LMFDB - Group of Dirichlet characters of modulus 407

Show commands: PariGP / SageMath

sage: H = DirichletGroup(407)

pari: g = idealstar(,407,2)

Character group

sage: G.order() pari: g.no
Order	=	360
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{180}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{407}(112,\cdot)$, $\chi_{407}(298,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{407}(1,\cdot)$	407.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{407}(2,\cdot)$	407.bj	180	yes	$1$	$1$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{407}(3,\cdot)$	407.bg	90	yes	$1$	$1$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{407}(4,\cdot)$	407.bg	90	yes	$1$	$1$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{407}(5,\cdot)$	407.bi	180	yes	$-1$	$1$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{407}(6,\cdot)$	407.w	20	yes	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$1$
$\chi_{407}(7,\cdot)$	407.bh	90	yes	$-1$	$1$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{407}(8,\cdot)$	407.bd	60	yes	$1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{15}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{407}(9,\cdot)$	407.bc	45	yes	$1$	$1$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{407}(10,\cdot)$	407.j	6	yes	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{407}(12,\cdot)$	407.l	9	no	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{407}(13,\cdot)$	407.bj	180	yes	$1$	$1$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{407}(14,\cdot)$	407.be	60	yes	$-1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{15}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{407}(15,\cdot)$	407.bi	180	yes	$-1$	$1$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{407}(16,\cdot)$	407.bc	45	yes	$1$	$1$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{407}(17,\cdot)$	407.bj	180	yes	$1$	$1$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{407}(18,\cdot)$	407.bj	180	yes	$1$	$1$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{407}(19,\cdot)$	407.bj	180	yes	$1$	$1$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{407}(20,\cdot)$	407.bi	180	yes	$-1$	$1$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{407}(21,\cdot)$	407.u	18	yes	$-1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{18}\right)$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{407}(23,\cdot)$	407.p	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{407}(24,\cdot)$	407.bj	180	yes	$1$	$1$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{407}(25,\cdot)$	407.bg	90	yes	$1$	$1$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{407}(26,\cdot)$	407.r	15	yes	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{15}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{407}(27,\cdot)$	407.x	30	yes	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{15}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{407}(28,\cdot)$	407.bf	90	yes	$-1$	$1$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{407}(29,\cdot)$	407.bd	60	yes	$1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{8}{15}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{407}(30,\cdot)$	407.bf	90	yes	$-1$	$1$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{407}(31,\cdot)$	407.v	20	yes	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$1$
$\chi_{407}(32,\cdot)$	407.bb	36	yes	$1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{36}\right)$	$i$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{407}(34,\cdot)$	407.l	9	no	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{9}\right)$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{407}(35,\cdot)$	407.bj	180	yes	$1$	$1$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{9}\right)$

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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	$407$
Structure	\(C_{2}\times C_{180}\)
Order	$360$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{407}(1,\cdot)\)	407.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{407}(2,\cdot)\)	407.bj	180	yes	\(1\)	\(1\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{407}(3,\cdot)\)	407.bg	90	yes	\(1\)	\(1\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{407}(4,\cdot)\)	407.bg	90	yes	\(1\)	\(1\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{407}(5,\cdot)\)	407.bi	180	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{407}(6,\cdot)\)	407.w	20	yes	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(1\)
\(\chi_{407}(7,\cdot)\)	407.bh	90	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{407}(8,\cdot)\)	407.bd	60	yes	\(1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{407}(9,\cdot)\)	407.bc	45	yes	\(1\)	\(1\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{407}(10,\cdot)\)	407.j	6	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{407}(12,\cdot)\)	407.l	9	no	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{407}(13,\cdot)\)	407.bj	180	yes	\(1\)	\(1\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{407}(14,\cdot)\)	407.be	60	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{407}(15,\cdot)\)	407.bi	180	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{407}(16,\cdot)\)	407.bc	45	yes	\(1\)	\(1\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{407}(17,\cdot)\)	407.bj	180	yes	\(1\)	\(1\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{407}(18,\cdot)\)	407.bj	180	yes	\(1\)	\(1\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{407}(19,\cdot)\)	407.bj	180	yes	\(1\)	\(1\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{407}(20,\cdot)\)	407.bi	180	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{407}(21,\cdot)\)	407.u	18	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{407}(23,\cdot)\)	407.p	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{407}(24,\cdot)\)	407.bj	180	yes	\(1\)	\(1\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{407}(25,\cdot)\)	407.bg	90	yes	\(1\)	\(1\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{407}(26,\cdot)\)	407.r	15	yes	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{407}(27,\cdot)\)	407.x	30	yes	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{407}(28,\cdot)\)	407.bf	90	yes	\(-1\)	\(1\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{407}(29,\cdot)\)	407.bd	60	yes	\(1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{407}(30,\cdot)\)	407.bf	90	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{407}(31,\cdot)\)	407.v	20	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(1\)
\(\chi_{407}(32,\cdot)\)	407.bb	36	yes	\(1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(i\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{407}(34,\cdot)\)	407.l	9	no	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{407}(35,\cdot)\)	407.bj	180	yes	\(1\)	\(1\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{9}\right)\)

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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.