LMFDB - Group of Dirichlet characters of modulus 425

sage:H = DirichletGroup(425)

pari:g = idealstar(,425,2)

Character group

sage:G.order() pari:g.no
Order	=	320
sage:H.invariants() pari:g.cyc
Structure	=	$C_{4}\times C_{80}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{425}(52,\cdot)$, $\chi_{425}(326,\cdot)$

First 32 of 320 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{425}(1,\cdot)$	425.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{425}(2,\cdot)$	425.bf	40	yes	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{425}(3,\cdot)$	425.bj	80	yes	$1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{425}(4,\cdot)$	425.w	20	yes	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{20}\right)$	$-i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{425}(6,\cdot)$	425.bi	80	yes	$-1$	$1$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{425}(7,\cdot)$	425.s	16	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{16}\right)$	$-i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-1$
$\chi_{425}(8,\cdot)$	425.bf	40	yes	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{425}(9,\cdot)$	425.bd	40	yes	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{425}(11,\cdot)$	425.bi	80	yes	$-1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{425}(12,\cdot)$	425.bg	80	yes	$1$	$1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{425}(13,\cdot)$	425.ba	20	yes	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$-1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{425}(14,\cdot)$	425.bh	80	yes	$-1$	$1$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{425}(16,\cdot)$	425.p	10	yes	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{425}(18,\cdot)$	425.h	4	no	$-1$	$1$	$-i$	$i$	$-1$	$1$	$-i$	$i$	$-1$	$1$	$-i$	$i$
$\chi_{425}(19,\cdot)$	425.bd	40	yes	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{425}(21,\cdot)$	425.bb	20	yes	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{20}\right)$	$i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{425}(22,\cdot)$	425.bg	80	yes	$1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{425}(23,\cdot)$	425.bg	80	yes	$1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{425}(24,\cdot)$	425.t	16	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$	$i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$
$\chi_{425}(26,\cdot)$	425.m	8	no	$1$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$
$\chi_{425}(27,\cdot)$	425.bj	80	yes	$1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{425}(28,\cdot)$	425.bg	80	yes	$1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{425}(29,\cdot)$	425.bh	80	yes	$-1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{425}(31,\cdot)$	425.bi	80	yes	$-1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{425}(32,\cdot)$	425.l	8	no	$-1$	$1$	$-1$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$
$\chi_{425}(33,\cdot)$	425.z	20	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{425}(36,\cdot)$	425.be	40	yes	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{425}(37,\cdot)$	425.bg	80	yes	$1$	$1$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{425}(38,\cdot)$	425.x	20	yes	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{425}(39,\cdot)$	425.bh	80	yes	$-1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{425}(41,\cdot)$	425.bi	80	yes	$-1$	$1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{425}(42,\cdot)$	425.bc	40	yes	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{17}{20}\right)$

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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	$425$
Structure	\(C_{4}\times C_{80}\)
Order	$320$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{425}(1,\cdot)\)	425.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{425}(2,\cdot)\)	425.bf	40	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{425}(3,\cdot)\)	425.bj	80	yes	\(1\)	\(1\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{425}(4,\cdot)\)	425.w	20	yes	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(-i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{425}(6,\cdot)\)	425.bi	80	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{425}(7,\cdot)\)	425.s	16	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)
\(\chi_{425}(8,\cdot)\)	425.bf	40	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{425}(9,\cdot)\)	425.bd	40	yes	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{425}(11,\cdot)\)	425.bi	80	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{425}(12,\cdot)\)	425.bg	80	yes	\(1\)	\(1\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{425}(13,\cdot)\)	425.ba	20	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(-1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{425}(14,\cdot)\)	425.bh	80	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{425}(16,\cdot)\)	425.p	10	yes	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{425}(18,\cdot)\)	425.h	4	no	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(i\)
\(\chi_{425}(19,\cdot)\)	425.bd	40	yes	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{425}(21,\cdot)\)	425.bb	20	yes	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{425}(22,\cdot)\)	425.bg	80	yes	\(1\)	\(1\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{425}(23,\cdot)\)	425.bg	80	yes	\(1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{425}(24,\cdot)\)	425.t	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)
\(\chi_{425}(26,\cdot)\)	425.m	8	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)
\(\chi_{425}(27,\cdot)\)	425.bj	80	yes	\(1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{425}(28,\cdot)\)	425.bg	80	yes	\(1\)	\(1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{425}(29,\cdot)\)	425.bh	80	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{425}(31,\cdot)\)	425.bi	80	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{425}(32,\cdot)\)	425.l	8	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)
\(\chi_{425}(33,\cdot)\)	425.z	20	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{425}(36,\cdot)\)	425.be	40	yes	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{425}(37,\cdot)\)	425.bg	80	yes	\(1\)	\(1\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{425}(38,\cdot)\)	425.x	20	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{425}(39,\cdot)\)	425.bh	80	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{425}(41,\cdot)\)	425.bi	80	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{425}(42,\cdot)\)	425.bc	40	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)

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.