LMFDB - Group of Dirichlet characters of modulus 2975

sage:H = DirichletGroup(2975)

pari:g = idealstar(,2975,2)

Character group

sage:G.order() pari:g.no
Order	=	1920
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{240}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{2975}(477,\cdot)$, $\chi_{2975}(2551,\cdot)$, $\chi_{2975}(2451,\cdot)$

First 32 of 1920 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	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$11$	$12$	$13$	$16$
$\chi_{2975}(1,\cdot)$	2975.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2975}(2,\cdot)$	2975.ez	120	yes	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{2975}(3,\cdot)$	2975.fg	240	yes	$-1$	$1$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{169}{240}\right)$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{2975}(4,\cdot)$	2975.ep	60	yes	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{2975}(6,\cdot)$	2975.eu	80	yes	$1$	$1$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{2975}(8,\cdot)$	2975.dv	40	no	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{2975}(9,\cdot)$	2975.fb	120	yes	$1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{2975}(11,\cdot)$	2975.fi	240	yes	$-1$	$1$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{169}{240}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{53}{240}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{2975}(12,\cdot)$	2975.fm	240	yes	$-1$	$1$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{53}{240}\right)$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{2975}(13,\cdot)$	2975.cq	20	yes	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{2975}(16,\cdot)$	2975.dl	30	yes	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{2975}(18,\cdot)$	2975.by	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{2975}(19,\cdot)$	2975.fd	120	yes	$-1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{2975}(22,\cdot)$	2975.er	80	no	$1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{2975}(23,\cdot)$	2975.fh	240	yes	$1$	$1$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{2975}(24,\cdot)$	2975.eb	48	no	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{13}{48}\right)$	$-i$	$e\left(\frac{5}{6}\right)$
$\chi_{2975}(26,\cdot)$	2975.dd	24	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{19}{24}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{2975}(27,\cdot)$	2975.eq	80	yes	$-1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{2975}(29,\cdot)$	2975.es	80	no	$-1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{2975}(31,\cdot)$	2975.fj	240	yes	$1$	$1$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{179}{240}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{2975}(32,\cdot)$	2975.df	24	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{24}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{2975}(33,\cdot)$	2975.ei	60	yes	$1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{2975}(36,\cdot)$	2975.dt	40	no	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{2975}(37,\cdot)$	2975.fh	240	yes	$1$	$1$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{233}{240}\right)$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{2975}(38,\cdot)$	2975.eg	60	yes	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{2975}(39,\cdot)$	2975.fl	240	yes	$-1$	$1$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{19}{240}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{2975}(41,\cdot)$	2975.eu	80	yes	$1$	$1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{2975}(43,\cdot)$	2975.bd	8	no	$-1$	$1$	$-1$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$-1$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$1$
$\chi_{2975}(44,\cdot)$	2975.fl	240	yes	$-1$	$1$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{11}{240}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{2975}(46,\cdot)$	2975.fi	240	yes	$-1$	$1$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{71}{240}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{2975}(47,\cdot)$	2975.eg	60	yes	$1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{2975}(48,\cdot)$	2975.eq	80	yes	$-1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$2975$
Structure	\(C_{2}\times C_{4}\times C_{240}\)
Order	$1920$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\(\chi_{2975}(1,\cdot)\)	2975.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2975}(2,\cdot)\)	2975.ez	120	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{2975}(3,\cdot)\)	2975.fg	240	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{163}{240}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{169}{240}\right)\)	\(e\left(\frac{191}{240}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{2975}(4,\cdot)\)	2975.ep	60	yes	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{2975}(6,\cdot)\)	2975.eu	80	yes	\(1\)	\(1\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{2975}(8,\cdot)\)	2975.dv	40	no	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{2975}(9,\cdot)\)	2975.fb	120	yes	\(1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{2975}(11,\cdot)\)	2975.fi	240	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{169}{240}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{53}{240}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{2975}(12,\cdot)\)	2975.fm	240	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{191}{240}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{53}{240}\right)\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{2975}(13,\cdot)\)	2975.cq	20	yes	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{2975}(16,\cdot)\)	2975.dl	30	yes	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{2975}(18,\cdot)\)	2975.by	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2975}(19,\cdot)\)	2975.fd	120	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{2975}(22,\cdot)\)	2975.er	80	no	\(1\)	\(1\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{2975}(23,\cdot)\)	2975.fh	240	yes	\(1\)	\(1\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{2975}(24,\cdot)\)	2975.eb	48	no	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2975}(26,\cdot)\)	2975.dd	24	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2975}(27,\cdot)\)	2975.eq	80	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{2975}(29,\cdot)\)	2975.es	80	no	\(-1\)	\(1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{2975}(31,\cdot)\)	2975.fj	240	yes	\(1\)	\(1\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{179}{240}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{2975}(32,\cdot)\)	2975.df	24	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2975}(33,\cdot)\)	2975.ei	60	yes	\(1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{2975}(36,\cdot)\)	2975.dt	40	no	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{2975}(37,\cdot)\)	2975.fh	240	yes	\(1\)	\(1\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{233}{240}\right)\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{2975}(38,\cdot)\)	2975.eg	60	yes	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{2975}(39,\cdot)\)	2975.fl	240	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{19}{240}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{2975}(41,\cdot)\)	2975.eu	80	yes	\(1\)	\(1\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{2975}(43,\cdot)\)	2975.bd	8	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(1\)
\(\chi_{2975}(44,\cdot)\)	2975.fl	240	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{11}{240}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{2975}(46,\cdot)\)	2975.fi	240	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{163}{240}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{71}{240}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{2975}(47,\cdot)\)	2975.eg	60	yes	\(1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{2975}(48,\cdot)\)	2975.eq	80	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)

Introduction

L-functions

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Character group

First 32 of 1920 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.