LMFDB - Group of Dirichlet characters of modulus 881

sage:H = DirichletGroup(881)

pari:g = idealstar(,881,2)

Character group

sage:G.order() pari:g.no
Order	=	880
sage:H.invariants() pari:g.cyc
Structure	=	$C_{880}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{881}(3,\cdot)$

First 32 of 880 characters

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

Character	Orbit	Order	Primitive	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{881}(1,\cdot)$	881.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{881}(2,\cdot)$	881.m	55	yes	$1$	$1$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{881}(3,\cdot)$	881.t	880	yes	$-1$	$1$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{1}{880}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{31}{440}\right)$	$e\left(\frac{417}{880}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{1}{440}\right)$	$e\left(\frac{239}{440}\right)$	$e\left(\frac{237}{440}\right)$
$\chi_{881}(4,\cdot)$	881.m	55	yes	$1$	$1$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{881}(5,\cdot)$	881.s	440	yes	$1$	$1$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{31}{440}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{167}{440}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{87}{220}\right)$
$\chi_{881}(6,\cdot)$	881.t	880	yes	$-1$	$1$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{417}{880}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{167}{440}\right)$	$e\left(\frac{529}{880}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{417}{440}\right)$	$e\left(\frac{223}{440}\right)$	$e\left(\frac{269}{440}\right)$
$\chi_{881}(7,\cdot)$	881.n	80	yes	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{17}{40}\right)$
$\chi_{881}(8,\cdot)$	881.m	55	yes	$1$	$1$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{12}{55}\right)$
$\chi_{881}(9,\cdot)$	881.s	440	yes	$1$	$1$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{1}{440}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{417}{440}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{17}{220}\right)$
$\chi_{881}(10,\cdot)$	881.s	440	yes	$1$	$1$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{239}{440}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{223}{440}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{103}{220}\right)$
$\chi_{881}(11,\cdot)$	881.s	440	yes	$1$	$1$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{237}{440}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{269}{440}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{69}{220}\right)$
$\chi_{881}(12,\cdot)$	881.t	880	yes	$-1$	$1$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{833}{880}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{303}{440}\right)$	$e\left(\frac{641}{880}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{393}{440}\right)$	$e\left(\frac{207}{440}\right)$	$e\left(\frac{301}{440}\right)$
$\chi_{881}(13,\cdot)$	881.s	440	yes	$1$	$1$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{83}{440}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{291}{440}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{91}{220}\right)$
$\chi_{881}(14,\cdot)$	881.t	880	yes	$-1$	$1$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{207}{880}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{257}{440}\right)$	$e\left(\frac{79}{880}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{207}{440}\right)$	$e\left(\frac{193}{440}\right)$	$e\left(\frac{219}{440}\right)$
$\chi_{881}(15,\cdot)$	881.t	880	yes	$-1$	$1$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{63}{880}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{193}{440}\right)$	$e\left(\frac{751}{880}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{63}{440}\right)$	$e\left(\frac{97}{440}\right)$	$e\left(\frac{411}{440}\right)$
$\chi_{881}(16,\cdot)$	881.m	55	yes	$1$	$1$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{881}(17,\cdot)$	881.t	880	yes	$-1$	$1$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{763}{880}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{333}{440}\right)$	$e\left(\frac{491}{880}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{323}{440}\right)$	$e\left(\frac{197}{440}\right)$	$e\left(\frac{431}{440}\right)$
$\chi_{881}(18,\cdot)$	881.k	40	yes	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{881}(19,\cdot)$	881.s	440	yes	$1$	$1$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{39}{440}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{423}{440}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{3}{220}\right)$
$\chi_{881}(20,\cdot)$	881.s	440	yes	$1$	$1$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{7}{440}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{279}{440}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{119}{220}\right)$
$\chi_{881}(21,\cdot)$	881.m	55	yes	$1$	$1$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{53}{55}\right)$
$\chi_{881}(22,\cdot)$	881.o	88	yes	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{17}{44}\right)$
$\chi_{881}(23,\cdot)$	881.t	880	yes	$-1$	$1$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{617}{880}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{207}{440}\right)$	$e\left(\frac{329}{880}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{177}{440}\right)$	$e\left(\frac{63}{440}\right)$	$e\left(\frac{149}{440}\right)$
$\chi_{881}(24,\cdot)$	881.t	880	yes	$-1$	$1$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{369}{880}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{439}{440}\right)$	$e\left(\frac{753}{880}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{369}{440}\right)$	$e\left(\frac{191}{440}\right)$	$e\left(\frac{333}{440}\right)$
$\chi_{881}(25,\cdot)$	881.r	220	yes	$1$	$1$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{87}{110}\right)$
$\chi_{881}(26,\cdot)$	881.s	440	yes	$1$	$1$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{291}{440}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{347}{440}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{107}{220}\right)$
$\chi_{881}(27,\cdot)$	881.t	880	yes	$-1$	$1$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{3}{880}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{93}{440}\right)$	$e\left(\frac{371}{880}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{3}{440}\right)$	$e\left(\frac{277}{440}\right)$	$e\left(\frac{271}{440}\right)$
$\chi_{881}(28,\cdot)$	881.t	880	yes	$-1$	$1$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{623}{880}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{393}{440}\right)$	$e\left(\frac{191}{880}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{183}{440}\right)$	$e\left(\frac{177}{440}\right)$	$e\left(\frac{251}{440}\right)$
$\chi_{881}(29,\cdot)$	881.q	176	yes	$-1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{87}{176}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{23}{176}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{27}{88}\right)$
$\chi_{881}(30,\cdot)$	881.t	880	yes	$-1$	$1$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{479}{880}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{329}{440}\right)$	$e\left(\frac{863}{880}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{39}{440}\right)$	$e\left(\frac{81}{440}\right)$	$e\left(\frac{3}{440}\right)$
$\chi_{881}(31,\cdot)$	881.t	880	yes	$-1$	$1$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{863}{880}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{353}{440}\right)$	$e\left(\frac{831}{880}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{423}{440}\right)$	$e\left(\frac{337}{440}\right)$	$e\left(\frac{371}{440}\right)$
$\chi_{881}(32,\cdot)$	881.g	11	yes	$1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{4}{11}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$881$
Structure	\(C_{880}\)
Order	$880$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{881}(1,\cdot)\)	881.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{881}(2,\cdot)\)	881.m	55	yes	\(1\)	\(1\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{881}(3,\cdot)\)	881.t	880	yes	\(-1\)	\(1\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{1}{880}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{31}{440}\right)\)	\(e\left(\frac{417}{880}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{1}{440}\right)\)	\(e\left(\frac{239}{440}\right)\)	\(e\left(\frac{237}{440}\right)\)
\(\chi_{881}(4,\cdot)\)	881.m	55	yes	\(1\)	\(1\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{881}(5,\cdot)\)	881.s	440	yes	\(1\)	\(1\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{31}{440}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{167}{440}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{87}{220}\right)\)
\(\chi_{881}(6,\cdot)\)	881.t	880	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{417}{880}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{167}{440}\right)\)	\(e\left(\frac{529}{880}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{417}{440}\right)\)	\(e\left(\frac{223}{440}\right)\)	\(e\left(\frac{269}{440}\right)\)
\(\chi_{881}(7,\cdot)\)	881.n	80	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)
\(\chi_{881}(8,\cdot)\)	881.m	55	yes	\(1\)	\(1\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)
\(\chi_{881}(9,\cdot)\)	881.s	440	yes	\(1\)	\(1\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{1}{440}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{417}{440}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{17}{220}\right)\)
\(\chi_{881}(10,\cdot)\)	881.s	440	yes	\(1\)	\(1\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{239}{440}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{223}{440}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{103}{220}\right)\)
\(\chi_{881}(11,\cdot)\)	881.s	440	yes	\(1\)	\(1\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{237}{440}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{269}{440}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{69}{220}\right)\)
\(\chi_{881}(12,\cdot)\)	881.t	880	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{833}{880}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{303}{440}\right)\)	\(e\left(\frac{641}{880}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{393}{440}\right)\)	\(e\left(\frac{207}{440}\right)\)	\(e\left(\frac{301}{440}\right)\)
\(\chi_{881}(13,\cdot)\)	881.s	440	yes	\(1\)	\(1\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{83}{440}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{291}{440}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{91}{220}\right)\)
\(\chi_{881}(14,\cdot)\)	881.t	880	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{207}{880}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{257}{440}\right)\)	\(e\left(\frac{79}{880}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{207}{440}\right)\)	\(e\left(\frac{193}{440}\right)\)	\(e\left(\frac{219}{440}\right)\)
\(\chi_{881}(15,\cdot)\)	881.t	880	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{63}{880}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{193}{440}\right)\)	\(e\left(\frac{751}{880}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{63}{440}\right)\)	\(e\left(\frac{97}{440}\right)\)	\(e\left(\frac{411}{440}\right)\)
\(\chi_{881}(16,\cdot)\)	881.m	55	yes	\(1\)	\(1\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{881}(17,\cdot)\)	881.t	880	yes	\(-1\)	\(1\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{763}{880}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{333}{440}\right)\)	\(e\left(\frac{491}{880}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{323}{440}\right)\)	\(e\left(\frac{197}{440}\right)\)	\(e\left(\frac{431}{440}\right)\)
\(\chi_{881}(18,\cdot)\)	881.k	40	yes	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{881}(19,\cdot)\)	881.s	440	yes	\(1\)	\(1\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{39}{440}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{423}{440}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{3}{220}\right)\)
\(\chi_{881}(20,\cdot)\)	881.s	440	yes	\(1\)	\(1\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{7}{440}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{279}{440}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{119}{220}\right)\)
\(\chi_{881}(21,\cdot)\)	881.m	55	yes	\(1\)	\(1\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)
\(\chi_{881}(22,\cdot)\)	881.o	88	yes	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)
\(\chi_{881}(23,\cdot)\)	881.t	880	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{617}{880}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{207}{440}\right)\)	\(e\left(\frac{329}{880}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{177}{440}\right)\)	\(e\left(\frac{63}{440}\right)\)	\(e\left(\frac{149}{440}\right)\)
\(\chi_{881}(24,\cdot)\)	881.t	880	yes	\(-1\)	\(1\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{369}{880}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{439}{440}\right)\)	\(e\left(\frac{753}{880}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{369}{440}\right)\)	\(e\left(\frac{191}{440}\right)\)	\(e\left(\frac{333}{440}\right)\)
\(\chi_{881}(25,\cdot)\)	881.r	220	yes	\(1\)	\(1\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)
\(\chi_{881}(26,\cdot)\)	881.s	440	yes	\(1\)	\(1\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{291}{440}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{347}{440}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{107}{220}\right)\)
\(\chi_{881}(27,\cdot)\)	881.t	880	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{3}{880}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{93}{440}\right)\)	\(e\left(\frac{371}{880}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{3}{440}\right)\)	\(e\left(\frac{277}{440}\right)\)	\(e\left(\frac{271}{440}\right)\)
\(\chi_{881}(28,\cdot)\)	881.t	880	yes	\(-1\)	\(1\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{623}{880}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{393}{440}\right)\)	\(e\left(\frac{191}{880}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{183}{440}\right)\)	\(e\left(\frac{177}{440}\right)\)	\(e\left(\frac{251}{440}\right)\)
\(\chi_{881}(29,\cdot)\)	881.q	176	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{87}{176}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{23}{176}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{27}{88}\right)\)
\(\chi_{881}(30,\cdot)\)	881.t	880	yes	\(-1\)	\(1\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{479}{880}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{329}{440}\right)\)	\(e\left(\frac{863}{880}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{39}{440}\right)\)	\(e\left(\frac{81}{440}\right)\)	\(e\left(\frac{3}{440}\right)\)
\(\chi_{881}(31,\cdot)\)	881.t	880	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{863}{880}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{353}{440}\right)\)	\(e\left(\frac{831}{880}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{423}{440}\right)\)	\(e\left(\frac{337}{440}\right)\)	\(e\left(\frac{371}{440}\right)\)
\(\chi_{881}(32,\cdot)\)	881.g	11	yes	\(1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.