LMFDB - Group of Dirichlet characters of modulus 101

Show commands: PariGP / SageMath

sage: H = DirichletGroup(101)

pari: g = idealstar(,101,2)

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	=	$\chi_{101}(2,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{101}(1,\cdot)$	101.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{101}(2,\cdot)$	101.i	100	yes	$-1$	$1$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{19}{50}\right)$	$i$	$e\left(\frac{13}{100}\right)$
$\chi_{101}(3,\cdot)$	101.i	100	yes	$-1$	$1$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{11}{50}\right)$	$i$	$e\left(\frac{97}{100}\right)$
$\chi_{101}(4,\cdot)$	101.h	50	yes	$1$	$1$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{19}{25}\right)$	$-1$	$e\left(\frac{13}{50}\right)$
$\chi_{101}(5,\cdot)$	101.g	25	yes	$1$	$1$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{3}{25}\right)$	$1$	$e\left(\frac{3}{25}\right)$
$\chi_{101}(6,\cdot)$	101.e	10	yes	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{1}{10}\right)$
$\chi_{101}(7,\cdot)$	101.i	100	yes	$-1$	$1$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{21}{50}\right)$	$i$	$e\left(\frac{17}{100}\right)$
$\chi_{101}(8,\cdot)$	101.i	100	yes	$-1$	$1$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{7}{50}\right)$	$-i$	$e\left(\frac{39}{100}\right)$
$\chi_{101}(9,\cdot)$	101.h	50	yes	$1$	$1$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{11}{25}\right)$	$-1$	$e\left(\frac{47}{50}\right)$
$\chi_{101}(10,\cdot)$	101.c	4	yes	$-1$	$1$	$i$	$i$	$-1$	$1$	$-1$	$i$	$-i$	$-1$	$i$	$i$
$\chi_{101}(11,\cdot)$	101.i	100	yes	$-1$	$1$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{47}{50}\right)$	$i$	$e\left(\frac{69}{100}\right)$
$\chi_{101}(12,\cdot)$	101.i	100	yes	$-1$	$1$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{49}{50}\right)$	$-i$	$e\left(\frac{23}{100}\right)$
$\chi_{101}(13,\cdot)$	101.h	50	yes	$1$	$1$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{2}{25}\right)$	$-1$	$e\left(\frac{29}{50}\right)$
$\chi_{101}(14,\cdot)$	101.e	10	yes	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{3}{10}\right)$
$\chi_{101}(15,\cdot)$	101.i	100	yes	$-1$	$1$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{17}{50}\right)$	$i$	$e\left(\frac{9}{100}\right)$
$\chi_{101}(16,\cdot)$	101.g	25	yes	$1$	$1$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{13}{25}\right)$	$1$	$e\left(\frac{13}{25}\right)$
$\chi_{101}(17,\cdot)$	101.e	10	yes	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{9}{10}\right)$
$\chi_{101}(18,\cdot)$	101.i	100	yes	$-1$	$1$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{41}{50}\right)$	$-i$	$e\left(\frac{7}{100}\right)$
$\chi_{101}(19,\cdot)$	101.g	25	yes	$1$	$1$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{12}{25}\right)$	$1$	$e\left(\frac{12}{25}\right)$
$\chi_{101}(20,\cdot)$	101.h	50	yes	$1$	$1$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{22}{25}\right)$	$-1$	$e\left(\frac{19}{50}\right)$
$\chi_{101}(21,\cdot)$	101.h	50	yes	$1$	$1$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{16}{25}\right)$	$-1$	$e\left(\frac{7}{50}\right)$
$\chi_{101}(22,\cdot)$	101.h	50	yes	$1$	$1$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{8}{25}\right)$	$-1$	$e\left(\frac{41}{50}\right)$
$\chi_{101}(23,\cdot)$	101.h	50	yes	$1$	$1$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{17}{25}\right)$	$-1$	$e\left(\frac{9}{50}\right)$
$\chi_{101}(24,\cdot)$	101.g	25	yes	$1$	$1$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{9}{25}\right)$	$1$	$e\left(\frac{9}{25}\right)$
$\chi_{101}(25,\cdot)$	101.g	25	yes	$1$	$1$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{6}{25}\right)$	$1$	$e\left(\frac{6}{25}\right)$
$\chi_{101}(26,\cdot)$	101.i	100	yes	$-1$	$1$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{23}{50}\right)$	$-i$	$e\left(\frac{71}{100}\right)$
$\chi_{101}(27,\cdot)$	101.i	100	yes	$-1$	$1$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{33}{50}\right)$	$-i$	$e\left(\frac{91}{100}\right)$
$\chi_{101}(28,\cdot)$	101.i	100	yes	$-1$	$1$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{9}{50}\right)$	$-i$	$e\left(\frac{43}{100}\right)$
$\chi_{101}(29,\cdot)$	101.i	100	yes	$-1$	$1$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{29}{50}\right)$	$-i$	$e\left(\frac{83}{100}\right)$
$\chi_{101}(30,\cdot)$	101.h	50	yes	$1$	$1$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{18}{25}\right)$	$-1$	$e\left(\frac{11}{50}\right)$
$\chi_{101}(31,\cdot)$	101.g	25	yes	$1$	$1$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{23}{25}\right)$	$1$	$e\left(\frac{23}{25}\right)$
$\chi_{101}(32,\cdot)$	101.f	20	yes	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$i$	$e\left(\frac{13}{20}\right)$

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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 $\F_{q}$

Modulus	$101$
Structure	\(C_{100}\)
Order	$100$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{101}(1,\cdot)\)	101.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{101}(2,\cdot)\)	101.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(i\)	\(e\left(\frac{13}{100}\right)\)
\(\chi_{101}(3,\cdot)\)	101.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(i\)	\(e\left(\frac{97}{100}\right)\)
\(\chi_{101}(4,\cdot)\)	101.h	50	yes	\(1\)	\(1\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(-1\)	\(e\left(\frac{13}{50}\right)\)
\(\chi_{101}(5,\cdot)\)	101.g	25	yes	\(1\)	\(1\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(1\)	\(e\left(\frac{3}{25}\right)\)
\(\chi_{101}(6,\cdot)\)	101.e	10	yes	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{101}(7,\cdot)\)	101.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(i\)	\(e\left(\frac{17}{100}\right)\)
\(\chi_{101}(8,\cdot)\)	101.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(-i\)	\(e\left(\frac{39}{100}\right)\)
\(\chi_{101}(9,\cdot)\)	101.h	50	yes	\(1\)	\(1\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(-1\)	\(e\left(\frac{47}{50}\right)\)
\(\chi_{101}(10,\cdot)\)	101.c	4	yes	\(-1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(1\)	\(-1\)	\(i\)	\(-i\)	\(-1\)	\(i\)	\(i\)
\(\chi_{101}(11,\cdot)\)	101.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(i\)	\(e\left(\frac{69}{100}\right)\)
\(\chi_{101}(12,\cdot)\)	101.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(-i\)	\(e\left(\frac{23}{100}\right)\)
\(\chi_{101}(13,\cdot)\)	101.h	50	yes	\(1\)	\(1\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(-1\)	\(e\left(\frac{29}{50}\right)\)
\(\chi_{101}(14,\cdot)\)	101.e	10	yes	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{101}(15,\cdot)\)	101.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(i\)	\(e\left(\frac{9}{100}\right)\)
\(\chi_{101}(16,\cdot)\)	101.g	25	yes	\(1\)	\(1\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(1\)	\(e\left(\frac{13}{25}\right)\)
\(\chi_{101}(17,\cdot)\)	101.e	10	yes	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{101}(18,\cdot)\)	101.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(-i\)	\(e\left(\frac{7}{100}\right)\)
\(\chi_{101}(19,\cdot)\)	101.g	25	yes	\(1\)	\(1\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(1\)	\(e\left(\frac{12}{25}\right)\)
\(\chi_{101}(20,\cdot)\)	101.h	50	yes	\(1\)	\(1\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(-1\)	\(e\left(\frac{19}{50}\right)\)
\(\chi_{101}(21,\cdot)\)	101.h	50	yes	\(1\)	\(1\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(-1\)	\(e\left(\frac{7}{50}\right)\)
\(\chi_{101}(22,\cdot)\)	101.h	50	yes	\(1\)	\(1\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(-1\)	\(e\left(\frac{41}{50}\right)\)
\(\chi_{101}(23,\cdot)\)	101.h	50	yes	\(1\)	\(1\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(-1\)	\(e\left(\frac{9}{50}\right)\)
\(\chi_{101}(24,\cdot)\)	101.g	25	yes	\(1\)	\(1\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(1\)	\(e\left(\frac{9}{25}\right)\)
\(\chi_{101}(25,\cdot)\)	101.g	25	yes	\(1\)	\(1\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(1\)	\(e\left(\frac{6}{25}\right)\)
\(\chi_{101}(26,\cdot)\)	101.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(-i\)	\(e\left(\frac{71}{100}\right)\)
\(\chi_{101}(27,\cdot)\)	101.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(-i\)	\(e\left(\frac{91}{100}\right)\)
\(\chi_{101}(28,\cdot)\)	101.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(-i\)	\(e\left(\frac{43}{100}\right)\)
\(\chi_{101}(29,\cdot)\)	101.i	100	yes	\(-1\)	\(1\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(-i\)	\(e\left(\frac{83}{100}\right)\)
\(\chi_{101}(30,\cdot)\)	101.h	50	yes	\(1\)	\(1\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(-1\)	\(e\left(\frac{11}{50}\right)\)
\(\chi_{101}(31,\cdot)\)	101.g	25	yes	\(1\)	\(1\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(1\)	\(e\left(\frac{23}{25}\right)\)
\(\chi_{101}(32,\cdot)\)	101.f	20	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)	\(e\left(\frac{13}{20}\right)\)

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.