LMFDB - Group of Dirichlet characters of modulus 49

sage:H = DirichletGroup(49)

pari:g = idealstar(,49,2)

Character group

sage:G.order() pari:g.no
Order	=	42
sage:H.invariants() pari:g.cyc
Structure	=	$C_{42}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{49}(3,\cdot)$

First 32 of 42 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{49}(1,\cdot)$	49.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{49}(2,\cdot)$	49.g	21	yes	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{49}(3,\cdot)$	49.h	42	yes	$-1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{42}\right)$
$\chi_{49}(4,\cdot)$	49.g	21	yes	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{49}(5,\cdot)$	49.h	42	yes	$-1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{25}{42}\right)$
$\chi_{49}(6,\cdot)$	49.f	14	yes	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{49}(8,\cdot)$	49.e	7	yes	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{49}(9,\cdot)$	49.g	21	yes	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{49}(10,\cdot)$	49.h	42	yes	$-1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{42}\right)$
$\chi_{49}(11,\cdot)$	49.g	21	yes	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{49}(12,\cdot)$	49.h	42	yes	$-1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{37}{42}\right)$
$\chi_{49}(13,\cdot)$	49.f	14	yes	$-1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{49}(15,\cdot)$	49.e	7	yes	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{49}(16,\cdot)$	49.g	21	yes	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{49}(17,\cdot)$	49.h	42	yes	$-1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{23}{42}\right)$
$\chi_{49}(18,\cdot)$	49.c	3	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{49}(19,\cdot)$	49.d	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{49}(20,\cdot)$	49.f	14	yes	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{49}(22,\cdot)$	49.e	7	yes	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{49}(23,\cdot)$	49.g	21	yes	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{49}(24,\cdot)$	49.h	42	yes	$-1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{29}{42}\right)$
$\chi_{49}(25,\cdot)$	49.g	21	yes	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{49}(26,\cdot)$	49.h	42	yes	$-1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{19}{42}\right)$
$\chi_{49}(27,\cdot)$	49.f	14	yes	$-1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{49}(29,\cdot)$	49.e	7	yes	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{49}(30,\cdot)$	49.c	3	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{49}(31,\cdot)$	49.d	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{49}(32,\cdot)$	49.g	21	yes	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{49}(33,\cdot)$	49.h	42	yes	$-1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{31}{42}\right)$
$\chi_{49}(34,\cdot)$	49.f	14	yes	$-1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{49}(36,\cdot)$	49.e	7	yes	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{49}(37,\cdot)$	49.g	21	yes	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{8}{21}\right)$

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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	$49$
Structure	\(C_{42}\)
Order	$42$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{49}(1,\cdot)\)	49.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{49}(2,\cdot)\)	49.g	21	yes	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{49}(3,\cdot)\)	49.h	42	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)
\(\chi_{49}(4,\cdot)\)	49.g	21	yes	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{49}(5,\cdot)\)	49.h	42	yes	\(-1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)
\(\chi_{49}(6,\cdot)\)	49.f	14	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{49}(8,\cdot)\)	49.e	7	yes	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{49}(9,\cdot)\)	49.g	21	yes	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{49}(10,\cdot)\)	49.h	42	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)
\(\chi_{49}(11,\cdot)\)	49.g	21	yes	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{49}(12,\cdot)\)	49.h	42	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)
\(\chi_{49}(13,\cdot)\)	49.f	14	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{49}(15,\cdot)\)	49.e	7	yes	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{49}(16,\cdot)\)	49.g	21	yes	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{49}(17,\cdot)\)	49.h	42	yes	\(-1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)
\(\chi_{49}(18,\cdot)\)	49.c	3	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{49}(19,\cdot)\)	49.d	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{49}(20,\cdot)\)	49.f	14	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{49}(22,\cdot)\)	49.e	7	yes	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{49}(23,\cdot)\)	49.g	21	yes	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{49}(24,\cdot)\)	49.h	42	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)
\(\chi_{49}(25,\cdot)\)	49.g	21	yes	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{49}(26,\cdot)\)	49.h	42	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)
\(\chi_{49}(27,\cdot)\)	49.f	14	yes	\(-1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{49}(29,\cdot)\)	49.e	7	yes	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{49}(30,\cdot)\)	49.c	3	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{49}(31,\cdot)\)	49.d	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{49}(32,\cdot)\)	49.g	21	yes	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{49}(33,\cdot)\)	49.h	42	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)
\(\chi_{49}(34,\cdot)\)	49.f	14	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{49}(36,\cdot)\)	49.e	7	yes	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{49}(37,\cdot)\)	49.g	21	yes	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)

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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.