LMFDB - Group of Dirichlet characters of modulus 64400

Show commands: PariGP / SageMath

sage: H = DirichletGroup(64400)

pari: g = idealstar(,64400,2)

Character group

sage: G.order() pari: g.no
Order	=	21120
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{660}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{64400}(56351,\cdot)$, $\chi_{64400}(16101,\cdot)$, $\chi_{64400}(2577,\cdot)$, $\chi_{64400}(9201,\cdot)$, $\chi_{64400}(19601,\cdot)$

First 32 of 21120 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	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$27$	$29$	$31$	$33$
$\chi_{64400}(1,\cdot)$	64400.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{64400}(3,\cdot)$	64400.yn	660	yes	$-1$	$1$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{41}{660}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{533}{660}\right)$	$e\left(\frac{523}{660}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{43}{660}\right)$
$\chi_{64400}(9,\cdot)$	64400.wc	330	no	$1$	$1$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{43}{330}\right)$
$\chi_{64400}(11,\cdot)$	64400.xw	660	yes	$1$	$1$	$e\left(\frac{41}{660}\right)$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{593}{660}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{307}{330}\right)$	$e\left(\frac{79}{660}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{7}{330}\right)$	$e\left(\frac{317}{330}\right)$
$\chi_{64400}(13,\cdot)$	64400.vl	220	yes	$1$	$1$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{57}{220}\right)$
$\chi_{64400}(17,\cdot)$	64400.yf	660	no	$-1$	$1$	$e\left(\frac{533}{660}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{307}{330}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{557}{660}\right)$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{487}{660}\right)$
$\chi_{64400}(19,\cdot)$	64400.xs	660	yes	$-1$	$1$	$e\left(\frac{523}{660}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{79}{660}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{227}{660}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{301}{330}\right)$
$\chi_{64400}(27,\cdot)$	64400.tz	220	yes	$-1$	$1$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{43}{220}\right)$
$\chi_{64400}(29,\cdot)$	64400.uo	220	no	$1$	$1$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{83}{110}\right)$
$\chi_{64400}(31,\cdot)$	64400.vx	330	no	$1$	$1$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{7}{330}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{281}{330}\right)$
$\chi_{64400}(33,\cdot)$	64400.yf	660	no	$-1$	$1$	$e\left(\frac{43}{660}\right)$	$e\left(\frac{43}{330}\right)$	$e\left(\frac{317}{330}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{487}{660}\right)$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{281}{330}\right)$	$e\left(\frac{17}{660}\right)$
$\chi_{64400}(37,\cdot)$	64400.yi	660	yes	$1$	$1$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{247}{660}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{571}{660}\right)$	$e\left(\frac{551}{660}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{581}{660}\right)$
$\chi_{64400}(39,\cdot)$	64400.wi	330	no	$-1$	$1$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{247}{330}\right)$	$e\left(\frac{107}{330}\right)$
$\chi_{64400}(41,\cdot)$	64400.rn	110	no	$-1$	$1$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{81}{110}\right)$
$\chi_{64400}(43,\cdot)$	64400.nk	44	no	$-1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{41}{44}\right)$
$\chi_{64400}(47,\cdot)$	64400.ob	60	no	$-1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{43}{60}\right)$
$\chi_{64400}(51,\cdot)$	64400.sp	132	no	$1$	$1$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{53}{66}\right)$
$\chi_{64400}(53,\cdot)$	64400.wz	660	yes	$1$	$1$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{191}{660}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{173}{660}\right)$	$e\left(\frac{223}{660}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{107}{165}\right)$	$e\left(\frac{643}{660}\right)$
$\chi_{64400}(57,\cdot)$	64400.mf	44	no	$1$	$1$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{43}{44}\right)$
$\chi_{64400}(59,\cdot)$	64400.xk	660	yes	$1$	$1$	$e\left(\frac{329}{660}\right)$	$e\left(\frac{329}{330}\right)$	$e\left(\frac{227}{660}\right)$	$e\left(\frac{101}{220}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{151}{660}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{139}{165}\right)$
$\chi_{64400}(61,\cdot)$	64400.xq	660	yes	$1$	$1$	$e\left(\frac{31}{660}\right)$	$e\left(\frac{31}{330}\right)$	$e\left(\frac{553}{660}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{269}{660}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{287}{330}\right)$	$e\left(\frac{146}{165}\right)$
$\chi_{64400}(67,\cdot)$	64400.yp	660	yes	$-1$	$1$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{419}{660}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{167}{660}\right)$	$e\left(\frac{427}{660}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{37}{660}\right)$
$\chi_{64400}(71,\cdot)$	64400.rr	110	no	$-1$	$1$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{64400}(73,\cdot)$	64400.yh	660	no	$1$	$1$	$e\left(\frac{281}{660}\right)$	$e\left(\frac{281}{330}\right)$	$e\left(\frac{199}{330}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{389}{660}\right)$	$e\left(\frac{317}{330}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{217}{330}\right)$	$e\left(\frac{19}{660}\right)$
$\chi_{64400}(79,\cdot)$	64400.vq	330	no	$1$	$1$	$e\left(\frac{118}{165}\right)$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{62}{165}\right)$
$\chi_{64400}(81,\cdot)$	64400.ts	165	no	$1$	$1$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{43}{165}\right)$
$\chi_{64400}(83,\cdot)$	64400.ua	220	yes	$1$	$1$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{179}{220}\right)$
$\chi_{64400}(87,\cdot)$	64400.xe	660	no	$-1$	$1$	$e\left(\frac{29}{660}\right)$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{551}{660}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{541}{660}\right)$
$\chi_{64400}(89,\cdot)$	64400.wg	330	no	$1$	$1$	$e\left(\frac{23}{330}\right)$	$e\left(\frac{23}{165}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{107}{330}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{247}{330}\right)$
$\chi_{64400}(93,\cdot)$	64400.he	12	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{64400}(97,\cdot)$	64400.ub	220	no	$-1$	$1$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{41}{220}\right)$
$\chi_{64400}(99,\cdot)$	64400.mo	44	no	$1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{11}\right)$

Click here to search among the remaining 21088 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	$64400$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{660}\)
Order	$21120$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(27\)	\(29\)	\(31\)	\(33\)
\(\chi_{64400}(1,\cdot)\)	64400.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{64400}(3,\cdot)\)	64400.yn	660	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{41}{660}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{533}{660}\right)\)	\(e\left(\frac{523}{660}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{43}{660}\right)\)
\(\chi_{64400}(9,\cdot)\)	64400.wc	330	no	\(1\)	\(1\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{43}{330}\right)\)
\(\chi_{64400}(11,\cdot)\)	64400.xw	660	yes	\(1\)	\(1\)	\(e\left(\frac{41}{660}\right)\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{593}{660}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{307}{330}\right)\)	\(e\left(\frac{79}{660}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{7}{330}\right)\)	\(e\left(\frac{317}{330}\right)\)
\(\chi_{64400}(13,\cdot)\)	64400.vl	220	yes	\(1\)	\(1\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{57}{220}\right)\)
\(\chi_{64400}(17,\cdot)\)	64400.yf	660	no	\(-1\)	\(1\)	\(e\left(\frac{533}{660}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{307}{330}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{557}{660}\right)\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{487}{660}\right)\)
\(\chi_{64400}(19,\cdot)\)	64400.xs	660	yes	\(-1\)	\(1\)	\(e\left(\frac{523}{660}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{79}{660}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{227}{660}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{301}{330}\right)\)
\(\chi_{64400}(27,\cdot)\)	64400.tz	220	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{43}{220}\right)\)
\(\chi_{64400}(29,\cdot)\)	64400.uo	220	no	\(1\)	\(1\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{83}{110}\right)\)
\(\chi_{64400}(31,\cdot)\)	64400.vx	330	no	\(1\)	\(1\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{7}{330}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{281}{330}\right)\)
\(\chi_{64400}(33,\cdot)\)	64400.yf	660	no	\(-1\)	\(1\)	\(e\left(\frac{43}{660}\right)\)	\(e\left(\frac{43}{330}\right)\)	\(e\left(\frac{317}{330}\right)\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{487}{660}\right)\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{281}{330}\right)\)	\(e\left(\frac{17}{660}\right)\)
\(\chi_{64400}(37,\cdot)\)	64400.yi	660	yes	\(1\)	\(1\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{247}{660}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{571}{660}\right)\)	\(e\left(\frac{551}{660}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{581}{660}\right)\)
\(\chi_{64400}(39,\cdot)\)	64400.wi	330	no	\(-1\)	\(1\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{247}{330}\right)\)	\(e\left(\frac{107}{330}\right)\)
\(\chi_{64400}(41,\cdot)\)	64400.rn	110	no	\(-1\)	\(1\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)
\(\chi_{64400}(43,\cdot)\)	64400.nk	44	no	\(-1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{41}{44}\right)\)
\(\chi_{64400}(47,\cdot)\)	64400.ob	60	no	\(-1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)
\(\chi_{64400}(51,\cdot)\)	64400.sp	132	no	\(1\)	\(1\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{53}{66}\right)\)
\(\chi_{64400}(53,\cdot)\)	64400.wz	660	yes	\(1\)	\(1\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{191}{660}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{173}{660}\right)\)	\(e\left(\frac{223}{660}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{107}{165}\right)\)	\(e\left(\frac{643}{660}\right)\)
\(\chi_{64400}(57,\cdot)\)	64400.mf	44	no	\(1\)	\(1\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)
\(\chi_{64400}(59,\cdot)\)	64400.xk	660	yes	\(1\)	\(1\)	\(e\left(\frac{329}{660}\right)\)	\(e\left(\frac{329}{330}\right)\)	\(e\left(\frac{227}{660}\right)\)	\(e\left(\frac{101}{220}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{151}{660}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{139}{165}\right)\)
\(\chi_{64400}(61,\cdot)\)	64400.xq	660	yes	\(1\)	\(1\)	\(e\left(\frac{31}{660}\right)\)	\(e\left(\frac{31}{330}\right)\)	\(e\left(\frac{553}{660}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{269}{660}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{287}{330}\right)\)	\(e\left(\frac{146}{165}\right)\)
\(\chi_{64400}(67,\cdot)\)	64400.yp	660	yes	\(-1\)	\(1\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{419}{660}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{167}{660}\right)\)	\(e\left(\frac{427}{660}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{37}{660}\right)\)
\(\chi_{64400}(71,\cdot)\)	64400.rr	110	no	\(-1\)	\(1\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{64400}(73,\cdot)\)	64400.yh	660	no	\(1\)	\(1\)	\(e\left(\frac{281}{660}\right)\)	\(e\left(\frac{281}{330}\right)\)	\(e\left(\frac{199}{330}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{389}{660}\right)\)	\(e\left(\frac{317}{330}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{217}{330}\right)\)	\(e\left(\frac{19}{660}\right)\)
\(\chi_{64400}(79,\cdot)\)	64400.vq	330	no	\(1\)	\(1\)	\(e\left(\frac{118}{165}\right)\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{62}{165}\right)\)
\(\chi_{64400}(81,\cdot)\)	64400.ts	165	no	\(1\)	\(1\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{43}{165}\right)\)
\(\chi_{64400}(83,\cdot)\)	64400.ua	220	yes	\(1\)	\(1\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{179}{220}\right)\)
\(\chi_{64400}(87,\cdot)\)	64400.xe	660	no	\(-1\)	\(1\)	\(e\left(\frac{29}{660}\right)\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{551}{660}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{541}{660}\right)\)
\(\chi_{64400}(89,\cdot)\)	64400.wg	330	no	\(1\)	\(1\)	\(e\left(\frac{23}{330}\right)\)	\(e\left(\frac{23}{165}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{107}{330}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{247}{330}\right)\)
\(\chi_{64400}(93,\cdot)\)	64400.he	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{64400}(97,\cdot)\)	64400.ub	220	no	\(-1\)	\(1\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{41}{220}\right)\)
\(\chi_{64400}(99,\cdot)\)	64400.mo	44	no	\(1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 21120 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.