LMFDB - Group of Dirichlet characters of modulus 107

Show commands: PariGP / SageMath

sage: H = DirichletGroup(107)

pari: g = idealstar(,107,2)

Character group

sage: G.order() pari: g.no
Order	=	106
sage: H.invariants() pari: g.cyc
Structure	=	$C_{106}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{107}(2,\cdot)$

First 32 of 106 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{107}(1,\cdot)$	107.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{107}(2,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{1}{106}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{47}{106}\right)$	$e\left(\frac{71}{106}\right)$	$e\left(\frac{43}{106}\right)$	$e\left(\frac{3}{106}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{11}{53}\right)$
$\chi_{107}(3,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{28}{53}\right)$
$\chi_{107}(4,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{22}{53}\right)$
$\chi_{107}(5,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{47}{106}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{89}{106}\right)$	$e\left(\frac{51}{106}\right)$	$e\left(\frac{7}{106}\right)$	$e\left(\frac{35}{106}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{40}{53}\right)$
$\chi_{107}(6,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{71}{106}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{51}{106}\right)$	$e\left(\frac{59}{106}\right)$	$e\left(\frac{85}{106}\right)$	$e\left(\frac{1}{106}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{39}{53}\right)$
$\chi_{107}(7,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{43}{106}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{7}{106}\right)$	$e\left(\frac{85}{106}\right)$	$e\left(\frac{47}{106}\right)$	$e\left(\frac{23}{106}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{49}{53}\right)$
$\chi_{107}(8,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{3}{106}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{35}{106}\right)$	$e\left(\frac{1}{106}\right)$	$e\left(\frac{23}{106}\right)$	$e\left(\frac{9}{106}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{33}{53}\right)$
$\chi_{107}(9,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{3}{53}\right)$
$\chi_{107}(10,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{51}{53}\right)$
$\chi_{107}(11,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{30}{53}\right)$
$\chi_{107}(12,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{50}{53}\right)$
$\chi_{107}(13,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{48}{53}\right)$
$\chi_{107}(14,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{7}{53}\right)$
$\chi_{107}(15,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{11}{106}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{93}{106}\right)$	$e\left(\frac{39}{106}\right)$	$e\left(\frac{49}{106}\right)$	$e\left(\frac{33}{106}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{15}{53}\right)$
$\chi_{107}(16,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{44}{53}\right)$
$\chi_{107}(17,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{29}{106}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{91}{106}\right)$	$e\left(\frac{45}{106}\right)$	$e\left(\frac{81}{106}\right)$	$e\left(\frac{87}{106}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{1}{53}\right)$
$\chi_{107}(18,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{35}{106}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{55}{106}\right)$	$e\left(\frac{47}{106}\right)$	$e\left(\frac{21}{106}\right)$	$e\left(\frac{105}{106}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{14}{53}\right)$
$\chi_{107}(19,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{10}{53}\right)$
$\chi_{107}(20,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{49}{106}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{77}{106}\right)$	$e\left(\frac{87}{106}\right)$	$e\left(\frac{93}{106}\right)$	$e\left(\frac{41}{106}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{9}{53}\right)$
$\chi_{107}(21,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{7}{106}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{11}{106}\right)$	$e\left(\frac{73}{106}\right)$	$e\left(\frac{89}{106}\right)$	$e\left(\frac{21}{106}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{24}{53}\right)$
$\chi_{107}(22,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{23}{106}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{21}{106}\right)$	$e\left(\frac{43}{106}\right)$	$e\left(\frac{35}{106}\right)$	$e\left(\frac{69}{106}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{41}{53}\right)$
$\chi_{107}(23,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{46}{53}\right)$
$\chi_{107}(24,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{73}{106}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{39}{106}\right)$	$e\left(\frac{95}{106}\right)$	$e\left(\frac{65}{106}\right)$	$e\left(\frac{7}{106}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{8}{53}\right)$
$\chi_{107}(25,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{27}{53}\right)$
$\chi_{107}(26,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{15}{106}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{69}{106}\right)$	$e\left(\frac{5}{106}\right)$	$e\left(\frac{9}{106}\right)$	$e\left(\frac{45}{106}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{6}{53}\right)$
$\chi_{107}(27,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{31}{53}\right)$
$\chi_{107}(28,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{45}{106}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{101}{106}\right)$	$e\left(\frac{15}{106}\right)$	$e\left(\frac{27}{106}\right)$	$e\left(\frac{29}{106}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{18}{53}\right)$
$\chi_{107}(29,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{34}{53}\right)$
$\chi_{107}(30,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{26}{53}\right)$
$\chi_{107}(31,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{27}{106}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{103}{106}\right)$	$e\left(\frac{9}{106}\right)$	$e\left(\frac{101}{106}\right)$	$e\left(\frac{81}{106}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{32}{53}\right)$
$\chi_{107}(32,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{5}{106}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{23}{106}\right)$	$e\left(\frac{37}{106}\right)$	$e\left(\frac{3}{106}\right)$	$e\left(\frac{15}{106}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{2}{53}\right)$

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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	$107$
Structure	\(C_{106}\)
Order	$106$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{107}(1,\cdot)\)	107.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{107}(2,\cdot)\)	107.d	106	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{106}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{47}{106}\right)\)	\(e\left(\frac{71}{106}\right)\)	\(e\left(\frac{43}{106}\right)\)	\(e\left(\frac{3}{106}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{11}{53}\right)\)
\(\chi_{107}(3,\cdot)\)	107.c	53	yes	\(1\)	\(1\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{28}{53}\right)\)
\(\chi_{107}(4,\cdot)\)	107.c	53	yes	\(1\)	\(1\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{34}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{22}{53}\right)\)
\(\chi_{107}(5,\cdot)\)	107.d	106	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{106}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{89}{106}\right)\)	\(e\left(\frac{51}{106}\right)\)	\(e\left(\frac{7}{106}\right)\)	\(e\left(\frac{35}{106}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{40}{53}\right)\)
\(\chi_{107}(6,\cdot)\)	107.d	106	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{106}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{51}{106}\right)\)	\(e\left(\frac{59}{106}\right)\)	\(e\left(\frac{85}{106}\right)\)	\(e\left(\frac{1}{106}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{39}{53}\right)\)
\(\chi_{107}(7,\cdot)\)	107.d	106	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{106}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{7}{106}\right)\)	\(e\left(\frac{85}{106}\right)\)	\(e\left(\frac{47}{106}\right)\)	\(e\left(\frac{23}{106}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)
\(\chi_{107}(8,\cdot)\)	107.d	106	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{106}\right)\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{35}{106}\right)\)	\(e\left(\frac{1}{106}\right)\)	\(e\left(\frac{23}{106}\right)\)	\(e\left(\frac{9}{106}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{33}{53}\right)\)
\(\chi_{107}(9,\cdot)\)	107.c	53	yes	\(1\)	\(1\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{34}{53}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)
\(\chi_{107}(10,\cdot)\)	107.c	53	yes	\(1\)	\(1\)	\(e\left(\frac{24}{53}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{51}{53}\right)\)
\(\chi_{107}(11,\cdot)\)	107.c	53	yes	\(1\)	\(1\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{28}{53}\right)\)	\(e\left(\frac{22}{53}\right)\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{30}{53}\right)\)
\(\chi_{107}(12,\cdot)\)	107.c	53	yes	\(1\)	\(1\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{29}{53}\right)\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)
\(\chi_{107}(13,\cdot)\)	107.c	53	yes	\(1\)	\(1\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{21}{53}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)
\(\chi_{107}(14,\cdot)\)	107.c	53	yes	\(1\)	\(1\)	\(e\left(\frac{22}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{7}{53}\right)\)
\(\chi_{107}(15,\cdot)\)	107.d	106	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{106}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{93}{106}\right)\)	\(e\left(\frac{39}{106}\right)\)	\(e\left(\frac{49}{106}\right)\)	\(e\left(\frac{33}{106}\right)\)	\(e\left(\frac{28}{53}\right)\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{15}{53}\right)\)
\(\chi_{107}(16,\cdot)\)	107.c	53	yes	\(1\)	\(1\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{34}{53}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{44}{53}\right)\)
\(\chi_{107}(17,\cdot)\)	107.d	106	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{106}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{29}{53}\right)\)	\(e\left(\frac{91}{106}\right)\)	\(e\left(\frac{45}{106}\right)\)	\(e\left(\frac{81}{106}\right)\)	\(e\left(\frac{87}{106}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{1}{53}\right)\)
\(\chi_{107}(18,\cdot)\)	107.d	106	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{106}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{55}{106}\right)\)	\(e\left(\frac{47}{106}\right)\)	\(e\left(\frac{21}{106}\right)\)	\(e\left(\frac{105}{106}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{14}{53}\right)\)
\(\chi_{107}(19,\cdot)\)	107.c	53	yes	\(1\)	\(1\)	\(e\left(\frac{39}{53}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{25}{53}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{34}{53}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{1}{53}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{10}{53}\right)\)
\(\chi_{107}(20,\cdot)\)	107.d	106	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{106}\right)\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{77}{106}\right)\)	\(e\left(\frac{87}{106}\right)\)	\(e\left(\frac{93}{106}\right)\)	\(e\left(\frac{41}{106}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{9}{53}\right)\)
\(\chi_{107}(21,\cdot)\)	107.d	106	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{106}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{11}{106}\right)\)	\(e\left(\frac{73}{106}\right)\)	\(e\left(\frac{89}{106}\right)\)	\(e\left(\frac{21}{106}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{24}{53}\right)\)
\(\chi_{107}(22,\cdot)\)	107.d	106	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{106}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{21}{106}\right)\)	\(e\left(\frac{43}{106}\right)\)	\(e\left(\frac{35}{106}\right)\)	\(e\left(\frac{69}{106}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{22}{53}\right)\)	\(e\left(\frac{41}{53}\right)\)
\(\chi_{107}(23,\cdot)\)	107.c	53	yes	\(1\)	\(1\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{9}{53}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{28}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{40}{53}\right)\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{46}{53}\right)\)
\(\chi_{107}(24,\cdot)\)	107.d	106	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{106}\right)\)	\(e\left(\frac{11}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{39}{106}\right)\)	\(e\left(\frac{95}{106}\right)\)	\(e\left(\frac{65}{106}\right)\)	\(e\left(\frac{7}{106}\right)\)	\(e\left(\frac{22}{53}\right)\)	\(e\left(\frac{3}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)
\(\chi_{107}(25,\cdot)\)	107.c	53	yes	\(1\)	\(1\)	\(e\left(\frac{47}{53}\right)\)	\(e\left(\frac{4}{53}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{8}{53}\right)\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{27}{53}\right)\)
\(\chi_{107}(26,\cdot)\)	107.d	106	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{106}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{69}{106}\right)\)	\(e\left(\frac{5}{106}\right)\)	\(e\left(\frac{9}{106}\right)\)	\(e\left(\frac{45}{106}\right)\)	\(e\left(\frac{43}{53}\right)\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{6}{53}\right)\)
\(\chi_{107}(27,\cdot)\)	107.c	53	yes	\(1\)	\(1\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{51}{53}\right)\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{50}{53}\right)\)	\(e\left(\frac{19}{53}\right)\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{31}{53}\right)\)
\(\chi_{107}(28,\cdot)\)	107.d	106	yes	\(-1\)	\(1\)	\(e\left(\frac{45}{106}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{101}{106}\right)\)	\(e\left(\frac{15}{106}\right)\)	\(e\left(\frac{27}{106}\right)\)	\(e\left(\frac{29}{106}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)
\(\chi_{107}(29,\cdot)\)	107.c	53	yes	\(1\)	\(1\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{52}{53}\right)\)	\(e\left(\frac{48}{53}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{26}{53}\right)\)	\(e\left(\frac{34}{53}\right)\)
\(\chi_{107}(30,\cdot)\)	107.c	53	yes	\(1\)	\(1\)	\(e\left(\frac{6}{53}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)	\(e\left(\frac{46}{53}\right)\)	\(e\left(\frac{18}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{26}{53}\right)\)
\(\chi_{107}(31,\cdot)\)	107.d	106	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{106}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{27}{53}\right)\)	\(e\left(\frac{103}{106}\right)\)	\(e\left(\frac{9}{106}\right)\)	\(e\left(\frac{101}{106}\right)\)	\(e\left(\frac{81}{106}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{12}{53}\right)\)	\(e\left(\frac{32}{53}\right)\)
\(\chi_{107}(32,\cdot)\)	107.d	106	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{106}\right)\)	\(e\left(\frac{16}{53}\right)\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{23}{106}\right)\)	\(e\left(\frac{37}{106}\right)\)	\(e\left(\frac{3}{106}\right)\)	\(e\left(\frac{15}{106}\right)\)	\(e\left(\frac{32}{53}\right)\)	\(e\left(\frac{14}{53}\right)\)	\(e\left(\frac{2}{53}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 106 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.