LMFDB - Group of Dirichlet characters of modulus 1201

sage:H = DirichletGroup(1201)

pari:g = idealstar(,1201,2)

Character group

sage:G.order() pari:g.no
Order	=	1200
sage:H.invariants() pari:g.cyc
Structure	=	$C_{1200}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{1201}(11,\cdot)$

First 32 of 1200 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{1201}(1,\cdot)$	1201.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1201}(2,\cdot)$	1201.ba	300	yes	$1$	$1$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{13}{15}\right)$	$-1$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{283}{300}\right)$
$\chi_{1201}(3,\cdot)$	1201.ba	300	yes	$1$	$1$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{7}{15}\right)$	$-1$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{97}{300}\right)$
$\chi_{1201}(4,\cdot)$	1201.x	150	yes	$1$	$1$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{11}{15}\right)$	$1$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{133}{150}\right)$
$\chi_{1201}(5,\cdot)$	1201.bc	600	yes	$1$	$1$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{241}{300}\right)$	$e\left(\frac{8}{15}\right)$	$-i$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{421}{600}\right)$
$\chi_{1201}(6,\cdot)$	1201.j	15	yes	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{1201}(7,\cdot)$	1201.g	8	yes	$1$	$1$	$-1$	$-1$	$1$	$-i$	$1$	$-i$	$-1$	$1$	$i$	$e\left(\frac{3}{8}\right)$
$\chi_{1201}(8,\cdot)$	1201.v	100	yes	$1$	$1$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{83}{100}\right)$
$\chi_{1201}(9,\cdot)$	1201.x	150	yes	$1$	$1$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{14}{15}\right)$	$1$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{97}{150}\right)$
$\chi_{1201}(10,\cdot)$	1201.y	200	yes	$1$	$1$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{2}{5}\right)$	$i$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{129}{200}\right)$
$\chi_{1201}(11,\cdot)$	1201.bd	1200	yes	$-1$	$1$	$e\left(\frac{283}{300}\right)$	$e\left(\frac{97}{300}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{421}{600}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{129}{200}\right)$	$e\left(\frac{1}{1200}\right)$
$\chi_{1201}(12,\cdot)$	1201.v	100	yes	$1$	$1$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{21}{100}\right)$
$\chi_{1201}(13,\cdot)$	1201.bb	400	yes	$-1$	$1$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{3}{200}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{141}{200}\right)$	$e\left(\frac{143}{400}\right)$
$\chi_{1201}(14,\cdot)$	1201.bc	600	yes	$1$	$1$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{11}{300}\right)$	$e\left(\frac{13}{15}\right)$	$i$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{191}{600}\right)$
$\chi_{1201}(15,\cdot)$	1201.p	40	yes	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$1$	$i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{40}\right)$
$\chi_{1201}(16,\cdot)$	1201.t	75	yes	$1$	$1$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{7}{15}\right)$	$1$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{58}{75}\right)$
$\chi_{1201}(17,\cdot)$	1201.bd	1200	yes	$-1$	$1$	$e\left(\frac{91}{300}\right)$	$e\left(\frac{169}{300}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{517}{600}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{33}{200}\right)$	$e\left(\frac{577}{1200}\right)$
$\chi_{1201}(18,\cdot)$	1201.v	100	yes	$1$	$1$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{59}{100}\right)$
$\chi_{1201}(19,\cdot)$	1201.y	200	yes	$1$	$1$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{4}{5}\right)$	$i$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{73}{200}\right)$
$\chi_{1201}(20,\cdot)$	1201.bc	600	yes	$1$	$1$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{113}{300}\right)$	$e\left(\frac{4}{15}\right)$	$-i$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{353}{600}\right)$
$\chi_{1201}(21,\cdot)$	1201.bc	600	yes	$1$	$1$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{299}{300}\right)$	$e\left(\frac{7}{15}\right)$	$i$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{419}{600}\right)$
$\chi_{1201}(22,\cdot)$	1201.bd	1200	yes	$-1$	$1$	$e\left(\frac{239}{300}\right)$	$e\left(\frac{101}{300}\right)$	$e\left(\frac{89}{150}\right)$	$e\left(\frac{593}{600}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{157}{200}\right)$	$e\left(\frac{1133}{1200}\right)$
$\chi_{1201}(23,\cdot)$	1201.bb	400	yes	$-1$	$1$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{43}{200}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{21}{200}\right)$	$e\left(\frac{383}{400}\right)$
$\chi_{1201}(24,\cdot)$	1201.x	150	yes	$1$	$1$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{1}{15}\right)$	$1$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{23}{150}\right)$
$\chi_{1201}(25,\cdot)$	1201.ba	300	yes	$1$	$1$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{1}{15}\right)$	$-1$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{121}{300}\right)$
$\chi_{1201}(26,\cdot)$	1201.bd	1200	yes	$-1$	$1$	$e\left(\frac{163}{300}\right)$	$e\left(\frac{217}{300}\right)$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{181}{600}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{169}{200}\right)$	$e\left(\frac{361}{1200}\right)$
$\chi_{1201}(27,\cdot)$	1201.v	100	yes	$1$	$1$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{97}{100}\right)$
$\chi_{1201}(28,\cdot)$	1201.bc	600	yes	$1$	$1$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{97}{300}\right)$	$e\left(\frac{11}{15}\right)$	$-i$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{157}{600}\right)$
$\chi_{1201}(29,\cdot)$	1201.bd	1200	yes	$-1$	$1$	$e\left(\frac{281}{300}\right)$	$e\left(\frac{179}{300}\right)$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{347}{600}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{103}{200}\right)$	$e\left(\frac{1007}{1200}\right)$
$\chi_{1201}(30,\cdot)$	1201.bc	600	yes	$1$	$1$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{101}{300}\right)$	$e\left(\frac{13}{15}\right)$	$-i$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{581}{600}\right)$
$\chi_{1201}(31,\cdot)$	1201.bd	1200	yes	$-1$	$1$	$e\left(\frac{257}{300}\right)$	$e\left(\frac{263}{300}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{359}{600}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{113}{150}\right)$	$e\left(\frac{91}{200}\right)$	$e\left(\frac{179}{1200}\right)$
$\chi_{1201}(32,\cdot)$	1201.s	60	yes	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{43}{60}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$1201$
Structure	\(C_{1200}\)
Order	$1200$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{1201}(1,\cdot)\)	1201.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1201}(2,\cdot)\)	1201.ba	300	yes	\(1\)	\(1\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(-1\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{283}{300}\right)\)
\(\chi_{1201}(3,\cdot)\)	1201.ba	300	yes	\(1\)	\(1\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(-1\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{97}{300}\right)\)
\(\chi_{1201}(4,\cdot)\)	1201.x	150	yes	\(1\)	\(1\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(1\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{133}{150}\right)\)
\(\chi_{1201}(5,\cdot)\)	1201.bc	600	yes	\(1\)	\(1\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{241}{300}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(-i\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{421}{600}\right)\)
\(\chi_{1201}(6,\cdot)\)	1201.j	15	yes	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{1201}(7,\cdot)\)	1201.g	8	yes	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1201}(8,\cdot)\)	1201.v	100	yes	\(1\)	\(1\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{83}{100}\right)\)
\(\chi_{1201}(9,\cdot)\)	1201.x	150	yes	\(1\)	\(1\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(1\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{97}{150}\right)\)
\(\chi_{1201}(10,\cdot)\)	1201.y	200	yes	\(1\)	\(1\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(i\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{129}{200}\right)\)
\(\chi_{1201}(11,\cdot)\)	1201.bd	1200	yes	\(-1\)	\(1\)	\(e\left(\frac{283}{300}\right)\)	\(e\left(\frac{97}{300}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{421}{600}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{129}{200}\right)\)	\(e\left(\frac{1}{1200}\right)\)
\(\chi_{1201}(12,\cdot)\)	1201.v	100	yes	\(1\)	\(1\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{21}{100}\right)\)
\(\chi_{1201}(13,\cdot)\)	1201.bb	400	yes	\(-1\)	\(1\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{3}{200}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{141}{200}\right)\)	\(e\left(\frac{143}{400}\right)\)
\(\chi_{1201}(14,\cdot)\)	1201.bc	600	yes	\(1\)	\(1\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{11}{300}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(i\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{191}{600}\right)\)
\(\chi_{1201}(15,\cdot)\)	1201.p	40	yes	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(1\)	\(i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)
\(\chi_{1201}(16,\cdot)\)	1201.t	75	yes	\(1\)	\(1\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(1\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{58}{75}\right)\)
\(\chi_{1201}(17,\cdot)\)	1201.bd	1200	yes	\(-1\)	\(1\)	\(e\left(\frac{91}{300}\right)\)	\(e\left(\frac{169}{300}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{517}{600}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{33}{200}\right)\)	\(e\left(\frac{577}{1200}\right)\)
\(\chi_{1201}(18,\cdot)\)	1201.v	100	yes	\(1\)	\(1\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{59}{100}\right)\)
\(\chi_{1201}(19,\cdot)\)	1201.y	200	yes	\(1\)	\(1\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(i\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{73}{200}\right)\)
\(\chi_{1201}(20,\cdot)\)	1201.bc	600	yes	\(1\)	\(1\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{113}{300}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(-i\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{353}{600}\right)\)
\(\chi_{1201}(21,\cdot)\)	1201.bc	600	yes	\(1\)	\(1\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{299}{300}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(i\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{419}{600}\right)\)
\(\chi_{1201}(22,\cdot)\)	1201.bd	1200	yes	\(-1\)	\(1\)	\(e\left(\frac{239}{300}\right)\)	\(e\left(\frac{101}{300}\right)\)	\(e\left(\frac{89}{150}\right)\)	\(e\left(\frac{593}{600}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{157}{200}\right)\)	\(e\left(\frac{1133}{1200}\right)\)
\(\chi_{1201}(23,\cdot)\)	1201.bb	400	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{43}{200}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{21}{200}\right)\)	\(e\left(\frac{383}{400}\right)\)
\(\chi_{1201}(24,\cdot)\)	1201.x	150	yes	\(1\)	\(1\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(1\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{23}{150}\right)\)
\(\chi_{1201}(25,\cdot)\)	1201.ba	300	yes	\(1\)	\(1\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(-1\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{121}{300}\right)\)
\(\chi_{1201}(26,\cdot)\)	1201.bd	1200	yes	\(-1\)	\(1\)	\(e\left(\frac{163}{300}\right)\)	\(e\left(\frac{217}{300}\right)\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{181}{600}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{169}{200}\right)\)	\(e\left(\frac{361}{1200}\right)\)
\(\chi_{1201}(27,\cdot)\)	1201.v	100	yes	\(1\)	\(1\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{97}{100}\right)\)
\(\chi_{1201}(28,\cdot)\)	1201.bc	600	yes	\(1\)	\(1\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{97}{300}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(-i\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{157}{600}\right)\)
\(\chi_{1201}(29,\cdot)\)	1201.bd	1200	yes	\(-1\)	\(1\)	\(e\left(\frac{281}{300}\right)\)	\(e\left(\frac{179}{300}\right)\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{347}{600}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{103}{200}\right)\)	\(e\left(\frac{1007}{1200}\right)\)
\(\chi_{1201}(30,\cdot)\)	1201.bc	600	yes	\(1\)	\(1\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{101}{300}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(-i\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{581}{600}\right)\)
\(\chi_{1201}(31,\cdot)\)	1201.bd	1200	yes	\(-1\)	\(1\)	\(e\left(\frac{257}{300}\right)\)	\(e\left(\frac{263}{300}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{359}{600}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{113}{150}\right)\)	\(e\left(\frac{91}{200}\right)\)	\(e\left(\frac{179}{1200}\right)\)
\(\chi_{1201}(32,\cdot)\)	1201.s	60	yes	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{43}{60}\right)\)

Introduction

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.