LMFDB - Group of Dirichlet characters of modulus 1205

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1205)

pari: g = idealstar(,1205,2)

Character group

sage: G.order() pari: g.no
Order	=	960
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4}\times C_{240}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1205}(242,\cdot)$, $\chi_{1205}(971,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{1205}(1,\cdot)$	1205.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1205}(2,\cdot)$	1205.bn	24	yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{24}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{1205}(3,\cdot)$	1205.cp	120	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{61}{120}\right)$	$-1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{107}{120}\right)$
$\chi_{1205}(4,\cdot)$	1205.w	12	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{1205}(6,\cdot)$	1205.bh	20	no	$1$	$1$	$-1$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{1205}(7,\cdot)$	1205.cr	240	yes	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{227}{240}\right)$
$\chi_{1205}(8,\cdot)$	1205.s	8	yes	$-1$	$1$	$1$	$-1$	$1$	$-1$	$e\left(\frac{1}{8}\right)$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$
$\chi_{1205}(9,\cdot)$	1205.cc	60	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{60}\right)$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{47}{60}\right)$
$\chi_{1205}(11,\cdot)$	1205.bz	48	no	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{43}{48}\right)$
$\chi_{1205}(12,\cdot)$	1205.cp	120	yes	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{71}{120}\right)$	$-1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{97}{120}\right)$
$\chi_{1205}(13,\cdot)$	1205.cr	240	yes	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{109}{240}\right)$
$\chi_{1205}(14,\cdot)$	1205.ct	240	yes	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{71}{240}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{217}{240}\right)$
$\chi_{1205}(16,\cdot)$	1205.m	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1205}(17,\cdot)$	1205.cl	80	yes	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{37}{40}\right)$	$i$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{39}{80}\right)$
$\chi_{1205}(18,\cdot)$	1205.cm	120	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{120}\right)$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{89}{120}\right)$
$\chi_{1205}(19,\cdot)$	1205.by	48	yes	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{48}\right)$
$\chi_{1205}(21,\cdot)$	1205.cj	80	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{31}{40}\right)$	$-i$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{67}{80}\right)$
$\chi_{1205}(22,\cdot)$	1205.cb	48	yes	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{41}{48}\right)$
$\chi_{1205}(23,\cdot)$	1205.cl	80	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{19}{40}\right)$	$-i$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{33}{80}\right)$
$\chi_{1205}(24,\cdot)$	1205.bs	30	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{30}\right)$	$-1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{1205}(26,\cdot)$	1205.cj	80	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{29}{40}\right)$	$i$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{33}{80}\right)$
$\chi_{1205}(27,\cdot)$	1205.bu	40	yes	$-1$	$1$	$-1$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{21}{40}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{27}{40}\right)$
$\chi_{1205}(28,\cdot)$	1205.cl	80	yes	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{40}\right)$	$-i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{69}{80}\right)$
$\chi_{1205}(29,\cdot)$	1205.cn	120	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{120}\right)$	$i$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{79}{120}\right)$
$\chi_{1205}(31,\cdot)$	1205.cs	240	no	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{137}{240}\right)$
$\chi_{1205}(32,\cdot)$	1205.bn	24	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{24}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{1205}(33,\cdot)$	1205.ck	80	yes	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{40}\right)$	$i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{63}{80}\right)$
$\chi_{1205}(34,\cdot)$	1205.ct	240	yes	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{107}{240}\right)$
$\chi_{1205}(36,\cdot)$	1205.v	10	no	$1$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1205}(37,\cdot)$	1205.cr	240	yes	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{133}{240}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{11}{240}\right)$
$\chi_{1205}(38,\cdot)$	1205.ca	48	yes	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{48}\right)$
$\chi_{1205}(39,\cdot)$	1205.ct	240	yes	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{109}{240}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{83}{240}\right)$

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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	$1205$
Structure	\(C_{4}\times C_{240}\)
Order	$960$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{1205}(1,\cdot)\)	1205.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1205}(2,\cdot)\)	1205.bn	24	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{24}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{1205}(3,\cdot)\)	1205.cp	120	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(-1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{107}{120}\right)\)
\(\chi_{1205}(4,\cdot)\)	1205.w	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1205}(6,\cdot)\)	1205.bh	20	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{1205}(7,\cdot)\)	1205.cr	240	yes	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{227}{240}\right)\)
\(\chi_{1205}(8,\cdot)\)	1205.s	8	yes	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1205}(9,\cdot)\)	1205.cc	60	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)
\(\chi_{1205}(11,\cdot)\)	1205.bz	48	no	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)
\(\chi_{1205}(12,\cdot)\)	1205.cp	120	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(-1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{97}{120}\right)\)
\(\chi_{1205}(13,\cdot)\)	1205.cr	240	yes	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{109}{240}\right)\)
\(\chi_{1205}(14,\cdot)\)	1205.ct	240	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{71}{240}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{217}{240}\right)\)
\(\chi_{1205}(16,\cdot)\)	1205.m	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1205}(17,\cdot)\)	1205.cl	80	yes	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(i\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)
\(\chi_{1205}(18,\cdot)\)	1205.cm	120	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{89}{120}\right)\)
\(\chi_{1205}(19,\cdot)\)	1205.by	48	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)
\(\chi_{1205}(21,\cdot)\)	1205.cj	80	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(-i\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)
\(\chi_{1205}(22,\cdot)\)	1205.cb	48	yes	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)
\(\chi_{1205}(23,\cdot)\)	1205.cl	80	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(-i\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)
\(\chi_{1205}(24,\cdot)\)	1205.bs	30	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(-1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{1205}(26,\cdot)\)	1205.cj	80	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(i\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)
\(\chi_{1205}(27,\cdot)\)	1205.bu	40	yes	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{27}{40}\right)\)
\(\chi_{1205}(28,\cdot)\)	1205.cl	80	yes	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(-i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)
\(\chi_{1205}(29,\cdot)\)	1205.cn	120	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(i\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{79}{120}\right)\)
\(\chi_{1205}(31,\cdot)\)	1205.cs	240	no	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{137}{240}\right)\)
\(\chi_{1205}(32,\cdot)\)	1205.bn	24	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{24}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{1205}(33,\cdot)\)	1205.ck	80	yes	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)
\(\chi_{1205}(34,\cdot)\)	1205.ct	240	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{107}{240}\right)\)
\(\chi_{1205}(36,\cdot)\)	1205.v	10	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1205}(37,\cdot)\)	1205.cr	240	yes	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{133}{240}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{11}{240}\right)\)
\(\chi_{1205}(38,\cdot)\)	1205.ca	48	yes	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)
\(\chi_{1205}(39,\cdot)\)	1205.ct	240	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{109}{240}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{83}{240}\right)\)

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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.