LMFDB - Group of Dirichlet characters of modulus 1648

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1648)

pari: g = idealstar(,1648,2)

Character group

sage: G.order() pari: g.no
Order	=	816
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{204}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1648}(207,\cdot)$, $\chi_{1648}(1237,\cdot)$, $\chi_{1648}(417,\cdot)$

First 32 of 816 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{1648}(1,\cdot)$	1648.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1648}(3,\cdot)$	1648.bh	68	yes	$1$	$1$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{13}{68}\right)$
$\chi_{1648}(5,\cdot)$	1648.bt	204	yes	$-1$	$1$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{173}{204}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{137}{204}\right)$
$\chi_{1648}(7,\cdot)$	1648.bm	102	no	$-1$	$1$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{19}{102}\right)$
$\chi_{1648}(9,\cdot)$	1648.bf	34	no	$1$	$1$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{13}{34}\right)$
$\chi_{1648}(11,\cdot)$	1648.bu	204	yes	$1$	$1$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{173}{204}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{47}{204}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{19}{204}\right)$	$e\left(\frac{197}{204}\right)$
$\chi_{1648}(13,\cdot)$	1648.bj	68	yes	$1$	$1$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{7}{68}\right)$
$\chi_{1648}(15,\cdot)$	1648.bq	102	no	$-1$	$1$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{44}{51}\right)$
$\chi_{1648}(17,\cdot)$	1648.bg	51	no	$1$	$1$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{26}{51}\right)$
$\chi_{1648}(19,\cdot)$	1648.bv	204	yes	$-1$	$1$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{19}{204}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{101}{204}\right)$	$e\left(\frac{97}{204}\right)$
$\chi_{1648}(21,\cdot)$	1648.bt	204	yes	$-1$	$1$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{137}{204}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{197}{204}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{97}{204}\right)$	$e\left(\frac{77}{204}\right)$
$\chi_{1648}(23,\cdot)$	1648.bb	34	no	$-1$	$1$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{21}{34}\right)$
$\chi_{1648}(25,\cdot)$	1648.bp	102	no	$1$	$1$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{40}{51}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{35}{102}\right)$
$\chi_{1648}(27,\cdot)$	1648.bh	68	yes	$1$	$1$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{39}{68}\right)$
$\chi_{1648}(29,\cdot)$	1648.bs	204	yes	$1$	$1$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{121}{204}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{37}{204}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{143}{204}\right)$	$e\left(\frac{1}{204}\right)$
$\chi_{1648}(31,\cdot)$	1648.ba	34	no	$1$	$1$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{1}{34}\right)$
$\chi_{1648}(33,\cdot)$	1648.bg	51	no	$1$	$1$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{8}{51}\right)$
$\chi_{1648}(35,\cdot)$	1648.bu	204	yes	$1$	$1$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{137}{204}\right)$	$e\left(\frac{175}{204}\right)$
$\chi_{1648}(37,\cdot)$	1648.bk	68	yes	$-1$	$1$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{31}{68}\right)$
$\chi_{1648}(39,\cdot)$	1648.bd	34	no	$1$	$1$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{5}{17}\right)$
$\chi_{1648}(41,\cdot)$	1648.bp	102	no	$1$	$1$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{49}{51}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{59}{102}\right)$
$\chi_{1648}(43,\cdot)$	1648.bu	204	yes	$1$	$1$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{1}{204}\right)$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{131}{204}\right)$	$e\left(\frac{145}{204}\right)$
$\chi_{1648}(45,\cdot)$	1648.bt	204	yes	$-1$	$1$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{107}{204}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{203}{204}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{43}{204}\right)$	$e\left(\frac{11}{204}\right)$
$\chi_{1648}(47,\cdot)$	1648.t	6	no	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1648}(49,\cdot)$	1648.bg	51	no	$1$	$1$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{40}{51}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{25}{51}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{19}{51}\right)$
$\chi_{1648}(51,\cdot)$	1648.bu	204	yes	$1$	$1$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{167}{204}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{89}{204}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{143}{204}\right)$
$\chi_{1648}(53,\cdot)$	1648.bt	204	yes	$-1$	$1$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{41}{204}\right)$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{169}{204}\right)$	$e\left(\frac{29}{204}\right)$
$\chi_{1648}(55,\cdot)$	1648.bm	102	no	$-1$	$1$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{65}{102}\right)$
$\chi_{1648}(57,\cdot)$	1648.r	6	no	$-1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1648}(59,\cdot)$	1648.bv	204	yes	$-1$	$1$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{43}{204}\right)$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{73}{204}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{23}{204}\right)$	$e\left(\frac{115}{204}\right)$
$\chi_{1648}(61,\cdot)$	1648.bj	68	yes	$1$	$1$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{63}{68}\right)$
$\chi_{1648}(63,\cdot)$	1648.bq	102	no	$-1$	$1$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{29}{51}\right)$

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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	$1648$
Structure	\(C_{2}\times C_{2}\times C_{204}\)
Order	$816$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{1648}(1,\cdot)\)	1648.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1648}(3,\cdot)\)	1648.bh	68	yes	\(1\)	\(1\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{13}{68}\right)\)
\(\chi_{1648}(5,\cdot)\)	1648.bt	204	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{173}{204}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{20}{51}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{137}{204}\right)\)
\(\chi_{1648}(7,\cdot)\)	1648.bm	102	no	\(-1\)	\(1\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{20}{51}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{19}{102}\right)\)
\(\chi_{1648}(9,\cdot)\)	1648.bf	34	no	\(1\)	\(1\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{13}{34}\right)\)
\(\chi_{1648}(11,\cdot)\)	1648.bu	204	yes	\(1\)	\(1\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{173}{204}\right)\)	\(e\left(\frac{20}{51}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{47}{204}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{44}{51}\right)\)	\(e\left(\frac{19}{204}\right)\)	\(e\left(\frac{197}{204}\right)\)
\(\chi_{1648}(13,\cdot)\)	1648.bj	68	yes	\(1\)	\(1\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{7}{68}\right)\)
\(\chi_{1648}(15,\cdot)\)	1648.bq	102	no	\(-1\)	\(1\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{20}{51}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{43}{102}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{23}{51}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{44}{51}\right)\)
\(\chi_{1648}(17,\cdot)\)	1648.bg	51	no	\(1\)	\(1\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{44}{51}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{23}{51}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{26}{51}\right)\)
\(\chi_{1648}(19,\cdot)\)	1648.bv	204	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{19}{204}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{101}{204}\right)\)	\(e\left(\frac{97}{204}\right)\)
\(\chi_{1648}(21,\cdot)\)	1648.bt	204	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{137}{204}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{197}{204}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{44}{51}\right)\)	\(e\left(\frac{26}{51}\right)\)	\(e\left(\frac{97}{204}\right)\)	\(e\left(\frac{77}{204}\right)\)
\(\chi_{1648}(23,\cdot)\)	1648.bb	34	no	\(-1\)	\(1\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{21}{34}\right)\)
\(\chi_{1648}(25,\cdot)\)	1648.bp	102	no	\(1\)	\(1\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{40}{51}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{35}{102}\right)\)
\(\chi_{1648}(27,\cdot)\)	1648.bh	68	yes	\(1\)	\(1\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{39}{68}\right)\)
\(\chi_{1648}(29,\cdot)\)	1648.bs	204	yes	\(1\)	\(1\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{121}{204}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{37}{204}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{1}{51}\right)\)	\(e\left(\frac{143}{204}\right)\)	\(e\left(\frac{1}{204}\right)\)
\(\chi_{1648}(31,\cdot)\)	1648.ba	34	no	\(1\)	\(1\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{1}{34}\right)\)
\(\chi_{1648}(33,\cdot)\)	1648.bg	51	no	\(1\)	\(1\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{50}{51}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{8}{51}\right)\)
\(\chi_{1648}(35,\cdot)\)	1648.bu	204	yes	\(1\)	\(1\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{10}{51}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{137}{204}\right)\)	\(e\left(\frac{175}{204}\right)\)
\(\chi_{1648}(37,\cdot)\)	1648.bk	68	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{31}{68}\right)\)
\(\chi_{1648}(39,\cdot)\)	1648.bd	34	no	\(1\)	\(1\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{5}{17}\right)\)
\(\chi_{1648}(41,\cdot)\)	1648.bp	102	no	\(1\)	\(1\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{49}{51}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{31}{51}\right)\)	\(e\left(\frac{16}{51}\right)\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{59}{102}\right)\)
\(\chi_{1648}(43,\cdot)\)	1648.bu	204	yes	\(1\)	\(1\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{1}{204}\right)\)	\(e\left(\frac{1}{51}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{43}{51}\right)\)	\(e\left(\frac{131}{204}\right)\)	\(e\left(\frac{145}{204}\right)\)
\(\chi_{1648}(45,\cdot)\)	1648.bt	204	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{107}{204}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{203}{204}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{50}{51}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{43}{204}\right)\)	\(e\left(\frac{11}{204}\right)\)
\(\chi_{1648}(47,\cdot)\)	1648.t	6	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1648}(49,\cdot)\)	1648.bg	51	no	\(1\)	\(1\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{16}{51}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{40}{51}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{25}{51}\right)\)	\(e\left(\frac{14}{51}\right)\)	\(e\left(\frac{19}{51}\right)\)
\(\chi_{1648}(51,\cdot)\)	1648.bu	204	yes	\(1\)	\(1\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{167}{204}\right)\)	\(e\left(\frac{14}{51}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{89}{204}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{143}{204}\right)\)
\(\chi_{1648}(53,\cdot)\)	1648.bt	204	yes	\(-1\)	\(1\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{41}{204}\right)\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{29}{51}\right)\)	\(e\left(\frac{169}{204}\right)\)	\(e\left(\frac{29}{204}\right)\)
\(\chi_{1648}(55,\cdot)\)	1648.bm	102	no	\(-1\)	\(1\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{65}{102}\right)\)
\(\chi_{1648}(57,\cdot)\)	1648.r	6	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1648}(59,\cdot)\)	1648.bv	204	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{43}{204}\right)\)	\(e\left(\frac{43}{51}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{73}{204}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{23}{204}\right)\)	\(e\left(\frac{115}{204}\right)\)
\(\chi_{1648}(61,\cdot)\)	1648.bj	68	yes	\(1\)	\(1\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{63}{68}\right)\)
\(\chi_{1648}(63,\cdot)\)	1648.bq	102	no	\(-1\)	\(1\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{55}{102}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{14}{51}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{29}{51}\right)\)

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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.