LMFDB - Group of Dirichlet characters of modulus 1734

sage:H = DirichletGroup(1734)

pari:g = idealstar(,1734,2)

Character group

sage:G.order() pari:g.no
Order	=	544
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{272}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{1734}(1157,\cdot)$, $\chi_{1734}(1159,\cdot)$

First 32 of 544 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	$-1$	$1$	$5$	$7$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{1734}(1,\cdot)$	1734.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1734}(5,\cdot)$	1734.t	272	no	$1$	$1$	$e\left(\frac{81}{272}\right)$	$e\left(\frac{135}{272}\right)$	$e\left(\frac{235}{272}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{107}{136}\right)$	$e\left(\frac{67}{272}\right)$	$e\left(\frac{81}{136}\right)$	$e\left(\frac{201}{272}\right)$	$e\left(\frac{157}{272}\right)$	$e\left(\frac{27}{34}\right)$
$\chi_{1734}(7,\cdot)$	1734.s	272	no	$-1$	$1$	$e\left(\frac{135}{272}\right)$	$e\left(\frac{89}{272}\right)$	$e\left(\frac{29}{272}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{133}{136}\right)$	$e\left(\frac{21}{272}\right)$	$e\left(\frac{135}{136}\right)$	$e\left(\frac{63}{272}\right)$	$e\left(\frac{35}{272}\right)$	$e\left(\frac{14}{17}\right)$
$\chi_{1734}(11,\cdot)$	1734.t	272	no	$1$	$1$	$e\left(\frac{235}{272}\right)$	$e\left(\frac{29}{272}\right)$	$e\left(\frac{121}{272}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{97}{272}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{19}{272}\right)$	$e\left(\frac{207}{272}\right)$	$e\left(\frac{33}{34}\right)$
$\chi_{1734}(13,\cdot)$	1734.o	68	no	$1$	$1$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{12}{17}\right)$
$\chi_{1734}(19,\cdot)$	1734.q	136	no	$1$	$1$	$e\left(\frac{107}{136}\right)$	$e\left(\frac{133}{136}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{13}{17}\right)$
$\chi_{1734}(23,\cdot)$	1734.t	272	no	$1$	$1$	$e\left(\frac{67}{272}\right)$	$e\left(\frac{21}{272}\right)$	$e\left(\frac{97}{272}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{89}{272}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{267}{272}\right)$	$e\left(\frac{103}{272}\right)$	$e\left(\frac{11}{34}\right)$
$\chi_{1734}(25,\cdot)$	1734.q	136	no	$1$	$1$	$e\left(\frac{81}{136}\right)$	$e\left(\frac{135}{136}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{10}{17}\right)$
$\chi_{1734}(29,\cdot)$	1734.t	272	no	$1$	$1$	$e\left(\frac{201}{272}\right)$	$e\left(\frac{63}{272}\right)$	$e\left(\frac{19}{272}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{267}{272}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{257}{272}\right)$	$e\left(\frac{37}{272}\right)$	$e\left(\frac{33}{34}\right)$
$\chi_{1734}(31,\cdot)$	1734.s	272	no	$-1$	$1$	$e\left(\frac{157}{272}\right)$	$e\left(\frac{35}{272}\right)$	$e\left(\frac{207}{272}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{103}{272}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{37}{272}\right)$	$e\left(\frac{81}{272}\right)$	$e\left(\frac{12}{17}\right)$
$\chi_{1734}(35,\cdot)$	1734.m	34	no	$-1$	$1$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{21}{34}\right)$
$\chi_{1734}(37,\cdot)$	1734.s	272	no	$-1$	$1$	$e\left(\frac{165}{272}\right)$	$e\left(\frac{139}{272}\right)$	$e\left(\frac{247}{272}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{87}{136}\right)$	$e\left(\frac{207}{272}\right)$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{77}{272}\right)$	$e\left(\frac{73}{272}\right)$	$e\left(\frac{2}{17}\right)$
$\chi_{1734}(41,\cdot)$	1734.t	272	no	$1$	$1$	$e\left(\frac{127}{272}\right)$	$e\left(\frac{121}{272}\right)$	$e\left(\frac{261}{272}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{109}{136}\right)$	$e\left(\frac{189}{272}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{23}{272}\right)$	$e\left(\frac{179}{272}\right)$	$e\left(\frac{31}{34}\right)$
$\chi_{1734}(43,\cdot)$	1734.q	136	no	$1$	$1$	$e\left(\frac{37}{136}\right)$	$e\left(\frac{107}{136}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{39}{136}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{117}{136}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{1}{17}\right)$
$\chi_{1734}(47,\cdot)$	1734.p	68	no	$-1$	$1$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{23}{34}\right)$
$\chi_{1734}(49,\cdot)$	1734.q	136	no	$1$	$1$	$e\left(\frac{135}{136}\right)$	$e\left(\frac{89}{136}\right)$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{11}{17}\right)$
$\chi_{1734}(53,\cdot)$	1734.r	136	no	$-1$	$1$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{125}{136}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{11}{34}\right)$
$\chi_{1734}(55,\cdot)$	1734.o	68	no	$1$	$1$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{13}{17}\right)$
$\chi_{1734}(59,\cdot)$	1734.r	136	no	$-1$	$1$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{39}{136}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{101}{136}\right)$	$e\left(\frac{29}{34}\right)$
$\chi_{1734}(61,\cdot)$	1734.s	272	no	$-1$	$1$	$e\left(\frac{15}{272}\right)$	$e\left(\frac{161}{272}\right)$	$e\left(\frac{245}{272}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{45}{136}\right)$	$e\left(\frac{93}{272}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{7}{272}\right)$	$e\left(\frac{155}{272}\right)$	$e\left(\frac{11}{17}\right)$
$\chi_{1734}(65,\cdot)$	1734.i	16	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-1$
$\chi_{1734}(67,\cdot)$	1734.n	34	no	$1$	$1$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{13}{17}\right)$
$\chi_{1734}(71,\cdot)$	1734.t	272	no	$1$	$1$	$e\left(\frac{237}{272}\right)$	$e\left(\frac{123}{272}\right)$	$e\left(\frac{63}{272}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{31}{136}\right)$	$e\left(\frac{55}{272}\right)$	$e\left(\frac{101}{136}\right)$	$e\left(\frac{165}{272}\right)$	$e\left(\frac{137}{272}\right)$	$e\left(\frac{11}{34}\right)$
$\chi_{1734}(73,\cdot)$	1734.s	272	no	$-1$	$1$	$e\left(\frac{249}{272}\right)$	$e\left(\frac{7}{272}\right)$	$e\left(\frac{259}{272}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{75}{272}\right)$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{225}{272}\right)$	$e\left(\frac{125}{272}\right)$	$e\left(\frac{16}{17}\right)$
$\chi_{1734}(77,\cdot)$	1734.r	136	no	$-1$	$1$	$e\left(\frac{49}{136}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{75}{136}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{27}{34}\right)$
$\chi_{1734}(79,\cdot)$	1734.s	272	no	$-1$	$1$	$e\left(\frac{163}{272}\right)$	$e\left(\frac{45}{272}\right)$	$e\left(\frac{33}{272}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{81}{136}\right)$	$e\left(\frac{249}{272}\right)$	$e\left(\frac{27}{136}\right)$	$e\left(\frac{203}{272}\right)$	$e\left(\frac{143}{272}\right)$	$e\left(\frac{13}{17}\right)$
$\chi_{1734}(83,\cdot)$	1734.r	136	no	$-1$	$1$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{33}{136}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{33}{136}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{3}{34}\right)$
$\chi_{1734}(89,\cdot)$	1734.p	68	no	$-1$	$1$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{27}{34}\right)$
$\chi_{1734}(91,\cdot)$	1734.s	272	no	$-1$	$1$	$e\left(\frac{139}{272}\right)$	$e\left(\frac{5}{272}\right)$	$e\left(\frac{185}{272}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{209}{272}\right)$	$e\left(\frac{3}{136}\right)$	$e\left(\frac{83}{272}\right)$	$e\left(\frac{167}{272}\right)$	$e\left(\frac{9}{17}\right)$
$\chi_{1734}(95,\cdot)$	1734.t	272	no	$1$	$1$	$e\left(\frac{23}{272}\right)$	$e\left(\frac{129}{272}\right)$	$e\left(\frac{13}{272}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{197}{272}\right)$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{47}{272}\right)$	$e\left(\frac{11}{272}\right)$	$e\left(\frac{19}{34}\right)$
$\chi_{1734}(97,\cdot)$	1734.s	272	no	$-1$	$1$	$e\left(\frac{33}{272}\right)$	$e\left(\frac{191}{272}\right)$	$e\left(\frac{267}{272}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{259}{272}\right)$	$e\left(\frac{33}{136}\right)$	$e\left(\frac{233}{272}\right)$	$e\left(\frac{69}{272}\right)$	$e\left(\frac{14}{17}\right)$
$\chi_{1734}(101,\cdot)$	1734.l	34	no	$-1$	$1$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{5}{34}\right)$

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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	$1734$
Structure	\(C_{2}\times C_{272}\)
Order	$544$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{1734}(1,\cdot)\)	1734.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1734}(5,\cdot)\)	1734.t	272	no	\(1\)	\(1\)	\(e\left(\frac{81}{272}\right)\)	\(e\left(\frac{135}{272}\right)\)	\(e\left(\frac{235}{272}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{107}{136}\right)\)	\(e\left(\frac{67}{272}\right)\)	\(e\left(\frac{81}{136}\right)\)	\(e\left(\frac{201}{272}\right)\)	\(e\left(\frac{157}{272}\right)\)	\(e\left(\frac{27}{34}\right)\)
\(\chi_{1734}(7,\cdot)\)	1734.s	272	no	\(-1\)	\(1\)	\(e\left(\frac{135}{272}\right)\)	\(e\left(\frac{89}{272}\right)\)	\(e\left(\frac{29}{272}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{133}{136}\right)\)	\(e\left(\frac{21}{272}\right)\)	\(e\left(\frac{135}{136}\right)\)	\(e\left(\frac{63}{272}\right)\)	\(e\left(\frac{35}{272}\right)\)	\(e\left(\frac{14}{17}\right)\)
\(\chi_{1734}(11,\cdot)\)	1734.t	272	no	\(1\)	\(1\)	\(e\left(\frac{235}{272}\right)\)	\(e\left(\frac{29}{272}\right)\)	\(e\left(\frac{121}{272}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{97}{272}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{19}{272}\right)\)	\(e\left(\frac{207}{272}\right)\)	\(e\left(\frac{33}{34}\right)\)
\(\chi_{1734}(13,\cdot)\)	1734.o	68	no	\(1\)	\(1\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{12}{17}\right)\)
\(\chi_{1734}(19,\cdot)\)	1734.q	136	no	\(1\)	\(1\)	\(e\left(\frac{107}{136}\right)\)	\(e\left(\frac{133}{136}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{13}{17}\right)\)
\(\chi_{1734}(23,\cdot)\)	1734.t	272	no	\(1\)	\(1\)	\(e\left(\frac{67}{272}\right)\)	\(e\left(\frac{21}{272}\right)\)	\(e\left(\frac{97}{272}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{89}{272}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{267}{272}\right)\)	\(e\left(\frac{103}{272}\right)\)	\(e\left(\frac{11}{34}\right)\)
\(\chi_{1734}(25,\cdot)\)	1734.q	136	no	\(1\)	\(1\)	\(e\left(\frac{81}{136}\right)\)	\(e\left(\frac{135}{136}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{10}{17}\right)\)
\(\chi_{1734}(29,\cdot)\)	1734.t	272	no	\(1\)	\(1\)	\(e\left(\frac{201}{272}\right)\)	\(e\left(\frac{63}{272}\right)\)	\(e\left(\frac{19}{272}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{267}{272}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{257}{272}\right)\)	\(e\left(\frac{37}{272}\right)\)	\(e\left(\frac{33}{34}\right)\)
\(\chi_{1734}(31,\cdot)\)	1734.s	272	no	\(-1\)	\(1\)	\(e\left(\frac{157}{272}\right)\)	\(e\left(\frac{35}{272}\right)\)	\(e\left(\frac{207}{272}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{103}{272}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{37}{272}\right)\)	\(e\left(\frac{81}{272}\right)\)	\(e\left(\frac{12}{17}\right)\)
\(\chi_{1734}(35,\cdot)\)	1734.m	34	no	\(-1\)	\(1\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{21}{34}\right)\)
\(\chi_{1734}(37,\cdot)\)	1734.s	272	no	\(-1\)	\(1\)	\(e\left(\frac{165}{272}\right)\)	\(e\left(\frac{139}{272}\right)\)	\(e\left(\frac{247}{272}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{87}{136}\right)\)	\(e\left(\frac{207}{272}\right)\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{77}{272}\right)\)	\(e\left(\frac{73}{272}\right)\)	\(e\left(\frac{2}{17}\right)\)
\(\chi_{1734}(41,\cdot)\)	1734.t	272	no	\(1\)	\(1\)	\(e\left(\frac{127}{272}\right)\)	\(e\left(\frac{121}{272}\right)\)	\(e\left(\frac{261}{272}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{109}{136}\right)\)	\(e\left(\frac{189}{272}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{23}{272}\right)\)	\(e\left(\frac{179}{272}\right)\)	\(e\left(\frac{31}{34}\right)\)
\(\chi_{1734}(43,\cdot)\)	1734.q	136	no	\(1\)	\(1\)	\(e\left(\frac{37}{136}\right)\)	\(e\left(\frac{107}{136}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{39}{136}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{117}{136}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{1}{17}\right)\)
\(\chi_{1734}(47,\cdot)\)	1734.p	68	no	\(-1\)	\(1\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)
\(\chi_{1734}(49,\cdot)\)	1734.q	136	no	\(1\)	\(1\)	\(e\left(\frac{135}{136}\right)\)	\(e\left(\frac{89}{136}\right)\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{11}{17}\right)\)
\(\chi_{1734}(53,\cdot)\)	1734.r	136	no	\(-1\)	\(1\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{125}{136}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{11}{34}\right)\)
\(\chi_{1734}(55,\cdot)\)	1734.o	68	no	\(1\)	\(1\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{13}{17}\right)\)
\(\chi_{1734}(59,\cdot)\)	1734.r	136	no	\(-1\)	\(1\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{39}{136}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{101}{136}\right)\)	\(e\left(\frac{29}{34}\right)\)
\(\chi_{1734}(61,\cdot)\)	1734.s	272	no	\(-1\)	\(1\)	\(e\left(\frac{15}{272}\right)\)	\(e\left(\frac{161}{272}\right)\)	\(e\left(\frac{245}{272}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{45}{136}\right)\)	\(e\left(\frac{93}{272}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{7}{272}\right)\)	\(e\left(\frac{155}{272}\right)\)	\(e\left(\frac{11}{17}\right)\)
\(\chi_{1734}(65,\cdot)\)	1734.i	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)
\(\chi_{1734}(67,\cdot)\)	1734.n	34	no	\(1\)	\(1\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{13}{17}\right)\)
\(\chi_{1734}(71,\cdot)\)	1734.t	272	no	\(1\)	\(1\)	\(e\left(\frac{237}{272}\right)\)	\(e\left(\frac{123}{272}\right)\)	\(e\left(\frac{63}{272}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{31}{136}\right)\)	\(e\left(\frac{55}{272}\right)\)	\(e\left(\frac{101}{136}\right)\)	\(e\left(\frac{165}{272}\right)\)	\(e\left(\frac{137}{272}\right)\)	\(e\left(\frac{11}{34}\right)\)
\(\chi_{1734}(73,\cdot)\)	1734.s	272	no	\(-1\)	\(1\)	\(e\left(\frac{249}{272}\right)\)	\(e\left(\frac{7}{272}\right)\)	\(e\left(\frac{259}{272}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{75}{272}\right)\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{225}{272}\right)\)	\(e\left(\frac{125}{272}\right)\)	\(e\left(\frac{16}{17}\right)\)
\(\chi_{1734}(77,\cdot)\)	1734.r	136	no	\(-1\)	\(1\)	\(e\left(\frac{49}{136}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{75}{136}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{27}{34}\right)\)
\(\chi_{1734}(79,\cdot)\)	1734.s	272	no	\(-1\)	\(1\)	\(e\left(\frac{163}{272}\right)\)	\(e\left(\frac{45}{272}\right)\)	\(e\left(\frac{33}{272}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{81}{136}\right)\)	\(e\left(\frac{249}{272}\right)\)	\(e\left(\frac{27}{136}\right)\)	\(e\left(\frac{203}{272}\right)\)	\(e\left(\frac{143}{272}\right)\)	\(e\left(\frac{13}{17}\right)\)
\(\chi_{1734}(83,\cdot)\)	1734.r	136	no	\(-1\)	\(1\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{33}{136}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{33}{136}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{3}{34}\right)\)
\(\chi_{1734}(89,\cdot)\)	1734.p	68	no	\(-1\)	\(1\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)
\(\chi_{1734}(91,\cdot)\)	1734.s	272	no	\(-1\)	\(1\)	\(e\left(\frac{139}{272}\right)\)	\(e\left(\frac{5}{272}\right)\)	\(e\left(\frac{185}{272}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{209}{272}\right)\)	\(e\left(\frac{3}{136}\right)\)	\(e\left(\frac{83}{272}\right)\)	\(e\left(\frac{167}{272}\right)\)	\(e\left(\frac{9}{17}\right)\)
\(\chi_{1734}(95,\cdot)\)	1734.t	272	no	\(1\)	\(1\)	\(e\left(\frac{23}{272}\right)\)	\(e\left(\frac{129}{272}\right)\)	\(e\left(\frac{13}{272}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{197}{272}\right)\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{47}{272}\right)\)	\(e\left(\frac{11}{272}\right)\)	\(e\left(\frac{19}{34}\right)\)
\(\chi_{1734}(97,\cdot)\)	1734.s	272	no	\(-1\)	\(1\)	\(e\left(\frac{33}{272}\right)\)	\(e\left(\frac{191}{272}\right)\)	\(e\left(\frac{267}{272}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{259}{272}\right)\)	\(e\left(\frac{33}{136}\right)\)	\(e\left(\frac{233}{272}\right)\)	\(e\left(\frac{69}{272}\right)\)	\(e\left(\frac{14}{17}\right)\)
\(\chi_{1734}(101,\cdot)\)	1734.l	34	no	\(-1\)	\(1\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{5}{34}\right)\)

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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.