LMFDB - Group of Dirichlet characters of modulus 8029

sage:H = DirichletGroup(8029)

pari:g = idealstar(,8029,2)

Character group

sage:G.order() pari:g.no
Order	=	6480
sage:H.invariants() pari:g.cyc
Structure	=	$C_{6}\times C_{6}\times C_{180}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{8029}(5736,\cdot)$, $\chi_{8029}(778,\cdot)$, $\chi_{8029}(4775,\cdot)$

First 32 of 6480 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{8029}(1,\cdot)$	8029.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8029}(2,\cdot)$	8029.ty	180	yes	$-1$	$1$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{11}{36}\right)$	$-i$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{8029}(3,\cdot)$	8029.st	90	yes	$1$	$1$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{31}{45}\right)$
$\chi_{8029}(4,\cdot)$	8029.rl	90	yes	$1$	$1$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{11}{18}\right)$	$-1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{45}\right)$
$\chi_{8029}(5,\cdot)$	8029.nw	36	yes	$1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{9}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{8029}(6,\cdot)$	8029.gg	12	yes	$-1$	$1$	$-i$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{8029}(8,\cdot)$	8029.pu	60	no	$-1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{8029}(9,\cdot)$	8029.pe	45	yes	$1$	$1$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{8029}(10,\cdot)$	8029.kg	30	yes	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{8029}(11,\cdot)$	8029.ly	30	yes	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{8029}(12,\cdot)$	8029.sj	90	yes	$1$	$1$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{8029}(13,\cdot)$	8029.ue	180	yes	$-1$	$1$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{8029}(15,\cdot)$	8029.uv	180	no	$1$	$1$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{11}{36}\right)$	$i$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{37}{90}\right)$
$\chi_{8029}(16,\cdot)$	8029.pi	45	yes	$1$	$1$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{2}{9}\right)$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{8029}(17,\cdot)$	8029.ve	180	yes	$-1$	$1$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{8029}(18,\cdot)$	8029.us	180	yes	$-1$	$1$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{8029}(19,\cdot)$	8029.uf	180	yes	$1$	$1$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{83}{90}\right)$
$\chi_{8029}(20,\cdot)$	8029.vb	180	yes	$1$	$1$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{90}\right)$
$\chi_{8029}(22,\cdot)$	8029.ub	180	no	$1$	$1$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{79}{90}\right)$
$\chi_{8029}(23,\cdot)$	8029.qr	60	yes	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{30}\right)$	$i$	$-i$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{8029}(24,\cdot)$	8029.ud	180	yes	$-1$	$1$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{8029}(25,\cdot)$	8029.jq	18	yes	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{9}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{8029}(26,\cdot)$	8029.ef	6	yes	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{8029}(27,\cdot)$	8029.lm	30	yes	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{8029}(29,\cdot)$	8029.ql	60	no	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{8029}(30,\cdot)$	8029.jw	18	yes	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{18}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{18}\right)$
$\chi_{8029}(32,\cdot)$	8029.pb	36	no	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{19}{36}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{9}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{8029}(33,\cdot)$	8029.rs	90	yes	$-1$	$1$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{17}{18}\right)$	$-1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{83}{90}\right)$
$\chi_{8029}(34,\cdot)$	8029.sn	90	yes	$1$	$1$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{8029}(36,\cdot)$	8029.bg	6	no	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{8029}(38,\cdot)$	8029.mw	30	no	$-1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{15}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{8029}(39,\cdot)$	8029.ux	180	yes	$-1$	$1$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{35}{36}\right)$	$-i$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{32}{45}\right)$

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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	$8029$
Structure	\(C_{6}\times C_{6}\times C_{180}\)
Order	$6480$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{8029}(1,\cdot)\)	8029.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8029}(2,\cdot)\)	8029.ty	180	yes	\(-1\)	\(1\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(-i\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{29}{45}\right)\)
\(\chi_{8029}(3,\cdot)\)	8029.st	90	yes	\(1\)	\(1\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{31}{45}\right)\)
\(\chi_{8029}(4,\cdot)\)	8029.rl	90	yes	\(1\)	\(1\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(-1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{45}\right)\)
\(\chi_{8029}(5,\cdot)\)	8029.nw	36	yes	\(1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{8029}(6,\cdot)\)	8029.gg	12	yes	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{8029}(8,\cdot)\)	8029.pu	60	no	\(-1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{8029}(9,\cdot)\)	8029.pe	45	yes	\(1\)	\(1\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{45}\right)\)
\(\chi_{8029}(10,\cdot)\)	8029.kg	30	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{8029}(11,\cdot)\)	8029.ly	30	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{8029}(12,\cdot)\)	8029.sj	90	yes	\(1\)	\(1\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{8029}(13,\cdot)\)	8029.ue	180	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{8029}(15,\cdot)\)	8029.uv	180	no	\(1\)	\(1\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(i\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{37}{90}\right)\)
\(\chi_{8029}(16,\cdot)\)	8029.pi	45	yes	\(1\)	\(1\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{26}{45}\right)\)
\(\chi_{8029}(17,\cdot)\)	8029.ve	180	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{32}{45}\right)\)
\(\chi_{8029}(18,\cdot)\)	8029.us	180	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{8029}(19,\cdot)\)	8029.uf	180	yes	\(1\)	\(1\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{83}{90}\right)\)
\(\chi_{8029}(20,\cdot)\)	8029.vb	180	yes	\(1\)	\(1\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{90}\right)\)
\(\chi_{8029}(22,\cdot)\)	8029.ub	180	no	\(1\)	\(1\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{79}{90}\right)\)
\(\chi_{8029}(23,\cdot)\)	8029.qr	60	yes	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{8029}(24,\cdot)\)	8029.ud	180	yes	\(-1\)	\(1\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{8029}(25,\cdot)\)	8029.jq	18	yes	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{8029}(26,\cdot)\)	8029.ef	6	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{8029}(27,\cdot)\)	8029.lm	30	yes	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{8029}(29,\cdot)\)	8029.ql	60	no	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{8029}(30,\cdot)\)	8029.jw	18	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{8029}(32,\cdot)\)	8029.pb	36	no	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{8029}(33,\cdot)\)	8029.rs	90	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(-1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{83}{90}\right)\)
\(\chi_{8029}(34,\cdot)\)	8029.sn	90	yes	\(1\)	\(1\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{8029}(36,\cdot)\)	8029.bg	6	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{8029}(38,\cdot)\)	8029.mw	30	no	\(-1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{8029}(39,\cdot)\)	8029.ux	180	yes	\(-1\)	\(1\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(-i\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{32}{45}\right)\)

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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.