LMFDB - Group of Dirichlet characters of modulus 601

Show commands: PariGP / SageMath

sage: H = DirichletGroup(601)

pari: g = idealstar(,601,2)

Character group

sage: G.order() pari: g.no
Order	=	600
sage: H.invariants() pari: g.cyc
Structure	=	$C_{600}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{601}(7,\cdot)$

First 32 of 600 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{601}(1,\cdot)$	601.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{601}(2,\cdot)$	601.m	25	yes	$1$	$1$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{2}{25}\right)$	$1$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{1}{25}\right)$
$\chi_{601}(3,\cdot)$	601.r	75	yes	$1$	$1$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{41}{75}\right)$
$\chi_{601}(4,\cdot)$	601.m	25	yes	$1$	$1$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{4}{25}\right)$	$1$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{2}{25}\right)$
$\chi_{601}(5,\cdot)$	601.i	12	yes	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{601}(6,\cdot)$	601.r	75	yes	$1$	$1$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{44}{75}\right)$
$\chi_{601}(7,\cdot)$	601.x	600	yes	$-1$	$1$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{1}{600}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{191}{300}\right)$	$e\left(\frac{157}{600}\right)$
$\chi_{601}(8,\cdot)$	601.m	25	yes	$1$	$1$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{6}{25}\right)$	$1$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{3}{25}\right)$
$\chi_{601}(9,\cdot)$	601.r	75	yes	$1$	$1$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{7}{75}\right)$
$\chi_{601}(10,\cdot)$	601.w	300	yes	$1$	$1$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{191}{300}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{287}{300}\right)$
$\chi_{601}(11,\cdot)$	601.x	600	yes	$-1$	$1$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{157}{600}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{287}{300}\right)$	$e\left(\frac{49}{600}\right)$
$\chi_{601}(12,\cdot)$	601.r	75	yes	$1$	$1$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{47}{75}\right)$
$\chi_{601}(13,\cdot)$	601.k	20	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{601}(14,\cdot)$	601.x	600	yes	$-1$	$1$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{433}{600}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{203}{300}\right)$	$e\left(\frac{181}{600}\right)$
$\chi_{601}(15,\cdot)$	601.w	300	yes	$1$	$1$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{127}{300}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{139}{300}\right)$
$\chi_{601}(16,\cdot)$	601.m	25	yes	$1$	$1$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{8}{25}\right)$	$1$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{4}{25}\right)$
$\chi_{601}(17,\cdot)$	601.t	120	yes	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{109}{120}\right)$
$\chi_{601}(18,\cdot)$	601.j	15	yes	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{601}(19,\cdot)$	601.x	600	yes	$-1$	$1$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{241}{600}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{131}{300}\right)$	$e\left(\frac{37}{600}\right)$
$\chi_{601}(20,\cdot)$	601.w	300	yes	$1$	$1$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{107}{300}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{299}{300}\right)$
$\chi_{601}(21,\cdot)$	601.t	120	yes	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{97}{120}\right)$
$\chi_{601}(22,\cdot)$	601.x	600	yes	$-1$	$1$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{589}{600}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{299}{300}\right)$	$e\left(\frac{73}{600}\right)$
$\chi_{601}(23,\cdot)$	601.w	300	yes	$1$	$1$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{251}{300}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{107}{300}\right)$
$\chi_{601}(24,\cdot)$	601.c	3	yes	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{601}(25,\cdot)$	601.f	6	yes	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{601}(26,\cdot)$	601.s	100	yes	$1$	$1$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{22}{25}\right)$	$-1$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{69}{100}\right)$
$\chi_{601}(27,\cdot)$	601.m	25	yes	$1$	$1$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{7}{25}\right)$	$1$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{16}{25}\right)$
$\chi_{601}(28,\cdot)$	601.t	120	yes	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{41}{120}\right)$
$\chi_{601}(29,\cdot)$	601.x	600	yes	$-1$	$1$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{391}{600}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{281}{300}\right)$	$e\left(\frac{187}{600}\right)$
$\chi_{601}(30,\cdot)$	601.w	300	yes	$1$	$1$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{43}{300}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{113}{150}\right)$	$e\left(\frac{151}{300}\right)$
$\chi_{601}(31,\cdot)$	601.v	200	yes	$-1$	$1$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{22}{25}\right)$	$-i$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{9}{200}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{13}{200}\right)$
$\chi_{601}(32,\cdot)$	601.e	5	yes	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$

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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	$601$
Structure	\(C_{600}\)
Order	$600$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{601}(1,\cdot)\)	601.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{601}(2,\cdot)\)	601.m	25	yes	\(1\)	\(1\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(1\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{1}{25}\right)\)
\(\chi_{601}(3,\cdot)\)	601.r	75	yes	\(1\)	\(1\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{41}{75}\right)\)
\(\chi_{601}(4,\cdot)\)	601.m	25	yes	\(1\)	\(1\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(1\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)
\(\chi_{601}(5,\cdot)\)	601.i	12	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{601}(6,\cdot)\)	601.r	75	yes	\(1\)	\(1\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{44}{75}\right)\)
\(\chi_{601}(7,\cdot)\)	601.x	600	yes	\(-1\)	\(1\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{1}{600}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{191}{300}\right)\)	\(e\left(\frac{157}{600}\right)\)
\(\chi_{601}(8,\cdot)\)	601.m	25	yes	\(1\)	\(1\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(1\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)
\(\chi_{601}(9,\cdot)\)	601.r	75	yes	\(1\)	\(1\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{7}{75}\right)\)
\(\chi_{601}(10,\cdot)\)	601.w	300	yes	\(1\)	\(1\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{191}{300}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{287}{300}\right)\)
\(\chi_{601}(11,\cdot)\)	601.x	600	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{157}{600}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{287}{300}\right)\)	\(e\left(\frac{49}{600}\right)\)
\(\chi_{601}(12,\cdot)\)	601.r	75	yes	\(1\)	\(1\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{47}{75}\right)\)
\(\chi_{601}(13,\cdot)\)	601.k	20	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{601}(14,\cdot)\)	601.x	600	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{433}{600}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{203}{300}\right)\)	\(e\left(\frac{181}{600}\right)\)
\(\chi_{601}(15,\cdot)\)	601.w	300	yes	\(1\)	\(1\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{127}{300}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{139}{300}\right)\)
\(\chi_{601}(16,\cdot)\)	601.m	25	yes	\(1\)	\(1\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(1\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)
\(\chi_{601}(17,\cdot)\)	601.t	120	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{109}{120}\right)\)
\(\chi_{601}(18,\cdot)\)	601.j	15	yes	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{601}(19,\cdot)\)	601.x	600	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{241}{600}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{131}{300}\right)\)	\(e\left(\frac{37}{600}\right)\)
\(\chi_{601}(20,\cdot)\)	601.w	300	yes	\(1\)	\(1\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{107}{300}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{299}{300}\right)\)
\(\chi_{601}(21,\cdot)\)	601.t	120	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{97}{120}\right)\)
\(\chi_{601}(22,\cdot)\)	601.x	600	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{589}{600}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{299}{300}\right)\)	\(e\left(\frac{73}{600}\right)\)
\(\chi_{601}(23,\cdot)\)	601.w	300	yes	\(1\)	\(1\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{251}{300}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{107}{300}\right)\)
\(\chi_{601}(24,\cdot)\)	601.c	3	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{601}(25,\cdot)\)	601.f	6	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{601}(26,\cdot)\)	601.s	100	yes	\(1\)	\(1\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(-1\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{69}{100}\right)\)
\(\chi_{601}(27,\cdot)\)	601.m	25	yes	\(1\)	\(1\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(1\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)
\(\chi_{601}(28,\cdot)\)	601.t	120	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{41}{120}\right)\)
\(\chi_{601}(29,\cdot)\)	601.x	600	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{391}{600}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{281}{300}\right)\)	\(e\left(\frac{187}{600}\right)\)
\(\chi_{601}(30,\cdot)\)	601.w	300	yes	\(1\)	\(1\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{43}{300}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{113}{150}\right)\)	\(e\left(\frac{151}{300}\right)\)
\(\chi_{601}(31,\cdot)\)	601.v	200	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(-i\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{9}{200}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{13}{200}\right)\)
\(\chi_{601}(32,\cdot)\)	601.e	5	yes	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)

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L-functions

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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.