LMFDB - Group of Dirichlet characters of modulus 7448

Show commands: PariGP / SageMath

sage: H = DirichletGroup(7448)

pari: g = idealstar(,7448,2)

Character group

sage: G.order() pari: g.no
Order	=	3024
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{126}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{7448}(1863,\cdot)$, $\chi_{7448}(3725,\cdot)$, $\chi_{7448}(3041,\cdot)$, $\chi_{7448}(3137,\cdot)$

First 32 of 3024 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$23$	$25$	$27$
$\chi_{7448}(1,\cdot)$	7448.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{7448}(3,\cdot)$	7448.jj	126	yes	$-1$	$1$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{7448}(5,\cdot)$	7448.ju	126	yes	$-1$	$1$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{7448}(9,\cdot)$	7448.ic	63	no	$1$	$1$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{7448}(11,\cdot)$	7448.hq	42	yes	$-1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{7448}(13,\cdot)$	7448.im	126	yes	$1$	$1$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{29}{42}\right)$
$\chi_{7448}(15,\cdot)$	7448.iv	126	no	$1$	$1$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{7448}(17,\cdot)$	7448.jb	126	no	$-1$	$1$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{19}{42}\right)$
$\chi_{7448}(23,\cdot)$	7448.il	126	no	$-1$	$1$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{23}{42}\right)$
$\chi_{7448}(25,\cdot)$	7448.ia	63	no	$1$	$1$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{7448}(27,\cdot)$	7448.hi	42	yes	$-1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{7448}(29,\cdot)$	7448.iw	126	yes	$-1$	$1$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{7448}(31,\cdot)$	7448.ba	6	no	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{7448}(33,\cdot)$	7448.ih	126	no	$1$	$1$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{7448}(37,\cdot)$	7448.hc	42	yes	$-1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{7448}(39,\cdot)$	7448.gn	42	no	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{7448}(41,\cdot)$	7448.jk	126	no	$1$	$1$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{7448}(43,\cdot)$	7448.jm	126	yes	$-1$	$1$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{7448}(45,\cdot)$	7448.fx	42	yes	$-1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{7448}(47,\cdot)$	7448.iz	126	no	$1$	$1$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{7448}(51,\cdot)$	7448.jh	126	yes	$1$	$1$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{29}{42}\right)$
$\chi_{7448}(53,\cdot)$	7448.jv	126	yes	$-1$	$1$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{7448}(55,\cdot)$	7448.iu	126	no	$1$	$1$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{7448}(59,\cdot)$	7448.jj	126	yes	$-1$	$1$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{7448}(61,\cdot)$	7448.is	126	yes	$-1$	$1$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{7448}(65,\cdot)$	7448.hy	42	no	$-1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{7448}(67,\cdot)$	7448.fk	18	no	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{7448}(69,\cdot)$	7448.gr	42	yes	$1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{7448}(71,\cdot)$	7448.iv	126	no	$1$	$1$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{7448}(73,\cdot)$	7448.jb	126	no	$-1$	$1$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{13}{42}\right)$
$\chi_{7448}(75,\cdot)$	7448.hl	42	yes	$-1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{7448}(79,\cdot)$	7448.dw	18	no	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$-1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$

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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	$7448$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{126}\)
Order	$3024$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(23\)	\(25\)	\(27\)
\(\chi_{7448}(1,\cdot)\)	7448.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{7448}(3,\cdot)\)	7448.jj	126	yes	\(-1\)	\(1\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{7448}(5,\cdot)\)	7448.ju	126	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{7448}(9,\cdot)\)	7448.ic	63	no	\(1\)	\(1\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{7448}(11,\cdot)\)	7448.hq	42	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{7448}(13,\cdot)\)	7448.im	126	yes	\(1\)	\(1\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{29}{42}\right)\)
\(\chi_{7448}(15,\cdot)\)	7448.iv	126	no	\(1\)	\(1\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{7448}(17,\cdot)\)	7448.jb	126	no	\(-1\)	\(1\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{19}{42}\right)\)
\(\chi_{7448}(23,\cdot)\)	7448.il	126	no	\(-1\)	\(1\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{23}{42}\right)\)
\(\chi_{7448}(25,\cdot)\)	7448.ia	63	no	\(1\)	\(1\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{7448}(27,\cdot)\)	7448.hi	42	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{7448}(29,\cdot)\)	7448.iw	126	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{7448}(31,\cdot)\)	7448.ba	6	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{7448}(33,\cdot)\)	7448.ih	126	no	\(1\)	\(1\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{7448}(37,\cdot)\)	7448.hc	42	yes	\(-1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{7448}(39,\cdot)\)	7448.gn	42	no	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{7448}(41,\cdot)\)	7448.jk	126	no	\(1\)	\(1\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{7448}(43,\cdot)\)	7448.jm	126	yes	\(-1\)	\(1\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{7448}(45,\cdot)\)	7448.fx	42	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{7448}(47,\cdot)\)	7448.iz	126	no	\(1\)	\(1\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{7448}(51,\cdot)\)	7448.jh	126	yes	\(1\)	\(1\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{29}{42}\right)\)
\(\chi_{7448}(53,\cdot)\)	7448.jv	126	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{7448}(55,\cdot)\)	7448.iu	126	no	\(1\)	\(1\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{7448}(59,\cdot)\)	7448.jj	126	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{7448}(61,\cdot)\)	7448.is	126	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{7448}(65,\cdot)\)	7448.hy	42	no	\(-1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{7448}(67,\cdot)\)	7448.fk	18	no	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{7448}(69,\cdot)\)	7448.gr	42	yes	\(1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{7448}(71,\cdot)\)	7448.iv	126	no	\(1\)	\(1\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{7448}(73,\cdot)\)	7448.jb	126	no	\(-1\)	\(1\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{13}{42}\right)\)
\(\chi_{7448}(75,\cdot)\)	7448.hl	42	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{7448}(79,\cdot)\)	7448.dw	18	no	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(-1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)

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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.