LMFDB - Group of Dirichlet characters of modulus 20800

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(20800)

gp:g = idealstar(,20800,2)

magma:G = FullDirichletGroup(20800);

Character group

Order	=	7680	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{4}\times C_{4}\times C_{240}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{20800}(12351,\cdot)$, $\chi_{20800}(16901,\cdot)$, $\chi_{20800}(14977,\cdot)$, $\chi_{20800}(1601,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 7680 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	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{20800}(1,\cdot)$	20800.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{20800}(3,\cdot)$	20800.uq	240	yes	$1$	$1$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{23}{240}\right)$
$\chi_{20800}(7,\cdot)$	20800.ln	24	no	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{20800}(9,\cdot)$	20800.tg	120	no	$1$	$1$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{23}{120}\right)$
$\chi_{20800}(11,\cdot)$	20800.uh	240	yes	$1$	$1$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{89}{240}\right)$
$\chi_{20800}(17,\cdot)$	20800.rb	60	no	$-1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{60}\right)$
$\chi_{20800}(19,\cdot)$	20800.uk	240	yes	$1$	$1$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{67}{240}\right)$
$\chi_{20800}(21,\cdot)$	20800.rz	80	yes	$-1$	$1$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{11}{80}\right)$
$\chi_{20800}(23,\cdot)$	20800.to	120	no	$1$	$1$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{7}{120}\right)$
$\chi_{20800}(27,\cdot)$	20800.rh	80	no	$1$	$1$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{23}{80}\right)$
$\chi_{20800}(29,\cdot)$	20800.uo	240	yes	$1$	$1$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{23}{240}\right)$
$\chi_{20800}(31,\cdot)$	20800.iz	20	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{20800}(33,\cdot)$	20800.qr	60	no	$1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{20800}(37,\cdot)$	20800.tw	240	yes	$1$	$1$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{101}{240}\right)$
$\chi_{20800}(41,\cdot)$	20800.st	120	no	$-1$	$1$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{43}{120}\right)$
$\chi_{20800}(43,\cdot)$	20800.ov	48	no	$1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{48}\right)$
$\chi_{20800}(47,\cdot)$	20800.kt	20	no	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{20800}(49,\cdot)$	20800.gw	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{1}{12}\right)$
$\chi_{20800}(51,\cdot)$	20800.hw	16	no	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{20800}(53,\cdot)$	20800.sk	80	no	$-1$	$1$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{11}{80}\right)$
$\chi_{20800}(57,\cdot)$	20800.ed	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$-i$	$i$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{20800}(59,\cdot)$	20800.uk	240	yes	$1$	$1$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{103}{240}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{181}{240}\right)$
$\chi_{20800}(61,\cdot)$	20800.un	240	yes	$1$	$1$	$e\left(\frac{199}{240}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{97}{240}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{11}{240}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{79}{240}\right)$
$\chi_{20800}(63,\cdot)$	20800.pr	60	no	$-1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{20800}(67,\cdot)$	20800.us	240	yes	$-1$	$1$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{167}{240}\right)$
$\chi_{20800}(69,\cdot)$	20800.ub	240	yes	$1$	$1$	$e\left(\frac{37}{240}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{211}{240}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{37}{240}\right)$
$\chi_{20800}(71,\cdot)$	20800.ss	120	no	$1$	$1$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{89}{120}\right)$
$\chi_{20800}(73,\cdot)$	20800.nd	40	no	$1$	$1$	$e\left(\frac{39}{40}\right)$	$i$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{9}{40}\right)$
$\chi_{20800}(77,\cdot)$	20800.se	80	yes	$-1$	$1$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{33}{80}\right)$
$\chi_{20800}(79,\cdot)$	20800.jk	20	no	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{20800}(81,\cdot)$	20800.qs	60	no	$1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{23}{60}\right)$
$\chi_{20800}(83,\cdot)$	20800.sg	80	yes	$-1$	$1$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{9}{80}\right)$

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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	$20800$
Structure	\(C_{2}\times C_{4}\times C_{4}\times C_{240}\)
Order	$7680$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{20800}(1,\cdot)\)	20800.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{20800}(3,\cdot)\)	20800.uq	240	yes	\(1\)	\(1\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{23}{240}\right)\)
\(\chi_{20800}(7,\cdot)\)	20800.ln	24	no	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{20800}(9,\cdot)\)	20800.tg	120	no	\(1\)	\(1\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{23}{120}\right)\)
\(\chi_{20800}(11,\cdot)\)	20800.uh	240	yes	\(1\)	\(1\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{89}{240}\right)\)
\(\chi_{20800}(17,\cdot)\)	20800.rb	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{60}\right)\)
\(\chi_{20800}(19,\cdot)\)	20800.uk	240	yes	\(1\)	\(1\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{67}{240}\right)\)
\(\chi_{20800}(21,\cdot)\)	20800.rz	80	yes	\(-1\)	\(1\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)
\(\chi_{20800}(23,\cdot)\)	20800.to	120	no	\(1\)	\(1\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{7}{120}\right)\)
\(\chi_{20800}(27,\cdot)\)	20800.rh	80	no	\(1\)	\(1\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)
\(\chi_{20800}(29,\cdot)\)	20800.uo	240	yes	\(1\)	\(1\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{23}{240}\right)\)
\(\chi_{20800}(31,\cdot)\)	20800.iz	20	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{20800}(33,\cdot)\)	20800.qr	60	no	\(1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{20800}(37,\cdot)\)	20800.tw	240	yes	\(1\)	\(1\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{101}{240}\right)\)
\(\chi_{20800}(41,\cdot)\)	20800.st	120	no	\(-1\)	\(1\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{43}{120}\right)\)
\(\chi_{20800}(43,\cdot)\)	20800.ov	48	no	\(1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{48}\right)\)
\(\chi_{20800}(47,\cdot)\)	20800.kt	20	no	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{20800}(49,\cdot)\)	20800.gw	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{20800}(51,\cdot)\)	20800.hw	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{20800}(53,\cdot)\)	20800.sk	80	no	\(-1\)	\(1\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)
\(\chi_{20800}(57,\cdot)\)	20800.ed	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{20800}(59,\cdot)\)	20800.uk	240	yes	\(1\)	\(1\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{103}{240}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{181}{240}\right)\)
\(\chi_{20800}(61,\cdot)\)	20800.un	240	yes	\(1\)	\(1\)	\(e\left(\frac{199}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{11}{240}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{79}{240}\right)\)
\(\chi_{20800}(63,\cdot)\)	20800.pr	60	no	\(-1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{20800}(67,\cdot)\)	20800.us	240	yes	\(-1\)	\(1\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{167}{240}\right)\)
\(\chi_{20800}(69,\cdot)\)	20800.ub	240	yes	\(1\)	\(1\)	\(e\left(\frac{37}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{211}{240}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{113}{240}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{37}{240}\right)\)
\(\chi_{20800}(71,\cdot)\)	20800.ss	120	no	\(1\)	\(1\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{89}{120}\right)\)
\(\chi_{20800}(73,\cdot)\)	20800.nd	40	no	\(1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(i\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)
\(\chi_{20800}(77,\cdot)\)	20800.se	80	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{33}{80}\right)\)
\(\chi_{20800}(79,\cdot)\)	20800.jk	20	no	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{20800}(81,\cdot)\)	20800.qs	60	no	\(1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{23}{60}\right)\)
\(\chi_{20800}(83,\cdot)\)	20800.sg	80	yes	\(-1\)	\(1\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)

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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.