LMFDB - Group of Dirichlet characters of modulus 4224

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4224)

pari: g = idealstar(,4224,2)

Character group

sage: G.order() pari: g.no
Order	=	1280
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{160}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4224}(2047,\cdot)$, $\chi_{4224}(133,\cdot)$, $\chi_{4224}(1409,\cdot)$, $\chi_{4224}(3841,\cdot)$

First 32 of 1280 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	$-1$	$1$	$5$	$7$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{4224}(1,\cdot)$	4224.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4224}(5,\cdot)$	4224.dp	160	yes	$-1$	$1$	$e\left(\frac{21}{160}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{139}{160}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{147}{160}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{23}{160}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{39}{160}\right)$
$\chi_{4224}(7,\cdot)$	4224.dc	80	no	$1$	$1$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{51}{80}\right)$
$\chi_{4224}(13,\cdot)$	4224.dq	160	no	$-1$	$1$	$e\left(\frac{139}{160}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{21}{160}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{13}{160}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{57}{160}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{41}{160}\right)$
$\chi_{4224}(17,\cdot)$	4224.cy	40	no	$1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{33}{40}\right)$	$-i$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{40}\right)$
$\chi_{4224}(19,\cdot)$	4224.do	160	no	$1$	$1$	$e\left(\frac{147}{160}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{13}{160}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{149}{160}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{81}{160}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{113}{160}\right)$
$\chi_{4224}(23,\cdot)$	4224.ca	16	no	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$1$	$e\left(\frac{13}{16}\right)$
$\chi_{4224}(25,\cdot)$	4224.di	80	no	$1$	$1$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{80}\right)$
$\chi_{4224}(29,\cdot)$	4224.dm	160	yes	$1$	$1$	$e\left(\frac{23}{160}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{57}{160}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{81}{160}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{29}{160}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{77}{160}\right)$
$\chi_{4224}(31,\cdot)$	4224.cf	20	no	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{4224}(35,\cdot)$	4224.dk	160	yes	$-1$	$1$	$e\left(\frac{39}{160}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{41}{160}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{113}{160}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{77}{160}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{141}{160}\right)$
$\chi_{4224}(37,\cdot)$	4224.dl	160	no	$1$	$1$	$e\left(\frac{93}{160}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{147}{160}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{91}{160}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{79}{160}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{127}{160}\right)$
$\chi_{4224}(41,\cdot)$	4224.dj	80	no	$1$	$1$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{80}\right)$
$\chi_{4224}(43,\cdot)$	4224.ct	32	no	$1$	$1$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{31}{32}\right)$	$-i$	$e\left(\frac{31}{32}\right)$
$\chi_{4224}(47,\cdot)$	4224.cx	40	no	$1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{21}{40}\right)$	$i$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{37}{40}\right)$
$\chi_{4224}(49,\cdot)$	4224.cz	40	no	$1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{40}\right)$	$-i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{40}\right)$
$\chi_{4224}(53,\cdot)$	4224.dp	160	yes	$-1$	$1$	$e\left(\frac{9}{160}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{151}{160}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{63}{160}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{147}{160}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{131}{160}\right)$
$\chi_{4224}(59,\cdot)$	4224.dr	160	yes	$1$	$1$	$e\left(\frac{133}{160}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{27}{160}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{51}{160}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{39}{160}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{160}\right)$
$\chi_{4224}(61,\cdot)$	4224.dq	160	no	$-1$	$1$	$e\left(\frac{31}{160}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{129}{160}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{57}{160}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{53}{160}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{69}{160}\right)$
$\chi_{4224}(65,\cdot)$	4224.m	2	no	$1$	$1$	$1$	$-1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$-1$
$\chi_{4224}(67,\cdot)$	4224.cm	32	no	$-1$	$1$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{32}\right)$	$i$	$e\left(\frac{1}{32}\right)$
$\chi_{4224}(71,\cdot)$	4224.dd	80	no	$1$	$1$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{27}{80}\right)$
$\chi_{4224}(73,\cdot)$	4224.dh	80	no	$-1$	$1$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{21}{80}\right)$
$\chi_{4224}(79,\cdot)$	4224.cw	40	no	$1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{40}\right)$	$i$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{40}\right)$
$\chi_{4224}(83,\cdot)$	4224.dk	160	yes	$-1$	$1$	$e\left(\frac{51}{160}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{29}{160}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{37}{160}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{113}{160}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{49}{160}\right)$
$\chi_{4224}(85,\cdot)$	4224.dq	160	no	$-1$	$1$	$e\left(\frac{17}{160}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{143}{160}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{119}{160}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{91}{160}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{43}{160}\right)$
$\chi_{4224}(89,\cdot)$	4224.bx	16	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{16}\right)$	$-1$	$e\left(\frac{11}{16}\right)$
$\chi_{4224}(91,\cdot)$	4224.dn	160	no	$-1$	$1$	$e\left(\frac{157}{160}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{83}{160}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{139}{160}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{111}{160}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{143}{160}\right)$
$\chi_{4224}(95,\cdot)$	4224.cj	20	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{20}\right)$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{4224}(97,\cdot)$	4224.ci	20	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{20}\right)$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{4224}(101,\cdot)$	4224.dm	160	yes	$1$	$1$	$e\left(\frac{29}{160}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{51}{160}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{123}{160}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{127}{160}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{111}{160}\right)$
$\chi_{4224}(103,\cdot)$	4224.df	80	no	$-1$	$1$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{31}{80}\right)$

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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	$4224$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{160}\)
Order	$1280$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{4224}(1,\cdot)\)	4224.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4224}(5,\cdot)\)	4224.dp	160	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{160}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{139}{160}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{147}{160}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{23}{160}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{39}{160}\right)\)
\(\chi_{4224}(7,\cdot)\)	4224.dc	80	no	\(1\)	\(1\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{51}{80}\right)\)
\(\chi_{4224}(13,\cdot)\)	4224.dq	160	no	\(-1\)	\(1\)	\(e\left(\frac{139}{160}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{21}{160}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{13}{160}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{57}{160}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{41}{160}\right)\)
\(\chi_{4224}(17,\cdot)\)	4224.cy	40	no	\(1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(-i\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{40}\right)\)
\(\chi_{4224}(19,\cdot)\)	4224.do	160	no	\(1\)	\(1\)	\(e\left(\frac{147}{160}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{13}{160}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{149}{160}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{81}{160}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{113}{160}\right)\)
\(\chi_{4224}(23,\cdot)\)	4224.ca	16	no	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(1\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{4224}(25,\cdot)\)	4224.di	80	no	\(1\)	\(1\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{80}\right)\)
\(\chi_{4224}(29,\cdot)\)	4224.dm	160	yes	\(1\)	\(1\)	\(e\left(\frac{23}{160}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{57}{160}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{81}{160}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{29}{160}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{77}{160}\right)\)
\(\chi_{4224}(31,\cdot)\)	4224.cf	20	no	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{4224}(35,\cdot)\)	4224.dk	160	yes	\(-1\)	\(1\)	\(e\left(\frac{39}{160}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{41}{160}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{113}{160}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{77}{160}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{141}{160}\right)\)
\(\chi_{4224}(37,\cdot)\)	4224.dl	160	no	\(1\)	\(1\)	\(e\left(\frac{93}{160}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{147}{160}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{91}{160}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{79}{160}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{127}{160}\right)\)
\(\chi_{4224}(41,\cdot)\)	4224.dj	80	no	\(1\)	\(1\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{80}\right)\)
\(\chi_{4224}(43,\cdot)\)	4224.ct	32	no	\(1\)	\(1\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(-i\)	\(e\left(\frac{31}{32}\right)\)
\(\chi_{4224}(47,\cdot)\)	4224.cx	40	no	\(1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(i\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{37}{40}\right)\)
\(\chi_{4224}(49,\cdot)\)	4224.cz	40	no	\(1\)	\(1\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(-i\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{40}\right)\)
\(\chi_{4224}(53,\cdot)\)	4224.dp	160	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{160}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{151}{160}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{63}{160}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{147}{160}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{131}{160}\right)\)
\(\chi_{4224}(59,\cdot)\)	4224.dr	160	yes	\(1\)	\(1\)	\(e\left(\frac{133}{160}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{27}{160}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{51}{160}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{39}{160}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{160}\right)\)
\(\chi_{4224}(61,\cdot)\)	4224.dq	160	no	\(-1\)	\(1\)	\(e\left(\frac{31}{160}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{129}{160}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{57}{160}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{53}{160}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{69}{160}\right)\)
\(\chi_{4224}(65,\cdot)\)	4224.m	2	no	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)
\(\chi_{4224}(67,\cdot)\)	4224.cm	32	no	\(-1\)	\(1\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(i\)	\(e\left(\frac{1}{32}\right)\)
\(\chi_{4224}(71,\cdot)\)	4224.dd	80	no	\(1\)	\(1\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{27}{80}\right)\)
\(\chi_{4224}(73,\cdot)\)	4224.dh	80	no	\(-1\)	\(1\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{21}{80}\right)\)
\(\chi_{4224}(79,\cdot)\)	4224.cw	40	no	\(1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(i\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{40}\right)\)
\(\chi_{4224}(83,\cdot)\)	4224.dk	160	yes	\(-1\)	\(1\)	\(e\left(\frac{51}{160}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{29}{160}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{37}{160}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{113}{160}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{49}{160}\right)\)
\(\chi_{4224}(85,\cdot)\)	4224.dq	160	no	\(-1\)	\(1\)	\(e\left(\frac{17}{160}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{143}{160}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{119}{160}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{91}{160}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{43}{160}\right)\)
\(\chi_{4224}(89,\cdot)\)	4224.bx	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{4224}(91,\cdot)\)	4224.dn	160	no	\(-1\)	\(1\)	\(e\left(\frac{157}{160}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{83}{160}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{139}{160}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{111}{160}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{143}{160}\right)\)
\(\chi_{4224}(95,\cdot)\)	4224.cj	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{4224}(97,\cdot)\)	4224.ci	20	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{4224}(101,\cdot)\)	4224.dm	160	yes	\(1\)	\(1\)	\(e\left(\frac{29}{160}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{51}{160}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{123}{160}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{127}{160}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{111}{160}\right)\)
\(\chi_{4224}(103,\cdot)\)	4224.df	80	no	\(-1\)	\(1\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{31}{80}\right)\)

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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.