LMFDB - Group of Dirichlet characters of modulus 151

Show commands: PariGP / SageMath

sage: H = DirichletGroup(151)

pari: g = idealstar(,151,2)

Character group

sage: G.order() pari: g.no
Order	=	150
sage: H.invariants() pari: g.cyc
Structure	=	$C_{150}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{151}(6,\cdot)$

First 32 of 150 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{151}(1,\cdot)$	151.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{151}(2,\cdot)$	151.g	15	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{15}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{151}(3,\cdot)$	151.j	50	yes	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{19}{25}\right)$
$\chi_{151}(4,\cdot)$	151.g	15	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{15}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{151}(5,\cdot)$	151.k	75	yes	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{14}{75}\right)$
$\chi_{151}(6,\cdot)$	151.l	150	yes	$-1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{47}{75}\right)$
$\chi_{151}(7,\cdot)$	151.l	150	yes	$-1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{74}{75}\right)$
$\chi_{151}(8,\cdot)$	151.d	5	yes	$1$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{151}(9,\cdot)$	151.h	25	yes	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{13}{25}\right)$
$\chi_{151}(10,\cdot)$	151.k	75	yes	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{4}{75}\right)$
$\chi_{151}(11,\cdot)$	151.k	75	yes	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{68}{75}\right)$
$\chi_{151}(12,\cdot)$	151.l	150	yes	$-1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{37}{75}\right)$
$\chi_{151}(13,\cdot)$	151.l	150	yes	$-1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{52}{75}\right)$
$\chi_{151}(14,\cdot)$	151.l	150	yes	$-1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{137}{150}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{64}{75}\right)$
$\chi_{151}(15,\cdot)$	151.l	150	yes	$-1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{71}{75}\right)$
$\chi_{151}(16,\cdot)$	151.g	15	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{15}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{151}(17,\cdot)$	151.k	75	yes	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{26}{75}\right)$
$\chi_{151}(18,\cdot)$	151.k	75	yes	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{29}{75}\right)$
$\chi_{151}(19,\cdot)$	151.d	5	yes	$1$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{151}(20,\cdot)$	151.h	25	yes	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{23}{25}\right)$
$\chi_{151}(21,\cdot)$	151.k	75	yes	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{56}{75}\right)$
$\chi_{151}(22,\cdot)$	151.k	75	yes	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{58}{75}\right)$
$\chi_{151}(23,\cdot)$	151.i	30	yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{30}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{151}(24,\cdot)$	151.j	50	yes	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{9}{25}\right)$
$\chi_{151}(25,\cdot)$	151.k	75	yes	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{28}{75}\right)$
$\chi_{151}(26,\cdot)$	151.j	50	yes	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{14}{25}\right)$
$\chi_{151}(27,\cdot)$	151.j	50	yes	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{7}{25}\right)$
$\chi_{151}(28,\cdot)$	151.j	50	yes	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{18}{25}\right)$
$\chi_{151}(29,\cdot)$	151.h	25	yes	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{11}{25}\right)$
$\chi_{151}(30,\cdot)$	151.l	150	yes	$-1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{113}{150}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{61}{75}\right)$
$\chi_{151}(31,\cdot)$	151.k	75	yes	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{41}{75}\right)$
$\chi_{151}(32,\cdot)$	151.c	3	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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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	$151$
Structure	\(C_{150}\)
Order	$150$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{151}(1,\cdot)\)	151.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{151}(2,\cdot)\)	151.g	15	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{151}(3,\cdot)\)	151.j	50	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)
\(\chi_{151}(4,\cdot)\)	151.g	15	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{151}(5,\cdot)\)	151.k	75	yes	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{14}{75}\right)\)
\(\chi_{151}(6,\cdot)\)	151.l	150	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{47}{75}\right)\)
\(\chi_{151}(7,\cdot)\)	151.l	150	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{74}{75}\right)\)
\(\chi_{151}(8,\cdot)\)	151.d	5	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{151}(9,\cdot)\)	151.h	25	yes	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)
\(\chi_{151}(10,\cdot)\)	151.k	75	yes	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{4}{75}\right)\)
\(\chi_{151}(11,\cdot)\)	151.k	75	yes	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{68}{75}\right)\)
\(\chi_{151}(12,\cdot)\)	151.l	150	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{37}{75}\right)\)
\(\chi_{151}(13,\cdot)\)	151.l	150	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{47}{150}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{52}{75}\right)\)
\(\chi_{151}(14,\cdot)\)	151.l	150	yes	\(-1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{137}{150}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{64}{75}\right)\)
\(\chi_{151}(15,\cdot)\)	151.l	150	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{71}{75}\right)\)
\(\chi_{151}(16,\cdot)\)	151.g	15	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{151}(17,\cdot)\)	151.k	75	yes	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{26}{75}\right)\)
\(\chi_{151}(18,\cdot)\)	151.k	75	yes	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{29}{75}\right)\)
\(\chi_{151}(19,\cdot)\)	151.d	5	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{151}(20,\cdot)\)	151.h	25	yes	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{23}{25}\right)\)
\(\chi_{151}(21,\cdot)\)	151.k	75	yes	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{56}{75}\right)\)
\(\chi_{151}(22,\cdot)\)	151.k	75	yes	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{58}{75}\right)\)
\(\chi_{151}(23,\cdot)\)	151.i	30	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{151}(24,\cdot)\)	151.j	50	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)
\(\chi_{151}(25,\cdot)\)	151.k	75	yes	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{28}{75}\right)\)
\(\chi_{151}(26,\cdot)\)	151.j	50	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{14}{25}\right)\)
\(\chi_{151}(27,\cdot)\)	151.j	50	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)
\(\chi_{151}(28,\cdot)\)	151.j	50	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)
\(\chi_{151}(29,\cdot)\)	151.h	25	yes	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)
\(\chi_{151}(30,\cdot)\)	151.l	150	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{113}{150}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{61}{75}\right)\)
\(\chi_{151}(31,\cdot)\)	151.k	75	yes	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{41}{75}\right)\)
\(\chi_{151}(32,\cdot)\)	151.c	3	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)

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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.