LMFDB - Group of Dirichlet characters of modulus 27200

Show commands: PariGP / SageMath

sage: H = DirichletGroup(27200)

pari: g = idealstar(,27200,2)

Character group

sage: G.order() pari: g.no
Order	=	10240
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{16}\times C_{80}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{27200}(5951,\cdot)$, $\chi_{27200}(15301,\cdot)$, $\chi_{27200}(2177,\cdot)$, $\chi_{27200}(1601,\cdot)$

First 32 of 10240 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{27200}(1,\cdot)$	27200.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{27200}(3,\cdot)$	27200.yh	80	yes	$-1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{23}{40}\right)$
$\chi_{27200}(7,\cdot)$	27200.nl	16	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{27200}(9,\cdot)$	27200.tl	40	no	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{27200}(11,\cdot)$	27200.wk	80	yes	$1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{29}{40}\right)$
$\chi_{27200}(13,\cdot)$	27200.xm	80	yes	$-1$	$1$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{37}{80}\right)$
$\chi_{27200}(19,\cdot)$	27200.bbd	80	yes	$-1$	$1$	$e\left(\frac{79}{80}\right)$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{79}{80}\right)$
$\chi_{27200}(21,\cdot)$	27200.yt	80	yes	$1$	$1$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{71}{80}\right)$
$\chi_{27200}(23,\cdot)$	27200.yc	80	no	$-1$	$1$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{73}{80}\right)$
$\chi_{27200}(27,\cdot)$	27200.yh	80	yes	$-1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{29}{40}\right)$
$\chi_{27200}(29,\cdot)$	27200.za	80	yes	$-1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{13}{40}\right)$
$\chi_{27200}(31,\cdot)$	27200.yv	80	no	$1$	$1$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{49}{80}\right)$
$\chi_{27200}(33,\cdot)$	27200.ph	20	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{27200}(37,\cdot)$	27200.bbo	80	yes	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{27200}(39,\cdot)$	27200.ww	80	no	$1$	$1$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{3}{80}\right)$
$\chi_{27200}(41,\cdot)$	27200.yn	80	no	$-1$	$1$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{77}{80}\right)$
$\chi_{27200}(43,\cdot)$	27200.mw	16	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{27200}(47,\cdot)$	27200.pw	20	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{27200}(49,\cdot)$	27200.fm	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$-i$	$1$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{27200}(53,\cdot)$	27200.uu	80	yes	$-1$	$1$	$e\left(\frac{21}{80}\right)$	$-1$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{41}{80}\right)$
$\chi_{27200}(57,\cdot)$	27200.nj	16	no	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{27200}(59,\cdot)$	27200.uq	80	yes	$-1$	$1$	$e\left(\frac{17}{80}\right)$	$-1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{17}{80}\right)$
$\chi_{27200}(61,\cdot)$	27200.bau	80	yes	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{27200}(63,\cdot)$	27200.baj	80	no	$-1$	$1$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{37}{80}\right)$
$\chi_{27200}(67,\cdot)$	27200.ze	80	yes	$1$	$1$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{69}{80}\right)$
$\chi_{27200}(69,\cdot)$	27200.zc	80	no	$1$	$1$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{39}{80}\right)$
$\chi_{27200}(71,\cdot)$	27200.ym	80	no	$1$	$1$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{71}{80}\right)$
$\chi_{27200}(73,\cdot)$	27200.baa	80	no	$1$	$1$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{23}{80}\right)$
$\chi_{27200}(77,\cdot)$	27200.bbf	80	yes	$-1$	$1$	$e\left(\frac{23}{80}\right)$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{3}{80}\right)$
$\chi_{27200}(79,\cdot)$	27200.vf	80	no	$1$	$1$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{51}{80}\right)$
$\chi_{27200}(81,\cdot)$	27200.qn	20	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{27200}(83,\cdot)$	27200.zn	80	yes	$1$	$1$	$e\left(\frac{19}{80}\right)$	$-i$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{79}{80}\right)$

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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 $\F_{q}$

Modulus	$27200$
Structure	\(C_{2}\times C_{4}\times C_{16}\times C_{80}\)
Order	$10240$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{27200}(1,\cdot)\)	27200.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{27200}(3,\cdot)\)	27200.yh	80	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)
\(\chi_{27200}(7,\cdot)\)	27200.nl	16	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{27200}(9,\cdot)\)	27200.tl	40	no	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{27200}(11,\cdot)\)	27200.wk	80	yes	\(1\)	\(1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)
\(\chi_{27200}(13,\cdot)\)	27200.xm	80	yes	\(-1\)	\(1\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)
\(\chi_{27200}(19,\cdot)\)	27200.bbd	80	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{80}\right)\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)
\(\chi_{27200}(21,\cdot)\)	27200.yt	80	yes	\(1\)	\(1\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)
\(\chi_{27200}(23,\cdot)\)	27200.yc	80	no	\(-1\)	\(1\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)
\(\chi_{27200}(27,\cdot)\)	27200.yh	80	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)
\(\chi_{27200}(29,\cdot)\)	27200.za	80	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)
\(\chi_{27200}(31,\cdot)\)	27200.yv	80	no	\(1\)	\(1\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)
\(\chi_{27200}(33,\cdot)\)	27200.ph	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{27200}(37,\cdot)\)	27200.bbo	80	yes	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{27200}(39,\cdot)\)	27200.ww	80	no	\(1\)	\(1\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)
\(\chi_{27200}(41,\cdot)\)	27200.yn	80	no	\(-1\)	\(1\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)
\(\chi_{27200}(43,\cdot)\)	27200.mw	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{27200}(47,\cdot)\)	27200.pw	20	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{27200}(49,\cdot)\)	27200.fm	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(1\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{27200}(53,\cdot)\)	27200.uu	80	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{80}\right)\)	\(-1\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)
\(\chi_{27200}(57,\cdot)\)	27200.nj	16	no	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{27200}(59,\cdot)\)	27200.uq	80	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{80}\right)\)	\(-1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)
\(\chi_{27200}(61,\cdot)\)	27200.bau	80	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{27200}(63,\cdot)\)	27200.baj	80	no	\(-1\)	\(1\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)
\(\chi_{27200}(67,\cdot)\)	27200.ze	80	yes	\(1\)	\(1\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)
\(\chi_{27200}(69,\cdot)\)	27200.zc	80	no	\(1\)	\(1\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)
\(\chi_{27200}(71,\cdot)\)	27200.ym	80	no	\(1\)	\(1\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)
\(\chi_{27200}(73,\cdot)\)	27200.baa	80	no	\(1\)	\(1\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)
\(\chi_{27200}(77,\cdot)\)	27200.bbf	80	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{80}\right)\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)
\(\chi_{27200}(79,\cdot)\)	27200.vf	80	no	\(1\)	\(1\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)
\(\chi_{27200}(81,\cdot)\)	27200.qn	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{27200}(83,\cdot)\)	27200.zn	80	yes	\(1\)	\(1\)	\(e\left(\frac{19}{80}\right)\)	\(-i\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)

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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.