LMFDB - Group of Dirichlet characters of modulus 2420

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(2420)

gp:g = idealstar(,2420,2)

magma:G = FullDirichletGroup(2420);

Character group

Order	=	880	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{220}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{2420}(1211,\cdot)$, $\chi_{2420}(1937,\cdot)$, $\chi_{2420}(2301,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

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	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{2420}(1,\cdot)$	2420.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2420}(3,\cdot)$	2420.w	20	no	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$-i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{2420}(7,\cdot)$	2420.bt	220	yes	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{2420}(9,\cdot)$	2420.t	10	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{2420}(13,\cdot)$	2420.bv	220	no	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{6}{55}\right)$
$\chi_{2420}(17,\cdot)$	2420.bv	220	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{2420}(19,\cdot)$	2420.bm	110	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{91}{110}\right)$
$\chi_{2420}(21,\cdot)$	2420.bf	22	no	$-1$	$1$	$1$	$e\left(\frac{1}{22}\right)$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$	$1$	$e\left(\frac{15}{22}\right)$
$\chi_{2420}(23,\cdot)$	2420.bg	44	yes	$1$	$1$	$-i$	$e\left(\frac{31}{44}\right)$	$-1$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{13}{44}\right)$	$i$	$e\left(\frac{7}{22}\right)$
$\chi_{2420}(27,\cdot)$	2420.w	20	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$i$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{2420}(29,\cdot)$	2420.br	110	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{69}{110}\right)$
$\chi_{2420}(31,\cdot)$	2420.bp	110	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{2420}(37,\cdot)$	2420.bs	220	no	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{109}{110}\right)$
$\chi_{2420}(39,\cdot)$	2420.bm	110	yes	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{23}{110}\right)$
$\chi_{2420}(41,\cdot)$	2420.bl	110	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{61}{110}\right)$
$\chi_{2420}(43,\cdot)$	2420.bj	44	yes	$-1$	$1$	$-i$	$e\left(\frac{37}{44}\right)$	$-1$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{29}{44}\right)$	$i$	$e\left(\frac{4}{11}\right)$
$\chi_{2420}(47,\cdot)$	2420.bu	220	yes	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{71}{110}\right)$
$\chi_{2420}(49,\cdot)$	2420.bo	110	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{2420}(51,\cdot)$	2420.bq	110	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{110}\right)$
$\chi_{2420}(53,\cdot)$	2420.bs	220	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{97}{110}\right)$
$\chi_{2420}(57,\cdot)$	2420.bv	220	no	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{51}{55}\right)$
$\chi_{2420}(59,\cdot)$	2420.bn	110	yes	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{52}{55}\right)$
$\chi_{2420}(61,\cdot)$	2420.bl	110	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{93}{110}\right)$
$\chi_{2420}(63,\cdot)$	2420.bt	220	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{2420}(67,\cdot)$	2420.bg	44	yes	$1$	$1$	$i$	$e\left(\frac{5}{44}\right)$	$-1$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{39}{44}\right)$	$-i$	$e\left(\frac{21}{22}\right)$
$\chi_{2420}(69,\cdot)$	2420.bo	110	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{55}\right)$
$\chi_{2420}(71,\cdot)$	2420.bp	110	no	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{55}\right)$
$\chi_{2420}(73,\cdot)$	2420.bv	220	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{12}{55}\right)$
$\chi_{2420}(79,\cdot)$	2420.bm	110	yes	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{37}{110}\right)$
$\chi_{2420}(81,\cdot)$	2420.m	5	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{2420}(83,\cdot)$	2420.bt	220	yes	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{54}{55}\right)$
$\chi_{2420}(87,\cdot)$	2420.bj	44	yes	$-1$	$1$	$i$	$e\left(\frac{19}{44}\right)$	$-1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{3}{44}\right)$	$-i$	$e\left(\frac{8}{11}\right)$

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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	$2420$
Structure	\(C_{2}\times C_{2}\times C_{220}\)
Order	$880$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{2420}(1,\cdot)\)	2420.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2420}(3,\cdot)\)	2420.w	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{2420}(7,\cdot)\)	2420.bt	220	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{32}{55}\right)\)
\(\chi_{2420}(9,\cdot)\)	2420.t	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{2420}(13,\cdot)\)	2420.bv	220	no	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{6}{55}\right)\)
\(\chi_{2420}(17,\cdot)\)	2420.bv	220	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{2420}(19,\cdot)\)	2420.bm	110	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{91}{110}\right)\)
\(\chi_{2420}(21,\cdot)\)	2420.bf	22	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(1\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{2420}(23,\cdot)\)	2420.bg	44	yes	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{31}{44}\right)\)	\(-1\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(i\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{2420}(27,\cdot)\)	2420.w	20	no	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(i\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{2420}(29,\cdot)\)	2420.br	110	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{69}{110}\right)\)
\(\chi_{2420}(31,\cdot)\)	2420.bp	110	no	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{2420}(37,\cdot)\)	2420.bs	220	no	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{109}{110}\right)\)
\(\chi_{2420}(39,\cdot)\)	2420.bm	110	yes	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{23}{110}\right)\)
\(\chi_{2420}(41,\cdot)\)	2420.bl	110	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{61}{110}\right)\)
\(\chi_{2420}(43,\cdot)\)	2420.bj	44	yes	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{37}{44}\right)\)	\(-1\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(i\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{2420}(47,\cdot)\)	2420.bu	220	yes	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{71}{110}\right)\)
\(\chi_{2420}(49,\cdot)\)	2420.bo	110	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{55}\right)\)
\(\chi_{2420}(51,\cdot)\)	2420.bq	110	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{110}\right)\)
\(\chi_{2420}(53,\cdot)\)	2420.bs	220	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{97}{110}\right)\)
\(\chi_{2420}(57,\cdot)\)	2420.bv	220	no	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{51}{55}\right)\)
\(\chi_{2420}(59,\cdot)\)	2420.bn	110	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{52}{55}\right)\)
\(\chi_{2420}(61,\cdot)\)	2420.bl	110	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{93}{110}\right)\)
\(\chi_{2420}(63,\cdot)\)	2420.bt	220	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{2420}(67,\cdot)\)	2420.bg	44	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{5}{44}\right)\)	\(-1\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(-i\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{2420}(69,\cdot)\)	2420.bo	110	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{55}\right)\)
\(\chi_{2420}(71,\cdot)\)	2420.bp	110	no	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{29}{55}\right)\)
\(\chi_{2420}(73,\cdot)\)	2420.bv	220	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{12}{55}\right)\)
\(\chi_{2420}(79,\cdot)\)	2420.bm	110	yes	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{37}{110}\right)\)
\(\chi_{2420}(81,\cdot)\)	2420.m	5	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{2420}(83,\cdot)\)	2420.bt	220	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{54}{55}\right)\)
\(\chi_{2420}(87,\cdot)\)	2420.bj	44	yes	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{19}{44}\right)\)	\(-1\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(-i\)	\(e\left(\frac{8}{11}\right)\)

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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.