LMFDB - Group of Dirichlet characters of modulus 6724

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6724)

pari: g = idealstar(,6724,2)

Character group

sage: G.order() pari: g.no
Order	=	3280
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{1640}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6724}(3363,\cdot)$, $\chi_{6724}(5049,\cdot)$

First 32 of 3280 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{6724}(1,\cdot)$	6724.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6724}(3,\cdot)$	6724.x	328	yes	$1$	$1$	$e\left(\frac{305}{328}\right)$	$e\left(\frac{129}{164}\right)$	$e\left(\frac{225}{328}\right)$	$e\left(\frac{141}{164}\right)$	$e\left(\frac{277}{328}\right)$	$e\left(\frac{213}{328}\right)$	$e\left(\frac{235}{328}\right)$	$e\left(\frac{187}{328}\right)$	$e\left(\frac{63}{328}\right)$	$e\left(\frac{101}{164}\right)$
$\chi_{6724}(5,\cdot)$	6724.bd	820	no	$1$	$1$	$e\left(\frac{129}{164}\right)$	$e\left(\frac{51}{410}\right)$	$e\left(\frac{129}{820}\right)$	$e\left(\frac{47}{82}\right)$	$e\left(\frac{653}{820}\right)$	$e\left(\frac{601}{820}\right)$	$e\left(\frac{747}{820}\right)$	$e\left(\frac{503}{820}\right)$	$e\left(\frac{679}{820}\right)$	$e\left(\frac{387}{410}\right)$
$\chi_{6724}(7,\cdot)$	6724.bf	1640	yes	$1$	$1$	$e\left(\frac{225}{328}\right)$	$e\left(\frac{129}{820}\right)$	$e\left(\frac{61}{1640}\right)$	$e\left(\frac{61}{164}\right)$	$e\left(\frac{1097}{1640}\right)$	$e\left(\frac{49}{1640}\right)$	$e\left(\frac{1383}{1640}\right)$	$e\left(\frac{1007}{1640}\right)$	$e\left(\frac{1211}{1640}\right)$	$e\left(\frac{593}{820}\right)$
$\chi_{6724}(9,\cdot)$	6724.u	164	no	$1$	$1$	$e\left(\frac{141}{164}\right)$	$e\left(\frac{47}{82}\right)$	$e\left(\frac{61}{164}\right)$	$e\left(\frac{59}{82}\right)$	$e\left(\frac{113}{164}\right)$	$e\left(\frac{49}{164}\right)$	$e\left(\frac{71}{164}\right)$	$e\left(\frac{23}{164}\right)$	$e\left(\frac{63}{164}\right)$	$e\left(\frac{19}{82}\right)$
$\chi_{6724}(11,\cdot)$	6724.bf	1640	yes	$1$	$1$	$e\left(\frac{277}{328}\right)$	$e\left(\frac{653}{820}\right)$	$e\left(\frac{1097}{1640}\right)$	$e\left(\frac{113}{164}\right)$	$e\left(\frac{989}{1640}\right)$	$e\left(\frac{693}{1640}\right)$	$e\left(\frac{1051}{1640}\right)$	$e\left(\frac{419}{1640}\right)$	$e\left(\frac{727}{1640}\right)$	$e\left(\frac{421}{820}\right)$
$\chi_{6724}(13,\cdot)$	6724.be	1640	no	$-1$	$1$	$e\left(\frac{213}{328}\right)$	$e\left(\frac{601}{820}\right)$	$e\left(\frac{49}{1640}\right)$	$e\left(\frac{49}{164}\right)$	$e\left(\frac{693}{1640}\right)$	$e\left(\frac{241}{1640}\right)$	$e\left(\frac{627}{1640}\right)$	$e\left(\frac{903}{1640}\right)$	$e\left(\frac{919}{1640}\right)$	$e\left(\frac{557}{820}\right)$
$\chi_{6724}(15,\cdot)$	6724.bf	1640	yes	$1$	$1$	$e\left(\frac{235}{328}\right)$	$e\left(\frac{747}{820}\right)$	$e\left(\frac{1383}{1640}\right)$	$e\left(\frac{71}{164}\right)$	$e\left(\frac{1051}{1640}\right)$	$e\left(\frac{627}{1640}\right)$	$e\left(\frac{1029}{1640}\right)$	$e\left(\frac{301}{1640}\right)$	$e\left(\frac{33}{1640}\right)$	$e\left(\frac{459}{820}\right)$
$\chi_{6724}(17,\cdot)$	6724.be	1640	no	$-1$	$1$	$e\left(\frac{187}{328}\right)$	$e\left(\frac{503}{820}\right)$	$e\left(\frac{1007}{1640}\right)$	$e\left(\frac{23}{164}\right)$	$e\left(\frac{419}{1640}\right)$	$e\left(\frac{903}{1640}\right)$	$e\left(\frac{301}{1640}\right)$	$e\left(\frac{49}{1640}\right)$	$e\left(\frac{177}{1640}\right)$	$e\left(\frac{151}{820}\right)$
$\chi_{6724}(19,\cdot)$	6724.bf	1640	yes	$1$	$1$	$e\left(\frac{63}{328}\right)$	$e\left(\frac{679}{820}\right)$	$e\left(\frac{1211}{1640}\right)$	$e\left(\frac{63}{164}\right)$	$e\left(\frac{727}{1640}\right)$	$e\left(\frac{919}{1640}\right)$	$e\left(\frac{33}{1640}\right)$	$e\left(\frac{177}{1640}\right)$	$e\left(\frac{221}{1640}\right)$	$e\left(\frac{763}{820}\right)$
$\chi_{6724}(21,\cdot)$	6724.bd	820	no	$1$	$1$	$e\left(\frac{101}{164}\right)$	$e\left(\frac{387}{410}\right)$	$e\left(\frac{593}{820}\right)$	$e\left(\frac{19}{82}\right)$	$e\left(\frac{421}{820}\right)$	$e\left(\frac{557}{820}\right)$	$e\left(\frac{459}{820}\right)$	$e\left(\frac{151}{820}\right)$	$e\left(\frac{763}{820}\right)$	$e\left(\frac{139}{410}\right)$
$\chi_{6724}(23,\cdot)$	6724.z	410	yes	$-1$	$1$	$e\left(\frac{16}{41}\right)$	$e\left(\frac{149}{205}\right)$	$e\left(\frac{98}{205}\right)$	$e\left(\frac{32}{41}\right)$	$e\left(\frac{156}{205}\right)$	$e\left(\frac{349}{410}\right)$	$e\left(\frac{24}{205}\right)$	$e\left(\frac{127}{410}\right)$	$e\left(\frac{198}{205}\right)$	$e\left(\frac{178}{205}\right)$
$\chi_{6724}(25,\cdot)$	6724.ba	410	no	$1$	$1$	$e\left(\frac{47}{82}\right)$	$e\left(\frac{51}{205}\right)$	$e\left(\frac{129}{410}\right)$	$e\left(\frac{6}{41}\right)$	$e\left(\frac{243}{410}\right)$	$e\left(\frac{191}{410}\right)$	$e\left(\frac{337}{410}\right)$	$e\left(\frac{93}{410}\right)$	$e\left(\frac{269}{410}\right)$	$e\left(\frac{182}{205}\right)$
$\chi_{6724}(27,\cdot)$	6724.x	328	yes	$1$	$1$	$e\left(\frac{259}{328}\right)$	$e\left(\frac{59}{164}\right)$	$e\left(\frac{19}{328}\right)$	$e\left(\frac{95}{164}\right)$	$e\left(\frac{175}{328}\right)$	$e\left(\frac{311}{328}\right)$	$e\left(\frac{49}{328}\right)$	$e\left(\frac{233}{328}\right)$	$e\left(\frac{189}{328}\right)$	$e\left(\frac{139}{164}\right)$
$\chi_{6724}(29,\cdot)$	6724.be	1640	no	$-1$	$1$	$e\left(\frac{37}{328}\right)$	$e\left(\frac{417}{820}\right)$	$e\left(\frac{1513}{1640}\right)$	$e\left(\frac{37}{164}\right)$	$e\left(\frac{781}{1640}\right)$	$e\left(\frac{1417}{1640}\right)$	$e\left(\frac{1019}{1640}\right)$	$e\left(\frac{471}{1640}\right)$	$e\left(\frac{463}{1640}\right)$	$e\left(\frac{29}{820}\right)$
$\chi_{6724}(31,\cdot)$	6724.z	410	yes	$-1$	$1$	$e\left(\frac{5}{41}\right)$	$e\left(\frac{167}{205}\right)$	$e\left(\frac{169}{205}\right)$	$e\left(\frac{10}{41}\right)$	$e\left(\frac{18}{205}\right)$	$e\left(\frac{127}{410}\right)$	$e\left(\frac{192}{205}\right)$	$e\left(\frac{401}{410}\right)$	$e\left(\frac{149}{205}\right)$	$e\left(\frac{194}{205}\right)$
$\chi_{6724}(33,\cdot)$	6724.bd	820	no	$1$	$1$	$e\left(\frac{127}{164}\right)$	$e\left(\frac{239}{410}\right)$	$e\left(\frac{291}{820}\right)$	$e\left(\frac{45}{82}\right)$	$e\left(\frac{367}{820}\right)$	$e\left(\frac{59}{820}\right)$	$e\left(\frac{293}{820}\right)$	$e\left(\frac{677}{820}\right)$	$e\left(\frac{521}{820}\right)$	$e\left(\frac{53}{410}\right)$
$\chi_{6724}(35,\cdot)$	6724.bf	1640	yes	$1$	$1$	$e\left(\frac{155}{328}\right)$	$e\left(\frac{231}{820}\right)$	$e\left(\frac{319}{1640}\right)$	$e\left(\frac{155}{164}\right)$	$e\left(\frac{763}{1640}\right)$	$e\left(\frac{1251}{1640}\right)$	$e\left(\frac{1237}{1640}\right)$	$e\left(\frac{373}{1640}\right)$	$e\left(\frac{929}{1640}\right)$	$e\left(\frac{547}{820}\right)$
$\chi_{6724}(37,\cdot)$	6724.w	205	no	$1$	$1$	$e\left(\frac{39}{41}\right)$	$e\left(\frac{48}{205}\right)$	$e\left(\frac{121}{205}\right)$	$e\left(\frac{37}{41}\right)$	$e\left(\frac{42}{205}\right)$	$e\left(\frac{114}{205}\right)$	$e\left(\frac{38}{205}\right)$	$e\left(\frac{92}{205}\right)$	$e\left(\frac{6}{205}\right)$	$e\left(\frac{111}{205}\right)$
$\chi_{6724}(39,\cdot)$	6724.bc	820	yes	$-1$	$1$	$e\left(\frac{95}{164}\right)$	$e\left(\frac{213}{410}\right)$	$e\left(\frac{587}{820}\right)$	$e\left(\frac{13}{82}\right)$	$e\left(\frac{219}{820}\right)$	$e\left(\frac{653}{820}\right)$	$e\left(\frac{81}{820}\right)$	$e\left(\frac{99}{820}\right)$	$e\left(\frac{617}{820}\right)$	$e\left(\frac{121}{410}\right)$
$\chi_{6724}(43,\cdot)$	6724.bc	820	yes	$-1$	$1$	$e\left(\frac{77}{164}\right)$	$e\left(\frac{183}{410}\right)$	$e\left(\frac{77}{820}\right)$	$e\left(\frac{77}{82}\right)$	$e\left(\frac{269}{820}\right)$	$e\left(\frac{203}{820}\right)$	$e\left(\frac{751}{820}\right)$	$e\left(\frac{189}{820}\right)$	$e\left(\frac{507}{820}\right)$	$e\left(\frac{231}{410}\right)$
$\chi_{6724}(45,\cdot)$	6724.ba	410	no	$1$	$1$	$e\left(\frac{53}{82}\right)$	$e\left(\frac{143}{205}\right)$	$e\left(\frac{217}{410}\right)$	$e\left(\frac{12}{41}\right)$	$e\left(\frac{199}{410}\right)$	$e\left(\frac{13}{410}\right)$	$e\left(\frac{141}{410}\right)$	$e\left(\frac{309}{410}\right)$	$e\left(\frac{87}{410}\right)$	$e\left(\frac{36}{205}\right)$
$\chi_{6724}(47,\cdot)$	6724.bf	1640	yes	$1$	$1$	$e\left(\frac{143}{328}\right)$	$e\left(\frac{211}{820}\right)$	$e\left(\frac{1619}{1640}\right)$	$e\left(\frac{143}{164}\right)$	$e\left(\frac{1343}{1640}\right)$	$e\left(\frac{951}{1640}\right)$	$e\left(\frac{1137}{1640}\right)$	$e\left(\frac{433}{1640}\right)$	$e\left(\frac{309}{1640}\right)$	$e\left(\frac{347}{820}\right)$
$\chi_{6724}(49,\cdot)$	6724.bd	820	no	$1$	$1$	$e\left(\frac{61}{164}\right)$	$e\left(\frac{129}{410}\right)$	$e\left(\frac{61}{820}\right)$	$e\left(\frac{61}{82}\right)$	$e\left(\frac{277}{820}\right)$	$e\left(\frac{49}{820}\right)$	$e\left(\frac{563}{820}\right)$	$e\left(\frac{187}{820}\right)$	$e\left(\frac{391}{820}\right)$	$e\left(\frac{183}{410}\right)$
$\chi_{6724}(51,\cdot)$	6724.j	10	no	$-1$	$1$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{6724}(53,\cdot)$	6724.be	1640	no	$-1$	$1$	$e\left(\frac{113}{328}\right)$	$e\left(\frac{817}{820}\right)$	$e\left(\frac{933}{1640}\right)$	$e\left(\frac{113}{164}\right)$	$e\left(\frac{1481}{1640}\right)$	$e\left(\frac{37}{1640}\right)$	$e\left(\frac{559}{1640}\right)$	$e\left(\frac{91}{1640}\right)$	$e\left(\frac{563}{1640}\right)$	$e\left(\frac{749}{820}\right)$
$\chi_{6724}(55,\cdot)$	6724.x	328	yes	$1$	$1$	$e\left(\frac{207}{328}\right)$	$e\left(\frac{151}{164}\right)$	$e\left(\frac{271}{328}\right)$	$e\left(\frac{43}{164}\right)$	$e\left(\frac{131}{328}\right)$	$e\left(\frac{51}{328}\right)$	$e\left(\frac{181}{328}\right)$	$e\left(\frac{285}{328}\right)$	$e\left(\frac{89}{328}\right)$	$e\left(\frac{75}{164}\right)$
$\chi_{6724}(57,\cdot)$	6724.w	205	no	$1$	$1$	$e\left(\frac{5}{41}\right)$	$e\left(\frac{126}{205}\right)$	$e\left(\frac{87}{205}\right)$	$e\left(\frac{10}{41}\right)$	$e\left(\frac{59}{205}\right)$	$e\left(\frac{43}{205}\right)$	$e\left(\frac{151}{205}\right)$	$e\left(\frac{139}{205}\right)$	$e\left(\frac{67}{205}\right)$	$e\left(\frac{112}{205}\right)$
$\chi_{6724}(59,\cdot)$	6724.bb	410	yes	$-1$	$1$	$e\left(\frac{31}{82}\right)$	$e\left(\frac{79}{205}\right)$	$e\left(\frac{31}{410}\right)$	$e\left(\frac{31}{41}\right)$	$e\left(\frac{87}{410}\right)$	$e\left(\frac{162}{205}\right)$	$e\left(\frac{313}{410}\right)$	$e\left(\frac{66}{205}\right)$	$e\left(\frac{71}{410}\right)$	$e\left(\frac{93}{205}\right)$
$\chi_{6724}(61,\cdot)$	6724.bd	820	no	$1$	$1$	$e\left(\frac{91}{164}\right)$	$e\left(\frac{97}{410}\right)$	$e\left(\frac{583}{820}\right)$	$e\left(\frac{9}{82}\right)$	$e\left(\frac{631}{820}\right)$	$e\left(\frac{307}{820}\right)$	$e\left(\frac{649}{820}\right)$	$e\left(\frac{201}{820}\right)$	$e\left(\frac{793}{820}\right)$	$e\left(\frac{109}{410}\right)$
$\chi_{6724}(63,\cdot)$	6724.bf	1640	yes	$1$	$1$	$e\left(\frac{179}{328}\right)$	$e\left(\frac{599}{820}\right)$	$e\left(\frac{671}{1640}\right)$	$e\left(\frac{15}{164}\right)$	$e\left(\frac{587}{1640}\right)$	$e\left(\frac{539}{1640}\right)$	$e\left(\frac{453}{1640}\right)$	$e\left(\frac{1237}{1640}\right)$	$e\left(\frac{201}{1640}\right)$	$e\left(\frac{783}{820}\right)$
$\chi_{6724}(65,\cdot)$	6724.be	1640	no	$-1$	$1$	$e\left(\frac{143}{328}\right)$	$e\left(\frac{703}{820}\right)$	$e\left(\frac{307}{1640}\right)$	$e\left(\frac{143}{164}\right)$	$e\left(\frac{359}{1640}\right)$	$e\left(\frac{1443}{1640}\right)$	$e\left(\frac{481}{1640}\right)$	$e\left(\frac{269}{1640}\right)$	$e\left(\frac{637}{1640}\right)$	$e\left(\frac{511}{820}\right)$

Click here to search among the remaining 3248 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	$6724$
Structure	\(C_{2}\times C_{1640}\)
Order	$3280$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{6724}(1,\cdot)\)	6724.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6724}(3,\cdot)\)	6724.x	328	yes	\(1\)	\(1\)	\(e\left(\frac{305}{328}\right)\)	\(e\left(\frac{129}{164}\right)\)	\(e\left(\frac{225}{328}\right)\)	\(e\left(\frac{141}{164}\right)\)	\(e\left(\frac{277}{328}\right)\)	\(e\left(\frac{213}{328}\right)\)	\(e\left(\frac{235}{328}\right)\)	\(e\left(\frac{187}{328}\right)\)	\(e\left(\frac{63}{328}\right)\)	\(e\left(\frac{101}{164}\right)\)
\(\chi_{6724}(5,\cdot)\)	6724.bd	820	no	\(1\)	\(1\)	\(e\left(\frac{129}{164}\right)\)	\(e\left(\frac{51}{410}\right)\)	\(e\left(\frac{129}{820}\right)\)	\(e\left(\frac{47}{82}\right)\)	\(e\left(\frac{653}{820}\right)\)	\(e\left(\frac{601}{820}\right)\)	\(e\left(\frac{747}{820}\right)\)	\(e\left(\frac{503}{820}\right)\)	\(e\left(\frac{679}{820}\right)\)	\(e\left(\frac{387}{410}\right)\)
\(\chi_{6724}(7,\cdot)\)	6724.bf	1640	yes	\(1\)	\(1\)	\(e\left(\frac{225}{328}\right)\)	\(e\left(\frac{129}{820}\right)\)	\(e\left(\frac{61}{1640}\right)\)	\(e\left(\frac{61}{164}\right)\)	\(e\left(\frac{1097}{1640}\right)\)	\(e\left(\frac{49}{1640}\right)\)	\(e\left(\frac{1383}{1640}\right)\)	\(e\left(\frac{1007}{1640}\right)\)	\(e\left(\frac{1211}{1640}\right)\)	\(e\left(\frac{593}{820}\right)\)
\(\chi_{6724}(9,\cdot)\)	6724.u	164	no	\(1\)	\(1\)	\(e\left(\frac{141}{164}\right)\)	\(e\left(\frac{47}{82}\right)\)	\(e\left(\frac{61}{164}\right)\)	\(e\left(\frac{59}{82}\right)\)	\(e\left(\frac{113}{164}\right)\)	\(e\left(\frac{49}{164}\right)\)	\(e\left(\frac{71}{164}\right)\)	\(e\left(\frac{23}{164}\right)\)	\(e\left(\frac{63}{164}\right)\)	\(e\left(\frac{19}{82}\right)\)
\(\chi_{6724}(11,\cdot)\)	6724.bf	1640	yes	\(1\)	\(1\)	\(e\left(\frac{277}{328}\right)\)	\(e\left(\frac{653}{820}\right)\)	\(e\left(\frac{1097}{1640}\right)\)	\(e\left(\frac{113}{164}\right)\)	\(e\left(\frac{989}{1640}\right)\)	\(e\left(\frac{693}{1640}\right)\)	\(e\left(\frac{1051}{1640}\right)\)	\(e\left(\frac{419}{1640}\right)\)	\(e\left(\frac{727}{1640}\right)\)	\(e\left(\frac{421}{820}\right)\)
\(\chi_{6724}(13,\cdot)\)	6724.be	1640	no	\(-1\)	\(1\)	\(e\left(\frac{213}{328}\right)\)	\(e\left(\frac{601}{820}\right)\)	\(e\left(\frac{49}{1640}\right)\)	\(e\left(\frac{49}{164}\right)\)	\(e\left(\frac{693}{1640}\right)\)	\(e\left(\frac{241}{1640}\right)\)	\(e\left(\frac{627}{1640}\right)\)	\(e\left(\frac{903}{1640}\right)\)	\(e\left(\frac{919}{1640}\right)\)	\(e\left(\frac{557}{820}\right)\)
\(\chi_{6724}(15,\cdot)\)	6724.bf	1640	yes	\(1\)	\(1\)	\(e\left(\frac{235}{328}\right)\)	\(e\left(\frac{747}{820}\right)\)	\(e\left(\frac{1383}{1640}\right)\)	\(e\left(\frac{71}{164}\right)\)	\(e\left(\frac{1051}{1640}\right)\)	\(e\left(\frac{627}{1640}\right)\)	\(e\left(\frac{1029}{1640}\right)\)	\(e\left(\frac{301}{1640}\right)\)	\(e\left(\frac{33}{1640}\right)\)	\(e\left(\frac{459}{820}\right)\)
\(\chi_{6724}(17,\cdot)\)	6724.be	1640	no	\(-1\)	\(1\)	\(e\left(\frac{187}{328}\right)\)	\(e\left(\frac{503}{820}\right)\)	\(e\left(\frac{1007}{1640}\right)\)	\(e\left(\frac{23}{164}\right)\)	\(e\left(\frac{419}{1640}\right)\)	\(e\left(\frac{903}{1640}\right)\)	\(e\left(\frac{301}{1640}\right)\)	\(e\left(\frac{49}{1640}\right)\)	\(e\left(\frac{177}{1640}\right)\)	\(e\left(\frac{151}{820}\right)\)
\(\chi_{6724}(19,\cdot)\)	6724.bf	1640	yes	\(1\)	\(1\)	\(e\left(\frac{63}{328}\right)\)	\(e\left(\frac{679}{820}\right)\)	\(e\left(\frac{1211}{1640}\right)\)	\(e\left(\frac{63}{164}\right)\)	\(e\left(\frac{727}{1640}\right)\)	\(e\left(\frac{919}{1640}\right)\)	\(e\left(\frac{33}{1640}\right)\)	\(e\left(\frac{177}{1640}\right)\)	\(e\left(\frac{221}{1640}\right)\)	\(e\left(\frac{763}{820}\right)\)
\(\chi_{6724}(21,\cdot)\)	6724.bd	820	no	\(1\)	\(1\)	\(e\left(\frac{101}{164}\right)\)	\(e\left(\frac{387}{410}\right)\)	\(e\left(\frac{593}{820}\right)\)	\(e\left(\frac{19}{82}\right)\)	\(e\left(\frac{421}{820}\right)\)	\(e\left(\frac{557}{820}\right)\)	\(e\left(\frac{459}{820}\right)\)	\(e\left(\frac{151}{820}\right)\)	\(e\left(\frac{763}{820}\right)\)	\(e\left(\frac{139}{410}\right)\)
\(\chi_{6724}(23,\cdot)\)	6724.z	410	yes	\(-1\)	\(1\)	\(e\left(\frac{16}{41}\right)\)	\(e\left(\frac{149}{205}\right)\)	\(e\left(\frac{98}{205}\right)\)	\(e\left(\frac{32}{41}\right)\)	\(e\left(\frac{156}{205}\right)\)	\(e\left(\frac{349}{410}\right)\)	\(e\left(\frac{24}{205}\right)\)	\(e\left(\frac{127}{410}\right)\)	\(e\left(\frac{198}{205}\right)\)	\(e\left(\frac{178}{205}\right)\)
\(\chi_{6724}(25,\cdot)\)	6724.ba	410	no	\(1\)	\(1\)	\(e\left(\frac{47}{82}\right)\)	\(e\left(\frac{51}{205}\right)\)	\(e\left(\frac{129}{410}\right)\)	\(e\left(\frac{6}{41}\right)\)	\(e\left(\frac{243}{410}\right)\)	\(e\left(\frac{191}{410}\right)\)	\(e\left(\frac{337}{410}\right)\)	\(e\left(\frac{93}{410}\right)\)	\(e\left(\frac{269}{410}\right)\)	\(e\left(\frac{182}{205}\right)\)
\(\chi_{6724}(27,\cdot)\)	6724.x	328	yes	\(1\)	\(1\)	\(e\left(\frac{259}{328}\right)\)	\(e\left(\frac{59}{164}\right)\)	\(e\left(\frac{19}{328}\right)\)	\(e\left(\frac{95}{164}\right)\)	\(e\left(\frac{175}{328}\right)\)	\(e\left(\frac{311}{328}\right)\)	\(e\left(\frac{49}{328}\right)\)	\(e\left(\frac{233}{328}\right)\)	\(e\left(\frac{189}{328}\right)\)	\(e\left(\frac{139}{164}\right)\)
\(\chi_{6724}(29,\cdot)\)	6724.be	1640	no	\(-1\)	\(1\)	\(e\left(\frac{37}{328}\right)\)	\(e\left(\frac{417}{820}\right)\)	\(e\left(\frac{1513}{1640}\right)\)	\(e\left(\frac{37}{164}\right)\)	\(e\left(\frac{781}{1640}\right)\)	\(e\left(\frac{1417}{1640}\right)\)	\(e\left(\frac{1019}{1640}\right)\)	\(e\left(\frac{471}{1640}\right)\)	\(e\left(\frac{463}{1640}\right)\)	\(e\left(\frac{29}{820}\right)\)
\(\chi_{6724}(31,\cdot)\)	6724.z	410	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{41}\right)\)	\(e\left(\frac{167}{205}\right)\)	\(e\left(\frac{169}{205}\right)\)	\(e\left(\frac{10}{41}\right)\)	\(e\left(\frac{18}{205}\right)\)	\(e\left(\frac{127}{410}\right)\)	\(e\left(\frac{192}{205}\right)\)	\(e\left(\frac{401}{410}\right)\)	\(e\left(\frac{149}{205}\right)\)	\(e\left(\frac{194}{205}\right)\)
\(\chi_{6724}(33,\cdot)\)	6724.bd	820	no	\(1\)	\(1\)	\(e\left(\frac{127}{164}\right)\)	\(e\left(\frac{239}{410}\right)\)	\(e\left(\frac{291}{820}\right)\)	\(e\left(\frac{45}{82}\right)\)	\(e\left(\frac{367}{820}\right)\)	\(e\left(\frac{59}{820}\right)\)	\(e\left(\frac{293}{820}\right)\)	\(e\left(\frac{677}{820}\right)\)	\(e\left(\frac{521}{820}\right)\)	\(e\left(\frac{53}{410}\right)\)
\(\chi_{6724}(35,\cdot)\)	6724.bf	1640	yes	\(1\)	\(1\)	\(e\left(\frac{155}{328}\right)\)	\(e\left(\frac{231}{820}\right)\)	\(e\left(\frac{319}{1640}\right)\)	\(e\left(\frac{155}{164}\right)\)	\(e\left(\frac{763}{1640}\right)\)	\(e\left(\frac{1251}{1640}\right)\)	\(e\left(\frac{1237}{1640}\right)\)	\(e\left(\frac{373}{1640}\right)\)	\(e\left(\frac{929}{1640}\right)\)	\(e\left(\frac{547}{820}\right)\)
\(\chi_{6724}(37,\cdot)\)	6724.w	205	no	\(1\)	\(1\)	\(e\left(\frac{39}{41}\right)\)	\(e\left(\frac{48}{205}\right)\)	\(e\left(\frac{121}{205}\right)\)	\(e\left(\frac{37}{41}\right)\)	\(e\left(\frac{42}{205}\right)\)	\(e\left(\frac{114}{205}\right)\)	\(e\left(\frac{38}{205}\right)\)	\(e\left(\frac{92}{205}\right)\)	\(e\left(\frac{6}{205}\right)\)	\(e\left(\frac{111}{205}\right)\)
\(\chi_{6724}(39,\cdot)\)	6724.bc	820	yes	\(-1\)	\(1\)	\(e\left(\frac{95}{164}\right)\)	\(e\left(\frac{213}{410}\right)\)	\(e\left(\frac{587}{820}\right)\)	\(e\left(\frac{13}{82}\right)\)	\(e\left(\frac{219}{820}\right)\)	\(e\left(\frac{653}{820}\right)\)	\(e\left(\frac{81}{820}\right)\)	\(e\left(\frac{99}{820}\right)\)	\(e\left(\frac{617}{820}\right)\)	\(e\left(\frac{121}{410}\right)\)
\(\chi_{6724}(43,\cdot)\)	6724.bc	820	yes	\(-1\)	\(1\)	\(e\left(\frac{77}{164}\right)\)	\(e\left(\frac{183}{410}\right)\)	\(e\left(\frac{77}{820}\right)\)	\(e\left(\frac{77}{82}\right)\)	\(e\left(\frac{269}{820}\right)\)	\(e\left(\frac{203}{820}\right)\)	\(e\left(\frac{751}{820}\right)\)	\(e\left(\frac{189}{820}\right)\)	\(e\left(\frac{507}{820}\right)\)	\(e\left(\frac{231}{410}\right)\)
\(\chi_{6724}(45,\cdot)\)	6724.ba	410	no	\(1\)	\(1\)	\(e\left(\frac{53}{82}\right)\)	\(e\left(\frac{143}{205}\right)\)	\(e\left(\frac{217}{410}\right)\)	\(e\left(\frac{12}{41}\right)\)	\(e\left(\frac{199}{410}\right)\)	\(e\left(\frac{13}{410}\right)\)	\(e\left(\frac{141}{410}\right)\)	\(e\left(\frac{309}{410}\right)\)	\(e\left(\frac{87}{410}\right)\)	\(e\left(\frac{36}{205}\right)\)
\(\chi_{6724}(47,\cdot)\)	6724.bf	1640	yes	\(1\)	\(1\)	\(e\left(\frac{143}{328}\right)\)	\(e\left(\frac{211}{820}\right)\)	\(e\left(\frac{1619}{1640}\right)\)	\(e\left(\frac{143}{164}\right)\)	\(e\left(\frac{1343}{1640}\right)\)	\(e\left(\frac{951}{1640}\right)\)	\(e\left(\frac{1137}{1640}\right)\)	\(e\left(\frac{433}{1640}\right)\)	\(e\left(\frac{309}{1640}\right)\)	\(e\left(\frac{347}{820}\right)\)
\(\chi_{6724}(49,\cdot)\)	6724.bd	820	no	\(1\)	\(1\)	\(e\left(\frac{61}{164}\right)\)	\(e\left(\frac{129}{410}\right)\)	\(e\left(\frac{61}{820}\right)\)	\(e\left(\frac{61}{82}\right)\)	\(e\left(\frac{277}{820}\right)\)	\(e\left(\frac{49}{820}\right)\)	\(e\left(\frac{563}{820}\right)\)	\(e\left(\frac{187}{820}\right)\)	\(e\left(\frac{391}{820}\right)\)	\(e\left(\frac{183}{410}\right)\)
\(\chi_{6724}(51,\cdot)\)	6724.j	10	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{6724}(53,\cdot)\)	6724.be	1640	no	\(-1\)	\(1\)	\(e\left(\frac{113}{328}\right)\)	\(e\left(\frac{817}{820}\right)\)	\(e\left(\frac{933}{1640}\right)\)	\(e\left(\frac{113}{164}\right)\)	\(e\left(\frac{1481}{1640}\right)\)	\(e\left(\frac{37}{1640}\right)\)	\(e\left(\frac{559}{1640}\right)\)	\(e\left(\frac{91}{1640}\right)\)	\(e\left(\frac{563}{1640}\right)\)	\(e\left(\frac{749}{820}\right)\)
\(\chi_{6724}(55,\cdot)\)	6724.x	328	yes	\(1\)	\(1\)	\(e\left(\frac{207}{328}\right)\)	\(e\left(\frac{151}{164}\right)\)	\(e\left(\frac{271}{328}\right)\)	\(e\left(\frac{43}{164}\right)\)	\(e\left(\frac{131}{328}\right)\)	\(e\left(\frac{51}{328}\right)\)	\(e\left(\frac{181}{328}\right)\)	\(e\left(\frac{285}{328}\right)\)	\(e\left(\frac{89}{328}\right)\)	\(e\left(\frac{75}{164}\right)\)
\(\chi_{6724}(57,\cdot)\)	6724.w	205	no	\(1\)	\(1\)	\(e\left(\frac{5}{41}\right)\)	\(e\left(\frac{126}{205}\right)\)	\(e\left(\frac{87}{205}\right)\)	\(e\left(\frac{10}{41}\right)\)	\(e\left(\frac{59}{205}\right)\)	\(e\left(\frac{43}{205}\right)\)	\(e\left(\frac{151}{205}\right)\)	\(e\left(\frac{139}{205}\right)\)	\(e\left(\frac{67}{205}\right)\)	\(e\left(\frac{112}{205}\right)\)
\(\chi_{6724}(59,\cdot)\)	6724.bb	410	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{82}\right)\)	\(e\left(\frac{79}{205}\right)\)	\(e\left(\frac{31}{410}\right)\)	\(e\left(\frac{31}{41}\right)\)	\(e\left(\frac{87}{410}\right)\)	\(e\left(\frac{162}{205}\right)\)	\(e\left(\frac{313}{410}\right)\)	\(e\left(\frac{66}{205}\right)\)	\(e\left(\frac{71}{410}\right)\)	\(e\left(\frac{93}{205}\right)\)
\(\chi_{6724}(61,\cdot)\)	6724.bd	820	no	\(1\)	\(1\)	\(e\left(\frac{91}{164}\right)\)	\(e\left(\frac{97}{410}\right)\)	\(e\left(\frac{583}{820}\right)\)	\(e\left(\frac{9}{82}\right)\)	\(e\left(\frac{631}{820}\right)\)	\(e\left(\frac{307}{820}\right)\)	\(e\left(\frac{649}{820}\right)\)	\(e\left(\frac{201}{820}\right)\)	\(e\left(\frac{793}{820}\right)\)	\(e\left(\frac{109}{410}\right)\)
\(\chi_{6724}(63,\cdot)\)	6724.bf	1640	yes	\(1\)	\(1\)	\(e\left(\frac{179}{328}\right)\)	\(e\left(\frac{599}{820}\right)\)	\(e\left(\frac{671}{1640}\right)\)	\(e\left(\frac{15}{164}\right)\)	\(e\left(\frac{587}{1640}\right)\)	\(e\left(\frac{539}{1640}\right)\)	\(e\left(\frac{453}{1640}\right)\)	\(e\left(\frac{1237}{1640}\right)\)	\(e\left(\frac{201}{1640}\right)\)	\(e\left(\frac{783}{820}\right)\)
\(\chi_{6724}(65,\cdot)\)	6724.be	1640	no	\(-1\)	\(1\)	\(e\left(\frac{143}{328}\right)\)	\(e\left(\frac{703}{820}\right)\)	\(e\left(\frac{307}{1640}\right)\)	\(e\left(\frac{143}{164}\right)\)	\(e\left(\frac{359}{1640}\right)\)	\(e\left(\frac{1443}{1640}\right)\)	\(e\left(\frac{481}{1640}\right)\)	\(e\left(\frac{269}{1640}\right)\)	\(e\left(\frac{637}{1640}\right)\)	\(e\left(\frac{511}{820}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 3280 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.