LMFDB - Group of Dirichlet characters of modulus 6272

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6272)

pari: g = idealstar(,6272,2)

Character group

sage: G.order() pari: g.no
Order	=	2688
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{672}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6272}(4607,\cdot)$, $\chi_{6272}(3333,\cdot)$, $\chi_{6272}(4609,\cdot)$

First 32 of 2688 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{6272}(1,\cdot)$	6272.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6272}(3,\cdot)$	6272.dr	672	yes	$1$	$1$	$e\left(\frac{541}{672}\right)$	$e\left(\frac{527}{672}\right)$	$e\left(\frac{205}{336}\right)$	$e\left(\frac{283}{672}\right)$	$e\left(\frac{43}{224}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{241}{336}\right)$	$e\left(\frac{191}{336}\right)$
$\chi_{6272}(5,\cdot)$	6272.dp	672	yes	$-1$	$1$	$e\left(\frac{527}{672}\right)$	$e\left(\frac{37}{672}\right)$	$e\left(\frac{191}{336}\right)$	$e\left(\frac{185}{672}\right)$	$e\left(\frac{57}{224}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{227}{336}\right)$	$e\left(\frac{37}{336}\right)$
$\chi_{6272}(9,\cdot)$	6272.dm	336	no	$1$	$1$	$e\left(\frac{205}{336}\right)$	$e\left(\frac{191}{336}\right)$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{283}{336}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{23}{168}\right)$
$\chi_{6272}(11,\cdot)$	6272.dq	672	yes	$-1$	$1$	$e\left(\frac{283}{672}\right)$	$e\left(\frac{185}{672}\right)$	$e\left(\frac{283}{336}\right)$	$e\left(\frac{253}{672}\right)$	$e\left(\frac{61}{224}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{295}{336}\right)$	$e\left(\frac{185}{336}\right)$
$\chi_{6272}(13,\cdot)$	6272.dg	224	yes	$-1$	$1$	$e\left(\frac{43}{224}\right)$	$e\left(\frac{57}{224}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{61}{224}\right)$	$e\left(\frac{215}{224}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{57}{112}\right)$
$\chi_{6272}(15,\cdot)$	6272.cn	56	no	$-1$	$1$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{6272}(17,\cdot)$	6272.df	168	no	$-1$	$1$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{6272}(19,\cdot)$	6272.cv	96	no	$1$	$1$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{6272}(23,\cdot)$	6272.dk	336	no	$-1$	$1$	$e\left(\frac{241}{336}\right)$	$e\left(\frac{227}{336}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{295}{336}\right)$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{59}{168}\right)$
$\chi_{6272}(25,\cdot)$	6272.dm	336	no	$1$	$1$	$e\left(\frac{191}{336}\right)$	$e\left(\frac{37}{336}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{185}{336}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{37}{168}\right)$
$\chi_{6272}(27,\cdot)$	6272.di	224	yes	$1$	$1$	$e\left(\frac{93}{224}\right)$	$e\left(\frac{79}{224}\right)$	$e\left(\frac{93}{112}\right)$	$e\left(\frac{59}{224}\right)$	$e\left(\frac{129}{224}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{17}{112}\right)$	$e\left(\frac{79}{112}\right)$
$\chi_{6272}(29,\cdot)$	6272.dh	224	yes	$1$	$1$	$e\left(\frac{215}{224}\right)$	$e\left(\frac{61}{224}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{193}{224}\right)$	$e\left(\frac{179}{224}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{61}{112}\right)$
$\chi_{6272}(31,\cdot)$	6272.ba	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{6272}(33,\cdot)$	6272.cq	84	no	$-1$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{42}\right)$
$\chi_{6272}(37,\cdot)$	6272.do	672	yes	$1$	$1$	$e\left(\frac{71}{672}\right)$	$e\left(\frac{589}{672}\right)$	$e\left(\frac{71}{336}\right)$	$e\left(\frac{593}{672}\right)$	$e\left(\frac{193}{224}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{155}{168}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{299}{336}\right)$	$e\left(\frac{253}{336}\right)$
$\chi_{6272}(39,\cdot)$	6272.dk	336	no	$-1$	$1$	$e\left(\frac{335}{336}\right)$	$e\left(\frac{13}{336}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{17}{112}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{13}{168}\right)$
$\chi_{6272}(41,\cdot)$	6272.da	112	no	$-1$	$1$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{33}{56}\right)$
$\chi_{6272}(43,\cdot)$	6272.dj	224	yes	$-1$	$1$	$e\left(\frac{81}{224}\right)$	$e\left(\frac{11}{224}\right)$	$e\left(\frac{81}{112}\right)$	$e\left(\frac{55}{224}\right)$	$e\left(\frac{69}{224}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{69}{112}\right)$	$e\left(\frac{11}{112}\right)$
$\chi_{6272}(45,\cdot)$	6272.dp	672	yes	$-1$	$1$	$e\left(\frac{265}{672}\right)$	$e\left(\frac{419}{672}\right)$	$e\left(\frac{265}{336}\right)$	$e\left(\frac{79}{672}\right)$	$e\left(\frac{143}{224}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{37}{336}\right)$	$e\left(\frac{83}{336}\right)$
$\chi_{6272}(47,\cdot)$	6272.dd	168	no	$1$	$1$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{6272}(51,\cdot)$	6272.dq	672	yes	$-1$	$1$	$e\left(\frac{17}{672}\right)$	$e\left(\frac{619}{672}\right)$	$e\left(\frac{17}{336}\right)$	$e\left(\frac{407}{672}\right)$	$e\left(\frac{215}{224}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{283}{336}\right)$
$\chi_{6272}(53,\cdot)$	6272.do	672	yes	$1$	$1$	$e\left(\frac{475}{672}\right)$	$e\left(\frac{41}{672}\right)$	$e\left(\frac{139}{336}\right)$	$e\left(\frac{541}{672}\right)$	$e\left(\frac{45}{224}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{55}{168}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{79}{336}\right)$	$e\left(\frac{41}{336}\right)$
$\chi_{6272}(55,\cdot)$	6272.cy	112	no	$1$	$1$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{73}{112}\right)$	$e\left(\frac{59}{112}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{37}{56}\right)$
$\chi_{6272}(57,\cdot)$	6272.cz	112	no	$1$	$1$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{75}{112}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{39}{112}\right)$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{19}{56}\right)$
$\chi_{6272}(59,\cdot)$	6272.dr	672	yes	$1$	$1$	$e\left(\frac{271}{672}\right)$	$e\left(\frac{341}{672}\right)$	$e\left(\frac{271}{336}\right)$	$e\left(\frac{25}{672}\right)$	$e\left(\frac{41}{224}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{235}{336}\right)$	$e\left(\frac{5}{336}\right)$
$\chi_{6272}(61,\cdot)$	6272.dp	672	yes	$-1$	$1$	$e\left(\frac{29}{672}\right)$	$e\left(\frac{127}{672}\right)$	$e\left(\frac{29}{336}\right)$	$e\left(\frac{635}{672}\right)$	$e\left(\frac{123}{224}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{89}{336}\right)$	$e\left(\frac{127}{336}\right)$
$\chi_{6272}(65,\cdot)$	6272.cb	42	no	$1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{6272}(67,\cdot)$	6272.cu	96	no	$-1$	$1$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{41}{48}\right)$
$\chi_{6272}(69,\cdot)$	6272.dg	224	yes	$-1$	$1$	$e\left(\frac{117}{224}\right)$	$e\left(\frac{103}{224}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{67}{224}\right)$	$e\left(\frac{137}{224}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{81}{112}\right)$	$e\left(\frac{103}{112}\right)$
$\chi_{6272}(71,\cdot)$	6272.db	112	no	$-1$	$1$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{43}{56}\right)$
$\chi_{6272}(73,\cdot)$	6272.dl	336	no	$-1$	$1$	$e\left(\frac{317}{336}\right)$	$e\left(\frac{79}{336}\right)$	$e\left(\frac{149}{168}\right)$	$e\left(\frac{227}{336}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{79}{168}\right)$

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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	$6272$
Structure	\(C_{2}\times C_{2}\times C_{672}\)
Order	$2688$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{6272}(1,\cdot)\)	6272.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6272}(3,\cdot)\)	6272.dr	672	yes	\(1\)	\(1\)	\(e\left(\frac{541}{672}\right)\)	\(e\left(\frac{527}{672}\right)\)	\(e\left(\frac{205}{336}\right)\)	\(e\left(\frac{283}{672}\right)\)	\(e\left(\frac{43}{224}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{241}{336}\right)\)	\(e\left(\frac{191}{336}\right)\)
\(\chi_{6272}(5,\cdot)\)	6272.dp	672	yes	\(-1\)	\(1\)	\(e\left(\frac{527}{672}\right)\)	\(e\left(\frac{37}{672}\right)\)	\(e\left(\frac{191}{336}\right)\)	\(e\left(\frac{185}{672}\right)\)	\(e\left(\frac{57}{224}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{227}{336}\right)\)	\(e\left(\frac{37}{336}\right)\)
\(\chi_{6272}(9,\cdot)\)	6272.dm	336	no	\(1\)	\(1\)	\(e\left(\frac{205}{336}\right)\)	\(e\left(\frac{191}{336}\right)\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{283}{336}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{23}{168}\right)\)
\(\chi_{6272}(11,\cdot)\)	6272.dq	672	yes	\(-1\)	\(1\)	\(e\left(\frac{283}{672}\right)\)	\(e\left(\frac{185}{672}\right)\)	\(e\left(\frac{283}{336}\right)\)	\(e\left(\frac{253}{672}\right)\)	\(e\left(\frac{61}{224}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{295}{336}\right)\)	\(e\left(\frac{185}{336}\right)\)
\(\chi_{6272}(13,\cdot)\)	6272.dg	224	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{224}\right)\)	\(e\left(\frac{57}{224}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{61}{224}\right)\)	\(e\left(\frac{215}{224}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{57}{112}\right)\)
\(\chi_{6272}(15,\cdot)\)	6272.cn	56	no	\(-1\)	\(1\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{6272}(17,\cdot)\)	6272.df	168	no	\(-1\)	\(1\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{6272}(19,\cdot)\)	6272.cv	96	no	\(1\)	\(1\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{6272}(23,\cdot)\)	6272.dk	336	no	\(-1\)	\(1\)	\(e\left(\frac{241}{336}\right)\)	\(e\left(\frac{227}{336}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{295}{336}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{59}{168}\right)\)
\(\chi_{6272}(25,\cdot)\)	6272.dm	336	no	\(1\)	\(1\)	\(e\left(\frac{191}{336}\right)\)	\(e\left(\frac{37}{336}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{185}{336}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{37}{168}\right)\)
\(\chi_{6272}(27,\cdot)\)	6272.di	224	yes	\(1\)	\(1\)	\(e\left(\frac{93}{224}\right)\)	\(e\left(\frac{79}{224}\right)\)	\(e\left(\frac{93}{112}\right)\)	\(e\left(\frac{59}{224}\right)\)	\(e\left(\frac{129}{224}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{17}{112}\right)\)	\(e\left(\frac{79}{112}\right)\)
\(\chi_{6272}(29,\cdot)\)	6272.dh	224	yes	\(1\)	\(1\)	\(e\left(\frac{215}{224}\right)\)	\(e\left(\frac{61}{224}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{193}{224}\right)\)	\(e\left(\frac{179}{224}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{61}{112}\right)\)
\(\chi_{6272}(31,\cdot)\)	6272.ba	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{6272}(33,\cdot)\)	6272.cq	84	no	\(-1\)	\(1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)
\(\chi_{6272}(37,\cdot)\)	6272.do	672	yes	\(1\)	\(1\)	\(e\left(\frac{71}{672}\right)\)	\(e\left(\frac{589}{672}\right)\)	\(e\left(\frac{71}{336}\right)\)	\(e\left(\frac{593}{672}\right)\)	\(e\left(\frac{193}{224}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{155}{168}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{299}{336}\right)\)	\(e\left(\frac{253}{336}\right)\)
\(\chi_{6272}(39,\cdot)\)	6272.dk	336	no	\(-1\)	\(1\)	\(e\left(\frac{335}{336}\right)\)	\(e\left(\frac{13}{336}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{17}{112}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{13}{168}\right)\)
\(\chi_{6272}(41,\cdot)\)	6272.da	112	no	\(-1\)	\(1\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{33}{56}\right)\)
\(\chi_{6272}(43,\cdot)\)	6272.dj	224	yes	\(-1\)	\(1\)	\(e\left(\frac{81}{224}\right)\)	\(e\left(\frac{11}{224}\right)\)	\(e\left(\frac{81}{112}\right)\)	\(e\left(\frac{55}{224}\right)\)	\(e\left(\frac{69}{224}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{69}{112}\right)\)	\(e\left(\frac{11}{112}\right)\)
\(\chi_{6272}(45,\cdot)\)	6272.dp	672	yes	\(-1\)	\(1\)	\(e\left(\frac{265}{672}\right)\)	\(e\left(\frac{419}{672}\right)\)	\(e\left(\frac{265}{336}\right)\)	\(e\left(\frac{79}{672}\right)\)	\(e\left(\frac{143}{224}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{37}{336}\right)\)	\(e\left(\frac{83}{336}\right)\)
\(\chi_{6272}(47,\cdot)\)	6272.dd	168	no	\(1\)	\(1\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{55}{84}\right)\)
\(\chi_{6272}(51,\cdot)\)	6272.dq	672	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{672}\right)\)	\(e\left(\frac{619}{672}\right)\)	\(e\left(\frac{17}{336}\right)\)	\(e\left(\frac{407}{672}\right)\)	\(e\left(\frac{215}{224}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{283}{336}\right)\)
\(\chi_{6272}(53,\cdot)\)	6272.do	672	yes	\(1\)	\(1\)	\(e\left(\frac{475}{672}\right)\)	\(e\left(\frac{41}{672}\right)\)	\(e\left(\frac{139}{336}\right)\)	\(e\left(\frac{541}{672}\right)\)	\(e\left(\frac{45}{224}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{55}{168}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{79}{336}\right)\)	\(e\left(\frac{41}{336}\right)\)
\(\chi_{6272}(55,\cdot)\)	6272.cy	112	no	\(1\)	\(1\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{73}{112}\right)\)	\(e\left(\frac{59}{112}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{37}{56}\right)\)
\(\chi_{6272}(57,\cdot)\)	6272.cz	112	no	\(1\)	\(1\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{75}{112}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{39}{112}\right)\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{19}{56}\right)\)
\(\chi_{6272}(59,\cdot)\)	6272.dr	672	yes	\(1\)	\(1\)	\(e\left(\frac{271}{672}\right)\)	\(e\left(\frac{341}{672}\right)\)	\(e\left(\frac{271}{336}\right)\)	\(e\left(\frac{25}{672}\right)\)	\(e\left(\frac{41}{224}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{235}{336}\right)\)	\(e\left(\frac{5}{336}\right)\)
\(\chi_{6272}(61,\cdot)\)	6272.dp	672	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{672}\right)\)	\(e\left(\frac{127}{672}\right)\)	\(e\left(\frac{29}{336}\right)\)	\(e\left(\frac{635}{672}\right)\)	\(e\left(\frac{123}{224}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{89}{336}\right)\)	\(e\left(\frac{127}{336}\right)\)
\(\chi_{6272}(65,\cdot)\)	6272.cb	42	no	\(1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{6272}(67,\cdot)\)	6272.cu	96	no	\(-1\)	\(1\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)
\(\chi_{6272}(69,\cdot)\)	6272.dg	224	yes	\(-1\)	\(1\)	\(e\left(\frac{117}{224}\right)\)	\(e\left(\frac{103}{224}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{67}{224}\right)\)	\(e\left(\frac{137}{224}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{81}{112}\right)\)	\(e\left(\frac{103}{112}\right)\)
\(\chi_{6272}(71,\cdot)\)	6272.db	112	no	\(-1\)	\(1\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)
\(\chi_{6272}(73,\cdot)\)	6272.dl	336	no	\(-1\)	\(1\)	\(e\left(\frac{317}{336}\right)\)	\(e\left(\frac{79}{336}\right)\)	\(e\left(\frac{149}{168}\right)\)	\(e\left(\frac{227}{336}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{79}{168}\right)\)

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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.