LMFDB - Group of Dirichlet characters of modulus 191

Show commands: PariGP / SageMath

sage: H = DirichletGroup(191)

pari: g = idealstar(,191,2)

Character group

sage: G.order() pari: g.no
Order	=	190
sage: H.invariants() pari: g.cyc
Structure	=	$C_{190}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{191}(19,\cdot)$

First 32 of 190 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{191}(1,\cdot)$	191.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{191}(2,\cdot)$	191.g	95	yes	$1$	$1$	$e\left(\frac{18}{95}\right)$	$e\left(\frac{82}{95}\right)$	$e\left(\frac{36}{95}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{54}{95}\right)$	$e\left(\frac{69}{95}\right)$	$e\left(\frac{73}{95}\right)$	$e\left(\frac{13}{19}\right)$
$\chi_{191}(3,\cdot)$	191.g	95	yes	$1$	$1$	$e\left(\frac{82}{95}\right)$	$e\left(\frac{78}{95}\right)$	$e\left(\frac{69}{95}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{56}{95}\right)$	$e\left(\frac{61}{95}\right)$	$e\left(\frac{37}{95}\right)$	$e\left(\frac{17}{19}\right)$
$\chi_{191}(4,\cdot)$	191.g	95	yes	$1$	$1$	$e\left(\frac{36}{95}\right)$	$e\left(\frac{69}{95}\right)$	$e\left(\frac{72}{95}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{95}\right)$	$e\left(\frac{43}{95}\right)$	$e\left(\frac{51}{95}\right)$	$e\left(\frac{7}{19}\right)$
$\chi_{191}(5,\cdot)$	191.e	19	yes	$1$	$1$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{2}{19}\right)$	$1$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{7}{19}\right)$
$\chi_{191}(6,\cdot)$	191.e	19	yes	$1$	$1$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{14}{19}\right)$	$1$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{11}{19}\right)$
$\chi_{191}(7,\cdot)$	191.d	10	yes	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$-1$
$\chi_{191}(8,\cdot)$	191.g	95	yes	$1$	$1$	$e\left(\frac{54}{95}\right)$	$e\left(\frac{56}{95}\right)$	$e\left(\frac{13}{95}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{67}{95}\right)$	$e\left(\frac{17}{95}\right)$	$e\left(\frac{29}{95}\right)$	$e\left(\frac{1}{19}\right)$
$\chi_{191}(9,\cdot)$	191.g	95	yes	$1$	$1$	$e\left(\frac{69}{95}\right)$	$e\left(\frac{61}{95}\right)$	$e\left(\frac{43}{95}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{95}\right)$	$e\left(\frac{27}{95}\right)$	$e\left(\frac{74}{95}\right)$	$e\left(\frac{15}{19}\right)$
$\chi_{191}(10,\cdot)$	191.g	95	yes	$1$	$1$	$e\left(\frac{73}{95}\right)$	$e\left(\frac{37}{95}\right)$	$e\left(\frac{51}{95}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{29}{95}\right)$	$e\left(\frac{74}{95}\right)$	$e\left(\frac{48}{95}\right)$	$e\left(\frac{1}{19}\right)$
$\chi_{191}(11,\cdot)$	191.f	38	yes	$-1$	$1$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{11}{19}\right)$	$-1$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{1}{38}\right)$
$\chi_{191}(12,\cdot)$	191.g	95	yes	$1$	$1$	$e\left(\frac{23}{95}\right)$	$e\left(\frac{52}{95}\right)$	$e\left(\frac{46}{95}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{69}{95}\right)$	$e\left(\frac{9}{95}\right)$	$e\left(\frac{88}{95}\right)$	$e\left(\frac{5}{19}\right)$
$\chi_{191}(13,\cdot)$	191.g	95	yes	$1$	$1$	$e\left(\frac{89}{95}\right)$	$e\left(\frac{36}{95}\right)$	$e\left(\frac{83}{95}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{77}{95}\right)$	$e\left(\frac{72}{95}\right)$	$e\left(\frac{39}{95}\right)$	$e\left(\frac{2}{19}\right)$
$\chi_{191}(14,\cdot)$	191.f	38	yes	$-1$	$1$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{1}{19}\right)$	$-1$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{7}{38}\right)$
$\chi_{191}(15,\cdot)$	191.g	95	yes	$1$	$1$	$e\left(\frac{42}{95}\right)$	$e\left(\frac{33}{95}\right)$	$e\left(\frac{84}{95}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{31}{95}\right)$	$e\left(\frac{66}{95}\right)$	$e\left(\frac{12}{95}\right)$	$e\left(\frac{5}{19}\right)$
$\chi_{191}(16,\cdot)$	191.g	95	yes	$1$	$1$	$e\left(\frac{72}{95}\right)$	$e\left(\frac{43}{95}\right)$	$e\left(\frac{49}{95}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{26}{95}\right)$	$e\left(\frac{86}{95}\right)$	$e\left(\frac{7}{95}\right)$	$e\left(\frac{14}{19}\right)$
$\chi_{191}(17,\cdot)$	191.g	95	yes	$1$	$1$	$e\left(\frac{66}{95}\right)$	$e\left(\frac{79}{95}\right)$	$e\left(\frac{37}{95}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{95}\right)$	$e\left(\frac{63}{95}\right)$	$e\left(\frac{46}{95}\right)$	$e\left(\frac{16}{19}\right)$
$\chi_{191}(18,\cdot)$	191.g	95	yes	$1$	$1$	$e\left(\frac{87}{95}\right)$	$e\left(\frac{48}{95}\right)$	$e\left(\frac{79}{95}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{71}{95}\right)$	$e\left(\frac{1}{95}\right)$	$e\left(\frac{52}{95}\right)$	$e\left(\frac{9}{19}\right)$
$\chi_{191}(19,\cdot)$	191.h	190	yes	$-1$	$1$	$e\left(\frac{22}{95}\right)$	$e\left(\frac{58}{95}\right)$	$e\left(\frac{44}{95}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{66}{95}\right)$	$e\left(\frac{21}{95}\right)$	$e\left(\frac{47}{95}\right)$	$e\left(\frac{17}{38}\right)$
$\chi_{191}(20,\cdot)$	191.g	95	yes	$1$	$1$	$e\left(\frac{91}{95}\right)$	$e\left(\frac{24}{95}\right)$	$e\left(\frac{87}{95}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{83}{95}\right)$	$e\left(\frac{48}{95}\right)$	$e\left(\frac{26}{95}\right)$	$e\left(\frac{14}{19}\right)$
$\chi_{191}(21,\cdot)$	191.h	190	yes	$-1$	$1$	$e\left(\frac{44}{95}\right)$	$e\left(\frac{21}{95}\right)$	$e\left(\frac{88}{95}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{37}{95}\right)$	$e\left(\frac{42}{95}\right)$	$e\left(\frac{94}{95}\right)$	$e\left(\frac{15}{38}\right)$
$\chi_{191}(22,\cdot)$	191.h	190	yes	$-1$	$1$	$e\left(\frac{83}{95}\right)$	$e\left(\frac{72}{95}\right)$	$e\left(\frac{71}{95}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{59}{95}\right)$	$e\left(\frac{49}{95}\right)$	$e\left(\frac{78}{95}\right)$	$e\left(\frac{27}{38}\right)$
$\chi_{191}(23,\cdot)$	191.g	95	yes	$1$	$1$	$e\left(\frac{3}{95}\right)$	$e\left(\frac{77}{95}\right)$	$e\left(\frac{6}{95}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{95}\right)$	$e\left(\frac{59}{95}\right)$	$e\left(\frac{28}{95}\right)$	$e\left(\frac{18}{19}\right)$
$\chi_{191}(24,\cdot)$	191.g	95	yes	$1$	$1$	$e\left(\frac{41}{95}\right)$	$e\left(\frac{39}{95}\right)$	$e\left(\frac{82}{95}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{28}{95}\right)$	$e\left(\frac{78}{95}\right)$	$e\left(\frac{66}{95}\right)$	$e\left(\frac{18}{19}\right)$
$\chi_{191}(25,\cdot)$	191.e	19	yes	$1$	$1$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{4}{19}\right)$	$1$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{14}{19}\right)$
$\chi_{191}(26,\cdot)$	191.g	95	yes	$1$	$1$	$e\left(\frac{12}{95}\right)$	$e\left(\frac{23}{95}\right)$	$e\left(\frac{24}{95}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{36}{95}\right)$	$e\left(\frac{46}{95}\right)$	$e\left(\frac{17}{95}\right)$	$e\left(\frac{15}{19}\right)$
$\chi_{191}(27,\cdot)$	191.g	95	yes	$1$	$1$	$e\left(\frac{56}{95}\right)$	$e\left(\frac{44}{95}\right)$	$e\left(\frac{17}{95}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{73}{95}\right)$	$e\left(\frac{88}{95}\right)$	$e\left(\frac{16}{95}\right)$	$e\left(\frac{13}{19}\right)$
$\chi_{191}(28,\cdot)$	191.h	190	yes	$-1$	$1$	$e\left(\frac{93}{95}\right)$	$e\left(\frac{12}{95}\right)$	$e\left(\frac{91}{95}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{89}{95}\right)$	$e\left(\frac{24}{95}\right)$	$e\left(\frac{13}{95}\right)$	$e\left(\frac{33}{38}\right)$
$\chi_{191}(29,\cdot)$	191.h	190	yes	$-1$	$1$	$e\left(\frac{61}{95}\right)$	$e\left(\frac{14}{95}\right)$	$e\left(\frac{27}{95}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{88}{95}\right)$	$e\left(\frac{28}{95}\right)$	$e\left(\frac{31}{95}\right)$	$e\left(\frac{29}{38}\right)$
$\chi_{191}(30,\cdot)$	191.e	19	yes	$1$	$1$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{16}{19}\right)$	$1$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{18}{19}\right)$
$\chi_{191}(31,\cdot)$	191.f	38	yes	$-1$	$1$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{7}{19}\right)$	$-1$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{11}{38}\right)$
$\chi_{191}(32,\cdot)$	191.e	19	yes	$1$	$1$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{5}{19}\right)$	$1$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{8}{19}\right)$

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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	$191$
Structure	\(C_{190}\)
Order	$190$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{191}(1,\cdot)\)	191.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{191}(2,\cdot)\)	191.g	95	yes	\(1\)	\(1\)	\(e\left(\frac{18}{95}\right)\)	\(e\left(\frac{82}{95}\right)\)	\(e\left(\frac{36}{95}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{54}{95}\right)\)	\(e\left(\frac{69}{95}\right)\)	\(e\left(\frac{73}{95}\right)\)	\(e\left(\frac{13}{19}\right)\)
\(\chi_{191}(3,\cdot)\)	191.g	95	yes	\(1\)	\(1\)	\(e\left(\frac{82}{95}\right)\)	\(e\left(\frac{78}{95}\right)\)	\(e\left(\frac{69}{95}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{56}{95}\right)\)	\(e\left(\frac{61}{95}\right)\)	\(e\left(\frac{37}{95}\right)\)	\(e\left(\frac{17}{19}\right)\)
\(\chi_{191}(4,\cdot)\)	191.g	95	yes	\(1\)	\(1\)	\(e\left(\frac{36}{95}\right)\)	\(e\left(\frac{69}{95}\right)\)	\(e\left(\frac{72}{95}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{95}\right)\)	\(e\left(\frac{43}{95}\right)\)	\(e\left(\frac{51}{95}\right)\)	\(e\left(\frac{7}{19}\right)\)
\(\chi_{191}(5,\cdot)\)	191.e	19	yes	\(1\)	\(1\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(1\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)
\(\chi_{191}(6,\cdot)\)	191.e	19	yes	\(1\)	\(1\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(1\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)
\(\chi_{191}(7,\cdot)\)	191.d	10	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)
\(\chi_{191}(8,\cdot)\)	191.g	95	yes	\(1\)	\(1\)	\(e\left(\frac{54}{95}\right)\)	\(e\left(\frac{56}{95}\right)\)	\(e\left(\frac{13}{95}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{67}{95}\right)\)	\(e\left(\frac{17}{95}\right)\)	\(e\left(\frac{29}{95}\right)\)	\(e\left(\frac{1}{19}\right)\)
\(\chi_{191}(9,\cdot)\)	191.g	95	yes	\(1\)	\(1\)	\(e\left(\frac{69}{95}\right)\)	\(e\left(\frac{61}{95}\right)\)	\(e\left(\frac{43}{95}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{95}\right)\)	\(e\left(\frac{27}{95}\right)\)	\(e\left(\frac{74}{95}\right)\)	\(e\left(\frac{15}{19}\right)\)
\(\chi_{191}(10,\cdot)\)	191.g	95	yes	\(1\)	\(1\)	\(e\left(\frac{73}{95}\right)\)	\(e\left(\frac{37}{95}\right)\)	\(e\left(\frac{51}{95}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{29}{95}\right)\)	\(e\left(\frac{74}{95}\right)\)	\(e\left(\frac{48}{95}\right)\)	\(e\left(\frac{1}{19}\right)\)
\(\chi_{191}(11,\cdot)\)	191.f	38	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(-1\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{1}{38}\right)\)
\(\chi_{191}(12,\cdot)\)	191.g	95	yes	\(1\)	\(1\)	\(e\left(\frac{23}{95}\right)\)	\(e\left(\frac{52}{95}\right)\)	\(e\left(\frac{46}{95}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{69}{95}\right)\)	\(e\left(\frac{9}{95}\right)\)	\(e\left(\frac{88}{95}\right)\)	\(e\left(\frac{5}{19}\right)\)
\(\chi_{191}(13,\cdot)\)	191.g	95	yes	\(1\)	\(1\)	\(e\left(\frac{89}{95}\right)\)	\(e\left(\frac{36}{95}\right)\)	\(e\left(\frac{83}{95}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{77}{95}\right)\)	\(e\left(\frac{72}{95}\right)\)	\(e\left(\frac{39}{95}\right)\)	\(e\left(\frac{2}{19}\right)\)
\(\chi_{191}(14,\cdot)\)	191.f	38	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(-1\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{7}{38}\right)\)
\(\chi_{191}(15,\cdot)\)	191.g	95	yes	\(1\)	\(1\)	\(e\left(\frac{42}{95}\right)\)	\(e\left(\frac{33}{95}\right)\)	\(e\left(\frac{84}{95}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{31}{95}\right)\)	\(e\left(\frac{66}{95}\right)\)	\(e\left(\frac{12}{95}\right)\)	\(e\left(\frac{5}{19}\right)\)
\(\chi_{191}(16,\cdot)\)	191.g	95	yes	\(1\)	\(1\)	\(e\left(\frac{72}{95}\right)\)	\(e\left(\frac{43}{95}\right)\)	\(e\left(\frac{49}{95}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{26}{95}\right)\)	\(e\left(\frac{86}{95}\right)\)	\(e\left(\frac{7}{95}\right)\)	\(e\left(\frac{14}{19}\right)\)
\(\chi_{191}(17,\cdot)\)	191.g	95	yes	\(1\)	\(1\)	\(e\left(\frac{66}{95}\right)\)	\(e\left(\frac{79}{95}\right)\)	\(e\left(\frac{37}{95}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{95}\right)\)	\(e\left(\frac{63}{95}\right)\)	\(e\left(\frac{46}{95}\right)\)	\(e\left(\frac{16}{19}\right)\)
\(\chi_{191}(18,\cdot)\)	191.g	95	yes	\(1\)	\(1\)	\(e\left(\frac{87}{95}\right)\)	\(e\left(\frac{48}{95}\right)\)	\(e\left(\frac{79}{95}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{71}{95}\right)\)	\(e\left(\frac{1}{95}\right)\)	\(e\left(\frac{52}{95}\right)\)	\(e\left(\frac{9}{19}\right)\)
\(\chi_{191}(19,\cdot)\)	191.h	190	yes	\(-1\)	\(1\)	\(e\left(\frac{22}{95}\right)\)	\(e\left(\frac{58}{95}\right)\)	\(e\left(\frac{44}{95}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{66}{95}\right)\)	\(e\left(\frac{21}{95}\right)\)	\(e\left(\frac{47}{95}\right)\)	\(e\left(\frac{17}{38}\right)\)
\(\chi_{191}(20,\cdot)\)	191.g	95	yes	\(1\)	\(1\)	\(e\left(\frac{91}{95}\right)\)	\(e\left(\frac{24}{95}\right)\)	\(e\left(\frac{87}{95}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{83}{95}\right)\)	\(e\left(\frac{48}{95}\right)\)	\(e\left(\frac{26}{95}\right)\)	\(e\left(\frac{14}{19}\right)\)
\(\chi_{191}(21,\cdot)\)	191.h	190	yes	\(-1\)	\(1\)	\(e\left(\frac{44}{95}\right)\)	\(e\left(\frac{21}{95}\right)\)	\(e\left(\frac{88}{95}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{37}{95}\right)\)	\(e\left(\frac{42}{95}\right)\)	\(e\left(\frac{94}{95}\right)\)	\(e\left(\frac{15}{38}\right)\)
\(\chi_{191}(22,\cdot)\)	191.h	190	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{95}\right)\)	\(e\left(\frac{72}{95}\right)\)	\(e\left(\frac{71}{95}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{59}{95}\right)\)	\(e\left(\frac{49}{95}\right)\)	\(e\left(\frac{78}{95}\right)\)	\(e\left(\frac{27}{38}\right)\)
\(\chi_{191}(23,\cdot)\)	191.g	95	yes	\(1\)	\(1\)	\(e\left(\frac{3}{95}\right)\)	\(e\left(\frac{77}{95}\right)\)	\(e\left(\frac{6}{95}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{95}\right)\)	\(e\left(\frac{59}{95}\right)\)	\(e\left(\frac{28}{95}\right)\)	\(e\left(\frac{18}{19}\right)\)
\(\chi_{191}(24,\cdot)\)	191.g	95	yes	\(1\)	\(1\)	\(e\left(\frac{41}{95}\right)\)	\(e\left(\frac{39}{95}\right)\)	\(e\left(\frac{82}{95}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{28}{95}\right)\)	\(e\left(\frac{78}{95}\right)\)	\(e\left(\frac{66}{95}\right)\)	\(e\left(\frac{18}{19}\right)\)
\(\chi_{191}(25,\cdot)\)	191.e	19	yes	\(1\)	\(1\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(1\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)
\(\chi_{191}(26,\cdot)\)	191.g	95	yes	\(1\)	\(1\)	\(e\left(\frac{12}{95}\right)\)	\(e\left(\frac{23}{95}\right)\)	\(e\left(\frac{24}{95}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{36}{95}\right)\)	\(e\left(\frac{46}{95}\right)\)	\(e\left(\frac{17}{95}\right)\)	\(e\left(\frac{15}{19}\right)\)
\(\chi_{191}(27,\cdot)\)	191.g	95	yes	\(1\)	\(1\)	\(e\left(\frac{56}{95}\right)\)	\(e\left(\frac{44}{95}\right)\)	\(e\left(\frac{17}{95}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{73}{95}\right)\)	\(e\left(\frac{88}{95}\right)\)	\(e\left(\frac{16}{95}\right)\)	\(e\left(\frac{13}{19}\right)\)
\(\chi_{191}(28,\cdot)\)	191.h	190	yes	\(-1\)	\(1\)	\(e\left(\frac{93}{95}\right)\)	\(e\left(\frac{12}{95}\right)\)	\(e\left(\frac{91}{95}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{89}{95}\right)\)	\(e\left(\frac{24}{95}\right)\)	\(e\left(\frac{13}{95}\right)\)	\(e\left(\frac{33}{38}\right)\)
\(\chi_{191}(29,\cdot)\)	191.h	190	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{95}\right)\)	\(e\left(\frac{14}{95}\right)\)	\(e\left(\frac{27}{95}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{88}{95}\right)\)	\(e\left(\frac{28}{95}\right)\)	\(e\left(\frac{31}{95}\right)\)	\(e\left(\frac{29}{38}\right)\)
\(\chi_{191}(30,\cdot)\)	191.e	19	yes	\(1\)	\(1\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(1\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)
\(\chi_{191}(31,\cdot)\)	191.f	38	yes	\(-1\)	\(1\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(-1\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{11}{38}\right)\)
\(\chi_{191}(32,\cdot)\)	191.e	19	yes	\(1\)	\(1\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(1\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)

Introduction

L-functions

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Character group

First 32 of 190 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.