LMFDB - Group of Dirichlet characters of modulus 1309

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1309)

pari: g = idealstar(,1309,2)

Character group

sage: G.order() pari: g.no
Order	=	960
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{240}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1309}(1123,\cdot)$, $\chi_{1309}(596,\cdot)$, $\chi_{1309}(309,\cdot)$

First 32 of 960 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$12$	$13$
$\chi_{1309}(1,\cdot)$	1309.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1309}(2,\cdot)$	1309.cu	120	yes	$-1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1309}(3,\cdot)$	1309.da	240	yes	$1$	$1$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{1309}(4,\cdot)$	1309.cm	60	yes	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1309}(5,\cdot)$	1309.da	240	yes	$1$	$1$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{79}{240}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1309}(6,\cdot)$	1309.cs	80	yes	$-1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1309}(8,\cdot)$	1309.cf	40	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1309}(9,\cdot)$	1309.cx	120	yes	$1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{1309}(10,\cdot)$	1309.ck	48	yes	$-1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{13}{48}\right)$	$-i$
$\chi_{1309}(12,\cdot)$	1309.cj	48	no	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{35}{48}\right)$	$-i$
$\chi_{1309}(13,\cdot)$	1309.bp	20	yes	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$-i$	$-i$	$e\left(\frac{3}{5}\right)$
$\chi_{1309}(15,\cdot)$	1309.cg	40	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1309}(16,\cdot)$	1309.cb	30	yes	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1309}(18,\cdot)$	1309.ca	30	no	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1309}(19,\cdot)$	1309.cw	120	yes	$1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1309}(20,\cdot)$	1309.cr	80	yes	$1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{1309}(23,\cdot)$	1309.ci	48	no	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{41}{48}\right)$	$-i$
$\chi_{1309}(24,\cdot)$	1309.cz	240	yes	$-1$	$1$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{161}{240}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{1309}(25,\cdot)$	1309.cx	120	yes	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1309}(26,\cdot)$	1309.cv	120	yes	$-1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1309}(27,\cdot)$	1309.cr	80	yes	$1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{1309}(29,\cdot)$	1309.ct	80	no	$1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1309}(30,\cdot)$	1309.cp	60	yes	$-1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1309}(31,\cdot)$	1309.da	240	yes	$1$	$1$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{11}{240}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{1309}(32,\cdot)$	1309.bw	24	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$1$
$\chi_{1309}(36,\cdot)$	1309.cg	40	no	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1309}(37,\cdot)$	1309.db	240	yes	$-1$	$1$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{1309}(38,\cdot)$	1309.cn	60	yes	$-1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{1309}(39,\cdot)$	1309.cy	240	yes	$1$	$1$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{119}{240}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1309}(40,\cdot)$	1309.cz	240	yes	$-1$	$1$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1309}(41,\cdot)$	1309.cs	80	yes	$-1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{1309}(43,\cdot)$	1309.x	8	no	$-1$	$1$	$i$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$

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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	$1309$
Structure	\(C_{2}\times C_{2}\times C_{240}\)
Order	$960$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(12\)	\(13\)
\(\chi_{1309}(1,\cdot)\)	1309.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1309}(2,\cdot)\)	1309.cu	120	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1309}(3,\cdot)\)	1309.da	240	yes	\(1\)	\(1\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{83}{240}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{1309}(4,\cdot)\)	1309.cm	60	yes	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1309}(5,\cdot)\)	1309.da	240	yes	\(1\)	\(1\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{83}{240}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{79}{240}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{1309}(6,\cdot)\)	1309.cs	80	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{1309}(8,\cdot)\)	1309.cf	40	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1309}(9,\cdot)\)	1309.cx	120	yes	\(1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{1309}(10,\cdot)\)	1309.ck	48	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(-i\)
\(\chi_{1309}(12,\cdot)\)	1309.cj	48	no	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(-i\)
\(\chi_{1309}(13,\cdot)\)	1309.bp	20	yes	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1309}(15,\cdot)\)	1309.cg	40	no	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1309}(16,\cdot)\)	1309.cb	30	yes	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1309}(18,\cdot)\)	1309.ca	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1309}(19,\cdot)\)	1309.cw	120	yes	\(1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1309}(20,\cdot)\)	1309.cr	80	yes	\(1\)	\(1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{1309}(23,\cdot)\)	1309.ci	48	no	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(-i\)
\(\chi_{1309}(24,\cdot)\)	1309.cz	240	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{161}{240}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{1309}(25,\cdot)\)	1309.cx	120	yes	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1309}(26,\cdot)\)	1309.cv	120	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1309}(27,\cdot)\)	1309.cr	80	yes	\(1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{1309}(29,\cdot)\)	1309.ct	80	no	\(1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{1309}(30,\cdot)\)	1309.cp	60	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1309}(31,\cdot)\)	1309.da	240	yes	\(1\)	\(1\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{11}{240}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{1309}(32,\cdot)\)	1309.bw	24	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(1\)
\(\chi_{1309}(36,\cdot)\)	1309.cg	40	no	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1309}(37,\cdot)\)	1309.db	240	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{1309}(38,\cdot)\)	1309.cn	60	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1309}(39,\cdot)\)	1309.cy	240	yes	\(1\)	\(1\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{43}{240}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{119}{240}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{1309}(40,\cdot)\)	1309.cz	240	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{1309}(41,\cdot)\)	1309.cs	80	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{1309}(43,\cdot)\)	1309.x	8	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)

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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.