LMFDB - Group of Dirichlet characters of modulus 181

Show commands: PariGP / SageMath

sage: H = DirichletGroup(181)

pari: g = idealstar(,181,2)

Character group

sage: G.order() pari: g.no
Order	=	180
sage: H.invariants() pari: g.cyc
Structure	=	$C_{180}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{181}(2,\cdot)$

First 32 of 180 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{181}(1,\cdot)$	181.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{181}(2,\cdot)$	181.r	180	yes	$-1$	$1$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{31}{90}\right)$
$\chi_{181}(3,\cdot)$	181.o	45	yes	$1$	$1$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{13}{45}\right)$
$\chi_{181}(4,\cdot)$	181.q	90	yes	$1$	$1$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{31}{45}\right)$
$\chi_{181}(5,\cdot)$	181.j	15	yes	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{181}(6,\cdot)$	181.p	60	yes	$-1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$-i$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{181}(7,\cdot)$	181.i	12	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-i$	$i$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{181}(8,\cdot)$	181.p	60	yes	$-1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$i$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{181}(9,\cdot)$	181.o	45	yes	$1$	$1$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{181}(10,\cdot)$	181.r	180	yes	$-1$	$1$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{7}{90}\right)$
$\chi_{181}(11,\cdot)$	181.q	90	yes	$1$	$1$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{181}(12,\cdot)$	181.q	90	yes	$1$	$1$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{181}(13,\cdot)$	181.o	45	yes	$1$	$1$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{181}(14,\cdot)$	181.o	45	yes	$1$	$1$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{23}{45}\right)$
$\chi_{181}(15,\cdot)$	181.o	45	yes	$1$	$1$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{181}(16,\cdot)$	181.o	45	yes	$1$	$1$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{181}(17,\cdot)$	181.n	36	yes	$-1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{181}(18,\cdot)$	181.r	180	yes	$-1$	$1$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{83}{90}\right)$
$\chi_{181}(19,\cdot)$	181.d	4	yes	$-1$	$1$	$-i$	$1$	$-1$	$1$	$-i$	$i$	$i$	$1$	$-i$	$-1$
$\chi_{181}(20,\cdot)$	181.q	90	yes	$1$	$1$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{19}{45}\right)$
$\chi_{181}(21,\cdot)$	181.r	180	yes	$-1$	$1$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{41}{90}\right)$
$\chi_{181}(22,\cdot)$	181.l	20	yes	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$i$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{181}(23,\cdot)$	181.r	180	yes	$-1$	$1$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{23}{90}\right)$
$\chi_{181}(24,\cdot)$	181.r	180	yes	$-1$	$1$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{29}{90}\right)$
$\chi_{181}(25,\cdot)$	181.j	15	yes	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{181}(26,\cdot)$	181.i	12	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$i$	$-i$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{181}(27,\cdot)$	181.j	15	yes	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{181}(28,\cdot)$	181.r	180	yes	$-1$	$1$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{77}{90}\right)$
$\chi_{181}(29,\cdot)$	181.j	15	yes	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{181}(30,\cdot)$	181.p	60	yes	$-1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$-i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{181}(31,\cdot)$	181.l	20	yes	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$i$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{181}(32,\cdot)$	181.n	36	yes	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{13}{18}\right)$

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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	$181$
Structure	\(C_{180}\)
Order	$180$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{181}(1,\cdot)\)	181.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{181}(2,\cdot)\)	181.r	180	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{31}{90}\right)\)
\(\chi_{181}(3,\cdot)\)	181.o	45	yes	\(1\)	\(1\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)
\(\chi_{181}(4,\cdot)\)	181.q	90	yes	\(1\)	\(1\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)
\(\chi_{181}(5,\cdot)\)	181.j	15	yes	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{181}(6,\cdot)\)	181.p	60	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(-i\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{181}(7,\cdot)\)	181.i	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-i\)	\(i\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{181}(8,\cdot)\)	181.p	60	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(i\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{181}(9,\cdot)\)	181.o	45	yes	\(1\)	\(1\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)
\(\chi_{181}(10,\cdot)\)	181.r	180	yes	\(-1\)	\(1\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{7}{90}\right)\)
\(\chi_{181}(11,\cdot)\)	181.q	90	yes	\(1\)	\(1\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{181}(12,\cdot)\)	181.q	90	yes	\(1\)	\(1\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{181}(13,\cdot)\)	181.o	45	yes	\(1\)	\(1\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{181}(14,\cdot)\)	181.o	45	yes	\(1\)	\(1\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)
\(\chi_{181}(15,\cdot)\)	181.o	45	yes	\(1\)	\(1\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{181}(16,\cdot)\)	181.o	45	yes	\(1\)	\(1\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)
\(\chi_{181}(17,\cdot)\)	181.n	36	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{181}(18,\cdot)\)	181.r	180	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)
\(\chi_{181}(19,\cdot)\)	181.d	4	yes	\(-1\)	\(1\)	\(-i\)	\(1\)	\(-1\)	\(1\)	\(-i\)	\(i\)	\(i\)	\(1\)	\(-i\)	\(-1\)
\(\chi_{181}(20,\cdot)\)	181.q	90	yes	\(1\)	\(1\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)
\(\chi_{181}(21,\cdot)\)	181.r	180	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)
\(\chi_{181}(22,\cdot)\)	181.l	20	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(i\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{181}(23,\cdot)\)	181.r	180	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)
\(\chi_{181}(24,\cdot)\)	181.r	180	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{29}{90}\right)\)
\(\chi_{181}(25,\cdot)\)	181.j	15	yes	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{181}(26,\cdot)\)	181.i	12	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(i\)	\(-i\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{181}(27,\cdot)\)	181.j	15	yes	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{181}(28,\cdot)\)	181.r	180	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)
\(\chi_{181}(29,\cdot)\)	181.j	15	yes	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{181}(30,\cdot)\)	181.p	60	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(-i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{181}(31,\cdot)\)	181.l	20	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(i\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{181}(32,\cdot)\)	181.n	36	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)

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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.