LMFDB - Group of Dirichlet characters of modulus 6900

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6900)

pari: g = idealstar(,6900,2)

Character group

sage: G.order() pari: g.no
Order	=	1760
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{220}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6900}(3451,\cdot)$, $\chi_{6900}(4601,\cdot)$, $\chi_{6900}(277,\cdot)$, $\chi_{6900}(1201,\cdot)$

First 32 of 1760 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$29$	$31$	$37$	$41$	$43$
$\chi_{6900}(1,\cdot)$	6900.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6900}(7,\cdot)$	6900.cp	44	no	$-1$	$1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{25}{44}\right)$
$\chi_{6900}(11,\cdot)$	6900.cy	110	yes	$-1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{6900}(13,\cdot)$	6900.dp	220	no	$-1$	$1$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{6900}(17,\cdot)$	6900.dr	220	no	$-1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{15}{44}\right)$
$\chi_{6900}(19,\cdot)$	6900.dh	110	no	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{6900}(29,\cdot)$	6900.dd	110	no	$-1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{6900}(31,\cdot)$	6900.df	110	no	$-1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{6900}(37,\cdot)$	6900.dn	220	no	$1$	$1$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{6900}(41,\cdot)$	6900.cx	110	no	$-1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{6900}(43,\cdot)$	6900.cp	44	no	$-1$	$1$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{39}{44}\right)$
$\chi_{6900}(47,\cdot)$	6900.bq	20	no	$-1$	$1$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$	$i$
$\chi_{6900}(49,\cdot)$	6900.ch	22	no	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{6900}(53,\cdot)$	6900.dr	220	no	$-1$	$1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{25}{44}\right)$
$\chi_{6900}(59,\cdot)$	6900.da	110	yes	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{6900}(61,\cdot)$	6900.de	110	no	$-1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{6900}(67,\cdot)$	6900.do	220	no	$-1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{6900}(71,\cdot)$	6900.di	110	yes	$1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{6900}(73,\cdot)$	6900.dp	220	no	$-1$	$1$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{7}{44}\right)$
$\chi_{6900}(77,\cdot)$	6900.dl	220	no	$1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{5}{44}\right)$
$\chi_{6900}(79,\cdot)$	6900.dh	110	no	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{6900}(83,\cdot)$	6900.dk	220	yes	$1$	$1$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{6900}(89,\cdot)$	6900.cz	110	no	$1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{6900}(91,\cdot)$	6900.bh	10	no	$1$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$1$
$\chi_{6900}(97,\cdot)$	6900.dn	220	no	$1$	$1$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{43}{44}\right)$
$\chi_{6900}(101,\cdot)$	6900.cb	22	no	$-1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{6900}(103,\cdot)$	6900.do	220	no	$-1$	$1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{35}{44}\right)$
$\chi_{6900}(107,\cdot)$	6900.ct	44	no	$1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{44}\right)$
$\chi_{6900}(109,\cdot)$	6900.cw	110	no	$-1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{6900}(113,\cdot)$	6900.dr	220	no	$-1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{6900}(119,\cdot)$	6900.da	110	yes	$1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{6900}(121,\cdot)$	6900.cu	55	no	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{1}{11}\right)$

Click here to search among the remaining 1728 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	$6900$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{220}\)
Order	$1760$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{6900}(1,\cdot)\)	6900.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6900}(7,\cdot)\)	6900.cp	44	no	\(-1\)	\(1\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)
\(\chi_{6900}(11,\cdot)\)	6900.cy	110	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{6900}(13,\cdot)\)	6900.dp	220	no	\(-1\)	\(1\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{6900}(17,\cdot)\)	6900.dr	220	no	\(-1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{15}{44}\right)\)
\(\chi_{6900}(19,\cdot)\)	6900.dh	110	no	\(1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{6900}(29,\cdot)\)	6900.dd	110	no	\(-1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{6900}(31,\cdot)\)	6900.df	110	no	\(-1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{6900}(37,\cdot)\)	6900.dn	220	no	\(1\)	\(1\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{6900}(41,\cdot)\)	6900.cx	110	no	\(-1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{6900}(43,\cdot)\)	6900.cp	44	no	\(-1\)	\(1\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)
\(\chi_{6900}(47,\cdot)\)	6900.bq	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)
\(\chi_{6900}(49,\cdot)\)	6900.ch	22	no	\(1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{6900}(53,\cdot)\)	6900.dr	220	no	\(-1\)	\(1\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{25}{44}\right)\)
\(\chi_{6900}(59,\cdot)\)	6900.da	110	yes	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{6900}(61,\cdot)\)	6900.de	110	no	\(-1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{6900}(67,\cdot)\)	6900.do	220	no	\(-1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{6900}(71,\cdot)\)	6900.di	110	yes	\(1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{6900}(73,\cdot)\)	6900.dp	220	no	\(-1\)	\(1\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{7}{44}\right)\)
\(\chi_{6900}(77,\cdot)\)	6900.dl	220	no	\(1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{5}{44}\right)\)
\(\chi_{6900}(79,\cdot)\)	6900.dh	110	no	\(1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{6900}(83,\cdot)\)	6900.dk	220	yes	\(1\)	\(1\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{6900}(89,\cdot)\)	6900.cz	110	no	\(1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{6900}(91,\cdot)\)	6900.bh	10	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)
\(\chi_{6900}(97,\cdot)\)	6900.dn	220	no	\(1\)	\(1\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{43}{44}\right)\)
\(\chi_{6900}(101,\cdot)\)	6900.cb	22	no	\(-1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{6900}(103,\cdot)\)	6900.do	220	no	\(-1\)	\(1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{35}{44}\right)\)
\(\chi_{6900}(107,\cdot)\)	6900.ct	44	no	\(1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)
\(\chi_{6900}(109,\cdot)\)	6900.cw	110	no	\(-1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{6900}(113,\cdot)\)	6900.dr	220	no	\(-1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{6900}(119,\cdot)\)	6900.da	110	yes	\(1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{6900}(121,\cdot)\)	6900.cu	55	no	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 1760 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.