LMFDB - Group of Dirichlet characters of modulus 695

sage:H = DirichletGroup(695)

pari:g = idealstar(,695,2)

Character group

sage:G.order() pari:g.no
Order	=	552
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{276}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{695}(557,\cdot)$, $\chi_{695}(141,\cdot)$

First 32 of 552 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{695}(1,\cdot)$	695.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{695}(2,\cdot)$	695.w	276	yes	$1$	$1$	$e\left(\frac{71}{276}\right)$	$e\left(\frac{13}{276}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{169}{276}\right)$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{155}{276}\right)$	$e\left(\frac{59}{276}\right)$
$\chi_{695}(3,\cdot)$	695.w	276	yes	$1$	$1$	$e\left(\frac{13}{276}\right)$	$e\left(\frac{119}{276}\right)$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{167}{276}\right)$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{119}{138}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{145}{276}\right)$	$e\left(\frac{73}{276}\right)$
$\chi_{695}(4,\cdot)$	695.t	138	yes	$1$	$1$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{31}{138}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{59}{138}\right)$
$\chi_{695}(6,\cdot)$	695.m	23	no	$1$	$1$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{11}{23}\right)$
$\chi_{695}(7,\cdot)$	695.x	276	yes	$-1$	$1$	$e\left(\frac{169}{276}\right)$	$e\left(\frac{167}{276}\right)$	$e\left(\frac{31}{138}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{101}{276}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{29}{138}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{229}{276}\right)$	$e\left(\frac{259}{276}\right)$
$\chi_{695}(8,\cdot)$	695.r	92	yes	$1$	$1$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{59}{92}\right)$
$\chi_{695}(9,\cdot)$	695.t	138	yes	$1$	$1$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{119}{138}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{29}{138}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{73}{138}\right)$
$\chi_{695}(11,\cdot)$	695.q	69	no	$1$	$1$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{17}{69}\right)$
$\chi_{695}(12,\cdot)$	695.w	276	yes	$1$	$1$	$e\left(\frac{155}{276}\right)$	$e\left(\frac{145}{276}\right)$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{229}{276}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{179}{276}\right)$	$e\left(\frac{191}{276}\right)$
$\chi_{695}(13,\cdot)$	695.x	276	yes	$-1$	$1$	$e\left(\frac{59}{276}\right)$	$e\left(\frac{73}{276}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{259}{276}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{73}{138}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{191}{276}\right)$	$e\left(\frac{257}{276}\right)$
$\chi_{695}(14,\cdot)$	695.n	46	yes	$-1$	$1$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{7}{46}\right)$
$\chi_{695}(16,\cdot)$	695.q	69	no	$1$	$1$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{59}{69}\right)$
$\chi_{695}(17,\cdot)$	695.w	276	yes	$1$	$1$	$e\left(\frac{7}{276}\right)$	$e\left(\frac{149}{276}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{5}{276}\right)$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{163}{276}\right)$	$e\left(\frac{103}{276}\right)$
$\chi_{695}(18,\cdot)$	695.w	276	yes	$1$	$1$	$e\left(\frac{97}{276}\right)$	$e\left(\frac{251}{276}\right)$	$e\left(\frac{97}{138}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{227}{276}\right)$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{113}{138}\right)$	$e\left(\frac{49}{69}\right)$	$e\left(\frac{169}{276}\right)$	$e\left(\frac{205}{276}\right)$
$\chi_{695}(19,\cdot)$	695.v	138	yes	$-1$	$1$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{109}{138}\right)$
$\chi_{695}(21,\cdot)$	695.u	138	no	$-1$	$1$	$e\left(\frac{91}{138}\right)$	$e\left(\frac{5}{138}\right)$	$e\left(\frac{22}{69}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{49}{138}\right)$	$e\left(\frac{14}{69}\right)$
$\chi_{695}(22,\cdot)$	695.w	276	yes	$1$	$1$	$e\left(\frac{223}{276}\right)$	$e\left(\frac{173}{276}\right)$	$e\left(\frac{85}{138}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{41}{276}\right)$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{67}{276}\right)$	$e\left(\frac{127}{276}\right)$
$\chi_{695}(23,\cdot)$	695.r	92	yes	$1$	$1$	$e\left(\frac{87}{92}\right)$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{49}{92}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{71}{92}\right)$
$\chi_{695}(24,\cdot)$	695.t	138	yes	$1$	$1$	$e\left(\frac{113}{138}\right)$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{61}{138}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{29}{138}\right)$	$e\left(\frac{125}{138}\right)$
$\chi_{695}(26,\cdot)$	695.u	138	no	$-1$	$1$	$e\left(\frac{65}{138}\right)$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{10}{69}\right)$
$\chi_{695}(27,\cdot)$	695.r	92	yes	$1$	$1$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{73}{92}\right)$
$\chi_{695}(28,\cdot)$	695.x	276	yes	$-1$	$1$	$e\left(\frac{35}{276}\right)$	$e\left(\frac{193}{276}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{163}{276}\right)$	$e\left(\frac{35}{92}\right)$	$e\left(\frac{55}{138}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{263}{276}\right)$	$e\left(\frac{101}{276}\right)$
$\chi_{695}(29,\cdot)$	695.t	138	yes	$1$	$1$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{77}{138}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{109}{138}\right)$	$e\left(\frac{13}{138}\right)$
$\chi_{695}(31,\cdot)$	695.q	69	no	$1$	$1$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{67}{69}\right)$
$\chi_{695}(32,\cdot)$	695.w	276	yes	$1$	$1$	$e\left(\frac{79}{276}\right)$	$e\left(\frac{65}{276}\right)$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{17}{276}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{65}{138}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{223}{276}\right)$	$e\left(\frac{19}{276}\right)$
$\chi_{695}(33,\cdot)$	695.r	92	yes	$1$	$1$	$e\left(\frac{55}{92}\right)$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{19}{92}\right)$	$e\left(\frac{47}{92}\right)$
$\chi_{695}(34,\cdot)$	695.p	46	yes	$1$	$1$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{27}{46}\right)$
$\chi_{695}(36,\cdot)$	695.m	23	no	$1$	$1$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{22}{23}\right)$
$\chi_{695}(37,\cdot)$	695.x	276	yes	$-1$	$1$	$e\left(\frac{229}{276}\right)$	$e\left(\frac{143}{276}\right)$	$e\left(\frac{91}{138}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{65}{276}\right)$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{5}{138}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{49}{276}\right)$	$e\left(\frac{235}{276}\right)$
$\chi_{695}(38,\cdot)$	695.x	276	yes	$-1$	$1$	$e\left(\frac{55}{276}\right)$	$e\left(\frac{185}{276}\right)$	$e\left(\frac{55}{138}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{59}{276}\right)$	$e\left(\frac{55}{92}\right)$	$e\left(\frac{47}{138}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{19}{276}\right)$	$e\left(\frac{1}{276}\right)$
$\chi_{695}(39,\cdot)$	695.n	46	yes	$-1$	$1$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{9}{46}\right)$

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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	$695$
Structure	\(C_{2}\times C_{276}\)
Order	$552$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{695}(1,\cdot)\)	695.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{695}(2,\cdot)\)	695.w	276	yes	\(1\)	\(1\)	\(e\left(\frac{71}{276}\right)\)	\(e\left(\frac{13}{276}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{169}{276}\right)\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{155}{276}\right)\)	\(e\left(\frac{59}{276}\right)\)
\(\chi_{695}(3,\cdot)\)	695.w	276	yes	\(1\)	\(1\)	\(e\left(\frac{13}{276}\right)\)	\(e\left(\frac{119}{276}\right)\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{167}{276}\right)\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{119}{138}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{145}{276}\right)\)	\(e\left(\frac{73}{276}\right)\)
\(\chi_{695}(4,\cdot)\)	695.t	138	yes	\(1\)	\(1\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{31}{138}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{59}{138}\right)\)
\(\chi_{695}(6,\cdot)\)	695.m	23	no	\(1\)	\(1\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)
\(\chi_{695}(7,\cdot)\)	695.x	276	yes	\(-1\)	\(1\)	\(e\left(\frac{169}{276}\right)\)	\(e\left(\frac{167}{276}\right)\)	\(e\left(\frac{31}{138}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{101}{276}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{29}{138}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{229}{276}\right)\)	\(e\left(\frac{259}{276}\right)\)
\(\chi_{695}(8,\cdot)\)	695.r	92	yes	\(1\)	\(1\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{59}{92}\right)\)
\(\chi_{695}(9,\cdot)\)	695.t	138	yes	\(1\)	\(1\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{119}{138}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{29}{138}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{73}{138}\right)\)
\(\chi_{695}(11,\cdot)\)	695.q	69	no	\(1\)	\(1\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{17}{69}\right)\)
\(\chi_{695}(12,\cdot)\)	695.w	276	yes	\(1\)	\(1\)	\(e\left(\frac{155}{276}\right)\)	\(e\left(\frac{145}{276}\right)\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{229}{276}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{179}{276}\right)\)	\(e\left(\frac{191}{276}\right)\)
\(\chi_{695}(13,\cdot)\)	695.x	276	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{276}\right)\)	\(e\left(\frac{73}{276}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{259}{276}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{73}{138}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{191}{276}\right)\)	\(e\left(\frac{257}{276}\right)\)
\(\chi_{695}(14,\cdot)\)	695.n	46	yes	\(-1\)	\(1\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{7}{46}\right)\)
\(\chi_{695}(16,\cdot)\)	695.q	69	no	\(1\)	\(1\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{59}{69}\right)\)
\(\chi_{695}(17,\cdot)\)	695.w	276	yes	\(1\)	\(1\)	\(e\left(\frac{7}{276}\right)\)	\(e\left(\frac{149}{276}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{5}{276}\right)\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{163}{276}\right)\)	\(e\left(\frac{103}{276}\right)\)
\(\chi_{695}(18,\cdot)\)	695.w	276	yes	\(1\)	\(1\)	\(e\left(\frac{97}{276}\right)\)	\(e\left(\frac{251}{276}\right)\)	\(e\left(\frac{97}{138}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{227}{276}\right)\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{113}{138}\right)\)	\(e\left(\frac{49}{69}\right)\)	\(e\left(\frac{169}{276}\right)\)	\(e\left(\frac{205}{276}\right)\)
\(\chi_{695}(19,\cdot)\)	695.v	138	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{109}{138}\right)\)
\(\chi_{695}(21,\cdot)\)	695.u	138	no	\(-1\)	\(1\)	\(e\left(\frac{91}{138}\right)\)	\(e\left(\frac{5}{138}\right)\)	\(e\left(\frac{22}{69}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{49}{138}\right)\)	\(e\left(\frac{14}{69}\right)\)
\(\chi_{695}(22,\cdot)\)	695.w	276	yes	\(1\)	\(1\)	\(e\left(\frac{223}{276}\right)\)	\(e\left(\frac{173}{276}\right)\)	\(e\left(\frac{85}{138}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{41}{276}\right)\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{67}{276}\right)\)	\(e\left(\frac{127}{276}\right)\)
\(\chi_{695}(23,\cdot)\)	695.r	92	yes	\(1\)	\(1\)	\(e\left(\frac{87}{92}\right)\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{49}{92}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{71}{92}\right)\)
\(\chi_{695}(24,\cdot)\)	695.t	138	yes	\(1\)	\(1\)	\(e\left(\frac{113}{138}\right)\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{61}{138}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{29}{138}\right)\)	\(e\left(\frac{125}{138}\right)\)
\(\chi_{695}(26,\cdot)\)	695.u	138	no	\(-1\)	\(1\)	\(e\left(\frac{65}{138}\right)\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{10}{69}\right)\)
\(\chi_{695}(27,\cdot)\)	695.r	92	yes	\(1\)	\(1\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{73}{92}\right)\)
\(\chi_{695}(28,\cdot)\)	695.x	276	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{276}\right)\)	\(e\left(\frac{193}{276}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{163}{276}\right)\)	\(e\left(\frac{35}{92}\right)\)	\(e\left(\frac{55}{138}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{263}{276}\right)\)	\(e\left(\frac{101}{276}\right)\)
\(\chi_{695}(29,\cdot)\)	695.t	138	yes	\(1\)	\(1\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{77}{138}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{109}{138}\right)\)	\(e\left(\frac{13}{138}\right)\)
\(\chi_{695}(31,\cdot)\)	695.q	69	no	\(1\)	\(1\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{67}{69}\right)\)
\(\chi_{695}(32,\cdot)\)	695.w	276	yes	\(1\)	\(1\)	\(e\left(\frac{79}{276}\right)\)	\(e\left(\frac{65}{276}\right)\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{17}{276}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{65}{138}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{223}{276}\right)\)	\(e\left(\frac{19}{276}\right)\)
\(\chi_{695}(33,\cdot)\)	695.r	92	yes	\(1\)	\(1\)	\(e\left(\frac{55}{92}\right)\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{19}{92}\right)\)	\(e\left(\frac{47}{92}\right)\)
\(\chi_{695}(34,\cdot)\)	695.p	46	yes	\(1\)	\(1\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{27}{46}\right)\)
\(\chi_{695}(36,\cdot)\)	695.m	23	no	\(1\)	\(1\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)
\(\chi_{695}(37,\cdot)\)	695.x	276	yes	\(-1\)	\(1\)	\(e\left(\frac{229}{276}\right)\)	\(e\left(\frac{143}{276}\right)\)	\(e\left(\frac{91}{138}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{65}{276}\right)\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{5}{138}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{49}{276}\right)\)	\(e\left(\frac{235}{276}\right)\)
\(\chi_{695}(38,\cdot)\)	695.x	276	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{276}\right)\)	\(e\left(\frac{185}{276}\right)\)	\(e\left(\frac{55}{138}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{59}{276}\right)\)	\(e\left(\frac{55}{92}\right)\)	\(e\left(\frac{47}{138}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{19}{276}\right)\)	\(e\left(\frac{1}{276}\right)\)
\(\chi_{695}(39,\cdot)\)	695.n	46	yes	\(-1\)	\(1\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{9}{46}\right)\)

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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.