LMFDB - Group of Dirichlet characters of modulus 1073

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1073)

pari: g = idealstar(,1073,2)

Character group

sage: G.order() pari: g.no
Order	=	1008
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4}\times C_{252}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1073}(408,\cdot)$, $\chi_{1073}(668,\cdot)$

First 32 of 1008 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{1073}(1,\cdot)$	1073.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1073}(2,\cdot)$	1073.cg	252	yes	$1$	$1$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{227}{252}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{107}{252}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{61}{84}\right)$
$\chi_{1073}(3,\cdot)$	1073.cc	252	yes	$-1$	$1$	$e\left(\frac{227}{252}\right)$	$e\left(\frac{169}{252}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{1073}(4,\cdot)$	1073.cb	126	yes	$1$	$1$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{19}{42}\right)$
$\chi_{1073}(5,\cdot)$	1073.ce	252	yes	$-1$	$1$	$e\left(\frac{107}{252}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{247}{252}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{1073}(6,\cdot)$	1073.be	28	yes	$-1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{1073}(7,\cdot)$	1073.bs	63	yes	$1$	$1$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{1073}(8,\cdot)$	1073.by	84	yes	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{28}\right)$
$\chi_{1073}(9,\cdot)$	1073.bz	126	yes	$1$	$1$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{11}{42}\right)$
$\chi_{1073}(10,\cdot)$	1073.bv	84	yes	$-1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{1073}(11,\cdot)$	1073.bw	84	yes	$-1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{1073}(12,\cdot)$	1073.bj	36	yes	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{18}\right)$	$-1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{1073}(13,\cdot)$	1073.ce	252	yes	$-1$	$1$	$e\left(\frac{239}{252}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{43}{252}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{1073}(14,\cdot)$	1073.by	84	yes	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{1073}(15,\cdot)$	1073.cd	252	yes	$1$	$1$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{53}{252}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{131}{252}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{79}{84}\right)$
$\chi_{1073}(16,\cdot)$	1073.bs	63	yes	$1$	$1$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{1073}(17,\cdot)$	1073.bn	36	yes	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{35}{36}\right)$	$-i$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{1073}(18,\cdot)$	1073.cd	252	yes	$1$	$1$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{61}{252}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{127}{252}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{83}{84}\right)$
$\chi_{1073}(19,\cdot)$	1073.cd	252	yes	$1$	$1$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{223}{252}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{109}{252}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{1073}(20,\cdot)$	1073.cf	252	yes	$-1$	$1$	$e\left(\frac{139}{252}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{209}{252}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{11}{42}\right)$
$\chi_{1073}(21,\cdot)$	1073.cc	252	yes	$-1$	$1$	$e\left(\frac{55}{252}\right)$	$e\left(\frac{233}{252}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{1073}(22,\cdot)$	1073.ce	252	yes	$-1$	$1$	$e\left(\frac{199}{252}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{59}{252}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{1073}(23,\cdot)$	1073.bu	84	yes	$-1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{1073}(24,\cdot)$	1073.cf	252	yes	$-1$	$1$	$e\left(\frac{23}{252}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{205}{252}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{13}{42}\right)$
$\chi_{1073}(25,\cdot)$	1073.ca	126	yes	$1$	$1$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{1073}(26,\cdot)$	1073.bv	84	yes	$-1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{1073}(27,\cdot)$	1073.bw	84	yes	$-1$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{1073}(28,\cdot)$	1073.z	18	yes	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{18}\right)$	$-1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1073}(30,\cdot)$	1073.ba	18	no	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{18}\right)$	$-1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1073}(31,\cdot)$	1073.bd	28	yes	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{1073}(32,\cdot)$	1073.cg	252	yes	$1$	$1$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{127}{252}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{31}{252}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{53}{84}\right)$
$\chi_{1073}(33,\cdot)$	1073.bz	126	yes	$1$	$1$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{19}{42}\right)$

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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	$1073$
Structure	\(C_{4}\times C_{252}\)
Order	$1008$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{1073}(1,\cdot)\)	1073.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1073}(2,\cdot)\)	1073.cg	252	yes	\(1\)	\(1\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{227}{252}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{107}{252}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)
\(\chi_{1073}(3,\cdot)\)	1073.cc	252	yes	\(-1\)	\(1\)	\(e\left(\frac{227}{252}\right)\)	\(e\left(\frac{169}{252}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{1073}(4,\cdot)\)	1073.cb	126	yes	\(1\)	\(1\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)
\(\chi_{1073}(5,\cdot)\)	1073.ce	252	yes	\(-1\)	\(1\)	\(e\left(\frac{107}{252}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{247}{252}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{1073}(6,\cdot)\)	1073.be	28	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{1073}(7,\cdot)\)	1073.bs	63	yes	\(1\)	\(1\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{1073}(8,\cdot)\)	1073.by	84	yes	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{1073}(9,\cdot)\)	1073.bz	126	yes	\(1\)	\(1\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)
\(\chi_{1073}(10,\cdot)\)	1073.bv	84	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{1073}(11,\cdot)\)	1073.bw	84	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{1073}(12,\cdot)\)	1073.bj	36	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(-1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1073}(13,\cdot)\)	1073.ce	252	yes	\(-1\)	\(1\)	\(e\left(\frac{239}{252}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{43}{252}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{1073}(14,\cdot)\)	1073.by	84	yes	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{1073}(15,\cdot)\)	1073.cd	252	yes	\(1\)	\(1\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{53}{252}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{131}{252}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{79}{84}\right)\)
\(\chi_{1073}(16,\cdot)\)	1073.bs	63	yes	\(1\)	\(1\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{1073}(17,\cdot)\)	1073.bn	36	yes	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(-i\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1073}(18,\cdot)\)	1073.cd	252	yes	\(1\)	\(1\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{61}{252}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{127}{252}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{83}{84}\right)\)
\(\chi_{1073}(19,\cdot)\)	1073.cd	252	yes	\(1\)	\(1\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{223}{252}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{109}{252}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)
\(\chi_{1073}(20,\cdot)\)	1073.cf	252	yes	\(-1\)	\(1\)	\(e\left(\frac{139}{252}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{209}{252}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)
\(\chi_{1073}(21,\cdot)\)	1073.cc	252	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{252}\right)\)	\(e\left(\frac{233}{252}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{1073}(22,\cdot)\)	1073.ce	252	yes	\(-1\)	\(1\)	\(e\left(\frac{199}{252}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{59}{252}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{1073}(23,\cdot)\)	1073.bu	84	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{1073}(24,\cdot)\)	1073.cf	252	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{252}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{205}{252}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)
\(\chi_{1073}(25,\cdot)\)	1073.ca	126	yes	\(1\)	\(1\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{1073}(26,\cdot)\)	1073.bv	84	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{1073}(27,\cdot)\)	1073.bw	84	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{1073}(28,\cdot)\)	1073.z	18	yes	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(-1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1073}(30,\cdot)\)	1073.ba	18	no	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(-1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1073}(31,\cdot)\)	1073.bd	28	yes	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{1073}(32,\cdot)\)	1073.cg	252	yes	\(1\)	\(1\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{127}{252}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{31}{252}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{53}{84}\right)\)
\(\chi_{1073}(33,\cdot)\)	1073.bz	126	yes	\(1\)	\(1\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)

Introduction

L-functions

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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.