$e\left(\frac{63}{208}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{145}{208}\right)$	$e\left(\frac{81}{208}\right)$	$e\left(\frac{185}{208}\right)$	$e\left(\frac{131}{208}\right)$	$e\left(\frac{5}{104}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{344760}(37,\cdot)$	344760.dcc	624	no	$-1$	$1$	$e\left(\frac{317}{624}\right)$	$e\left(\frac{397}{624}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{331}{624}\right)$	$e\left(\frac{185}{208}\right)$	$e\left(\frac{607}{624}\right)$	$e\left(\frac{601}{624}\right)$	$e\left(\frac{145}{312}\right)$	$e\left(\frac{25}{52}\right)$
$\chi_{344760}(41,\cdot)$	344760.dep	624	no	$-1$	$1$	$e\left(\frac{539}{624}\right)$	$e\left(\frac{271}{624}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{145}{624}\right)$	$e\left(\frac{131}{208}\right)$	$e\left(\frac{601}{624}\right)$	$e\left(\frac{235}{624}\right)$	$e\left(\frac{265}{312}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{344760}(43,\cdot)$	344760.cxo	312	no	$1$	$1$	$e\left(\frac{95}{312}\right)$	$e\left(\frac{133}{312}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{283}{312}\right)$	$e\left(\frac{5}{104}\right)$	$e\left(\frac{145}{312}\right)$	$e\left(\frac{265}{312}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{1}{52}\right)$
$\chi_{344760}(47,\cdot)$	344760.byp	52	no	$1$	$1$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{9}{26}\right)$	$-i$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{344760}(49,\cdot)$	344760.cyt	312	no	$1$	$1$	$e\left(\frac{127}{312}\right)$	$e\left(\frac{287}{312}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{233}{312}\right)$	$e\left(\frac{19}{104}\right)$	$e\left(\frac{5}{312}\right)$	$e\left(\frac{227}{312}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{344760}(53,\cdot)$	344760.cgz	104	yes	$1$	$1$	$e\left(\frac{71}{104}\right)$	$e\left(\frac{37}{104}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{67}{104}\right)$	$e\left(\frac{3}{104}\right)$	$e\left(\frac{29}{104}\right)$	$e\left(\frac{53}{104}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{11}{52}\right)$
$\chi_{344760}(59,\cdot)$	344760.cwf	312	yes	$-1$	$1$	$e\left(\frac{275}{312}\right)$	$e\left(\frac{307}{312}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{31}{312}\right)$	$e\left(\frac{87}{104}\right)$	$e\left(\frac{157}{312}\right)$	$e\left(\frac{139}{312}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{7}{52}\right)$
$\chi_{344760}(61,\cdot)$	344760.ddy	624	no	$-1$	$1$	$e\left(\frac{55}{624}\right)$	$e\left(\frac{155}{624}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{521}{624}\right)$	$e\left(\frac{111}{208}\right)$	$e\left(\frac{125}{624}\right)$	$e\left(\frac{215}{624}\right)$	$e\left(\frac{113}{312}\right)$	$e\left(\frac{15}{52}\right)$
$\chi_{344760}(67,\cdot)$	344760.ciz	156	no	$-1$	$1$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{344760}(71,\cdot)$	344760.dfk	624	no	$1$	$1$	$e\left(\frac{97}{624}\right)$	$e\left(\frac{557}{624}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{275}{624}\right)$	$e\left(\frac{105}{208}\right)$	$e\left(\frac{419}{624}\right)$	$e\left(\frac{521}{624}\right)$	$e\left(\frac{239}{312}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{344760}(73,\cdot)$	344760.cuk	208	no	$-1$	$1$	$e\left(\frac{35}{208}\right)$	$e\left(\frac{179}{208}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{133}{208}\right)$	$e\left(\frac{141}{208}\right)$	$e\left(\frac{89}{208}\right)$	$e\left(\frac{47}{208}\right)$	$e\left(\frac{79}{104}\right)$	$e\left(\frac{31}{52}\right)$
$\chi_{344760}(77,\cdot)$	344760.cgv	104	yes	$1$	$1$	$e\left(\frac{69}{104}\right)$	$e\left(\frac{55}{104}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{101}{104}\right)$	$e\left(\frac{41}{104}\right)$	$e\left(\frac{15}{104}\right)$	$e\left(\frac{31}{104}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{3}{52}\right)$
$\chi_{344760}(79,\cdot)$	344760.cud	208	no	$1$	$1$	$e\left(\frac{57}{208}\right)$	$e\left(\frac{85}{208}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{175}{208}\right)$	$e\left(\frac{139}{208}\right)$	$e\left(\frac{35}{208}\right)$	$e\left(\frac{185}{208}\right)$	$e\left(\frac{67}{104}\right)$	$e\left(\frac{23}{52}\right)$
$\chi_{344760}(83,\cdot)$	344760.cen	104	yes	$1$	$1$	$e\left(\frac{25}{104}\right)$	$e\left(\frac{87}{104}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{95}{104}\right)$	$e\left(\frac{97}{104}\right)$	$e\left(\frac{19}{104}\right)$	$e\left(\frac{15}{104}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{344760}(89,\cdot)$	344760.baz	12	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-i$
$\chi_{344760}(97,\cdot)$	344760.ddc	624	no	$-1$	$1$	$e\left(\frac{529}{624}\right)$	$e\left(\frac{569}{624}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{263}{624}\right)$	$e\left(\frac{125}{208}\right)$	$e\left(\frac{323}{624}\right)$	$e\left(\frac{125}{624}\right)$	$e\left(\frac{209}{312}\right)$	$e\left(\frac{19}{52}\right)$
$\chi_{344760}(101,\cdot)$	344760.ccv	78	no	$-1$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{344760}(103,\cdot)$	344760.buk	52	no	$1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{7}{13}\right)$	$-1$	$-i$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{43}{52}\right)$
$\chi_{344760}(107,\cdot)$	344760.dey	624	yes	$1$	$1$	$e\left(\frac{485}{624}\right)$	$e\left(\frac{445}{624}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{127}{624}\right)$	$e\left(\frac{161}{208}\right)$	$e\left(\frac{535}{624}\right)$	$e\left(\frac{265}{624}\right)$	$e\left(\frac{181}{312}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{344760}(109,\cdot)$	344760.cuv	208	no	$1$	$1$	$e\left(\frac{33}{208}\right)$	$e\left(\frac{197}{208}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{208}\right)$	$e\left(\frac{179}{208}\right)$	$e\left(\frac{179}{208}\right)$	$e\left(\frac{129}{208}\right)$	$e\left(\frac{99}{104}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{344760}(113,\cdot)$	344760.dbl	624	no	$-1$	$1$	$e\left(\frac{319}{624}\right)$	$e\left(\frac{431}{624}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{557}{624}\right)$	$e\left(\frac{51}{208}\right)$	$e\left(\frac{101}{624}\right)$	$e\left(\frac{467}{624}\right)$	$e\left(\frac{47}{312}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{344760}(121,\cdot)$	344760.cxt	312	no	$1$	$1$	$e\left(\frac{287}{312}\right)$	$e\left(\frac{43}{312}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{61}{312}\right)$	$e\left(\frac{63}{104}\right)$	$e\left(\frac{85}{312}\right)$	$e\left(\frac{271}{312}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{344760}(127,\cdot)$	344760.cxr	312	no	$1$	$1$	$e\left(\frac{79}{312}\right)$	$e\left(\frac{173}{312}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{35}{312}\right)$	$e\left(\frac{89}{104}\right)$	$e\left(\frac{293}{312}\right)$	$e\left(\frac{245}{312}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{23}{52}\right)$
$\chi_{344760}(131,\cdot)$	344760.cug	208	no	$-1$	$1$	$e\left(\frac{43}{208}\right)$	$e\left(\frac{55}{208}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{101}{208}\right)$	$e\left(\frac{41}{208}\right)$	$e\left(\frac{145}{208}\right)$	$e\left(\frac{187}{208}\right)$	$e\left(\frac{25}{104}\right)$	$e\left(\frac{21}{52}\right)$
$\chi_{344760}(133,\cdot)$	344760.dbm	624	no	$1$	$1$	$e\left(\frac{569}{624}\right)$	$e\left(\frac{1}{624}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{259}{624}\right)$	$e\left(\frac{45}{208}\right)$	$e\left(\frac{187}{624}\right)$	$e\left(\frac{565}{624}\right)$	$e\left(\frac{121}{312}\right)$	$e\left(\frac{6}{13}\right)$

Click here to search among the remaining 79840 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	$344760$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{4}\times C_{624}\)
Order	$79872$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{344760}(1,\cdot)\)	344760.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{344760}(7,\cdot)\)	344760.dde	624	no	\(1\)	\(1\)	\(e\left(\frac{439}{624}\right)\)	\(e\left(\frac{599}{624}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{545}{624}\right)\)	\(e\left(\frac{19}{208}\right)\)	\(e\left(\frac{317}{624}\right)\)	\(e\left(\frac{539}{624}\right)\)	\(e\left(\frac{95}{312}\right)\)	\(e\left(\frac{37}{52}\right)\)
\(\chi_{344760}(11,\cdot)\)	344760.dfr	624	no	\(1\)	\(1\)	\(e\left(\frac{599}{624}\right)\)	\(e\left(\frac{355}{624}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{61}{624}\right)\)	\(e\left(\frac{63}{208}\right)\)	\(e\left(\frac{397}{624}\right)\)	\(e\left(\frac{271}{624}\right)\)	\(e\left(\frac{133}{312}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{344760}(19,\cdot)\)	344760.bgj	24	no	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)
\(\chi_{344760}(23,\cdot)\)	344760.brs	48	no	\(1\)	\(1\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(1\)
\(\chi_{344760}(29,\cdot)\)	344760.dco	624	yes	\(1\)	\(1\)	\(e\left(\frac{545}{624}\right)\)	\(e\left(\frac{61}{624}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{511}{624}\right)\)	\(e\left(\frac{145}{208}\right)\)	\(e\left(\frac{331}{624}\right)\)	\(e\left(\frac{145}{624}\right)\)	\(e\left(\frac{283}{312}\right)\)	\(e\left(\frac{21}{52}\right)\)
\(\chi_{344760}(31,\cdot)\)	344760.crw	208	no	\(-1\)	\(1\)	\(e\left(\frac{19}{208}\right)\)	\(e\left(\frac{63}{208}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{145}{208}\right)\)	\(e\left(\frac{81}{208}\right)\)	\(e\left(\frac{185}{208}\right)\)	\(e\left(\frac{131}{208}\right)\)	\(e\left(\frac{5}{104}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{344760}(37,\cdot)\)	344760.dcc	624	no	\(-1\)	\(1\)	\(e\left(\frac{317}{624}\right)\)	\(e\left(\frac{397}{624}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{331}{624}\right)\)	\(e\left(\frac{185}{208}\right)\)	\(e\left(\frac{607}{624}\right)\)	\(e\left(\frac{601}{624}\right)\)	\(e\left(\frac{145}{312}\right)\)	\(e\left(\frac{25}{52}\right)\)
\(\chi_{344760}(41,\cdot)\)	344760.dep	624	no	\(-1\)	\(1\)	\(e\left(\frac{539}{624}\right)\)	\(e\left(\frac{271}{624}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{145}{624}\right)\)	\(e\left(\frac{131}{208}\right)\)	\(e\left(\frac{601}{624}\right)\)	\(e\left(\frac{235}{624}\right)\)	\(e\left(\frac{265}{312}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{344760}(43,\cdot)\)	344760.cxo	312	no	\(1\)	\(1\)	\(e\left(\frac{95}{312}\right)\)	\(e\left(\frac{133}{312}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{283}{312}\right)\)	\(e\left(\frac{5}{104}\right)\)	\(e\left(\frac{145}{312}\right)\)	\(e\left(\frac{265}{312}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{1}{52}\right)\)
\(\chi_{344760}(47,\cdot)\)	344760.byp	52	no	\(1\)	\(1\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{344760}(49,\cdot)\)	344760.cyt	312	no	\(1\)	\(1\)	\(e\left(\frac{127}{312}\right)\)	\(e\left(\frac{287}{312}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{233}{312}\right)\)	\(e\left(\frac{19}{104}\right)\)	\(e\left(\frac{5}{312}\right)\)	\(e\left(\frac{227}{312}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{344760}(53,\cdot)\)	344760.cgz	104	yes	\(1\)	\(1\)	\(e\left(\frac{71}{104}\right)\)	\(e\left(\frac{37}{104}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{67}{104}\right)\)	\(e\left(\frac{3}{104}\right)\)	\(e\left(\frac{29}{104}\right)\)	\(e\left(\frac{53}{104}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{11}{52}\right)\)
\(\chi_{344760}(59,\cdot)\)	344760.cwf	312	yes	\(-1\)	\(1\)	\(e\left(\frac{275}{312}\right)\)	\(e\left(\frac{307}{312}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{31}{312}\right)\)	\(e\left(\frac{87}{104}\right)\)	\(e\left(\frac{157}{312}\right)\)	\(e\left(\frac{139}{312}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{7}{52}\right)\)
\(\chi_{344760}(61,\cdot)\)	344760.ddy	624	no	\(-1\)	\(1\)	\(e\left(\frac{55}{624}\right)\)	\(e\left(\frac{155}{624}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{521}{624}\right)\)	\(e\left(\frac{111}{208}\right)\)	\(e\left(\frac{125}{624}\right)\)	\(e\left(\frac{215}{624}\right)\)	\(e\left(\frac{113}{312}\right)\)	\(e\left(\frac{15}{52}\right)\)
\(\chi_{344760}(67,\cdot)\)	344760.ciz	156	no	\(-1\)	\(1\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{344760}(71,\cdot)\)	344760.dfk	624	no	\(1\)	\(1\)	\(e\left(\frac{97}{624}\right)\)	\(e\left(\frac{557}{624}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{275}{624}\right)\)	\(e\left(\frac{105}{208}\right)\)	\(e\left(\frac{419}{624}\right)\)	\(e\left(\frac{521}{624}\right)\)	\(e\left(\frac{239}{312}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{344760}(73,\cdot)\)	344760.cuk	208	no	\(-1\)	\(1\)	\(e\left(\frac{35}{208}\right)\)	\(e\left(\frac{179}{208}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{133}{208}\right)\)	\(e\left(\frac{141}{208}\right)\)	\(e\left(\frac{89}{208}\right)\)	\(e\left(\frac{47}{208}\right)\)	\(e\left(\frac{79}{104}\right)\)	\(e\left(\frac{31}{52}\right)\)
\(\chi_{344760}(77,\cdot)\)	344760.cgv	104	yes	\(1\)	\(1\)	\(e\left(\frac{69}{104}\right)\)	\(e\left(\frac{55}{104}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{101}{104}\right)\)	\(e\left(\frac{41}{104}\right)\)	\(e\left(\frac{15}{104}\right)\)	\(e\left(\frac{31}{104}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{3}{52}\right)\)
\(\chi_{344760}(79,\cdot)\)	344760.cud	208	no	\(1\)	\(1\)	\(e\left(\frac{57}{208}\right)\)	\(e\left(\frac{85}{208}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{175}{208}\right)\)	\(e\left(\frac{139}{208}\right)\)	\(e\left(\frac{35}{208}\right)\)	\(e\left(\frac{185}{208}\right)\)	\(e\left(\frac{67}{104}\right)\)	\(e\left(\frac{23}{52}\right)\)
\(\chi_{344760}(83,\cdot)\)	344760.cen	104	yes	\(1\)	\(1\)	\(e\left(\frac{25}{104}\right)\)	\(e\left(\frac{87}{104}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{95}{104}\right)\)	\(e\left(\frac{97}{104}\right)\)	\(e\left(\frac{19}{104}\right)\)	\(e\left(\frac{15}{104}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{344760}(89,\cdot)\)	344760.baz	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)
\(\chi_{344760}(97,\cdot)\)	344760.ddc	624	no	\(-1\)	\(1\)	\(e\left(\frac{529}{624}\right)\)	\(e\left(\frac{569}{624}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{263}{624}\right)\)	\(e\left(\frac{125}{208}\right)\)	\(e\left(\frac{323}{624}\right)\)	\(e\left(\frac{125}{624}\right)\)	\(e\left(\frac{209}{312}\right)\)	\(e\left(\frac{19}{52}\right)\)
\(\chi_{344760}(101,\cdot)\)	344760.ccv	78	no	\(-1\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{344760}(103,\cdot)\)	344760.buk	52	no	\(1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)
\(\chi_{344760}(107,\cdot)\)	344760.dey	624	yes	\(1\)	\(1\)	\(e\left(\frac{485}{624}\right)\)	\(e\left(\frac{445}{624}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{127}{624}\right)\)	\(e\left(\frac{161}{208}\right)\)	\(e\left(\frac{535}{624}\right)\)	\(e\left(\frac{265}{624}\right)\)	\(e\left(\frac{181}{312}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{344760}(109,\cdot)\)	344760.cuv	208	no	\(1\)	\(1\)	\(e\left(\frac{33}{208}\right)\)	\(e\left(\frac{197}{208}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{208}\right)\)	\(e\left(\frac{179}{208}\right)\)	\(e\left(\frac{179}{208}\right)\)	\(e\left(\frac{129}{208}\right)\)	\(e\left(\frac{99}{104}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{344760}(113,\cdot)\)	344760.dbl	624	no	\(-1\)	\(1\)	\(e\left(\frac{319}{624}\right)\)	\(e\left(\frac{431}{624}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{557}{624}\right)\)	\(e\left(\frac{51}{208}\right)\)	\(e\left(\frac{101}{624}\right)\)	\(e\left(\frac{467}{624}\right)\)	\(e\left(\frac{47}{312}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{344760}(121,\cdot)\)	344760.cxt	312	no	\(1\)	\(1\)	\(e\left(\frac{287}{312}\right)\)	\(e\left(\frac{43}{312}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{61}{312}\right)\)	\(e\left(\frac{63}{104}\right)\)	\(e\left(\frac{85}{312}\right)\)	\(e\left(\frac{271}{312}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{344760}(127,\cdot)\)	344760.cxr	312	no	\(1\)	\(1\)	\(e\left(\frac{79}{312}\right)\)	\(e\left(\frac{173}{312}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{35}{312}\right)\)	\(e\left(\frac{89}{104}\right)\)	\(e\left(\frac{293}{312}\right)\)	\(e\left(\frac{245}{312}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{23}{52}\right)\)
\(\chi_{344760}(131,\cdot)\)	344760.cug	208	no	\(-1\)	\(1\)	\(e\left(\frac{43}{208}\right)\)	\(e\left(\frac{55}{208}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{101}{208}\right)\)	\(e\left(\frac{41}{208}\right)\)	\(e\left(\frac{145}{208}\right)\)	\(e\left(\frac{187}{208}\right)\)	\(e\left(\frac{25}{104}\right)\)	\(e\left(\frac{21}{52}\right)\)
\(\chi_{344760}(133,\cdot)\)	344760.dbm	624	no	\(1\)	\(1\)	\(e\left(\frac{569}{624}\right)\)	\(e\left(\frac{1}{624}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{259}{624}\right)\)	\(e\left(\frac{45}{208}\right)\)	\(e\left(\frac{187}{624}\right)\)	\(e\left(\frac{565}{624}\right)\)	\(e\left(\frac{121}{312}\right)\)	\(e\left(\frac{6}{13}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 79872 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.