LMFDB - Group of Dirichlet characters of modulus 9405

Show commands: PariGP / SageMath

sage: H = DirichletGroup(9405)

pari: g = idealstar(,9405,2)

Character group

sage: G.order() pari: g.no
Order	=	4320
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{180}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{9405}(1046,\cdot)$, $\chi_{9405}(1882,\cdot)$, $\chi_{9405}(5986,\cdot)$, $\chi_{9405}(496,\cdot)$

First 32 of 4320 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	$-1$	$1$	$2$	$4$	$7$	$8$	$13$	$14$	$16$	$17$	$23$	$26$
$\chi_{9405}(1,\cdot)$	9405.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{9405}(2,\cdot)$	9405.ob	180	yes	$1$	$1$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{9405}(4,\cdot)$	9405.nr	90	yes	$1$	$1$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{9405}(7,\cdot)$	9405.lw	60	yes	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{53}{60}\right)$	$-i$	$e\left(\frac{2}{5}\right)$
$\chi_{9405}(8,\cdot)$	9405.li	60	no	$1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{9405}(13,\cdot)$	9405.on	180	yes	$-1$	$1$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{9405}(14,\cdot)$	9405.mm	90	yes	$1$	$1$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{9405}(16,\cdot)$	9405.ku	45	no	$1$	$1$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{9405}(17,\cdot)$	9405.oc	180	no	$-1$	$1$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{9405}(23,\cdot)$	9405.kk	36	no	$1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{18}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9405}(26,\cdot)$	9405.hy	30	no	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{9405}(28,\cdot)$	9405.oo	180	no	$1$	$1$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{9405}(29,\cdot)$	9405.nk	90	yes	$-1$	$1$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{9405}(31,\cdot)$	9405.ij	30	no	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{9405}(32,\cdot)$	9405.ko	36	yes	$1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{13}{18}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9405}(34,\cdot)$	9405.gk	18	no	$-1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{9405}(37,\cdot)$	9405.hg	20	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{20}\right)$	$-i$	$e\left(\frac{2}{5}\right)$
$\chi_{9405}(41,\cdot)$	9405.mn	90	no	$-1$	$1$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{9405}(43,\cdot)$	9405.ka	36	yes	$1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{11}{18}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{9405}(46,\cdot)$	9405.jm	30	no	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{9405}(47,\cdot)$	9405.nx	180	yes	$1$	$1$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{9405}(49,\cdot)$	9405.jq	30	yes	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{23}{30}\right)$	$-1$	$e\left(\frac{4}{5}\right)$
$\chi_{9405}(52,\cdot)$	9405.on	180	yes	$-1$	$1$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{9405}(53,\cdot)$	9405.ny	180	no	$-1$	$1$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{9405}(56,\cdot)$	9405.bs	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$
$\chi_{9405}(58,\cdot)$	9405.lc	60	no	$-1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{9405}(59,\cdot)$	9405.mm	90	yes	$1$	$1$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{9405}(61,\cdot)$	9405.mo	90	no	$-1$	$1$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{9405}(62,\cdot)$	9405.oc	180	no	$-1$	$1$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{9405}(64,\cdot)$	9405.iq	30	no	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{9405}(67,\cdot)$	9405.ke	36	no	$1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{18}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{9405}(68,\cdot)$	9405.mb	60	yes	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{49}{60}\right)$	$-i$	$e\left(\frac{7}{10}\right)$

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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	$9405$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{180}\)
Order	$4320$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(13\)	\(14\)	\(16\)	\(17\)	\(23\)	\(26\)
\(\chi_{9405}(1,\cdot)\)	9405.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{9405}(2,\cdot)\)	9405.ob	180	yes	\(1\)	\(1\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{9405}(4,\cdot)\)	9405.nr	90	yes	\(1\)	\(1\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{9405}(7,\cdot)\)	9405.lw	60	yes	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(-i\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{9405}(8,\cdot)\)	9405.li	60	no	\(1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{9405}(13,\cdot)\)	9405.on	180	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{9405}(14,\cdot)\)	9405.mm	90	yes	\(1\)	\(1\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{9405}(16,\cdot)\)	9405.ku	45	no	\(1\)	\(1\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{9405}(17,\cdot)\)	9405.oc	180	no	\(-1\)	\(1\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{9405}(23,\cdot)\)	9405.kk	36	no	\(1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9405}(26,\cdot)\)	9405.hy	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{9405}(28,\cdot)\)	9405.oo	180	no	\(1\)	\(1\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{9405}(29,\cdot)\)	9405.nk	90	yes	\(-1\)	\(1\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{9405}(31,\cdot)\)	9405.ij	30	no	\(-1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{9405}(32,\cdot)\)	9405.ko	36	yes	\(1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9405}(34,\cdot)\)	9405.gk	18	no	\(-1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{9405}(37,\cdot)\)	9405.hg	20	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(-i\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{9405}(41,\cdot)\)	9405.mn	90	no	\(-1\)	\(1\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{9405}(43,\cdot)\)	9405.ka	36	yes	\(1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{9405}(46,\cdot)\)	9405.jm	30	no	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{9405}(47,\cdot)\)	9405.nx	180	yes	\(1\)	\(1\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{9405}(49,\cdot)\)	9405.jq	30	yes	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{9405}(52,\cdot)\)	9405.on	180	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{9405}(53,\cdot)\)	9405.ny	180	no	\(-1\)	\(1\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{9405}(56,\cdot)\)	9405.bs	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)
\(\chi_{9405}(58,\cdot)\)	9405.lc	60	no	\(-1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{9405}(59,\cdot)\)	9405.mm	90	yes	\(1\)	\(1\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{9405}(61,\cdot)\)	9405.mo	90	no	\(-1\)	\(1\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{9405}(62,\cdot)\)	9405.oc	180	no	\(-1\)	\(1\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{9405}(64,\cdot)\)	9405.iq	30	no	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{9405}(67,\cdot)\)	9405.ke	36	no	\(1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{9405}(68,\cdot)\)	9405.mb	60	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(-i\)	\(e\left(\frac{7}{10}\right)\)

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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.