LMFDB - Group of Dirichlet characters of modulus 1084

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1084)

pari: g = idealstar(,1084,2)

Character group

sage: G.order() pari: g.no
Order	=	540
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{270}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1084}(543,\cdot)$, $\chi_{1084}(277,\cdot)$

First 32 of 540 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{1084}(1,\cdot)$	1084.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1084}(3,\cdot)$	1084.s	30	yes	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{30}\right)$	$-1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{1084}(5,\cdot)$	1084.r	27	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{27}\right)$
$\chi_{1084}(7,\cdot)$	1084.bd	270	yes	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{49}{270}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{181}{270}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{119}{270}\right)$	$e\left(\frac{4}{135}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{29}{135}\right)$
$\chi_{1084}(9,\cdot)$	1084.n	15	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{15}\right)$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{1084}(11,\cdot)$	1084.bd	270	yes	$-1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{181}{270}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{79}{270}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{131}{270}\right)$	$e\left(\frac{1}{135}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{41}{135}\right)$
$\chi_{1084}(13,\cdot)$	1084.p	18	no	$-1$	$1$	$-1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{9}\right)$	$-1$	$e\left(\frac{5}{18}\right)$
$\chi_{1084}(15,\cdot)$	1084.bf	270	yes	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{119}{270}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{131}{270}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{77}{135}\right)$	$e\left(\frac{29}{135}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{83}{270}\right)$
$\chi_{1084}(17,\cdot)$	1084.bc	135	no	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{4}{135}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{135}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{29}{135}\right)$	$e\left(\frac{53}{135}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{135}\right)$
$\chi_{1084}(19,\cdot)$	1084.s	30	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{30}\right)$	$-1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{1084}(21,\cdot)$	1084.be	270	no	$-1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{29}{135}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{41}{135}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{83}{270}\right)$	$e\left(\frac{13}{135}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{121}{270}\right)$
$\chi_{1084}(23,\cdot)$	1084.q	18	yes	$1$	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{18}\right)$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{9}\right)$	$1$	$e\left(\frac{7}{18}\right)$
$\chi_{1084}(25,\cdot)$	1084.r	27	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{27}\right)$
$\chi_{1084}(27,\cdot)$	1084.k	10	yes	$1$	$1$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1084}(29,\cdot)$	1084.g	6	no	$-1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{1084}(31,\cdot)$	1084.ba	90	yes	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{1084}(33,\cdot)$	1084.y	54	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{54}\right)$
$\chi_{1084}(35,\cdot)$	1084.ba	90	yes	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{45}\right)$
$\chi_{1084}(37,\cdot)$	1084.bc	135	no	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{113}{135}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{62}{135}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{43}{135}\right)$	$e\left(\frac{46}{135}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{131}{135}\right)$
$\chi_{1084}(39,\cdot)$	1084.ba	90	yes	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{45}\right)$
$\chi_{1084}(41,\cdot)$	1084.v	45	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{45}\right)$
$\chi_{1084}(43,\cdot)$	1084.bf	270	yes	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{203}{270}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{270}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{44}{135}\right)$	$e\left(\frac{113}{135}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{221}{270}\right)$
$\chi_{1084}(45,\cdot)$	1084.bc	135	no	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{64}{135}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{16}{135}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{59}{135}\right)$	$e\left(\frac{38}{135}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{73}{135}\right)$
$\chi_{1084}(47,\cdot)$	1084.z	90	yes	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{31}{90}\right)$
$\chi_{1084}(49,\cdot)$	1084.bc	135	no	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{49}{135}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{46}{135}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{119}{135}\right)$	$e\left(\frac{8}{135}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{58}{135}\right)$
$\chi_{1084}(51,\cdot)$	1084.bf	270	yes	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{17}{270}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{173}{270}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{135}\right)$	$e\left(\frac{62}{135}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{89}{270}\right)$
$\chi_{1084}(53,\cdot)$	1084.bc	135	no	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{16}{135}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{135}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{116}{135}\right)$	$e\left(\frac{77}{135}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{52}{135}\right)$
$\chi_{1084}(55,\cdot)$	1084.ba	90	yes	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{1084}(57,\cdot)$	1084.n	15	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{15}\right)$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{1084}(59,\cdot)$	1084.bf	270	yes	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{163}{270}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{270}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{34}{135}\right)$	$e\left(\frac{118}{135}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{91}{270}\right)$
$\chi_{1084}(61,\cdot)$	1084.bc	135	no	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{83}{135}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{122}{135}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{28}{135}\right)$	$e\left(\frac{121}{135}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{101}{135}\right)$
$\chi_{1084}(63,\cdot)$	1084.bd	270	yes	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{67}{270}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{253}{270}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{47}{270}\right)$	$e\left(\frac{22}{135}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{92}{135}\right)$

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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	$1084$
Structure	\(C_{2}\times C_{270}\)
Order	$540$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{1084}(1,\cdot)\)	1084.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1084}(3,\cdot)\)	1084.s	30	yes	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(-1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{1084}(5,\cdot)\)	1084.r	27	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{27}\right)\)
\(\chi_{1084}(7,\cdot)\)	1084.bd	270	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{49}{270}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{181}{270}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{119}{270}\right)\)	\(e\left(\frac{4}{135}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{29}{135}\right)\)
\(\chi_{1084}(9,\cdot)\)	1084.n	15	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{1084}(11,\cdot)\)	1084.bd	270	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{181}{270}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{79}{270}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{131}{270}\right)\)	\(e\left(\frac{1}{135}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{41}{135}\right)\)
\(\chi_{1084}(13,\cdot)\)	1084.p	18	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(-1\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{1084}(15,\cdot)\)	1084.bf	270	yes	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{119}{270}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{131}{270}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{77}{135}\right)\)	\(e\left(\frac{29}{135}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{83}{270}\right)\)
\(\chi_{1084}(17,\cdot)\)	1084.bc	135	no	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{4}{135}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{135}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{29}{135}\right)\)	\(e\left(\frac{53}{135}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{135}\right)\)
\(\chi_{1084}(19,\cdot)\)	1084.s	30	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(-1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{1084}(21,\cdot)\)	1084.be	270	no	\(-1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{29}{135}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{41}{135}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{83}{270}\right)\)	\(e\left(\frac{13}{135}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{121}{270}\right)\)
\(\chi_{1084}(23,\cdot)\)	1084.q	18	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(1\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{1084}(25,\cdot)\)	1084.r	27	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{27}\right)\)
\(\chi_{1084}(27,\cdot)\)	1084.k	10	yes	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1084}(29,\cdot)\)	1084.g	6	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1084}(31,\cdot)\)	1084.ba	90	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{32}{45}\right)\)
\(\chi_{1084}(33,\cdot)\)	1084.y	54	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{54}\right)\)
\(\chi_{1084}(35,\cdot)\)	1084.ba	90	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{45}\right)\)
\(\chi_{1084}(37,\cdot)\)	1084.bc	135	no	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{113}{135}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{62}{135}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{43}{135}\right)\)	\(e\left(\frac{46}{135}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{131}{135}\right)\)
\(\chi_{1084}(39,\cdot)\)	1084.ba	90	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{45}\right)\)
\(\chi_{1084}(41,\cdot)\)	1084.v	45	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{45}\right)\)
\(\chi_{1084}(43,\cdot)\)	1084.bf	270	yes	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{203}{270}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{270}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{44}{135}\right)\)	\(e\left(\frac{113}{135}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{221}{270}\right)\)
\(\chi_{1084}(45,\cdot)\)	1084.bc	135	no	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{64}{135}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{16}{135}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{59}{135}\right)\)	\(e\left(\frac{38}{135}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{73}{135}\right)\)
\(\chi_{1084}(47,\cdot)\)	1084.z	90	yes	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{31}{90}\right)\)
\(\chi_{1084}(49,\cdot)\)	1084.bc	135	no	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{49}{135}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{46}{135}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{119}{135}\right)\)	\(e\left(\frac{8}{135}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{58}{135}\right)\)
\(\chi_{1084}(51,\cdot)\)	1084.bf	270	yes	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{17}{270}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{173}{270}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{11}{135}\right)\)	\(e\left(\frac{62}{135}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{89}{270}\right)\)
\(\chi_{1084}(53,\cdot)\)	1084.bc	135	no	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{16}{135}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{135}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{116}{135}\right)\)	\(e\left(\frac{77}{135}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{52}{135}\right)\)
\(\chi_{1084}(55,\cdot)\)	1084.ba	90	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{45}\right)\)
\(\chi_{1084}(57,\cdot)\)	1084.n	15	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{1084}(59,\cdot)\)	1084.bf	270	yes	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{163}{270}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{270}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{34}{135}\right)\)	\(e\left(\frac{118}{135}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{91}{270}\right)\)
\(\chi_{1084}(61,\cdot)\)	1084.bc	135	no	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{83}{135}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{122}{135}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{28}{135}\right)\)	\(e\left(\frac{121}{135}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{101}{135}\right)\)
\(\chi_{1084}(63,\cdot)\)	1084.bd	270	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{67}{270}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{253}{270}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{47}{270}\right)\)	\(e\left(\frac{22}{135}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{92}{135}\right)\)

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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.