LMFDB - Group of Dirichlet characters of modulus 4195

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4195)

pari: g = idealstar(,4195,2)

Character group

sage: G.order() pari: g.no
Order	=	3352
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{1676}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4195}(3357,\cdot)$, $\chi_{4195}(11,\cdot)$

First 32 of 3352 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{4195}(1,\cdot)$	4195.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4195}(2,\cdot)$	4195.k	1676	yes	$-1$	$1$	$e\left(\frac{179}{1676}\right)$	$e\left(\frac{169}{1676}\right)$	$e\left(\frac{179}{838}\right)$	$e\left(\frac{87}{419}\right)$	$e\left(\frac{1107}{1676}\right)$	$e\left(\frac{537}{1676}\right)$	$e\left(\frac{169}{838}\right)$	$e\left(\frac{243}{419}\right)$	$e\left(\frac{527}{1676}\right)$	$e\left(\frac{33}{1676}\right)$
$\chi_{4195}(3,\cdot)$	4195.k	1676	yes	$-1$	$1$	$e\left(\frac{169}{1676}\right)$	$e\left(\frac{403}{1676}\right)$	$e\left(\frac{169}{838}\right)$	$e\left(\frac{143}{419}\right)$	$e\left(\frac{577}{1676}\right)$	$e\left(\frac{507}{1676}\right)$	$e\left(\frac{403}{838}\right)$	$e\left(\frac{96}{419}\right)$	$e\left(\frac{741}{1676}\right)$	$e\left(\frac{1239}{1676}\right)$
$\chi_{4195}(4,\cdot)$	4195.i	838	yes	$1$	$1$	$e\left(\frac{179}{838}\right)$	$e\left(\frac{169}{838}\right)$	$e\left(\frac{179}{419}\right)$	$e\left(\frac{174}{419}\right)$	$e\left(\frac{269}{838}\right)$	$e\left(\frac{537}{838}\right)$	$e\left(\frac{169}{419}\right)$	$e\left(\frac{67}{419}\right)$	$e\left(\frac{527}{838}\right)$	$e\left(\frac{33}{838}\right)$
$\chi_{4195}(6,\cdot)$	4195.g	419	no	$1$	$1$	$e\left(\frac{87}{419}\right)$	$e\left(\frac{143}{419}\right)$	$e\left(\frac{174}{419}\right)$	$e\left(\frac{230}{419}\right)$	$e\left(\frac{2}{419}\right)$	$e\left(\frac{261}{419}\right)$	$e\left(\frac{286}{419}\right)$	$e\left(\frac{339}{419}\right)$	$e\left(\frac{317}{419}\right)$	$e\left(\frac{318}{419}\right)$
$\chi_{4195}(7,\cdot)$	4195.k	1676	yes	$-1$	$1$	$e\left(\frac{1107}{1676}\right)$	$e\left(\frac{577}{1676}\right)$	$e\left(\frac{269}{838}\right)$	$e\left(\frac{2}{419}\right)$	$e\left(\frac{11}{1676}\right)$	$e\left(\frac{1645}{1676}\right)$	$e\left(\frac{577}{838}\right)$	$e\left(\frac{309}{419}\right)$	$e\left(\frac{1115}{1676}\right)$	$e\left(\frac{73}{1676}\right)$
$\chi_{4195}(8,\cdot)$	4195.k	1676	yes	$-1$	$1$	$e\left(\frac{537}{1676}\right)$	$e\left(\frac{507}{1676}\right)$	$e\left(\frac{537}{838}\right)$	$e\left(\frac{261}{419}\right)$	$e\left(\frac{1645}{1676}\right)$	$e\left(\frac{1611}{1676}\right)$	$e\left(\frac{507}{838}\right)$	$e\left(\frac{310}{419}\right)$	$e\left(\frac{1581}{1676}\right)$	$e\left(\frac{99}{1676}\right)$
$\chi_{4195}(9,\cdot)$	4195.i	838	yes	$1$	$1$	$e\left(\frac{169}{838}\right)$	$e\left(\frac{403}{838}\right)$	$e\left(\frac{169}{419}\right)$	$e\left(\frac{286}{419}\right)$	$e\left(\frac{577}{838}\right)$	$e\left(\frac{507}{838}\right)$	$e\left(\frac{403}{419}\right)$	$e\left(\frac{192}{419}\right)$	$e\left(\frac{741}{838}\right)$	$e\left(\frac{401}{838}\right)$
$\chi_{4195}(11,\cdot)$	4195.h	838	no	$-1$	$1$	$e\left(\frac{243}{419}\right)$	$e\left(\frac{96}{419}\right)$	$e\left(\frac{67}{419}\right)$	$e\left(\frac{339}{419}\right)$	$e\left(\frac{309}{419}\right)$	$e\left(\frac{310}{419}\right)$	$e\left(\frac{192}{419}\right)$	$e\left(\frac{1}{838}\right)$	$e\left(\frac{163}{419}\right)$	$e\left(\frac{635}{838}\right)$
$\chi_{4195}(12,\cdot)$	4195.k	1676	yes	$-1$	$1$	$e\left(\frac{527}{1676}\right)$	$e\left(\frac{741}{1676}\right)$	$e\left(\frac{527}{838}\right)$	$e\left(\frac{317}{419}\right)$	$e\left(\frac{1115}{1676}\right)$	$e\left(\frac{1581}{1676}\right)$	$e\left(\frac{741}{838}\right)$	$e\left(\frac{163}{419}\right)$	$e\left(\frac{119}{1676}\right)$	$e\left(\frac{1305}{1676}\right)$
$\chi_{4195}(13,\cdot)$	4195.l	1676	yes	$1$	$1$	$e\left(\frac{33}{1676}\right)$	$e\left(\frac{1239}{1676}\right)$	$e\left(\frac{33}{838}\right)$	$e\left(\frac{318}{419}\right)$	$e\left(\frac{73}{1676}\right)$	$e\left(\frac{99}{1676}\right)$	$e\left(\frac{401}{838}\right)$	$e\left(\frac{635}{838}\right)$	$e\left(\frac{1305}{1676}\right)$	$e\left(\frac{713}{1676}\right)$
$\chi_{4195}(14,\cdot)$	4195.i	838	yes	$1$	$1$	$e\left(\frac{643}{838}\right)$	$e\left(\frac{373}{838}\right)$	$e\left(\frac{224}{419}\right)$	$e\left(\frac{89}{419}\right)$	$e\left(\frac{559}{838}\right)$	$e\left(\frac{253}{838}\right)$	$e\left(\frac{373}{419}\right)$	$e\left(\frac{133}{419}\right)$	$e\left(\frac{821}{838}\right)$	$e\left(\frac{53}{838}\right)$
$\chi_{4195}(16,\cdot)$	4195.g	419	no	$1$	$1$	$e\left(\frac{179}{419}\right)$	$e\left(\frac{169}{419}\right)$	$e\left(\frac{358}{419}\right)$	$e\left(\frac{348}{419}\right)$	$e\left(\frac{269}{419}\right)$	$e\left(\frac{118}{419}\right)$	$e\left(\frac{338}{419}\right)$	$e\left(\frac{134}{419}\right)$	$e\left(\frac{108}{419}\right)$	$e\left(\frac{33}{419}\right)$
$\chi_{4195}(17,\cdot)$	4195.l	1676	yes	$1$	$1$	$e\left(\frac{1067}{1676}\right)$	$e\left(\frac{1513}{1676}\right)$	$e\left(\frac{229}{838}\right)$	$e\left(\frac{226}{419}\right)$	$e\left(\frac{1243}{1676}\right)$	$e\left(\frac{1525}{1676}\right)$	$e\left(\frac{675}{838}\right)$	$e\left(\frac{699}{838}\right)$	$e\left(\frac{295}{1676}\right)$	$e\left(\frac{707}{1676}\right)$
$\chi_{4195}(18,\cdot)$	4195.k	1676	yes	$-1$	$1$	$e\left(\frac{517}{1676}\right)$	$e\left(\frac{975}{1676}\right)$	$e\left(\frac{517}{838}\right)$	$e\left(\frac{373}{419}\right)$	$e\left(\frac{585}{1676}\right)$	$e\left(\frac{1551}{1676}\right)$	$e\left(\frac{137}{838}\right)$	$e\left(\frac{16}{419}\right)$	$e\left(\frac{333}{1676}\right)$	$e\left(\frac{835}{1676}\right)$
$\chi_{4195}(19,\cdot)$	4195.i	838	yes	$1$	$1$	$e\left(\frac{467}{838}\right)$	$e\left(\frac{469}{838}\right)$	$e\left(\frac{48}{419}\right)$	$e\left(\frac{49}{419}\right)$	$e\left(\frac{449}{838}\right)$	$e\left(\frac{563}{838}\right)$	$e\left(\frac{50}{419}\right)$	$e\left(\frac{238}{419}\right)$	$e\left(\frac{565}{838}\right)$	$e\left(\frac{161}{838}\right)$
$\chi_{4195}(21,\cdot)$	4195.g	419	no	$1$	$1$	$e\left(\frac{319}{419}\right)$	$e\left(\frac{245}{419}\right)$	$e\left(\frac{219}{419}\right)$	$e\left(\frac{145}{419}\right)$	$e\left(\frac{147}{419}\right)$	$e\left(\frac{119}{419}\right)$	$e\left(\frac{71}{419}\right)$	$e\left(\frac{405}{419}\right)$	$e\left(\frac{45}{419}\right)$	$e\left(\frac{328}{419}\right)$
$\chi_{4195}(22,\cdot)$	4195.l	1676	yes	$1$	$1$	$e\left(\frac{1151}{1676}\right)$	$e\left(\frac{553}{1676}\right)$	$e\left(\frac{313}{838}\right)$	$e\left(\frac{7}{419}\right)$	$e\left(\frac{667}{1676}\right)$	$e\left(\frac{101}{1676}\right)$	$e\left(\frac{553}{838}\right)$	$e\left(\frac{487}{838}\right)$	$e\left(\frac{1179}{1676}\right)$	$e\left(\frac{1303}{1676}\right)$
$\chi_{4195}(23,\cdot)$	4195.k	1676	yes	$-1$	$1$	$e\left(\frac{1533}{1676}\right)$	$e\left(\frac{1335}{1676}\right)$	$e\left(\frac{695}{838}\right)$	$e\left(\frac{298}{419}\right)$	$e\left(\frac{801}{1676}\right)$	$e\left(\frac{1247}{1676}\right)$	$e\left(\frac{497}{838}\right)$	$e\left(\frac{370}{419}\right)$	$e\left(\frac{1049}{1676}\right)$	$e\left(\frac{1659}{1676}\right)$
$\chi_{4195}(24,\cdot)$	4195.i	838	yes	$1$	$1$	$e\left(\frac{353}{838}\right)$	$e\left(\frac{455}{838}\right)$	$e\left(\frac{353}{419}\right)$	$e\left(\frac{404}{419}\right)$	$e\left(\frac{273}{838}\right)$	$e\left(\frac{221}{838}\right)$	$e\left(\frac{36}{419}\right)$	$e\left(\frac{406}{419}\right)$	$e\left(\frac{323}{838}\right)$	$e\left(\frac{669}{838}\right)$
$\chi_{4195}(26,\cdot)$	4195.h	838	no	$-1$	$1$	$e\left(\frac{53}{419}\right)$	$e\left(\frac{352}{419}\right)$	$e\left(\frac{106}{419}\right)$	$e\left(\frac{405}{419}\right)$	$e\left(\frac{295}{419}\right)$	$e\left(\frac{159}{419}\right)$	$e\left(\frac{285}{419}\right)$	$e\left(\frac{283}{838}\right)$	$e\left(\frac{39}{419}\right)$	$e\left(\frac{373}{838}\right)$
$\chi_{4195}(27,\cdot)$	4195.k	1676	yes	$-1$	$1$	$e\left(\frac{507}{1676}\right)$	$e\left(\frac{1209}{1676}\right)$	$e\left(\frac{507}{838}\right)$	$e\left(\frac{10}{419}\right)$	$e\left(\frac{55}{1676}\right)$	$e\left(\frac{1521}{1676}\right)$	$e\left(\frac{371}{838}\right)$	$e\left(\frac{288}{419}\right)$	$e\left(\frac{547}{1676}\right)$	$e\left(\frac{365}{1676}\right)$
$\chi_{4195}(28,\cdot)$	4195.k	1676	yes	$-1$	$1$	$e\left(\frac{1465}{1676}\right)$	$e\left(\frac{915}{1676}\right)$	$e\left(\frac{627}{838}\right)$	$e\left(\frac{176}{419}\right)$	$e\left(\frac{549}{1676}\right)$	$e\left(\frac{1043}{1676}\right)$	$e\left(\frac{77}{838}\right)$	$e\left(\frac{376}{419}\right)$	$e\left(\frac{493}{1676}\right)$	$e\left(\frac{139}{1676}\right)$
$\chi_{4195}(29,\cdot)$	4195.j	838	yes	$-1$	$1$	$e\left(\frac{359}{838}\right)$	$e\left(\frac{147}{838}\right)$	$e\left(\frac{359}{419}\right)$	$e\left(\frac{253}{419}\right)$	$e\left(\frac{591}{838}\right)$	$e\left(\frac{239}{838}\right)$	$e\left(\frac{147}{419}\right)$	$e\left(\frac{243}{838}\right)$	$e\left(\frac{27}{838}\right)$	$e\left(\frac{266}{419}\right)$
$\chi_{4195}(31,\cdot)$	4195.h	838	no	$-1$	$1$	$e\left(\frac{337}{419}\right)$	$e\left(\frac{159}{419}\right)$	$e\left(\frac{255}{419}\right)$	$e\left(\frac{77}{419}\right)$	$e\left(\frac{263}{419}\right)$	$e\left(\frac{173}{419}\right)$	$e\left(\frac{318}{419}\right)$	$e\left(\frac{329}{838}\right)$	$e\left(\frac{414}{419}\right)$	$e\left(\frac{253}{838}\right)$
$\chi_{4195}(32,\cdot)$	4195.k	1676	yes	$-1$	$1$	$e\left(\frac{895}{1676}\right)$	$e\left(\frac{845}{1676}\right)$	$e\left(\frac{57}{838}\right)$	$e\left(\frac{16}{419}\right)$	$e\left(\frac{507}{1676}\right)$	$e\left(\frac{1009}{1676}\right)$	$e\left(\frac{7}{838}\right)$	$e\left(\frac{377}{419}\right)$	$e\left(\frac{959}{1676}\right)$	$e\left(\frac{165}{1676}\right)$
$\chi_{4195}(33,\cdot)$	4195.l	1676	yes	$1$	$1$	$e\left(\frac{1141}{1676}\right)$	$e\left(\frac{787}{1676}\right)$	$e\left(\frac{303}{838}\right)$	$e\left(\frac{63}{419}\right)$	$e\left(\frac{137}{1676}\right)$	$e\left(\frac{71}{1676}\right)$	$e\left(\frac{787}{838}\right)$	$e\left(\frac{193}{838}\right)$	$e\left(\frac{1393}{1676}\right)$	$e\left(\frac{833}{1676}\right)$
$\chi_{4195}(34,\cdot)$	4195.j	838	yes	$-1$	$1$	$e\left(\frac{623}{838}\right)$	$e\left(\frac{3}{838}\right)$	$e\left(\frac{204}{419}\right)$	$e\left(\frac{313}{419}\right)$	$e\left(\frac{337}{838}\right)$	$e\left(\frac{193}{838}\right)$	$e\left(\frac{3}{419}\right)$	$e\left(\frac{347}{838}\right)$	$e\left(\frac{411}{838}\right)$	$e\left(\frac{185}{419}\right)$
$\chi_{4195}(36,\cdot)$	4195.g	419	no	$1$	$1$	$e\left(\frac{174}{419}\right)$	$e\left(\frac{286}{419}\right)$	$e\left(\frac{348}{419}\right)$	$e\left(\frac{41}{419}\right)$	$e\left(\frac{4}{419}\right)$	$e\left(\frac{103}{419}\right)$	$e\left(\frac{153}{419}\right)$	$e\left(\frac{259}{419}\right)$	$e\left(\frac{215}{419}\right)$	$e\left(\frac{217}{419}\right)$
$\chi_{4195}(37,\cdot)$	4195.k	1676	yes	$-1$	$1$	$e\left(\frac{251}{1676}\right)$	$e\left(\frac{1501}{1676}\right)$	$e\left(\frac{251}{838}\right)$	$e\left(\frac{19}{419}\right)$	$e\left(\frac{1571}{1676}\right)$	$e\left(\frac{753}{1676}\right)$	$e\left(\frac{663}{838}\right)$	$e\left(\frac{212}{419}\right)$	$e\left(\frac{327}{1676}\right)$	$e\left(\frac{65}{1676}\right)$
$\chi_{4195}(38,\cdot)$	4195.k	1676	yes	$-1$	$1$	$e\left(\frac{1113}{1676}\right)$	$e\left(\frac{1107}{1676}\right)$	$e\left(\frac{275}{838}\right)$	$e\left(\frac{136}{419}\right)$	$e\left(\frac{329}{1676}\right)$	$e\left(\frac{1663}{1676}\right)$	$e\left(\frac{269}{838}\right)$	$e\left(\frac{62}{419}\right)$	$e\left(\frac{1657}{1676}\right)$	$e\left(\frac{355}{1676}\right)$
$\chi_{4195}(39,\cdot)$	4195.j	838	yes	$-1$	$1$	$e\left(\frac{101}{838}\right)$	$e\left(\frac{821}{838}\right)$	$e\left(\frac{101}{419}\right)$	$e\left(\frac{42}{419}\right)$	$e\left(\frac{325}{838}\right)$	$e\left(\frac{303}{838}\right)$	$e\left(\frac{402}{419}\right)$	$e\left(\frac{827}{838}\right)$	$e\left(\frac{185}{838}\right)$	$e\left(\frac{69}{419}\right)$

Click here to search among the remaining 3320 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	$4195$
Structure	\(C_{2}\times C_{1676}\)
Order	$3352$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{4195}(1,\cdot)\)	4195.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4195}(2,\cdot)\)	4195.k	1676	yes	\(-1\)	\(1\)	\(e\left(\frac{179}{1676}\right)\)	\(e\left(\frac{169}{1676}\right)\)	\(e\left(\frac{179}{838}\right)\)	\(e\left(\frac{87}{419}\right)\)	\(e\left(\frac{1107}{1676}\right)\)	\(e\left(\frac{537}{1676}\right)\)	\(e\left(\frac{169}{838}\right)\)	\(e\left(\frac{243}{419}\right)\)	\(e\left(\frac{527}{1676}\right)\)	\(e\left(\frac{33}{1676}\right)\)
\(\chi_{4195}(3,\cdot)\)	4195.k	1676	yes	\(-1\)	\(1\)	\(e\left(\frac{169}{1676}\right)\)	\(e\left(\frac{403}{1676}\right)\)	\(e\left(\frac{169}{838}\right)\)	\(e\left(\frac{143}{419}\right)\)	\(e\left(\frac{577}{1676}\right)\)	\(e\left(\frac{507}{1676}\right)\)	\(e\left(\frac{403}{838}\right)\)	\(e\left(\frac{96}{419}\right)\)	\(e\left(\frac{741}{1676}\right)\)	\(e\left(\frac{1239}{1676}\right)\)
\(\chi_{4195}(4,\cdot)\)	4195.i	838	yes	\(1\)	\(1\)	\(e\left(\frac{179}{838}\right)\)	\(e\left(\frac{169}{838}\right)\)	\(e\left(\frac{179}{419}\right)\)	\(e\left(\frac{174}{419}\right)\)	\(e\left(\frac{269}{838}\right)\)	\(e\left(\frac{537}{838}\right)\)	\(e\left(\frac{169}{419}\right)\)	\(e\left(\frac{67}{419}\right)\)	\(e\left(\frac{527}{838}\right)\)	\(e\left(\frac{33}{838}\right)\)
\(\chi_{4195}(6,\cdot)\)	4195.g	419	no	\(1\)	\(1\)	\(e\left(\frac{87}{419}\right)\)	\(e\left(\frac{143}{419}\right)\)	\(e\left(\frac{174}{419}\right)\)	\(e\left(\frac{230}{419}\right)\)	\(e\left(\frac{2}{419}\right)\)	\(e\left(\frac{261}{419}\right)\)	\(e\left(\frac{286}{419}\right)\)	\(e\left(\frac{339}{419}\right)\)	\(e\left(\frac{317}{419}\right)\)	\(e\left(\frac{318}{419}\right)\)
\(\chi_{4195}(7,\cdot)\)	4195.k	1676	yes	\(-1\)	\(1\)	\(e\left(\frac{1107}{1676}\right)\)	\(e\left(\frac{577}{1676}\right)\)	\(e\left(\frac{269}{838}\right)\)	\(e\left(\frac{2}{419}\right)\)	\(e\left(\frac{11}{1676}\right)\)	\(e\left(\frac{1645}{1676}\right)\)	\(e\left(\frac{577}{838}\right)\)	\(e\left(\frac{309}{419}\right)\)	\(e\left(\frac{1115}{1676}\right)\)	\(e\left(\frac{73}{1676}\right)\)
\(\chi_{4195}(8,\cdot)\)	4195.k	1676	yes	\(-1\)	\(1\)	\(e\left(\frac{537}{1676}\right)\)	\(e\left(\frac{507}{1676}\right)\)	\(e\left(\frac{537}{838}\right)\)	\(e\left(\frac{261}{419}\right)\)	\(e\left(\frac{1645}{1676}\right)\)	\(e\left(\frac{1611}{1676}\right)\)	\(e\left(\frac{507}{838}\right)\)	\(e\left(\frac{310}{419}\right)\)	\(e\left(\frac{1581}{1676}\right)\)	\(e\left(\frac{99}{1676}\right)\)
\(\chi_{4195}(9,\cdot)\)	4195.i	838	yes	\(1\)	\(1\)	\(e\left(\frac{169}{838}\right)\)	\(e\left(\frac{403}{838}\right)\)	\(e\left(\frac{169}{419}\right)\)	\(e\left(\frac{286}{419}\right)\)	\(e\left(\frac{577}{838}\right)\)	\(e\left(\frac{507}{838}\right)\)	\(e\left(\frac{403}{419}\right)\)	\(e\left(\frac{192}{419}\right)\)	\(e\left(\frac{741}{838}\right)\)	\(e\left(\frac{401}{838}\right)\)
\(\chi_{4195}(11,\cdot)\)	4195.h	838	no	\(-1\)	\(1\)	\(e\left(\frac{243}{419}\right)\)	\(e\left(\frac{96}{419}\right)\)	\(e\left(\frac{67}{419}\right)\)	\(e\left(\frac{339}{419}\right)\)	\(e\left(\frac{309}{419}\right)\)	\(e\left(\frac{310}{419}\right)\)	\(e\left(\frac{192}{419}\right)\)	\(e\left(\frac{1}{838}\right)\)	\(e\left(\frac{163}{419}\right)\)	\(e\left(\frac{635}{838}\right)\)
\(\chi_{4195}(12,\cdot)\)	4195.k	1676	yes	\(-1\)	\(1\)	\(e\left(\frac{527}{1676}\right)\)	\(e\left(\frac{741}{1676}\right)\)	\(e\left(\frac{527}{838}\right)\)	\(e\left(\frac{317}{419}\right)\)	\(e\left(\frac{1115}{1676}\right)\)	\(e\left(\frac{1581}{1676}\right)\)	\(e\left(\frac{741}{838}\right)\)	\(e\left(\frac{163}{419}\right)\)	\(e\left(\frac{119}{1676}\right)\)	\(e\left(\frac{1305}{1676}\right)\)
\(\chi_{4195}(13,\cdot)\)	4195.l	1676	yes	\(1\)	\(1\)	\(e\left(\frac{33}{1676}\right)\)	\(e\left(\frac{1239}{1676}\right)\)	\(e\left(\frac{33}{838}\right)\)	\(e\left(\frac{318}{419}\right)\)	\(e\left(\frac{73}{1676}\right)\)	\(e\left(\frac{99}{1676}\right)\)	\(e\left(\frac{401}{838}\right)\)	\(e\left(\frac{635}{838}\right)\)	\(e\left(\frac{1305}{1676}\right)\)	\(e\left(\frac{713}{1676}\right)\)
\(\chi_{4195}(14,\cdot)\)	4195.i	838	yes	\(1\)	\(1\)	\(e\left(\frac{643}{838}\right)\)	\(e\left(\frac{373}{838}\right)\)	\(e\left(\frac{224}{419}\right)\)	\(e\left(\frac{89}{419}\right)\)	\(e\left(\frac{559}{838}\right)\)	\(e\left(\frac{253}{838}\right)\)	\(e\left(\frac{373}{419}\right)\)	\(e\left(\frac{133}{419}\right)\)	\(e\left(\frac{821}{838}\right)\)	\(e\left(\frac{53}{838}\right)\)
\(\chi_{4195}(16,\cdot)\)	4195.g	419	no	\(1\)	\(1\)	\(e\left(\frac{179}{419}\right)\)	\(e\left(\frac{169}{419}\right)\)	\(e\left(\frac{358}{419}\right)\)	\(e\left(\frac{348}{419}\right)\)	\(e\left(\frac{269}{419}\right)\)	\(e\left(\frac{118}{419}\right)\)	\(e\left(\frac{338}{419}\right)\)	\(e\left(\frac{134}{419}\right)\)	\(e\left(\frac{108}{419}\right)\)	\(e\left(\frac{33}{419}\right)\)
\(\chi_{4195}(17,\cdot)\)	4195.l	1676	yes	\(1\)	\(1\)	\(e\left(\frac{1067}{1676}\right)\)	\(e\left(\frac{1513}{1676}\right)\)	\(e\left(\frac{229}{838}\right)\)	\(e\left(\frac{226}{419}\right)\)	\(e\left(\frac{1243}{1676}\right)\)	\(e\left(\frac{1525}{1676}\right)\)	\(e\left(\frac{675}{838}\right)\)	\(e\left(\frac{699}{838}\right)\)	\(e\left(\frac{295}{1676}\right)\)	\(e\left(\frac{707}{1676}\right)\)
\(\chi_{4195}(18,\cdot)\)	4195.k	1676	yes	\(-1\)	\(1\)	\(e\left(\frac{517}{1676}\right)\)	\(e\left(\frac{975}{1676}\right)\)	\(e\left(\frac{517}{838}\right)\)	\(e\left(\frac{373}{419}\right)\)	\(e\left(\frac{585}{1676}\right)\)	\(e\left(\frac{1551}{1676}\right)\)	\(e\left(\frac{137}{838}\right)\)	\(e\left(\frac{16}{419}\right)\)	\(e\left(\frac{333}{1676}\right)\)	\(e\left(\frac{835}{1676}\right)\)
\(\chi_{4195}(19,\cdot)\)	4195.i	838	yes	\(1\)	\(1\)	\(e\left(\frac{467}{838}\right)\)	\(e\left(\frac{469}{838}\right)\)	\(e\left(\frac{48}{419}\right)\)	\(e\left(\frac{49}{419}\right)\)	\(e\left(\frac{449}{838}\right)\)	\(e\left(\frac{563}{838}\right)\)	\(e\left(\frac{50}{419}\right)\)	\(e\left(\frac{238}{419}\right)\)	\(e\left(\frac{565}{838}\right)\)	\(e\left(\frac{161}{838}\right)\)
\(\chi_{4195}(21,\cdot)\)	4195.g	419	no	\(1\)	\(1\)	\(e\left(\frac{319}{419}\right)\)	\(e\left(\frac{245}{419}\right)\)	\(e\left(\frac{219}{419}\right)\)	\(e\left(\frac{145}{419}\right)\)	\(e\left(\frac{147}{419}\right)\)	\(e\left(\frac{119}{419}\right)\)	\(e\left(\frac{71}{419}\right)\)	\(e\left(\frac{405}{419}\right)\)	\(e\left(\frac{45}{419}\right)\)	\(e\left(\frac{328}{419}\right)\)
\(\chi_{4195}(22,\cdot)\)	4195.l	1676	yes	\(1\)	\(1\)	\(e\left(\frac{1151}{1676}\right)\)	\(e\left(\frac{553}{1676}\right)\)	\(e\left(\frac{313}{838}\right)\)	\(e\left(\frac{7}{419}\right)\)	\(e\left(\frac{667}{1676}\right)\)	\(e\left(\frac{101}{1676}\right)\)	\(e\left(\frac{553}{838}\right)\)	\(e\left(\frac{487}{838}\right)\)	\(e\left(\frac{1179}{1676}\right)\)	\(e\left(\frac{1303}{1676}\right)\)
\(\chi_{4195}(23,\cdot)\)	4195.k	1676	yes	\(-1\)	\(1\)	\(e\left(\frac{1533}{1676}\right)\)	\(e\left(\frac{1335}{1676}\right)\)	\(e\left(\frac{695}{838}\right)\)	\(e\left(\frac{298}{419}\right)\)	\(e\left(\frac{801}{1676}\right)\)	\(e\left(\frac{1247}{1676}\right)\)	\(e\left(\frac{497}{838}\right)\)	\(e\left(\frac{370}{419}\right)\)	\(e\left(\frac{1049}{1676}\right)\)	\(e\left(\frac{1659}{1676}\right)\)
\(\chi_{4195}(24,\cdot)\)	4195.i	838	yes	\(1\)	\(1\)	\(e\left(\frac{353}{838}\right)\)	\(e\left(\frac{455}{838}\right)\)	\(e\left(\frac{353}{419}\right)\)	\(e\left(\frac{404}{419}\right)\)	\(e\left(\frac{273}{838}\right)\)	\(e\left(\frac{221}{838}\right)\)	\(e\left(\frac{36}{419}\right)\)	\(e\left(\frac{406}{419}\right)\)	\(e\left(\frac{323}{838}\right)\)	\(e\left(\frac{669}{838}\right)\)
\(\chi_{4195}(26,\cdot)\)	4195.h	838	no	\(-1\)	\(1\)	\(e\left(\frac{53}{419}\right)\)	\(e\left(\frac{352}{419}\right)\)	\(e\left(\frac{106}{419}\right)\)	\(e\left(\frac{405}{419}\right)\)	\(e\left(\frac{295}{419}\right)\)	\(e\left(\frac{159}{419}\right)\)	\(e\left(\frac{285}{419}\right)\)	\(e\left(\frac{283}{838}\right)\)	\(e\left(\frac{39}{419}\right)\)	\(e\left(\frac{373}{838}\right)\)
\(\chi_{4195}(27,\cdot)\)	4195.k	1676	yes	\(-1\)	\(1\)	\(e\left(\frac{507}{1676}\right)\)	\(e\left(\frac{1209}{1676}\right)\)	\(e\left(\frac{507}{838}\right)\)	\(e\left(\frac{10}{419}\right)\)	\(e\left(\frac{55}{1676}\right)\)	\(e\left(\frac{1521}{1676}\right)\)	\(e\left(\frac{371}{838}\right)\)	\(e\left(\frac{288}{419}\right)\)	\(e\left(\frac{547}{1676}\right)\)	\(e\left(\frac{365}{1676}\right)\)
\(\chi_{4195}(28,\cdot)\)	4195.k	1676	yes	\(-1\)	\(1\)	\(e\left(\frac{1465}{1676}\right)\)	\(e\left(\frac{915}{1676}\right)\)	\(e\left(\frac{627}{838}\right)\)	\(e\left(\frac{176}{419}\right)\)	\(e\left(\frac{549}{1676}\right)\)	\(e\left(\frac{1043}{1676}\right)\)	\(e\left(\frac{77}{838}\right)\)	\(e\left(\frac{376}{419}\right)\)	\(e\left(\frac{493}{1676}\right)\)	\(e\left(\frac{139}{1676}\right)\)
\(\chi_{4195}(29,\cdot)\)	4195.j	838	yes	\(-1\)	\(1\)	\(e\left(\frac{359}{838}\right)\)	\(e\left(\frac{147}{838}\right)\)	\(e\left(\frac{359}{419}\right)\)	\(e\left(\frac{253}{419}\right)\)	\(e\left(\frac{591}{838}\right)\)	\(e\left(\frac{239}{838}\right)\)	\(e\left(\frac{147}{419}\right)\)	\(e\left(\frac{243}{838}\right)\)	\(e\left(\frac{27}{838}\right)\)	\(e\left(\frac{266}{419}\right)\)
\(\chi_{4195}(31,\cdot)\)	4195.h	838	no	\(-1\)	\(1\)	\(e\left(\frac{337}{419}\right)\)	\(e\left(\frac{159}{419}\right)\)	\(e\left(\frac{255}{419}\right)\)	\(e\left(\frac{77}{419}\right)\)	\(e\left(\frac{263}{419}\right)\)	\(e\left(\frac{173}{419}\right)\)	\(e\left(\frac{318}{419}\right)\)	\(e\left(\frac{329}{838}\right)\)	\(e\left(\frac{414}{419}\right)\)	\(e\left(\frac{253}{838}\right)\)
\(\chi_{4195}(32,\cdot)\)	4195.k	1676	yes	\(-1\)	\(1\)	\(e\left(\frac{895}{1676}\right)\)	\(e\left(\frac{845}{1676}\right)\)	\(e\left(\frac{57}{838}\right)\)	\(e\left(\frac{16}{419}\right)\)	\(e\left(\frac{507}{1676}\right)\)	\(e\left(\frac{1009}{1676}\right)\)	\(e\left(\frac{7}{838}\right)\)	\(e\left(\frac{377}{419}\right)\)	\(e\left(\frac{959}{1676}\right)\)	\(e\left(\frac{165}{1676}\right)\)
\(\chi_{4195}(33,\cdot)\)	4195.l	1676	yes	\(1\)	\(1\)	\(e\left(\frac{1141}{1676}\right)\)	\(e\left(\frac{787}{1676}\right)\)	\(e\left(\frac{303}{838}\right)\)	\(e\left(\frac{63}{419}\right)\)	\(e\left(\frac{137}{1676}\right)\)	\(e\left(\frac{71}{1676}\right)\)	\(e\left(\frac{787}{838}\right)\)	\(e\left(\frac{193}{838}\right)\)	\(e\left(\frac{1393}{1676}\right)\)	\(e\left(\frac{833}{1676}\right)\)
\(\chi_{4195}(34,\cdot)\)	4195.j	838	yes	\(-1\)	\(1\)	\(e\left(\frac{623}{838}\right)\)	\(e\left(\frac{3}{838}\right)\)	\(e\left(\frac{204}{419}\right)\)	\(e\left(\frac{313}{419}\right)\)	\(e\left(\frac{337}{838}\right)\)	\(e\left(\frac{193}{838}\right)\)	\(e\left(\frac{3}{419}\right)\)	\(e\left(\frac{347}{838}\right)\)	\(e\left(\frac{411}{838}\right)\)	\(e\left(\frac{185}{419}\right)\)
\(\chi_{4195}(36,\cdot)\)	4195.g	419	no	\(1\)	\(1\)	\(e\left(\frac{174}{419}\right)\)	\(e\left(\frac{286}{419}\right)\)	\(e\left(\frac{348}{419}\right)\)	\(e\left(\frac{41}{419}\right)\)	\(e\left(\frac{4}{419}\right)\)	\(e\left(\frac{103}{419}\right)\)	\(e\left(\frac{153}{419}\right)\)	\(e\left(\frac{259}{419}\right)\)	\(e\left(\frac{215}{419}\right)\)	\(e\left(\frac{217}{419}\right)\)
\(\chi_{4195}(37,\cdot)\)	4195.k	1676	yes	\(-1\)	\(1\)	\(e\left(\frac{251}{1676}\right)\)	\(e\left(\frac{1501}{1676}\right)\)	\(e\left(\frac{251}{838}\right)\)	\(e\left(\frac{19}{419}\right)\)	\(e\left(\frac{1571}{1676}\right)\)	\(e\left(\frac{753}{1676}\right)\)	\(e\left(\frac{663}{838}\right)\)	\(e\left(\frac{212}{419}\right)\)	\(e\left(\frac{327}{1676}\right)\)	\(e\left(\frac{65}{1676}\right)\)
\(\chi_{4195}(38,\cdot)\)	4195.k	1676	yes	\(-1\)	\(1\)	\(e\left(\frac{1113}{1676}\right)\)	\(e\left(\frac{1107}{1676}\right)\)	\(e\left(\frac{275}{838}\right)\)	\(e\left(\frac{136}{419}\right)\)	\(e\left(\frac{329}{1676}\right)\)	\(e\left(\frac{1663}{1676}\right)\)	\(e\left(\frac{269}{838}\right)\)	\(e\left(\frac{62}{419}\right)\)	\(e\left(\frac{1657}{1676}\right)\)	\(e\left(\frac{355}{1676}\right)\)
\(\chi_{4195}(39,\cdot)\)	4195.j	838	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{838}\right)\)	\(e\left(\frac{821}{838}\right)\)	\(e\left(\frac{101}{419}\right)\)	\(e\left(\frac{42}{419}\right)\)	\(e\left(\frac{325}{838}\right)\)	\(e\left(\frac{303}{838}\right)\)	\(e\left(\frac{402}{419}\right)\)	\(e\left(\frac{827}{838}\right)\)	\(e\left(\frac{185}{838}\right)\)	\(e\left(\frac{69}{419}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 3352 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.