LMFDB - Group of Dirichlet characters of modulus 125

Show commands: PariGP / SageMath

sage: H = DirichletGroup(125)

pari: g = idealstar(,125,2)

Character group

sage: G.order() pari: g.no
Order	=	100
sage: H.invariants() pari: g.cyc
Structure	=	$C_{100}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{125}(2,\cdot)$

First 32 of 100 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{125}(1,\cdot)$	125.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{125}(2,\cdot)$	125.i	100	yes	$-1$	$1$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{39}{100}\right)$
$\chi_{125}(3,\cdot)$	125.i	100	yes	$-1$	$1$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{73}{100}\right)$
$\chi_{125}(4,\cdot)$	125.h	50	yes	$1$	$1$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{39}{50}\right)$
$\chi_{125}(6,\cdot)$	125.g	25	yes	$1$	$1$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{3}{25}\right)$
$\chi_{125}(7,\cdot)$	125.f	20	no	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{125}(8,\cdot)$	125.i	100	yes	$-1$	$1$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{17}{100}\right)$
$\chi_{125}(9,\cdot)$	125.h	50	yes	$1$	$1$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{23}{50}\right)$
$\chi_{125}(11,\cdot)$	125.g	25	yes	$1$	$1$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{16}{25}\right)$
$\chi_{125}(12,\cdot)$	125.i	100	yes	$-1$	$1$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{51}{100}\right)$
$\chi_{125}(13,\cdot)$	125.i	100	yes	$-1$	$1$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{21}{100}\right)$
$\chi_{125}(14,\cdot)$	125.h	50	yes	$1$	$1$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{27}{50}\right)$
$\chi_{125}(16,\cdot)$	125.g	25	yes	$1$	$1$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{14}{25}\right)$
$\chi_{125}(17,\cdot)$	125.i	100	yes	$-1$	$1$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{47}{100}\right)$
$\chi_{125}(18,\cdot)$	125.f	20	no	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$-i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{125}(19,\cdot)$	125.h	50	yes	$1$	$1$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{1}{50}\right)$
$\chi_{125}(21,\cdot)$	125.g	25	yes	$1$	$1$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{22}{25}\right)$
$\chi_{125}(22,\cdot)$	125.i	100	yes	$-1$	$1$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{3}{100}\right)$
$\chi_{125}(23,\cdot)$	125.i	100	yes	$-1$	$1$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{9}{100}\right)$
$\chi_{125}(24,\cdot)$	125.e	10	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{125}(26,\cdot)$	125.d	5	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{125}(27,\cdot)$	125.i	100	yes	$-1$	$1$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{19}{100}\right)$
$\chi_{125}(28,\cdot)$	125.i	100	yes	$-1$	$1$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{93}{100}\right)$
$\chi_{125}(29,\cdot)$	125.h	50	yes	$1$	$1$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{9}{50}\right)$
$\chi_{125}(31,\cdot)$	125.g	25	yes	$1$	$1$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{18}{25}\right)$
$\chi_{125}(32,\cdot)$	125.f	20	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$i$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{125}(33,\cdot)$	125.i	100	yes	$-1$	$1$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{37}{100}\right)$
$\chi_{125}(34,\cdot)$	125.h	50	yes	$1$	$1$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{43}{50}\right)$
$\chi_{125}(36,\cdot)$	125.g	25	yes	$1$	$1$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{6}{25}\right)$
$\chi_{125}(37,\cdot)$	125.i	100	yes	$-1$	$1$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{31}{100}\right)$
$\chi_{125}(38,\cdot)$	125.i	100	yes	$-1$	$1$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{41}{100}\right)$
$\chi_{125}(39,\cdot)$	125.h	50	yes	$1$	$1$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{47}{50}\right)$

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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	$125$
Structure	\(C_{100}\)
Order	$100$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{125}(1,\cdot)\)	125.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{125}(2,\cdot)\)	125.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{39}{100}\right)\)
\(\chi_{125}(3,\cdot)\)	125.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{73}{100}\right)\)
\(\chi_{125}(4,\cdot)\)	125.h	50	yes	\(1\)	\(1\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{39}{50}\right)\)
\(\chi_{125}(6,\cdot)\)	125.g	25	yes	\(1\)	\(1\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)
\(\chi_{125}(7,\cdot)\)	125.f	20	no	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{125}(8,\cdot)\)	125.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{17}{100}\right)\)
\(\chi_{125}(9,\cdot)\)	125.h	50	yes	\(1\)	\(1\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{23}{50}\right)\)
\(\chi_{125}(11,\cdot)\)	125.g	25	yes	\(1\)	\(1\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)
\(\chi_{125}(12,\cdot)\)	125.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{51}{100}\right)\)
\(\chi_{125}(13,\cdot)\)	125.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{21}{100}\right)\)
\(\chi_{125}(14,\cdot)\)	125.h	50	yes	\(1\)	\(1\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{27}{50}\right)\)
\(\chi_{125}(16,\cdot)\)	125.g	25	yes	\(1\)	\(1\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{14}{25}\right)\)
\(\chi_{125}(17,\cdot)\)	125.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{47}{100}\right)\)
\(\chi_{125}(18,\cdot)\)	125.f	20	no	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-i\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{125}(19,\cdot)\)	125.h	50	yes	\(1\)	\(1\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{1}{50}\right)\)
\(\chi_{125}(21,\cdot)\)	125.g	25	yes	\(1\)	\(1\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)
\(\chi_{125}(22,\cdot)\)	125.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{3}{100}\right)\)
\(\chi_{125}(23,\cdot)\)	125.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{9}{100}\right)\)
\(\chi_{125}(24,\cdot)\)	125.e	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{125}(26,\cdot)\)	125.d	5	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{125}(27,\cdot)\)	125.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{19}{100}\right)\)
\(\chi_{125}(28,\cdot)\)	125.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{93}{100}\right)\)
\(\chi_{125}(29,\cdot)\)	125.h	50	yes	\(1\)	\(1\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{9}{50}\right)\)
\(\chi_{125}(31,\cdot)\)	125.g	25	yes	\(1\)	\(1\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)
\(\chi_{125}(32,\cdot)\)	125.f	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(i\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{125}(33,\cdot)\)	125.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{37}{100}\right)\)
\(\chi_{125}(34,\cdot)\)	125.h	50	yes	\(1\)	\(1\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{43}{50}\right)\)
\(\chi_{125}(36,\cdot)\)	125.g	25	yes	\(1\)	\(1\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{6}{25}\right)\)
\(\chi_{125}(37,\cdot)\)	125.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{31}{100}\right)\)
\(\chi_{125}(38,\cdot)\)	125.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{41}{100}\right)\)
\(\chi_{125}(39,\cdot)\)	125.h	50	yes	\(1\)	\(1\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{47}{50}\right)\)

Introduction

L-functions

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Character group

First 32 of 100 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.