LMFDB - Group of Dirichlet characters of modulus 405

Show commands: PariGP / SageMath

sage: H = DirichletGroup(405)

pari: g = idealstar(,405,2)

Character group

sage: G.order() pari: g.no
Order	=	216
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{108}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{405}(326,\cdot)$, $\chi_{405}(82,\cdot)$

First 32 of 216 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{405}(1,\cdot)$	405.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{405}(2,\cdot)$	405.x	108	yes	$1$	$1$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{405}(4,\cdot)$	405.t	54	yes	$1$	$1$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{405}(7,\cdot)$	405.w	108	yes	$-1$	$1$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{405}(8,\cdot)$	405.r	36	no	$1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{405}(11,\cdot)$	405.u	54	no	$-1$	$1$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{405}(13,\cdot)$	405.w	108	yes	$-1$	$1$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{405}(14,\cdot)$	405.v	54	yes	$-1$	$1$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{405}(16,\cdot)$	405.q	27	no	$1$	$1$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{405}(17,\cdot)$	405.r	36	no	$1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{405}(19,\cdot)$	405.p	18	no	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{405}(22,\cdot)$	405.w	108	yes	$-1$	$1$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{405}(23,\cdot)$	405.x	108	yes	$1$	$1$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{405}(26,\cdot)$	405.i	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$
$\chi_{405}(28,\cdot)$	405.l	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$-1$
$\chi_{405}(29,\cdot)$	405.v	54	yes	$-1$	$1$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{405}(31,\cdot)$	405.q	27	no	$1$	$1$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{405}(32,\cdot)$	405.x	108	yes	$1$	$1$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{405}(34,\cdot)$	405.t	54	yes	$1$	$1$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{405}(37,\cdot)$	405.s	36	no	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{405}(38,\cdot)$	405.x	108	yes	$1$	$1$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{405}(41,\cdot)$	405.u	54	no	$-1$	$1$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{405}(43,\cdot)$	405.w	108	yes	$-1$	$1$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{405}(44,\cdot)$	405.n	18	no	$-1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{405}(46,\cdot)$	405.k	9	no	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{405}(47,\cdot)$	405.x	108	yes	$1$	$1$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{405}(49,\cdot)$	405.t	54	yes	$1$	$1$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{405}(52,\cdot)$	405.w	108	yes	$-1$	$1$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{405}(53,\cdot)$	405.m	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$-1$
$\chi_{405}(56,\cdot)$	405.u	54	no	$-1$	$1$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{405}(58,\cdot)$	405.w	108	yes	$-1$	$1$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{405}(59,\cdot)$	405.v	54	yes	$-1$	$1$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{9}\right)$

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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	$405$
Structure	\(C_{2}\times C_{108}\)
Order	$216$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{405}(1,\cdot)\)	405.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{405}(2,\cdot)\)	405.x	108	yes	\(1\)	\(1\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{405}(4,\cdot)\)	405.t	54	yes	\(1\)	\(1\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{405}(7,\cdot)\)	405.w	108	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{405}(8,\cdot)\)	405.r	36	no	\(1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{405}(11,\cdot)\)	405.u	54	no	\(-1\)	\(1\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{405}(13,\cdot)\)	405.w	108	yes	\(-1\)	\(1\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{405}(14,\cdot)\)	405.v	54	yes	\(-1\)	\(1\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{405}(16,\cdot)\)	405.q	27	no	\(1\)	\(1\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{405}(17,\cdot)\)	405.r	36	no	\(1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{405}(19,\cdot)\)	405.p	18	no	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{405}(22,\cdot)\)	405.w	108	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{405}(23,\cdot)\)	405.x	108	yes	\(1\)	\(1\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{405}(26,\cdot)\)	405.i	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)
\(\chi_{405}(28,\cdot)\)	405.l	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(-1\)
\(\chi_{405}(29,\cdot)\)	405.v	54	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{405}(31,\cdot)\)	405.q	27	no	\(1\)	\(1\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{405}(32,\cdot)\)	405.x	108	yes	\(1\)	\(1\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{405}(34,\cdot)\)	405.t	54	yes	\(1\)	\(1\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{405}(37,\cdot)\)	405.s	36	no	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{405}(38,\cdot)\)	405.x	108	yes	\(1\)	\(1\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{405}(41,\cdot)\)	405.u	54	no	\(-1\)	\(1\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{405}(43,\cdot)\)	405.w	108	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{405}(44,\cdot)\)	405.n	18	no	\(-1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{405}(46,\cdot)\)	405.k	9	no	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{405}(47,\cdot)\)	405.x	108	yes	\(1\)	\(1\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{405}(49,\cdot)\)	405.t	54	yes	\(1\)	\(1\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{405}(52,\cdot)\)	405.w	108	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{405}(53,\cdot)\)	405.m	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(-1\)
\(\chi_{405}(56,\cdot)\)	405.u	54	no	\(-1\)	\(1\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{405}(58,\cdot)\)	405.w	108	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{405}(59,\cdot)\)	405.v	54	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)

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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.