LMFDB - Group of Dirichlet characters of modulus 290145

Show commands: PariGP / SageMath

sage: H = DirichletGroup(290145)

pari: g = idealstar(,290145,2)

Character group

sage: G.order() pari: g.no
Order	=	142912
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{8932}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{290145}(96716,\cdot)$, $\chi_{290145}(232117,\cdot)$, $\chi_{290145}(189226,\cdot)$, $\chi_{290145}(276691,\cdot)$

First 32 of 142912 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{290145}(1,\cdot)$	290145.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{290145}(2,\cdot)$	290145.mf	8932	yes	$-1$	$1$	$e\left(\frac{4167}{4466}\right)$	$e\left(\frac{1934}{2233}\right)$	$e\left(\frac{3933}{8932}\right)$	$e\left(\frac{3569}{4466}\right)$	$e\left(\frac{3733}{8932}\right)$	$e\left(\frac{7485}{8932}\right)$	$e\left(\frac{115}{308}\right)$	$e\left(\frac{1635}{2233}\right)$	$e\left(\frac{615}{638}\right)$	$e\left(\frac{5657}{8932}\right)$
$\chi_{290145}(4,\cdot)$	290145.lb	4466	no	$1$	$1$	$e\left(\frac{1934}{2233}\right)$	$e\left(\frac{1635}{2233}\right)$	$e\left(\frac{3933}{4466}\right)$	$e\left(\frac{1336}{2233}\right)$	$e\left(\frac{3733}{4466}\right)$	$e\left(\frac{3019}{4466}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{1037}{2233}\right)$	$e\left(\frac{296}{319}\right)$	$e\left(\frac{1191}{4466}\right)$
$\chi_{290145}(7,\cdot)$	290145.lw	8932	no	$1$	$1$	$e\left(\frac{3933}{8932}\right)$	$e\left(\frac{3933}{4466}\right)$	$e\left(\frac{6855}{8932}\right)$	$e\left(\frac{2867}{8932}\right)$	$e\left(\frac{1251}{4466}\right)$	$e\left(\frac{3419}{8932}\right)$	$e\left(\frac{16}{77}\right)$	$e\left(\frac{1700}{2233}\right)$	$e\left(\frac{597}{1276}\right)$	$e\left(\frac{1928}{2233}\right)$
$\chi_{290145}(8,\cdot)$	290145.mf	8932	yes	$-1$	$1$	$e\left(\frac{3569}{4466}\right)$	$e\left(\frac{1336}{2233}\right)$	$e\left(\frac{2867}{8932}\right)$	$e\left(\frac{1775}{4466}\right)$	$e\left(\frac{2267}{8932}\right)$	$e\left(\frac{4591}{8932}\right)$	$e\left(\frac{37}{308}\right)$	$e\left(\frac{439}{2233}\right)$	$e\left(\frac{569}{638}\right)$	$e\left(\frac{8039}{8932}\right)$
$\chi_{290145}(11,\cdot)$	290145.md	8932	no	$-1$	$1$	$e\left(\frac{3733}{8932}\right)$	$e\left(\frac{3733}{4466}\right)$	$e\left(\frac{1251}{4466}\right)$	$e\left(\frac{2267}{8932}\right)$	$e\left(\frac{2339}{8932}\right)$	$e\left(\frac{3413}{4466}\right)$	$e\left(\frac{215}{308}\right)$	$e\left(\frac{1500}{2233}\right)$	$e\left(\frac{189}{1276}\right)$	$e\left(\frac{4309}{8932}\right)$
$\chi_{290145}(13,\cdot)$	290145.lx	8932	no	$-1$	$1$	$e\left(\frac{7485}{8932}\right)$	$e\left(\frac{3019}{4466}\right)$	$e\left(\frac{3419}{8932}\right)$	$e\left(\frac{4591}{8932}\right)$	$e\left(\frac{3413}{4466}\right)$	$e\left(\frac{7757}{8932}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{786}{2233}\right)$	$e\left(\frac{723}{1276}\right)$	$e\left(\frac{1317}{2233}\right)$
$\chi_{290145}(14,\cdot)$	290145.ho	308	no	$-1$	$1$	$e\left(\frac{115}{308}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{16}{77}\right)$	$e\left(\frac{37}{308}\right)$	$e\left(\frac{215}{308}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{179}{308}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{153}{308}\right)$
$\chi_{290145}(16,\cdot)$	290145.ku	2233	no	$1$	$1$	$e\left(\frac{1635}{2233}\right)$	$e\left(\frac{1037}{2233}\right)$	$e\left(\frac{1700}{2233}\right)$	$e\left(\frac{439}{2233}\right)$	$e\left(\frac{1500}{2233}\right)$	$e\left(\frac{786}{2233}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{2074}{2233}\right)$	$e\left(\frac{273}{319}\right)$	$e\left(\frac{1191}{2233}\right)$
$\chi_{290145}(17,\cdot)$	290145.jz	1276	yes	$1$	$1$	$e\left(\frac{615}{638}\right)$	$e\left(\frac{296}{319}\right)$	$e\left(\frac{597}{1276}\right)$	$e\left(\frac{569}{638}\right)$	$e\left(\frac{189}{1276}\right)$	$e\left(\frac{723}{1276}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{273}{319}\right)$	$e\left(\frac{276}{319}\right)$	$e\left(\frac{337}{1276}\right)$
$\chi_{290145}(19,\cdot)$	290145.lp	8932	no	$1$	$1$	$e\left(\frac{5657}{8932}\right)$	$e\left(\frac{1191}{4466}\right)$	$e\left(\frac{1928}{2233}\right)$	$e\left(\frac{8039}{8932}\right)$	$e\left(\frac{4309}{8932}\right)$	$e\left(\frac{1317}{2233}\right)$	$e\left(\frac{153}{308}\right)$	$e\left(\frac{1191}{2233}\right)$	$e\left(\frac{337}{1276}\right)$	$e\left(\frac{2613}{8932}\right)$
$\chi_{290145}(22,\cdot)$	290145.jk	812	no	$1$	$1$	$e\left(\frac{285}{812}\right)$	$e\left(\frac{285}{406}\right)$	$e\left(\frac{585}{812}\right)$	$e\left(\frac{43}{812}\right)$	$e\left(\frac{138}{203}\right)$	$e\left(\frac{489}{812}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{82}{203}\right)$	$e\left(\frac{13}{116}\right)$	$e\left(\frac{47}{406}\right)$
$\chi_{290145}(26,\cdot)$	290145.lq	8932	no	$1$	$1$	$e\left(\frac{6887}{8932}\right)$	$e\left(\frac{2421}{4466}\right)$	$e\left(\frac{1838}{2233}\right)$	$e\left(\frac{2797}{8932}\right)$	$e\left(\frac{1627}{8932}\right)$	$e\left(\frac{3155}{4466}\right)$	$e\left(\frac{183}{308}\right)$	$e\left(\frac{188}{2233}\right)$	$e\left(\frac{677}{1276}\right)$	$e\left(\frac{1993}{8932}\right)$
$\chi_{290145}(28,\cdot)$	290145.ki	1276	no	$1$	$1$	$e\left(\frac{391}{1276}\right)$	$e\left(\frac{391}{638}\right)$	$e\left(\frac{827}{1276}\right)$	$e\left(\frac{1173}{1276}\right)$	$e\left(\frac{37}{319}\right)$	$e\left(\frac{75}{1276}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{72}{319}\right)$	$e\left(\frac{505}{1276}\right)$	$e\left(\frac{83}{638}\right)$
$\chi_{290145}(31,\cdot)$	290145.lr	8932	no	$-1$	$1$	$e\left(\frac{571}{8932}\right)$	$e\left(\frac{571}{4466}\right)$	$e\left(\frac{285}{2233}\right)$	$e\left(\frac{1713}{8932}\right)$	$e\left(\frac{4027}{8932}\right)$	$e\left(\frac{211}{4466}\right)$	$e\left(\frac{59}{308}\right)$	$e\left(\frac{571}{2233}\right)$	$e\left(\frac{93}{1276}\right)$	$e\left(\frac{1219}{8932}\right)$
$\chi_{290145}(32,\cdot)$	290145.mf	8932	yes	$-1$	$1$	$e\left(\frac{2971}{4466}\right)$	$e\left(\frac{738}{2233}\right)$	$e\left(\frac{1801}{8932}\right)$	$e\left(\frac{4447}{4466}\right)$	$e\left(\frac{801}{8932}\right)$	$e\left(\frac{1697}{8932}\right)$	$e\left(\frac{267}{308}\right)$	$e\left(\frac{1476}{2233}\right)$	$e\left(\frac{523}{638}\right)$	$e\left(\frac{1489}{8932}\right)$
$\chi_{290145}(34,\cdot)$	290145.kw	4466	no	$-1$	$1$	$e\left(\frac{2003}{2233}\right)$	$e\left(\frac{1773}{2233}\right)$	$e\left(\frac{2028}{2233}\right)$	$e\left(\frac{1543}{2233}\right)$	$e\left(\frac{1264}{2233}\right)$	$e\left(\frac{1807}{4466}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{1313}{2233}\right)$	$e\left(\frac{529}{638}\right)$	$e\left(\frac{2004}{2233}\right)$
$\chi_{290145}(37,\cdot)$	290145.mh	8932	no	$-1$	$1$	$e\left(\frac{2421}{4466}\right)$	$e\left(\frac{188}{2233}\right)$	$e\left(\frac{3539}{8932}\right)$	$e\left(\frac{2797}{4466}\right)$	$e\left(\frac{5487}{8932}\right)$	$e\left(\frac{5921}{8932}\right)$	$e\left(\frac{289}{308}\right)$	$e\left(\frac{376}{2233}\right)$	$e\left(\frac{179}{319}\right)$	$e\left(\frac{1753}{8932}\right)$
$\chi_{290145}(38,\cdot)$	290145.ly	8932	yes	$-1$	$1$	$e\left(\frac{5059}{8932}\right)$	$e\left(\frac{593}{4466}\right)$	$e\left(\frac{2713}{8932}\right)$	$e\left(\frac{6245}{8932}\right)$	$e\left(\frac{4021}{4466}\right)$	$e\left(\frac{3821}{8932}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{593}{2233}\right)$	$e\left(\frac{291}{1276}\right)$	$e\left(\frac{4135}{4466}\right)$
$\chi_{290145}(41,\cdot)$	290145.dz	44	no	$1$	$1$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{290145}(43,\cdot)$	290145.mh	8932	no	$-1$	$1$	$e\left(\frac{2679}{4466}\right)$	$e\left(\frac{446}{2233}\right)$	$e\left(\frac{6329}{8932}\right)$	$e\left(\frac{3571}{4466}\right)$	$e\left(\frac{593}{8932}\right)$	$e\left(\frac{1195}{8932}\right)$	$e\left(\frac{95}{308}\right)$	$e\left(\frac{892}{2233}\right)$	$e\left(\frac{238}{319}\right)$	$e\left(\frac{8791}{8932}\right)$
$\chi_{290145}(44,\cdot)$	290145.lo	8932	yes	$-1$	$1$	$e\left(\frac{2537}{8932}\right)$	$e\left(\frac{2537}{4466}\right)$	$e\left(\frac{359}{2233}\right)$	$e\left(\frac{7611}{8932}\right)$	$e\left(\frac{873}{8932}\right)$	$e\left(\frac{983}{2233}\right)$	$e\left(\frac{137}{308}\right)$	$e\left(\frac{304}{2233}\right)$	$e\left(\frac{97}{1276}\right)$	$e\left(\frac{6691}{8932}\right)$
$\chi_{290145}(47,\cdot)$	290145.jt	812	no	$-1$	$1$	$e\left(\frac{162}{203}\right)$	$e\left(\frac{121}{203}\right)$	$e\left(\frac{251}{812}\right)$	$e\left(\frac{80}{203}\right)$	$e\left(\frac{317}{812}\right)$	$e\left(\frac{443}{812}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{39}{203}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{421}{812}\right)$
$\chi_{290145}(49,\cdot)$	290145.li	4466	no	$1$	$1$	$e\left(\frac{3933}{4466}\right)$	$e\left(\frac{1700}{2233}\right)$	$e\left(\frac{2389}{4466}\right)$	$e\left(\frac{2867}{4466}\right)$	$e\left(\frac{1251}{2233}\right)$	$e\left(\frac{3419}{4466}\right)$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{1167}{2233}\right)$	$e\left(\frac{597}{638}\right)$	$e\left(\frac{1623}{2233}\right)$
$\chi_{290145}(52,\cdot)$	290145.lu	8932	no	$-1$	$1$	$e\left(\frac{6289}{8932}\right)$	$e\left(\frac{1823}{4466}\right)$	$e\left(\frac{2353}{8932}\right)$	$e\left(\frac{1003}{8932}\right)$	$e\left(\frac{1340}{2233}\right)$	$e\left(\frac{4863}{8932}\right)$	$e\left(\frac{149}{154}\right)$	$e\left(\frac{1823}{2233}\right)$	$e\left(\frac{631}{1276}\right)$	$e\left(\frac{3825}{4466}\right)$
$\chi_{290145}(53,\cdot)$	290145.lt	8932	yes	$-1$	$1$	$e\left(\frac{3889}{8932}\right)$	$e\left(\frac{3889}{4466}\right)$	$e\left(\frac{3709}{8932}\right)$	$e\left(\frac{2735}{8932}\right)$	$e\left(\frac{851}{2233}\right)$	$e\left(\frac{5553}{8932}\right)$	$e\left(\frac{131}{154}\right)$	$e\left(\frac{1656}{2233}\right)$	$e\left(\frac{201}{1276}\right)$	$e\left(\frac{1752}{2233}\right)$
$\chi_{290145}(56,\cdot)$	290145.md	8932	no	$-1$	$1$	$e\left(\frac{2139}{8932}\right)$	$e\left(\frac{2139}{4466}\right)$	$e\left(\frac{395}{4466}\right)$	$e\left(\frac{6417}{8932}\right)$	$e\left(\frac{4769}{8932}\right)$	$e\left(\frac{4005}{4466}\right)$	$e\left(\frac{101}{308}\right)$	$e\left(\frac{2139}{2233}\right)$	$e\left(\frac{459}{1276}\right)$	$e\left(\frac{6819}{8932}\right)$
$\chi_{290145}(59,\cdot)$	290145.is	638	yes	$-1$	$1$	$e\left(\frac{109}{319}\right)$	$e\left(\frac{218}{319}\right)$	$e\left(\frac{333}{638}\right)$	$e\left(\frac{8}{319}\right)$	$e\left(\frac{519}{638}\right)$	$e\left(\frac{41}{638}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{117}{319}\right)$	$e\left(\frac{255}{319}\right)$	$e\left(\frac{207}{319}\right)$
$\chi_{290145}(61,\cdot)$	290145.mc	8932	no	$1$	$1$	$e\left(\frac{8007}{8932}\right)$	$e\left(\frac{3541}{4466}\right)$	$e\left(\frac{2913}{4466}\right)$	$e\left(\frac{6157}{8932}\right)$	$e\left(\frac{3433}{8932}\right)$	$e\left(\frac{761}{4466}\right)$	$e\left(\frac{169}{308}\right)$	$e\left(\frac{1308}{2233}\right)$	$e\left(\frac{27}{1276}\right)$	$e\left(\frac{8545}{8932}\right)$
$\chi_{290145}(62,\cdot)$	290145.ls	8932	yes	$1$	$1$	$e\left(\frac{8905}{8932}\right)$	$e\left(\frac{4439}{4466}\right)$	$e\left(\frac{5073}{8932}\right)$	$e\left(\frac{8851}{8932}\right)$	$e\left(\frac{1940}{2233}\right)$	$e\left(\frac{7907}{8932}\right)$	$e\left(\frac{87}{154}\right)$	$e\left(\frac{2206}{2233}\right)$	$e\left(\frac{47}{1276}\right)$	$e\left(\frac{1719}{2233}\right)$
$\chi_{290145}(64,\cdot)$	290145.lb	4466	no	$1$	$1$	$e\left(\frac{1336}{2233}\right)$	$e\left(\frac{439}{2233}\right)$	$e\left(\frac{2867}{4466}\right)$	$e\left(\frac{1775}{2233}\right)$	$e\left(\frac{2267}{4466}\right)$	$e\left(\frac{125}{4466}\right)$	$e\left(\frac{37}{154}\right)$	$e\left(\frac{878}{2233}\right)$	$e\left(\frac{250}{319}\right)$	$e\left(\frac{3573}{4466}\right)$
$\chi_{290145}(67,\cdot)$	290145.lv	8932	no	$1$	$1$	$e\left(\frac{5815}{8932}\right)$	$e\left(\frac{1349}{4466}\right)$	$e\left(\frac{8047}{8932}\right)$	$e\left(\frac{8513}{8932}\right)$	$e\left(\frac{166}{2233}\right)$	$e\left(\frac{1259}{8932}\right)$	$e\left(\frac{85}{154}\right)$	$e\left(\frac{1349}{2233}\right)$	$e\left(\frac{251}{1276}\right)$	$e\left(\frac{1657}{4466}\right)$

Click here to search among the remaining 142880 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	$290145$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{8932}\)
Order	$142912$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{290145}(1,\cdot)\)	290145.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{290145}(2,\cdot)\)	290145.mf	8932	yes	\(-1\)	\(1\)	\(e\left(\frac{4167}{4466}\right)\)	\(e\left(\frac{1934}{2233}\right)\)	\(e\left(\frac{3933}{8932}\right)\)	\(e\left(\frac{3569}{4466}\right)\)	\(e\left(\frac{3733}{8932}\right)\)	\(e\left(\frac{7485}{8932}\right)\)	\(e\left(\frac{115}{308}\right)\)	\(e\left(\frac{1635}{2233}\right)\)	\(e\left(\frac{615}{638}\right)\)	\(e\left(\frac{5657}{8932}\right)\)
\(\chi_{290145}(4,\cdot)\)	290145.lb	4466	no	\(1\)	\(1\)	\(e\left(\frac{1934}{2233}\right)\)	\(e\left(\frac{1635}{2233}\right)\)	\(e\left(\frac{3933}{4466}\right)\)	\(e\left(\frac{1336}{2233}\right)\)	\(e\left(\frac{3733}{4466}\right)\)	\(e\left(\frac{3019}{4466}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{1037}{2233}\right)\)	\(e\left(\frac{296}{319}\right)\)	\(e\left(\frac{1191}{4466}\right)\)
\(\chi_{290145}(7,\cdot)\)	290145.lw	8932	no	\(1\)	\(1\)	\(e\left(\frac{3933}{8932}\right)\)	\(e\left(\frac{3933}{4466}\right)\)	\(e\left(\frac{6855}{8932}\right)\)	\(e\left(\frac{2867}{8932}\right)\)	\(e\left(\frac{1251}{4466}\right)\)	\(e\left(\frac{3419}{8932}\right)\)	\(e\left(\frac{16}{77}\right)\)	\(e\left(\frac{1700}{2233}\right)\)	\(e\left(\frac{597}{1276}\right)\)	\(e\left(\frac{1928}{2233}\right)\)
\(\chi_{290145}(8,\cdot)\)	290145.mf	8932	yes	\(-1\)	\(1\)	\(e\left(\frac{3569}{4466}\right)\)	\(e\left(\frac{1336}{2233}\right)\)	\(e\left(\frac{2867}{8932}\right)\)	\(e\left(\frac{1775}{4466}\right)\)	\(e\left(\frac{2267}{8932}\right)\)	\(e\left(\frac{4591}{8932}\right)\)	\(e\left(\frac{37}{308}\right)\)	\(e\left(\frac{439}{2233}\right)\)	\(e\left(\frac{569}{638}\right)\)	\(e\left(\frac{8039}{8932}\right)\)
\(\chi_{290145}(11,\cdot)\)	290145.md	8932	no	\(-1\)	\(1\)	\(e\left(\frac{3733}{8932}\right)\)	\(e\left(\frac{3733}{4466}\right)\)	\(e\left(\frac{1251}{4466}\right)\)	\(e\left(\frac{2267}{8932}\right)\)	\(e\left(\frac{2339}{8932}\right)\)	\(e\left(\frac{3413}{4466}\right)\)	\(e\left(\frac{215}{308}\right)\)	\(e\left(\frac{1500}{2233}\right)\)	\(e\left(\frac{189}{1276}\right)\)	\(e\left(\frac{4309}{8932}\right)\)
\(\chi_{290145}(13,\cdot)\)	290145.lx	8932	no	\(-1\)	\(1\)	\(e\left(\frac{7485}{8932}\right)\)	\(e\left(\frac{3019}{4466}\right)\)	\(e\left(\frac{3419}{8932}\right)\)	\(e\left(\frac{4591}{8932}\right)\)	\(e\left(\frac{3413}{4466}\right)\)	\(e\left(\frac{7757}{8932}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{786}{2233}\right)\)	\(e\left(\frac{723}{1276}\right)\)	\(e\left(\frac{1317}{2233}\right)\)
\(\chi_{290145}(14,\cdot)\)	290145.ho	308	no	\(-1\)	\(1\)	\(e\left(\frac{115}{308}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{16}{77}\right)\)	\(e\left(\frac{37}{308}\right)\)	\(e\left(\frac{215}{308}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{179}{308}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{153}{308}\right)\)
\(\chi_{290145}(16,\cdot)\)	290145.ku	2233	no	\(1\)	\(1\)	\(e\left(\frac{1635}{2233}\right)\)	\(e\left(\frac{1037}{2233}\right)\)	\(e\left(\frac{1700}{2233}\right)\)	\(e\left(\frac{439}{2233}\right)\)	\(e\left(\frac{1500}{2233}\right)\)	\(e\left(\frac{786}{2233}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{2074}{2233}\right)\)	\(e\left(\frac{273}{319}\right)\)	\(e\left(\frac{1191}{2233}\right)\)
\(\chi_{290145}(17,\cdot)\)	290145.jz	1276	yes	\(1\)	\(1\)	\(e\left(\frac{615}{638}\right)\)	\(e\left(\frac{296}{319}\right)\)	\(e\left(\frac{597}{1276}\right)\)	\(e\left(\frac{569}{638}\right)\)	\(e\left(\frac{189}{1276}\right)\)	\(e\left(\frac{723}{1276}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{273}{319}\right)\)	\(e\left(\frac{276}{319}\right)\)	\(e\left(\frac{337}{1276}\right)\)
\(\chi_{290145}(19,\cdot)\)	290145.lp	8932	no	\(1\)	\(1\)	\(e\left(\frac{5657}{8932}\right)\)	\(e\left(\frac{1191}{4466}\right)\)	\(e\left(\frac{1928}{2233}\right)\)	\(e\left(\frac{8039}{8932}\right)\)	\(e\left(\frac{4309}{8932}\right)\)	\(e\left(\frac{1317}{2233}\right)\)	\(e\left(\frac{153}{308}\right)\)	\(e\left(\frac{1191}{2233}\right)\)	\(e\left(\frac{337}{1276}\right)\)	\(e\left(\frac{2613}{8932}\right)\)
\(\chi_{290145}(22,\cdot)\)	290145.jk	812	no	\(1\)	\(1\)	\(e\left(\frac{285}{812}\right)\)	\(e\left(\frac{285}{406}\right)\)	\(e\left(\frac{585}{812}\right)\)	\(e\left(\frac{43}{812}\right)\)	\(e\left(\frac{138}{203}\right)\)	\(e\left(\frac{489}{812}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{82}{203}\right)\)	\(e\left(\frac{13}{116}\right)\)	\(e\left(\frac{47}{406}\right)\)
\(\chi_{290145}(26,\cdot)\)	290145.lq	8932	no	\(1\)	\(1\)	\(e\left(\frac{6887}{8932}\right)\)	\(e\left(\frac{2421}{4466}\right)\)	\(e\left(\frac{1838}{2233}\right)\)	\(e\left(\frac{2797}{8932}\right)\)	\(e\left(\frac{1627}{8932}\right)\)	\(e\left(\frac{3155}{4466}\right)\)	\(e\left(\frac{183}{308}\right)\)	\(e\left(\frac{188}{2233}\right)\)	\(e\left(\frac{677}{1276}\right)\)	\(e\left(\frac{1993}{8932}\right)\)
\(\chi_{290145}(28,\cdot)\)	290145.ki	1276	no	\(1\)	\(1\)	\(e\left(\frac{391}{1276}\right)\)	\(e\left(\frac{391}{638}\right)\)	\(e\left(\frac{827}{1276}\right)\)	\(e\left(\frac{1173}{1276}\right)\)	\(e\left(\frac{37}{319}\right)\)	\(e\left(\frac{75}{1276}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{72}{319}\right)\)	\(e\left(\frac{505}{1276}\right)\)	\(e\left(\frac{83}{638}\right)\)
\(\chi_{290145}(31,\cdot)\)	290145.lr	8932	no	\(-1\)	\(1\)	\(e\left(\frac{571}{8932}\right)\)	\(e\left(\frac{571}{4466}\right)\)	\(e\left(\frac{285}{2233}\right)\)	\(e\left(\frac{1713}{8932}\right)\)	\(e\left(\frac{4027}{8932}\right)\)	\(e\left(\frac{211}{4466}\right)\)	\(e\left(\frac{59}{308}\right)\)	\(e\left(\frac{571}{2233}\right)\)	\(e\left(\frac{93}{1276}\right)\)	\(e\left(\frac{1219}{8932}\right)\)
\(\chi_{290145}(32,\cdot)\)	290145.mf	8932	yes	\(-1\)	\(1\)	\(e\left(\frac{2971}{4466}\right)\)	\(e\left(\frac{738}{2233}\right)\)	\(e\left(\frac{1801}{8932}\right)\)	\(e\left(\frac{4447}{4466}\right)\)	\(e\left(\frac{801}{8932}\right)\)	\(e\left(\frac{1697}{8932}\right)\)	\(e\left(\frac{267}{308}\right)\)	\(e\left(\frac{1476}{2233}\right)\)	\(e\left(\frac{523}{638}\right)\)	\(e\left(\frac{1489}{8932}\right)\)
\(\chi_{290145}(34,\cdot)\)	290145.kw	4466	no	\(-1\)	\(1\)	\(e\left(\frac{2003}{2233}\right)\)	\(e\left(\frac{1773}{2233}\right)\)	\(e\left(\frac{2028}{2233}\right)\)	\(e\left(\frac{1543}{2233}\right)\)	\(e\left(\frac{1264}{2233}\right)\)	\(e\left(\frac{1807}{4466}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{1313}{2233}\right)\)	\(e\left(\frac{529}{638}\right)\)	\(e\left(\frac{2004}{2233}\right)\)
\(\chi_{290145}(37,\cdot)\)	290145.mh	8932	no	\(-1\)	\(1\)	\(e\left(\frac{2421}{4466}\right)\)	\(e\left(\frac{188}{2233}\right)\)	\(e\left(\frac{3539}{8932}\right)\)	\(e\left(\frac{2797}{4466}\right)\)	\(e\left(\frac{5487}{8932}\right)\)	\(e\left(\frac{5921}{8932}\right)\)	\(e\left(\frac{289}{308}\right)\)	\(e\left(\frac{376}{2233}\right)\)	\(e\left(\frac{179}{319}\right)\)	\(e\left(\frac{1753}{8932}\right)\)
\(\chi_{290145}(38,\cdot)\)	290145.ly	8932	yes	\(-1\)	\(1\)	\(e\left(\frac{5059}{8932}\right)\)	\(e\left(\frac{593}{4466}\right)\)	\(e\left(\frac{2713}{8932}\right)\)	\(e\left(\frac{6245}{8932}\right)\)	\(e\left(\frac{4021}{4466}\right)\)	\(e\left(\frac{3821}{8932}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{593}{2233}\right)\)	\(e\left(\frac{291}{1276}\right)\)	\(e\left(\frac{4135}{4466}\right)\)
\(\chi_{290145}(41,\cdot)\)	290145.dz	44	no	\(1\)	\(1\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{290145}(43,\cdot)\)	290145.mh	8932	no	\(-1\)	\(1\)	\(e\left(\frac{2679}{4466}\right)\)	\(e\left(\frac{446}{2233}\right)\)	\(e\left(\frac{6329}{8932}\right)\)	\(e\left(\frac{3571}{4466}\right)\)	\(e\left(\frac{593}{8932}\right)\)	\(e\left(\frac{1195}{8932}\right)\)	\(e\left(\frac{95}{308}\right)\)	\(e\left(\frac{892}{2233}\right)\)	\(e\left(\frac{238}{319}\right)\)	\(e\left(\frac{8791}{8932}\right)\)
\(\chi_{290145}(44,\cdot)\)	290145.lo	8932	yes	\(-1\)	\(1\)	\(e\left(\frac{2537}{8932}\right)\)	\(e\left(\frac{2537}{4466}\right)\)	\(e\left(\frac{359}{2233}\right)\)	\(e\left(\frac{7611}{8932}\right)\)	\(e\left(\frac{873}{8932}\right)\)	\(e\left(\frac{983}{2233}\right)\)	\(e\left(\frac{137}{308}\right)\)	\(e\left(\frac{304}{2233}\right)\)	\(e\left(\frac{97}{1276}\right)\)	\(e\left(\frac{6691}{8932}\right)\)
\(\chi_{290145}(47,\cdot)\)	290145.jt	812	no	\(-1\)	\(1\)	\(e\left(\frac{162}{203}\right)\)	\(e\left(\frac{121}{203}\right)\)	\(e\left(\frac{251}{812}\right)\)	\(e\left(\frac{80}{203}\right)\)	\(e\left(\frac{317}{812}\right)\)	\(e\left(\frac{443}{812}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{39}{203}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{421}{812}\right)\)
\(\chi_{290145}(49,\cdot)\)	290145.li	4466	no	\(1\)	\(1\)	\(e\left(\frac{3933}{4466}\right)\)	\(e\left(\frac{1700}{2233}\right)\)	\(e\left(\frac{2389}{4466}\right)\)	\(e\left(\frac{2867}{4466}\right)\)	\(e\left(\frac{1251}{2233}\right)\)	\(e\left(\frac{3419}{4466}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{1167}{2233}\right)\)	\(e\left(\frac{597}{638}\right)\)	\(e\left(\frac{1623}{2233}\right)\)
\(\chi_{290145}(52,\cdot)\)	290145.lu	8932	no	\(-1\)	\(1\)	\(e\left(\frac{6289}{8932}\right)\)	\(e\left(\frac{1823}{4466}\right)\)	\(e\left(\frac{2353}{8932}\right)\)	\(e\left(\frac{1003}{8932}\right)\)	\(e\left(\frac{1340}{2233}\right)\)	\(e\left(\frac{4863}{8932}\right)\)	\(e\left(\frac{149}{154}\right)\)	\(e\left(\frac{1823}{2233}\right)\)	\(e\left(\frac{631}{1276}\right)\)	\(e\left(\frac{3825}{4466}\right)\)
\(\chi_{290145}(53,\cdot)\)	290145.lt	8932	yes	\(-1\)	\(1\)	\(e\left(\frac{3889}{8932}\right)\)	\(e\left(\frac{3889}{4466}\right)\)	\(e\left(\frac{3709}{8932}\right)\)	\(e\left(\frac{2735}{8932}\right)\)	\(e\left(\frac{851}{2233}\right)\)	\(e\left(\frac{5553}{8932}\right)\)	\(e\left(\frac{131}{154}\right)\)	\(e\left(\frac{1656}{2233}\right)\)	\(e\left(\frac{201}{1276}\right)\)	\(e\left(\frac{1752}{2233}\right)\)
\(\chi_{290145}(56,\cdot)\)	290145.md	8932	no	\(-1\)	\(1\)	\(e\left(\frac{2139}{8932}\right)\)	\(e\left(\frac{2139}{4466}\right)\)	\(e\left(\frac{395}{4466}\right)\)	\(e\left(\frac{6417}{8932}\right)\)	\(e\left(\frac{4769}{8932}\right)\)	\(e\left(\frac{4005}{4466}\right)\)	\(e\left(\frac{101}{308}\right)\)	\(e\left(\frac{2139}{2233}\right)\)	\(e\left(\frac{459}{1276}\right)\)	\(e\left(\frac{6819}{8932}\right)\)
\(\chi_{290145}(59,\cdot)\)	290145.is	638	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{319}\right)\)	\(e\left(\frac{218}{319}\right)\)	\(e\left(\frac{333}{638}\right)\)	\(e\left(\frac{8}{319}\right)\)	\(e\left(\frac{519}{638}\right)\)	\(e\left(\frac{41}{638}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{117}{319}\right)\)	\(e\left(\frac{255}{319}\right)\)	\(e\left(\frac{207}{319}\right)\)
\(\chi_{290145}(61,\cdot)\)	290145.mc	8932	no	\(1\)	\(1\)	\(e\left(\frac{8007}{8932}\right)\)	\(e\left(\frac{3541}{4466}\right)\)	\(e\left(\frac{2913}{4466}\right)\)	\(e\left(\frac{6157}{8932}\right)\)	\(e\left(\frac{3433}{8932}\right)\)	\(e\left(\frac{761}{4466}\right)\)	\(e\left(\frac{169}{308}\right)\)	\(e\left(\frac{1308}{2233}\right)\)	\(e\left(\frac{27}{1276}\right)\)	\(e\left(\frac{8545}{8932}\right)\)
\(\chi_{290145}(62,\cdot)\)	290145.ls	8932	yes	\(1\)	\(1\)	\(e\left(\frac{8905}{8932}\right)\)	\(e\left(\frac{4439}{4466}\right)\)	\(e\left(\frac{5073}{8932}\right)\)	\(e\left(\frac{8851}{8932}\right)\)	\(e\left(\frac{1940}{2233}\right)\)	\(e\left(\frac{7907}{8932}\right)\)	\(e\left(\frac{87}{154}\right)\)	\(e\left(\frac{2206}{2233}\right)\)	\(e\left(\frac{47}{1276}\right)\)	\(e\left(\frac{1719}{2233}\right)\)
\(\chi_{290145}(64,\cdot)\)	290145.lb	4466	no	\(1\)	\(1\)	\(e\left(\frac{1336}{2233}\right)\)	\(e\left(\frac{439}{2233}\right)\)	\(e\left(\frac{2867}{4466}\right)\)	\(e\left(\frac{1775}{2233}\right)\)	\(e\left(\frac{2267}{4466}\right)\)	\(e\left(\frac{125}{4466}\right)\)	\(e\left(\frac{37}{154}\right)\)	\(e\left(\frac{878}{2233}\right)\)	\(e\left(\frac{250}{319}\right)\)	\(e\left(\frac{3573}{4466}\right)\)
\(\chi_{290145}(67,\cdot)\)	290145.lv	8932	no	\(1\)	\(1\)	\(e\left(\frac{5815}{8932}\right)\)	\(e\left(\frac{1349}{4466}\right)\)	\(e\left(\frac{8047}{8932}\right)\)	\(e\left(\frac{8513}{8932}\right)\)	\(e\left(\frac{166}{2233}\right)\)	\(e\left(\frac{1259}{8932}\right)\)	\(e\left(\frac{85}{154}\right)\)	\(e\left(\frac{1349}{2233}\right)\)	\(e\left(\frac{251}{1276}\right)\)	\(e\left(\frac{1657}{4466}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 142912 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.