LMFDB - Group of Dirichlet characters of modulus 549

Show commands: PariGP / SageMath

sage: H = DirichletGroup(549)

pari: g = idealstar(,549,2)

Character group

sage: G.order() pari: g.no
Order	=	360
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{60}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{549}(245,\cdot)$, $\chi_{549}(307,\cdot)$

First 32 of 360 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{549}(1,\cdot)$	549.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{549}(2,\cdot)$	549.ca	60	yes	$1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{549}(4,\cdot)$	549.bp	30	yes	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{549}(5,\cdot)$	549.bo	30	yes	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{4}{5}\right)$
$\chi_{549}(7,\cdot)$	549.cf	60	yes	$-1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{549}(8,\cdot)$	549.bm	20	no	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$	$i$	$1$	$1$	$e\left(\frac{1}{5}\right)$
$\chi_{549}(10,\cdot)$	549.cb	60	no	$-1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{49}{60}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{549}(11,\cdot)$	549.bd	12	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{549}(13,\cdot)$	549.h	3	yes	$1$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$
$\chi_{549}(14,\cdot)$	549.n	6	yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{549}(16,\cdot)$	549.bj	15	yes	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{549}(17,\cdot)$	549.cd	60	no	$1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{60}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{549}(19,\cdot)$	549.bs	30	no	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{30}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{549}(20,\cdot)$	549.bq	30	yes	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{549}(22,\cdot)$	549.bi	15	yes	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{5}\right)$
$\chi_{549}(23,\cdot)$	549.ce	60	yes	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{549}(25,\cdot)$	549.bi	15	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{3}{5}\right)$
$\chi_{549}(26,\cdot)$	549.cd	60	no	$1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{43}{60}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{549}(28,\cdot)$	549.bn	20	no	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{20}\right)$	$-i$	$1$	$-1$	$e\left(\frac{2}{5}\right)$
$\chi_{549}(29,\cdot)$	549.ba	12	yes	$1$	$1$	$-i$	$-1$	$e\left(\frac{2}{3}\right)$	$i$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$
$\chi_{549}(31,\cdot)$	549.cf	60	yes	$-1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{549}(32,\cdot)$	549.bh	12	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{549}(34,\cdot)$	549.bk	15	yes	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{549}(35,\cdot)$	549.cd	60	no	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{60}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{549}(37,\cdot)$	549.bn	20	no	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{20}\right)$	$-i$	$1$	$-1$	$e\left(\frac{3}{5}\right)$
$\chi_{549}(38,\cdot)$	549.ce	60	yes	$1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{549}(40,\cdot)$	549.bb	12	yes	$-1$	$1$	$-i$	$-1$	$e\left(\frac{5}{6}\right)$	$-i$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$
$\chi_{549}(41,\cdot)$	549.bw	30	yes	$-1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{549}(43,\cdot)$	549.cf	60	yes	$-1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{549}(44,\cdot)$	549.cd	60	no	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{31}{60}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{549}(46,\cdot)$	549.bs	30	no	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{30}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{549}(47,\cdot)$	549.m	6	yes	$-1$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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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	$549$
Structure	\(C_{6}\times C_{60}\)
Order	$360$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{549}(1,\cdot)\)	549.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{549}(2,\cdot)\)	549.ca	60	yes	\(1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{549}(4,\cdot)\)	549.bp	30	yes	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{549}(5,\cdot)\)	549.bo	30	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{549}(7,\cdot)\)	549.cf	60	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{549}(8,\cdot)\)	549.bm	20	no	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(i\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{549}(10,\cdot)\)	549.cb	60	no	\(-1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{549}(11,\cdot)\)	549.bd	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{549}(13,\cdot)\)	549.h	3	yes	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)
\(\chi_{549}(14,\cdot)\)	549.n	6	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{549}(16,\cdot)\)	549.bj	15	yes	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{549}(17,\cdot)\)	549.cd	60	no	\(1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{549}(19,\cdot)\)	549.bs	30	no	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{549}(20,\cdot)\)	549.bq	30	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{549}(22,\cdot)\)	549.bi	15	yes	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{549}(23,\cdot)\)	549.ce	60	yes	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{549}(25,\cdot)\)	549.bi	15	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{549}(26,\cdot)\)	549.cd	60	no	\(1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{549}(28,\cdot)\)	549.bn	20	no	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(-i\)	\(1\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{549}(29,\cdot)\)	549.ba	12	yes	\(1\)	\(1\)	\(-i\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)
\(\chi_{549}(31,\cdot)\)	549.cf	60	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{549}(32,\cdot)\)	549.bh	12	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{549}(34,\cdot)\)	549.bk	15	yes	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{549}(35,\cdot)\)	549.cd	60	no	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{549}(37,\cdot)\)	549.bn	20	no	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(-i\)	\(1\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{549}(38,\cdot)\)	549.ce	60	yes	\(1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{549}(40,\cdot)\)	549.bb	12	yes	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)
\(\chi_{549}(41,\cdot)\)	549.bw	30	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{549}(43,\cdot)\)	549.cf	60	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{549}(44,\cdot)\)	549.cd	60	no	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{549}(46,\cdot)\)	549.bs	30	no	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{549}(47,\cdot)\)	549.m	6	yes	\(-1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)

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