LMFDB - Group of Dirichlet characters of modulus 1997

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1997)

pari: g = idealstar(,1997,2)

Character group

sage: G.order() pari: g.no
Order	=	1996
sage: H.invariants() pari: g.cyc
Structure	=	$C_{1996}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1997}(2,\cdot)$

First 32 of 1996 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{1997}(1,\cdot)$	1997.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1997}(2,\cdot)$	1997.f	1996	yes	$-1$	$1$	$e\left(\frac{1}{1996}\right)$	$e\left(\frac{447}{1996}\right)$	$e\left(\frac{1}{998}\right)$	$e\left(\frac{813}{1996}\right)$	$e\left(\frac{112}{499}\right)$	$e\left(\frac{354}{499}\right)$	$e\left(\frac{3}{1996}\right)$	$e\left(\frac{447}{998}\right)$	$e\left(\frac{407}{998}\right)$	$e\left(\frac{849}{1996}\right)$
$\chi_{1997}(3,\cdot)$	1997.f	1996	yes	$-1$	$1$	$e\left(\frac{447}{1996}\right)$	$e\left(\frac{209}{1996}\right)$	$e\left(\frac{447}{998}\right)$	$e\left(\frac{139}{1996}\right)$	$e\left(\frac{164}{499}\right)$	$e\left(\frac{55}{499}\right)$	$e\left(\frac{1341}{1996}\right)$	$e\left(\frac{209}{998}\right)$	$e\left(\frac{293}{998}\right)$	$e\left(\frac{263}{1996}\right)$
$\chi_{1997}(4,\cdot)$	1997.e	998	yes	$1$	$1$	$e\left(\frac{1}{998}\right)$	$e\left(\frac{447}{998}\right)$	$e\left(\frac{1}{499}\right)$	$e\left(\frac{813}{998}\right)$	$e\left(\frac{224}{499}\right)$	$e\left(\frac{209}{499}\right)$	$e\left(\frac{3}{998}\right)$	$e\left(\frac{447}{499}\right)$	$e\left(\frac{407}{499}\right)$	$e\left(\frac{849}{998}\right)$
$\chi_{1997}(5,\cdot)$	1997.f	1996	yes	$-1$	$1$	$e\left(\frac{813}{1996}\right)$	$e\left(\frac{139}{1996}\right)$	$e\left(\frac{813}{998}\right)$	$e\left(\frac{293}{1996}\right)$	$e\left(\frac{238}{499}\right)$	$e\left(\frac{378}{499}\right)$	$e\left(\frac{443}{1996}\right)$	$e\left(\frac{139}{998}\right)$	$e\left(\frac{553}{998}\right)$	$e\left(\frac{1617}{1996}\right)$
$\chi_{1997}(6,\cdot)$	1997.d	499	yes	$1$	$1$	$e\left(\frac{112}{499}\right)$	$e\left(\frac{164}{499}\right)$	$e\left(\frac{224}{499}\right)$	$e\left(\frac{238}{499}\right)$	$e\left(\frac{276}{499}\right)$	$e\left(\frac{409}{499}\right)$	$e\left(\frac{336}{499}\right)$	$e\left(\frac{328}{499}\right)$	$e\left(\frac{350}{499}\right)$	$e\left(\frac{278}{499}\right)$
$\chi_{1997}(7,\cdot)$	1997.d	499	yes	$1$	$1$	$e\left(\frac{354}{499}\right)$	$e\left(\frac{55}{499}\right)$	$e\left(\frac{209}{499}\right)$	$e\left(\frac{378}{499}\right)$	$e\left(\frac{409}{499}\right)$	$e\left(\frac{268}{499}\right)$	$e\left(\frac{64}{499}\right)$	$e\left(\frac{110}{499}\right)$	$e\left(\frac{233}{499}\right)$	$e\left(\frac{148}{499}\right)$
$\chi_{1997}(8,\cdot)$	1997.f	1996	yes	$-1$	$1$	$e\left(\frac{3}{1996}\right)$	$e\left(\frac{1341}{1996}\right)$	$e\left(\frac{3}{998}\right)$	$e\left(\frac{443}{1996}\right)$	$e\left(\frac{336}{499}\right)$	$e\left(\frac{64}{499}\right)$	$e\left(\frac{9}{1996}\right)$	$e\left(\frac{343}{998}\right)$	$e\left(\frac{223}{998}\right)$	$e\left(\frac{551}{1996}\right)$
$\chi_{1997}(9,\cdot)$	1997.e	998	yes	$1$	$1$	$e\left(\frac{447}{998}\right)$	$e\left(\frac{209}{998}\right)$	$e\left(\frac{447}{499}\right)$	$e\left(\frac{139}{998}\right)$	$e\left(\frac{328}{499}\right)$	$e\left(\frac{110}{499}\right)$	$e\left(\frac{343}{998}\right)$	$e\left(\frac{209}{499}\right)$	$e\left(\frac{293}{499}\right)$	$e\left(\frac{263}{998}\right)$
$\chi_{1997}(10,\cdot)$	1997.e	998	yes	$1$	$1$	$e\left(\frac{407}{998}\right)$	$e\left(\frac{293}{998}\right)$	$e\left(\frac{407}{499}\right)$	$e\left(\frac{553}{998}\right)$	$e\left(\frac{350}{499}\right)$	$e\left(\frac{233}{499}\right)$	$e\left(\frac{223}{998}\right)$	$e\left(\frac{293}{499}\right)$	$e\left(\frac{480}{499}\right)$	$e\left(\frac{235}{998}\right)$
$\chi_{1997}(11,\cdot)$	1997.f	1996	yes	$-1$	$1$	$e\left(\frac{849}{1996}\right)$	$e\left(\frac{263}{1996}\right)$	$e\left(\frac{849}{998}\right)$	$e\left(\frac{1617}{1996}\right)$	$e\left(\frac{278}{499}\right)$	$e\left(\frac{148}{499}\right)$	$e\left(\frac{551}{1996}\right)$	$e\left(\frac{263}{998}\right)$	$e\left(\frac{235}{998}\right)$	$e\left(\frac{245}{1996}\right)$
$\chi_{1997}(12,\cdot)$	1997.f	1996	yes	$-1$	$1$	$e\left(\frac{449}{1996}\right)$	$e\left(\frac{1103}{1996}\right)$	$e\left(\frac{449}{998}\right)$	$e\left(\frac{1765}{1996}\right)$	$e\left(\frac{388}{499}\right)$	$e\left(\frac{264}{499}\right)$	$e\left(\frac{1347}{1996}\right)$	$e\left(\frac{105}{998}\right)$	$e\left(\frac{109}{998}\right)$	$e\left(\frac{1961}{1996}\right)$
$\chi_{1997}(13,\cdot)$	1997.f	1996	yes	$-1$	$1$	$e\left(\frac{543}{1996}\right)$	$e\left(\frac{1205}{1996}\right)$	$e\left(\frac{543}{998}\right)$	$e\left(\frac{343}{1996}\right)$	$e\left(\frac{437}{499}\right)$	$e\left(\frac{107}{499}\right)$	$e\left(\frac{1629}{1996}\right)$	$e\left(\frac{207}{998}\right)$	$e\left(\frac{443}{998}\right)$	$e\left(\frac{1927}{1996}\right)$
$\chi_{1997}(14,\cdot)$	1997.f	1996	yes	$-1$	$1$	$e\left(\frac{1417}{1996}\right)$	$e\left(\frac{667}{1996}\right)$	$e\left(\frac{419}{998}\right)$	$e\left(\frac{329}{1996}\right)$	$e\left(\frac{22}{499}\right)$	$e\left(\frac{123}{499}\right)$	$e\left(\frac{259}{1996}\right)$	$e\left(\frac{667}{998}\right)$	$e\left(\frac{873}{998}\right)$	$e\left(\frac{1441}{1996}\right)$
$\chi_{1997}(15,\cdot)$	1997.d	499	yes	$1$	$1$	$e\left(\frac{315}{499}\right)$	$e\left(\frac{87}{499}\right)$	$e\left(\frac{131}{499}\right)$	$e\left(\frac{108}{499}\right)$	$e\left(\frac{402}{499}\right)$	$e\left(\frac{433}{499}\right)$	$e\left(\frac{446}{499}\right)$	$e\left(\frac{174}{499}\right)$	$e\left(\frac{423}{499}\right)$	$e\left(\frac{470}{499}\right)$
$\chi_{1997}(16,\cdot)$	1997.d	499	yes	$1$	$1$	$e\left(\frac{1}{499}\right)$	$e\left(\frac{447}{499}\right)$	$e\left(\frac{2}{499}\right)$	$e\left(\frac{314}{499}\right)$	$e\left(\frac{448}{499}\right)$	$e\left(\frac{418}{499}\right)$	$e\left(\frac{3}{499}\right)$	$e\left(\frac{395}{499}\right)$	$e\left(\frac{315}{499}\right)$	$e\left(\frac{350}{499}\right)$
$\chi_{1997}(17,\cdot)$	1997.d	499	yes	$1$	$1$	$e\left(\frac{390}{499}\right)$	$e\left(\frac{179}{499}\right)$	$e\left(\frac{281}{499}\right)$	$e\left(\frac{205}{499}\right)$	$e\left(\frac{70}{499}\right)$	$e\left(\frac{346}{499}\right)$	$e\left(\frac{172}{499}\right)$	$e\left(\frac{358}{499}\right)$	$e\left(\frac{96}{499}\right)$	$e\left(\frac{273}{499}\right)$
$\chi_{1997}(18,\cdot)$	1997.f	1996	yes	$-1$	$1$	$e\left(\frac{895}{1996}\right)$	$e\left(\frac{865}{1996}\right)$	$e\left(\frac{895}{998}\right)$	$e\left(\frac{1091}{1996}\right)$	$e\left(\frac{440}{499}\right)$	$e\left(\frac{464}{499}\right)$	$e\left(\frac{689}{1996}\right)$	$e\left(\frac{865}{998}\right)$	$e\left(\frac{993}{998}\right)$	$e\left(\frac{1375}{1996}\right)$
$\chi_{1997}(19,\cdot)$	1997.f	1996	yes	$-1$	$1$	$e\left(\frac{319}{1996}\right)$	$e\left(\frac{877}{1996}\right)$	$e\left(\frac{319}{998}\right)$	$e\left(\frac{1863}{1996}\right)$	$e\left(\frac{299}{499}\right)$	$e\left(\frac{152}{499}\right)$	$e\left(\frac{957}{1996}\right)$	$e\left(\frac{877}{998}\right)$	$e\left(\frac{93}{998}\right)$	$e\left(\frac{1371}{1996}\right)$
$\chi_{1997}(20,\cdot)$	1997.f	1996	yes	$-1$	$1$	$e\left(\frac{815}{1996}\right)$	$e\left(\frac{1033}{1996}\right)$	$e\left(\frac{815}{998}\right)$	$e\left(\frac{1919}{1996}\right)$	$e\left(\frac{462}{499}\right)$	$e\left(\frac{88}{499}\right)$	$e\left(\frac{449}{1996}\right)$	$e\left(\frac{35}{998}\right)$	$e\left(\frac{369}{998}\right)$	$e\left(\frac{1319}{1996}\right)$
$\chi_{1997}(21,\cdot)$	1997.f	1996	yes	$-1$	$1$	$e\left(\frac{1863}{1996}\right)$	$e\left(\frac{429}{1996}\right)$	$e\left(\frac{865}{998}\right)$	$e\left(\frac{1651}{1996}\right)$	$e\left(\frac{74}{499}\right)$	$e\left(\frac{323}{499}\right)$	$e\left(\frac{1597}{1996}\right)$	$e\left(\frac{429}{998}\right)$	$e\left(\frac{759}{998}\right)$	$e\left(\frac{855}{1996}\right)$
$\chi_{1997}(22,\cdot)$	1997.e	998	yes	$1$	$1$	$e\left(\frac{425}{998}\right)$	$e\left(\frac{355}{998}\right)$	$e\left(\frac{425}{499}\right)$	$e\left(\frac{217}{998}\right)$	$e\left(\frac{390}{499}\right)$	$e\left(\frac{3}{499}\right)$	$e\left(\frac{277}{998}\right)$	$e\left(\frac{355}{499}\right)$	$e\left(\frac{321}{499}\right)$	$e\left(\frac{547}{998}\right)$
$\chi_{1997}(23,\cdot)$	1997.f	1996	yes	$-1$	$1$	$e\left(\frac{489}{1996}\right)$	$e\left(\frac{1019}{1996}\right)$	$e\left(\frac{489}{998}\right)$	$e\left(\frac{353}{1996}\right)$	$e\left(\frac{377}{499}\right)$	$e\left(\frac{452}{499}\right)$	$e\left(\frac{1467}{1996}\right)$	$e\left(\frac{21}{998}\right)$	$e\left(\frac{421}{998}\right)$	$e\left(\frac{1989}{1996}\right)$
$\chi_{1997}(24,\cdot)$	1997.e	998	yes	$1$	$1$	$e\left(\frac{225}{998}\right)$	$e\left(\frac{775}{998}\right)$	$e\left(\frac{225}{499}\right)$	$e\left(\frac{291}{998}\right)$	$e\left(\frac{1}{499}\right)$	$e\left(\frac{119}{499}\right)$	$e\left(\frac{675}{998}\right)$	$e\left(\frac{276}{499}\right)$	$e\left(\frac{258}{499}\right)$	$e\left(\frac{407}{998}\right)$
$\chi_{1997}(25,\cdot)$	1997.e	998	yes	$1$	$1$	$e\left(\frac{813}{998}\right)$	$e\left(\frac{139}{998}\right)$	$e\left(\frac{314}{499}\right)$	$e\left(\frac{293}{998}\right)$	$e\left(\frac{476}{499}\right)$	$e\left(\frac{257}{499}\right)$	$e\left(\frac{443}{998}\right)$	$e\left(\frac{139}{499}\right)$	$e\left(\frac{54}{499}\right)$	$e\left(\frac{619}{998}\right)$
$\chi_{1997}(26,\cdot)$	1997.d	499	yes	$1$	$1$	$e\left(\frac{136}{499}\right)$	$e\left(\frac{413}{499}\right)$	$e\left(\frac{272}{499}\right)$	$e\left(\frac{289}{499}\right)$	$e\left(\frac{50}{499}\right)$	$e\left(\frac{461}{499}\right)$	$e\left(\frac{408}{499}\right)$	$e\left(\frac{327}{499}\right)$	$e\left(\frac{425}{499}\right)$	$e\left(\frac{195}{499}\right)$
$\chi_{1997}(27,\cdot)$	1997.f	1996	yes	$-1$	$1$	$e\left(\frac{1341}{1996}\right)$	$e\left(\frac{627}{1996}\right)$	$e\left(\frac{343}{998}\right)$	$e\left(\frac{417}{1996}\right)$	$e\left(\frac{492}{499}\right)$	$e\left(\frac{165}{499}\right)$	$e\left(\frac{31}{1996}\right)$	$e\left(\frac{627}{998}\right)$	$e\left(\frac{879}{998}\right)$	$e\left(\frac{789}{1996}\right)$
$\chi_{1997}(28,\cdot)$	1997.e	998	yes	$1$	$1$	$e\left(\frac{709}{998}\right)$	$e\left(\frac{557}{998}\right)$	$e\left(\frac{210}{499}\right)$	$e\left(\frac{571}{998}\right)$	$e\left(\frac{134}{499}\right)$	$e\left(\frac{477}{499}\right)$	$e\left(\frac{131}{998}\right)$	$e\left(\frac{58}{499}\right)$	$e\left(\frac{141}{499}\right)$	$e\left(\frac{147}{998}\right)$
$\chi_{1997}(29,\cdot)$	1997.e	998	yes	$1$	$1$	$e\left(\frac{531}{998}\right)$	$e\left(\frac{831}{998}\right)$	$e\left(\frac{32}{499}\right)$	$e\left(\frac{567}{998}\right)$	$e\left(\frac{182}{499}\right)$	$e\left(\frac{201}{499}\right)$	$e\left(\frac{595}{998}\right)$	$e\left(\frac{332}{499}\right)$	$e\left(\frac{50}{499}\right)$	$e\left(\frac{721}{998}\right)$
$\chi_{1997}(30,\cdot)$	1997.f	1996	yes	$-1$	$1$	$e\left(\frac{1261}{1996}\right)$	$e\left(\frac{795}{1996}\right)$	$e\left(\frac{263}{998}\right)$	$e\left(\frac{1245}{1996}\right)$	$e\left(\frac{15}{499}\right)$	$e\left(\frac{288}{499}\right)$	$e\left(\frac{1787}{1996}\right)$	$e\left(\frac{795}{998}\right)$	$e\left(\frac{255}{998}\right)$	$e\left(\frac{733}{1996}\right)$
$\chi_{1997}(31,\cdot)$	1997.f	1996	yes	$-1$	$1$	$e\left(\frac{1535}{1996}\right)$	$e\left(\frac{1517}{1996}\right)$	$e\left(\frac{537}{998}\right)$	$e\left(\frac{455}{1996}\right)$	$e\left(\frac{264}{499}\right)$	$e\left(\frac{478}{499}\right)$	$e\left(\frac{613}{1996}\right)$	$e\left(\frac{519}{998}\right)$	$e\left(\frac{995}{998}\right)$	$e\left(\frac{1823}{1996}\right)$
$\chi_{1997}(32,\cdot)$	1997.f	1996	yes	$-1$	$1$	$e\left(\frac{5}{1996}\right)$	$e\left(\frac{239}{1996}\right)$	$e\left(\frac{5}{998}\right)$	$e\left(\frac{73}{1996}\right)$	$e\left(\frac{61}{499}\right)$	$e\left(\frac{273}{499}\right)$	$e\left(\frac{15}{1996}\right)$	$e\left(\frac{239}{998}\right)$	$e\left(\frac{39}{998}\right)$	$e\left(\frac{253}{1996}\right)$

Click here to search among the remaining 1964 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	$1997$
Structure	\(C_{1996}\)
Order	$1996$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{1997}(1,\cdot)\)	1997.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1997}(2,\cdot)\)	1997.f	1996	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{1996}\right)\)	\(e\left(\frac{447}{1996}\right)\)	\(e\left(\frac{1}{998}\right)\)	\(e\left(\frac{813}{1996}\right)\)	\(e\left(\frac{112}{499}\right)\)	\(e\left(\frac{354}{499}\right)\)	\(e\left(\frac{3}{1996}\right)\)	\(e\left(\frac{447}{998}\right)\)	\(e\left(\frac{407}{998}\right)\)	\(e\left(\frac{849}{1996}\right)\)
\(\chi_{1997}(3,\cdot)\)	1997.f	1996	yes	\(-1\)	\(1\)	\(e\left(\frac{447}{1996}\right)\)	\(e\left(\frac{209}{1996}\right)\)	\(e\left(\frac{447}{998}\right)\)	\(e\left(\frac{139}{1996}\right)\)	\(e\left(\frac{164}{499}\right)\)	\(e\left(\frac{55}{499}\right)\)	\(e\left(\frac{1341}{1996}\right)\)	\(e\left(\frac{209}{998}\right)\)	\(e\left(\frac{293}{998}\right)\)	\(e\left(\frac{263}{1996}\right)\)
\(\chi_{1997}(4,\cdot)\)	1997.e	998	yes	\(1\)	\(1\)	\(e\left(\frac{1}{998}\right)\)	\(e\left(\frac{447}{998}\right)\)	\(e\left(\frac{1}{499}\right)\)	\(e\left(\frac{813}{998}\right)\)	\(e\left(\frac{224}{499}\right)\)	\(e\left(\frac{209}{499}\right)\)	\(e\left(\frac{3}{998}\right)\)	\(e\left(\frac{447}{499}\right)\)	\(e\left(\frac{407}{499}\right)\)	\(e\left(\frac{849}{998}\right)\)
\(\chi_{1997}(5,\cdot)\)	1997.f	1996	yes	\(-1\)	\(1\)	\(e\left(\frac{813}{1996}\right)\)	\(e\left(\frac{139}{1996}\right)\)	\(e\left(\frac{813}{998}\right)\)	\(e\left(\frac{293}{1996}\right)\)	\(e\left(\frac{238}{499}\right)\)	\(e\left(\frac{378}{499}\right)\)	\(e\left(\frac{443}{1996}\right)\)	\(e\left(\frac{139}{998}\right)\)	\(e\left(\frac{553}{998}\right)\)	\(e\left(\frac{1617}{1996}\right)\)
\(\chi_{1997}(6,\cdot)\)	1997.d	499	yes	\(1\)	\(1\)	\(e\left(\frac{112}{499}\right)\)	\(e\left(\frac{164}{499}\right)\)	\(e\left(\frac{224}{499}\right)\)	\(e\left(\frac{238}{499}\right)\)	\(e\left(\frac{276}{499}\right)\)	\(e\left(\frac{409}{499}\right)\)	\(e\left(\frac{336}{499}\right)\)	\(e\left(\frac{328}{499}\right)\)	\(e\left(\frac{350}{499}\right)\)	\(e\left(\frac{278}{499}\right)\)
\(\chi_{1997}(7,\cdot)\)	1997.d	499	yes	\(1\)	\(1\)	\(e\left(\frac{354}{499}\right)\)	\(e\left(\frac{55}{499}\right)\)	\(e\left(\frac{209}{499}\right)\)	\(e\left(\frac{378}{499}\right)\)	\(e\left(\frac{409}{499}\right)\)	\(e\left(\frac{268}{499}\right)\)	\(e\left(\frac{64}{499}\right)\)	\(e\left(\frac{110}{499}\right)\)	\(e\left(\frac{233}{499}\right)\)	\(e\left(\frac{148}{499}\right)\)
\(\chi_{1997}(8,\cdot)\)	1997.f	1996	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{1996}\right)\)	\(e\left(\frac{1341}{1996}\right)\)	\(e\left(\frac{3}{998}\right)\)	\(e\left(\frac{443}{1996}\right)\)	\(e\left(\frac{336}{499}\right)\)	\(e\left(\frac{64}{499}\right)\)	\(e\left(\frac{9}{1996}\right)\)	\(e\left(\frac{343}{998}\right)\)	\(e\left(\frac{223}{998}\right)\)	\(e\left(\frac{551}{1996}\right)\)
\(\chi_{1997}(9,\cdot)\)	1997.e	998	yes	\(1\)	\(1\)	\(e\left(\frac{447}{998}\right)\)	\(e\left(\frac{209}{998}\right)\)	\(e\left(\frac{447}{499}\right)\)	\(e\left(\frac{139}{998}\right)\)	\(e\left(\frac{328}{499}\right)\)	\(e\left(\frac{110}{499}\right)\)	\(e\left(\frac{343}{998}\right)\)	\(e\left(\frac{209}{499}\right)\)	\(e\left(\frac{293}{499}\right)\)	\(e\left(\frac{263}{998}\right)\)
\(\chi_{1997}(10,\cdot)\)	1997.e	998	yes	\(1\)	\(1\)	\(e\left(\frac{407}{998}\right)\)	\(e\left(\frac{293}{998}\right)\)	\(e\left(\frac{407}{499}\right)\)	\(e\left(\frac{553}{998}\right)\)	\(e\left(\frac{350}{499}\right)\)	\(e\left(\frac{233}{499}\right)\)	\(e\left(\frac{223}{998}\right)\)	\(e\left(\frac{293}{499}\right)\)	\(e\left(\frac{480}{499}\right)\)	\(e\left(\frac{235}{998}\right)\)
\(\chi_{1997}(11,\cdot)\)	1997.f	1996	yes	\(-1\)	\(1\)	\(e\left(\frac{849}{1996}\right)\)	\(e\left(\frac{263}{1996}\right)\)	\(e\left(\frac{849}{998}\right)\)	\(e\left(\frac{1617}{1996}\right)\)	\(e\left(\frac{278}{499}\right)\)	\(e\left(\frac{148}{499}\right)\)	\(e\left(\frac{551}{1996}\right)\)	\(e\left(\frac{263}{998}\right)\)	\(e\left(\frac{235}{998}\right)\)	\(e\left(\frac{245}{1996}\right)\)
\(\chi_{1997}(12,\cdot)\)	1997.f	1996	yes	\(-1\)	\(1\)	\(e\left(\frac{449}{1996}\right)\)	\(e\left(\frac{1103}{1996}\right)\)	\(e\left(\frac{449}{998}\right)\)	\(e\left(\frac{1765}{1996}\right)\)	\(e\left(\frac{388}{499}\right)\)	\(e\left(\frac{264}{499}\right)\)	\(e\left(\frac{1347}{1996}\right)\)	\(e\left(\frac{105}{998}\right)\)	\(e\left(\frac{109}{998}\right)\)	\(e\left(\frac{1961}{1996}\right)\)
\(\chi_{1997}(13,\cdot)\)	1997.f	1996	yes	\(-1\)	\(1\)	\(e\left(\frac{543}{1996}\right)\)	\(e\left(\frac{1205}{1996}\right)\)	\(e\left(\frac{543}{998}\right)\)	\(e\left(\frac{343}{1996}\right)\)	\(e\left(\frac{437}{499}\right)\)	\(e\left(\frac{107}{499}\right)\)	\(e\left(\frac{1629}{1996}\right)\)	\(e\left(\frac{207}{998}\right)\)	\(e\left(\frac{443}{998}\right)\)	\(e\left(\frac{1927}{1996}\right)\)
\(\chi_{1997}(14,\cdot)\)	1997.f	1996	yes	\(-1\)	\(1\)	\(e\left(\frac{1417}{1996}\right)\)	\(e\left(\frac{667}{1996}\right)\)	\(e\left(\frac{419}{998}\right)\)	\(e\left(\frac{329}{1996}\right)\)	\(e\left(\frac{22}{499}\right)\)	\(e\left(\frac{123}{499}\right)\)	\(e\left(\frac{259}{1996}\right)\)	\(e\left(\frac{667}{998}\right)\)	\(e\left(\frac{873}{998}\right)\)	\(e\left(\frac{1441}{1996}\right)\)
\(\chi_{1997}(15,\cdot)\)	1997.d	499	yes	\(1\)	\(1\)	\(e\left(\frac{315}{499}\right)\)	\(e\left(\frac{87}{499}\right)\)	\(e\left(\frac{131}{499}\right)\)	\(e\left(\frac{108}{499}\right)\)	\(e\left(\frac{402}{499}\right)\)	\(e\left(\frac{433}{499}\right)\)	\(e\left(\frac{446}{499}\right)\)	\(e\left(\frac{174}{499}\right)\)	\(e\left(\frac{423}{499}\right)\)	\(e\left(\frac{470}{499}\right)\)
\(\chi_{1997}(16,\cdot)\)	1997.d	499	yes	\(1\)	\(1\)	\(e\left(\frac{1}{499}\right)\)	\(e\left(\frac{447}{499}\right)\)	\(e\left(\frac{2}{499}\right)\)	\(e\left(\frac{314}{499}\right)\)	\(e\left(\frac{448}{499}\right)\)	\(e\left(\frac{418}{499}\right)\)	\(e\left(\frac{3}{499}\right)\)	\(e\left(\frac{395}{499}\right)\)	\(e\left(\frac{315}{499}\right)\)	\(e\left(\frac{350}{499}\right)\)
\(\chi_{1997}(17,\cdot)\)	1997.d	499	yes	\(1\)	\(1\)	\(e\left(\frac{390}{499}\right)\)	\(e\left(\frac{179}{499}\right)\)	\(e\left(\frac{281}{499}\right)\)	\(e\left(\frac{205}{499}\right)\)	\(e\left(\frac{70}{499}\right)\)	\(e\left(\frac{346}{499}\right)\)	\(e\left(\frac{172}{499}\right)\)	\(e\left(\frac{358}{499}\right)\)	\(e\left(\frac{96}{499}\right)\)	\(e\left(\frac{273}{499}\right)\)
\(\chi_{1997}(18,\cdot)\)	1997.f	1996	yes	\(-1\)	\(1\)	\(e\left(\frac{895}{1996}\right)\)	\(e\left(\frac{865}{1996}\right)\)	\(e\left(\frac{895}{998}\right)\)	\(e\left(\frac{1091}{1996}\right)\)	\(e\left(\frac{440}{499}\right)\)	\(e\left(\frac{464}{499}\right)\)	\(e\left(\frac{689}{1996}\right)\)	\(e\left(\frac{865}{998}\right)\)	\(e\left(\frac{993}{998}\right)\)	\(e\left(\frac{1375}{1996}\right)\)
\(\chi_{1997}(19,\cdot)\)	1997.f	1996	yes	\(-1\)	\(1\)	\(e\left(\frac{319}{1996}\right)\)	\(e\left(\frac{877}{1996}\right)\)	\(e\left(\frac{319}{998}\right)\)	\(e\left(\frac{1863}{1996}\right)\)	\(e\left(\frac{299}{499}\right)\)	\(e\left(\frac{152}{499}\right)\)	\(e\left(\frac{957}{1996}\right)\)	\(e\left(\frac{877}{998}\right)\)	\(e\left(\frac{93}{998}\right)\)	\(e\left(\frac{1371}{1996}\right)\)
\(\chi_{1997}(20,\cdot)\)	1997.f	1996	yes	\(-1\)	\(1\)	\(e\left(\frac{815}{1996}\right)\)	\(e\left(\frac{1033}{1996}\right)\)	\(e\left(\frac{815}{998}\right)\)	\(e\left(\frac{1919}{1996}\right)\)	\(e\left(\frac{462}{499}\right)\)	\(e\left(\frac{88}{499}\right)\)	\(e\left(\frac{449}{1996}\right)\)	\(e\left(\frac{35}{998}\right)\)	\(e\left(\frac{369}{998}\right)\)	\(e\left(\frac{1319}{1996}\right)\)
\(\chi_{1997}(21,\cdot)\)	1997.f	1996	yes	\(-1\)	\(1\)	\(e\left(\frac{1863}{1996}\right)\)	\(e\left(\frac{429}{1996}\right)\)	\(e\left(\frac{865}{998}\right)\)	\(e\left(\frac{1651}{1996}\right)\)	\(e\left(\frac{74}{499}\right)\)	\(e\left(\frac{323}{499}\right)\)	\(e\left(\frac{1597}{1996}\right)\)	\(e\left(\frac{429}{998}\right)\)	\(e\left(\frac{759}{998}\right)\)	\(e\left(\frac{855}{1996}\right)\)
\(\chi_{1997}(22,\cdot)\)	1997.e	998	yes	\(1\)	\(1\)	\(e\left(\frac{425}{998}\right)\)	\(e\left(\frac{355}{998}\right)\)	\(e\left(\frac{425}{499}\right)\)	\(e\left(\frac{217}{998}\right)\)	\(e\left(\frac{390}{499}\right)\)	\(e\left(\frac{3}{499}\right)\)	\(e\left(\frac{277}{998}\right)\)	\(e\left(\frac{355}{499}\right)\)	\(e\left(\frac{321}{499}\right)\)	\(e\left(\frac{547}{998}\right)\)
\(\chi_{1997}(23,\cdot)\)	1997.f	1996	yes	\(-1\)	\(1\)	\(e\left(\frac{489}{1996}\right)\)	\(e\left(\frac{1019}{1996}\right)\)	\(e\left(\frac{489}{998}\right)\)	\(e\left(\frac{353}{1996}\right)\)	\(e\left(\frac{377}{499}\right)\)	\(e\left(\frac{452}{499}\right)\)	\(e\left(\frac{1467}{1996}\right)\)	\(e\left(\frac{21}{998}\right)\)	\(e\left(\frac{421}{998}\right)\)	\(e\left(\frac{1989}{1996}\right)\)
\(\chi_{1997}(24,\cdot)\)	1997.e	998	yes	\(1\)	\(1\)	\(e\left(\frac{225}{998}\right)\)	\(e\left(\frac{775}{998}\right)\)	\(e\left(\frac{225}{499}\right)\)	\(e\left(\frac{291}{998}\right)\)	\(e\left(\frac{1}{499}\right)\)	\(e\left(\frac{119}{499}\right)\)	\(e\left(\frac{675}{998}\right)\)	\(e\left(\frac{276}{499}\right)\)	\(e\left(\frac{258}{499}\right)\)	\(e\left(\frac{407}{998}\right)\)
\(\chi_{1997}(25,\cdot)\)	1997.e	998	yes	\(1\)	\(1\)	\(e\left(\frac{813}{998}\right)\)	\(e\left(\frac{139}{998}\right)\)	\(e\left(\frac{314}{499}\right)\)	\(e\left(\frac{293}{998}\right)\)	\(e\left(\frac{476}{499}\right)\)	\(e\left(\frac{257}{499}\right)\)	\(e\left(\frac{443}{998}\right)\)	\(e\left(\frac{139}{499}\right)\)	\(e\left(\frac{54}{499}\right)\)	\(e\left(\frac{619}{998}\right)\)
\(\chi_{1997}(26,\cdot)\)	1997.d	499	yes	\(1\)	\(1\)	\(e\left(\frac{136}{499}\right)\)	\(e\left(\frac{413}{499}\right)\)	\(e\left(\frac{272}{499}\right)\)	\(e\left(\frac{289}{499}\right)\)	\(e\left(\frac{50}{499}\right)\)	\(e\left(\frac{461}{499}\right)\)	\(e\left(\frac{408}{499}\right)\)	\(e\left(\frac{327}{499}\right)\)	\(e\left(\frac{425}{499}\right)\)	\(e\left(\frac{195}{499}\right)\)
\(\chi_{1997}(27,\cdot)\)	1997.f	1996	yes	\(-1\)	\(1\)	\(e\left(\frac{1341}{1996}\right)\)	\(e\left(\frac{627}{1996}\right)\)	\(e\left(\frac{343}{998}\right)\)	\(e\left(\frac{417}{1996}\right)\)	\(e\left(\frac{492}{499}\right)\)	\(e\left(\frac{165}{499}\right)\)	\(e\left(\frac{31}{1996}\right)\)	\(e\left(\frac{627}{998}\right)\)	\(e\left(\frac{879}{998}\right)\)	\(e\left(\frac{789}{1996}\right)\)
\(\chi_{1997}(28,\cdot)\)	1997.e	998	yes	\(1\)	\(1\)	\(e\left(\frac{709}{998}\right)\)	\(e\left(\frac{557}{998}\right)\)	\(e\left(\frac{210}{499}\right)\)	\(e\left(\frac{571}{998}\right)\)	\(e\left(\frac{134}{499}\right)\)	\(e\left(\frac{477}{499}\right)\)	\(e\left(\frac{131}{998}\right)\)	\(e\left(\frac{58}{499}\right)\)	\(e\left(\frac{141}{499}\right)\)	\(e\left(\frac{147}{998}\right)\)
\(\chi_{1997}(29,\cdot)\)	1997.e	998	yes	\(1\)	\(1\)	\(e\left(\frac{531}{998}\right)\)	\(e\left(\frac{831}{998}\right)\)	\(e\left(\frac{32}{499}\right)\)	\(e\left(\frac{567}{998}\right)\)	\(e\left(\frac{182}{499}\right)\)	\(e\left(\frac{201}{499}\right)\)	\(e\left(\frac{595}{998}\right)\)	\(e\left(\frac{332}{499}\right)\)	\(e\left(\frac{50}{499}\right)\)	\(e\left(\frac{721}{998}\right)\)
\(\chi_{1997}(30,\cdot)\)	1997.f	1996	yes	\(-1\)	\(1\)	\(e\left(\frac{1261}{1996}\right)\)	\(e\left(\frac{795}{1996}\right)\)	\(e\left(\frac{263}{998}\right)\)	\(e\left(\frac{1245}{1996}\right)\)	\(e\left(\frac{15}{499}\right)\)	\(e\left(\frac{288}{499}\right)\)	\(e\left(\frac{1787}{1996}\right)\)	\(e\left(\frac{795}{998}\right)\)	\(e\left(\frac{255}{998}\right)\)	\(e\left(\frac{733}{1996}\right)\)
\(\chi_{1997}(31,\cdot)\)	1997.f	1996	yes	\(-1\)	\(1\)	\(e\left(\frac{1535}{1996}\right)\)	\(e\left(\frac{1517}{1996}\right)\)	\(e\left(\frac{537}{998}\right)\)	\(e\left(\frac{455}{1996}\right)\)	\(e\left(\frac{264}{499}\right)\)	\(e\left(\frac{478}{499}\right)\)	\(e\left(\frac{613}{1996}\right)\)	\(e\left(\frac{519}{998}\right)\)	\(e\left(\frac{995}{998}\right)\)	\(e\left(\frac{1823}{1996}\right)\)
\(\chi_{1997}(32,\cdot)\)	1997.f	1996	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{1996}\right)\)	\(e\left(\frac{239}{1996}\right)\)	\(e\left(\frac{5}{998}\right)\)	\(e\left(\frac{73}{1996}\right)\)	\(e\left(\frac{61}{499}\right)\)	\(e\left(\frac{273}{499}\right)\)	\(e\left(\frac{15}{1996}\right)\)	\(e\left(\frac{239}{998}\right)\)	\(e\left(\frac{39}{998}\right)\)	\(e\left(\frac{253}{1996}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 1996 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.