LMFDB - Group of Dirichlet characters of modulus 1075

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1075)

pari: g = idealstar(,1075,2)

Character group

sage: G.order() pari: g.no
Order	=	840
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{420}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1075}(302,\cdot)$, $\chi_{1075}(476,\cdot)$

First 32 of 840 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{1075}(1,\cdot)$	1075.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1075}(2,\cdot)$	1075.bq	140	yes	$1$	$1$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{2}{5}\right)$	$-i$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{73}{140}\right)$
$\chi_{1075}(3,\cdot)$	1075.bu	420	yes	$1$	$1$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{199}{420}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{193}{420}\right)$	$e\left(\frac{173}{420}\right)$
$\chi_{1075}(4,\cdot)$	1075.bj	70	yes	$1$	$1$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{3}{70}\right)$
$\chi_{1075}(6,\cdot)$	1075.u	15	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{1075}(7,\cdot)$	1075.p	12	no	$1$	$1$	$-i$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{1075}(8,\cdot)$	1075.bq	140	yes	$1$	$1$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{1}{5}\right)$	$i$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{79}{140}\right)$
$\chi_{1075}(9,\cdot)$	1075.bs	210	yes	$1$	$1$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{193}{210}\right)$	$e\left(\frac{173}{210}\right)$
$\chi_{1075}(11,\cdot)$	1075.bd	35	yes	$1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{1075}(12,\cdot)$	1075.bu	420	yes	$1$	$1$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{193}{420}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{193}{210}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{31}{420}\right)$	$e\left(\frac{191}{420}\right)$
$\chi_{1075}(13,\cdot)$	1075.bv	420	yes	$-1$	$1$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{173}{420}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{191}{420}\right)$	$e\left(\frac{181}{420}\right)$
$\chi_{1075}(14,\cdot)$	1075.bs	210	yes	$1$	$1$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{197}{210}\right)$
$\chi_{1075}(16,\cdot)$	1075.bd	35	yes	$1$	$1$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{1075}(17,\cdot)$	1075.bv	420	yes	$-1$	$1$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{191}{420}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{257}{420}\right)$	$e\left(\frac{127}{420}\right)$
$\chi_{1075}(18,\cdot)$	1075.bn	84	no	$1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{29}{84}\right)$
$\chi_{1075}(19,\cdot)$	1075.bt	210	yes	$-1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{121}{210}\right)$
$\chi_{1075}(21,\cdot)$	1075.bd	35	yes	$1$	$1$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{29}{35}\right)$
$\chi_{1075}(22,\cdot)$	1075.bq	140	yes	$1$	$1$	$e\left(\frac{69}{140}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{4}{5}\right)$	$-i$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{81}{140}\right)$
$\chi_{1075}(23,\cdot)$	1075.bv	420	yes	$-1$	$1$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{97}{420}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{269}{420}\right)$
$\chi_{1075}(24,\cdot)$	1075.bf	42	no	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{41}{42}\right)$
$\chi_{1075}(26,\cdot)$	1075.bg	42	no	$-1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{1075}(27,\cdot)$	1075.bq	140	yes	$1$	$1$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{2}{5}\right)$	$-i$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{33}{140}\right)$
$\chi_{1075}(28,\cdot)$	1075.bu	420	yes	$1$	$1$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{239}{420}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{29}{210}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{293}{420}\right)$	$e\left(\frac{193}{420}\right)$
$\chi_{1075}(29,\cdot)$	1075.bt	210	yes	$-1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{29}{210}\right)$
$\chi_{1075}(31,\cdot)$	1075.bo	105	yes	$1$	$1$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{53}{105}\right)$
$\chi_{1075}(32,\cdot)$	1075.y	28	no	$1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{14}\right)$	$1$	$-i$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{1075}(33,\cdot)$	1075.bu	420	yes	$1$	$1$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{331}{420}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{397}{420}\right)$	$e\left(\frac{197}{420}\right)$
$\chi_{1075}(34,\cdot)$	1075.bt	210	yes	$-1$	$1$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{173}{210}\right)$
$\chi_{1075}(36,\cdot)$	1075.u	15	yes	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{1075}(37,\cdot)$	1075.bi	60	yes	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{53}{60}\right)$
$\chi_{1075}(38,\cdot)$	1075.bv	420	yes	$-1$	$1$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{313}{420}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{331}{420}\right)$	$e\left(\frac{41}{420}\right)$
$\chi_{1075}(39,\cdot)$	1075.bl	70	yes	$-1$	$1$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{59}{70}\right)$

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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	$1075$
Structure	\(C_{2}\times C_{420}\)
Order	$840$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{1075}(1,\cdot)\)	1075.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1075}(2,\cdot)\)	1075.bq	140	yes	\(1\)	\(1\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-i\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{73}{140}\right)\)
\(\chi_{1075}(3,\cdot)\)	1075.bu	420	yes	\(1\)	\(1\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{199}{420}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{193}{420}\right)\)	\(e\left(\frac{173}{420}\right)\)
\(\chi_{1075}(4,\cdot)\)	1075.bj	70	yes	\(1\)	\(1\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{3}{70}\right)\)
\(\chi_{1075}(6,\cdot)\)	1075.u	15	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{1075}(7,\cdot)\)	1075.p	12	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1075}(8,\cdot)\)	1075.bq	140	yes	\(1\)	\(1\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(i\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{79}{140}\right)\)
\(\chi_{1075}(9,\cdot)\)	1075.bs	210	yes	\(1\)	\(1\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{193}{210}\right)\)	\(e\left(\frac{173}{210}\right)\)
\(\chi_{1075}(11,\cdot)\)	1075.bd	35	yes	\(1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{1075}(12,\cdot)\)	1075.bu	420	yes	\(1\)	\(1\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{193}{420}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{193}{210}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{31}{420}\right)\)	\(e\left(\frac{191}{420}\right)\)
\(\chi_{1075}(13,\cdot)\)	1075.bv	420	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{173}{420}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{191}{420}\right)\)	\(e\left(\frac{181}{420}\right)\)
\(\chi_{1075}(14,\cdot)\)	1075.bs	210	yes	\(1\)	\(1\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{197}{210}\right)\)
\(\chi_{1075}(16,\cdot)\)	1075.bd	35	yes	\(1\)	\(1\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{1075}(17,\cdot)\)	1075.bv	420	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{191}{420}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{257}{420}\right)\)	\(e\left(\frac{127}{420}\right)\)
\(\chi_{1075}(18,\cdot)\)	1075.bn	84	no	\(1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)
\(\chi_{1075}(19,\cdot)\)	1075.bt	210	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{121}{210}\right)\)
\(\chi_{1075}(21,\cdot)\)	1075.bd	35	yes	\(1\)	\(1\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)
\(\chi_{1075}(22,\cdot)\)	1075.bq	140	yes	\(1\)	\(1\)	\(e\left(\frac{69}{140}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{81}{140}\right)\)
\(\chi_{1075}(23,\cdot)\)	1075.bv	420	yes	\(-1\)	\(1\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{97}{420}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{269}{420}\right)\)
\(\chi_{1075}(24,\cdot)\)	1075.bf	42	no	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)
\(\chi_{1075}(26,\cdot)\)	1075.bg	42	no	\(-1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{1075}(27,\cdot)\)	1075.bq	140	yes	\(1\)	\(1\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-i\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{33}{140}\right)\)
\(\chi_{1075}(28,\cdot)\)	1075.bu	420	yes	\(1\)	\(1\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{239}{420}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{29}{210}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{293}{420}\right)\)	\(e\left(\frac{193}{420}\right)\)
\(\chi_{1075}(29,\cdot)\)	1075.bt	210	yes	\(-1\)	\(1\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{29}{210}\right)\)
\(\chi_{1075}(31,\cdot)\)	1075.bo	105	yes	\(1\)	\(1\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)
\(\chi_{1075}(32,\cdot)\)	1075.y	28	no	\(1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{1075}(33,\cdot)\)	1075.bu	420	yes	\(1\)	\(1\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{331}{420}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{397}{420}\right)\)	\(e\left(\frac{197}{420}\right)\)
\(\chi_{1075}(34,\cdot)\)	1075.bt	210	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{173}{210}\right)\)
\(\chi_{1075}(36,\cdot)\)	1075.u	15	yes	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{1075}(37,\cdot)\)	1075.bi	60	yes	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)
\(\chi_{1075}(38,\cdot)\)	1075.bv	420	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{313}{420}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{331}{420}\right)\)	\(e\left(\frac{41}{420}\right)\)
\(\chi_{1075}(39,\cdot)\)	1075.bl	70	yes	\(-1\)	\(1\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{59}{70}\right)\)

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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.