LMFDB - Group of Dirichlet characters of modulus 431

Show commands: PariGP / SageMath

sage: H = DirichletGroup(431)

pari: g = idealstar(,431,2)

Character group

sage: G.order() pari: g.no
Order	=	430
sage: H.invariants() pari: g.cyc
Structure	=	$C_{430}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{431}(7,\cdot)$

First 32 of 430 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{431}(1,\cdot)$	431.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{431}(2,\cdot)$	431.e	43	yes	$1$	$1$	$e\left(\frac{24}{43}\right)$	$e\left(\frac{11}{43}\right)$	$e\left(\frac{5}{43}\right)$	$e\left(\frac{42}{43}\right)$	$e\left(\frac{35}{43}\right)$	$e\left(\frac{22}{43}\right)$	$e\left(\frac{29}{43}\right)$	$e\left(\frac{22}{43}\right)$	$e\left(\frac{23}{43}\right)$	$e\left(\frac{37}{43}\right)$
$\chi_{431}(3,\cdot)$	431.e	43	yes	$1$	$1$	$e\left(\frac{11}{43}\right)$	$e\left(\frac{14}{43}\right)$	$e\left(\frac{22}{43}\right)$	$e\left(\frac{30}{43}\right)$	$e\left(\frac{25}{43}\right)$	$e\left(\frac{28}{43}\right)$	$e\left(\frac{33}{43}\right)$	$e\left(\frac{28}{43}\right)$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{8}{43}\right)$
$\chi_{431}(4,\cdot)$	431.e	43	yes	$1$	$1$	$e\left(\frac{5}{43}\right)$	$e\left(\frac{22}{43}\right)$	$e\left(\frac{10}{43}\right)$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{27}{43}\right)$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{15}{43}\right)$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{3}{43}\right)$	$e\left(\frac{31}{43}\right)$
$\chi_{431}(5,\cdot)$	431.g	215	yes	$1$	$1$	$e\left(\frac{42}{43}\right)$	$e\left(\frac{30}{43}\right)$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{2}{215}\right)$	$e\left(\frac{29}{43}\right)$	$e\left(\frac{171}{215}\right)$	$e\left(\frac{40}{43}\right)$	$e\left(\frac{17}{43}\right)$	$e\left(\frac{212}{215}\right)$	$e\left(\frac{98}{215}\right)$
$\chi_{431}(6,\cdot)$	431.e	43	yes	$1$	$1$	$e\left(\frac{35}{43}\right)$	$e\left(\frac{25}{43}\right)$	$e\left(\frac{27}{43}\right)$	$e\left(\frac{29}{43}\right)$	$e\left(\frac{17}{43}\right)$	$e\left(\frac{7}{43}\right)$	$e\left(\frac{19}{43}\right)$	$e\left(\frac{7}{43}\right)$	$e\left(\frac{21}{43}\right)$	$e\left(\frac{2}{43}\right)$
$\chi_{431}(7,\cdot)$	431.h	430	yes	$-1$	$1$	$e\left(\frac{22}{43}\right)$	$e\left(\frac{28}{43}\right)$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{171}{215}\right)$	$e\left(\frac{7}{43}\right)$	$e\left(\frac{1}{430}\right)$	$e\left(\frac{23}{43}\right)$	$e\left(\frac{13}{43}\right)$	$e\left(\frac{66}{215}\right)$	$e\left(\frac{209}{215}\right)$
$\chi_{431}(8,\cdot)$	431.e	43	yes	$1$	$1$	$e\left(\frac{29}{43}\right)$	$e\left(\frac{33}{43}\right)$	$e\left(\frac{15}{43}\right)$	$e\left(\frac{40}{43}\right)$	$e\left(\frac{19}{43}\right)$	$e\left(\frac{23}{43}\right)$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{23}{43}\right)$	$e\left(\frac{26}{43}\right)$	$e\left(\frac{25}{43}\right)$
$\chi_{431}(9,\cdot)$	431.e	43	yes	$1$	$1$	$e\left(\frac{22}{43}\right)$	$e\left(\frac{28}{43}\right)$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{17}{43}\right)$	$e\left(\frac{7}{43}\right)$	$e\left(\frac{13}{43}\right)$	$e\left(\frac{23}{43}\right)$	$e\left(\frac{13}{43}\right)$	$e\left(\frac{39}{43}\right)$	$e\left(\frac{16}{43}\right)$
$\chi_{431}(10,\cdot)$	431.g	215	yes	$1$	$1$	$e\left(\frac{23}{43}\right)$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{3}{43}\right)$	$e\left(\frac{212}{215}\right)$	$e\left(\frac{21}{43}\right)$	$e\left(\frac{66}{215}\right)$	$e\left(\frac{26}{43}\right)$	$e\left(\frac{39}{43}\right)$	$e\left(\frac{112}{215}\right)$	$e\left(\frac{68}{215}\right)$
$\chi_{431}(11,\cdot)$	431.g	215	yes	$1$	$1$	$e\left(\frac{37}{43}\right)$	$e\left(\frac{8}{43}\right)$	$e\left(\frac{31}{43}\right)$	$e\left(\frac{98}{215}\right)$	$e\left(\frac{2}{43}\right)$	$e\left(\frac{209}{215}\right)$	$e\left(\frac{25}{43}\right)$	$e\left(\frac{16}{43}\right)$	$e\left(\frac{68}{215}\right)$	$e\left(\frac{72}{215}\right)$
$\chi_{431}(12,\cdot)$	431.e	43	yes	$1$	$1$	$e\left(\frac{16}{43}\right)$	$e\left(\frac{36}{43}\right)$	$e\left(\frac{32}{43}\right)$	$e\left(\frac{28}{43}\right)$	$e\left(\frac{9}{43}\right)$	$e\left(\frac{29}{43}\right)$	$e\left(\frac{5}{43}\right)$	$e\left(\frac{29}{43}\right)$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{39}{43}\right)$
$\chi_{431}(13,\cdot)$	431.h	430	yes	$-1$	$1$	$e\left(\frac{19}{43}\right)$	$e\left(\frac{32}{43}\right)$	$e\left(\frac{38}{43}\right)$	$e\left(\frac{177}{215}\right)$	$e\left(\frac{8}{43}\right)$	$e\left(\frac{167}{430}\right)$	$e\left(\frac{14}{43}\right)$	$e\left(\frac{21}{43}\right)$	$e\left(\frac{57}{215}\right)$	$e\left(\frac{73}{215}\right)$
$\chi_{431}(14,\cdot)$	431.h	430	yes	$-1$	$1$	$e\left(\frac{3}{43}\right)$	$e\left(\frac{39}{43}\right)$	$e\left(\frac{6}{43}\right)$	$e\left(\frac{166}{215}\right)$	$e\left(\frac{42}{43}\right)$	$e\left(\frac{221}{430}\right)$	$e\left(\frac{9}{43}\right)$	$e\left(\frac{35}{43}\right)$	$e\left(\frac{181}{215}\right)$	$e\left(\frac{179}{215}\right)$
$\chi_{431}(15,\cdot)$	431.g	215	yes	$1$	$1$	$e\left(\frac{10}{43}\right)$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{20}{43}\right)$	$e\left(\frac{152}{215}\right)$	$e\left(\frac{11}{43}\right)$	$e\left(\frac{96}{215}\right)$	$e\left(\frac{30}{43}\right)$	$e\left(\frac{2}{43}\right)$	$e\left(\frac{202}{215}\right)$	$e\left(\frac{138}{215}\right)$
$\chi_{431}(16,\cdot)$	431.e	43	yes	$1$	$1$	$e\left(\frac{10}{43}\right)$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{20}{43}\right)$	$e\left(\frac{39}{43}\right)$	$e\left(\frac{11}{43}\right)$	$e\left(\frac{2}{43}\right)$	$e\left(\frac{30}{43}\right)$	$e\left(\frac{2}{43}\right)$	$e\left(\frac{6}{43}\right)$	$e\left(\frac{19}{43}\right)$
$\chi_{431}(17,\cdot)$	431.h	430	yes	$-1$	$1$	$e\left(\frac{37}{43}\right)$	$e\left(\frac{8}{43}\right)$	$e\left(\frac{31}{43}\right)$	$e\left(\frac{141}{215}\right)$	$e\left(\frac{2}{43}\right)$	$e\left(\frac{31}{430}\right)$	$e\left(\frac{25}{43}\right)$	$e\left(\frac{16}{43}\right)$	$e\left(\frac{111}{215}\right)$	$e\left(\frac{29}{215}\right)$
$\chi_{431}(18,\cdot)$	431.e	43	yes	$1$	$1$	$e\left(\frac{3}{43}\right)$	$e\left(\frac{39}{43}\right)$	$e\left(\frac{6}{43}\right)$	$e\left(\frac{16}{43}\right)$	$e\left(\frac{42}{43}\right)$	$e\left(\frac{35}{43}\right)$	$e\left(\frac{9}{43}\right)$	$e\left(\frac{35}{43}\right)$	$e\left(\frac{19}{43}\right)$	$e\left(\frac{10}{43}\right)$
$\chi_{431}(19,\cdot)$	431.g	215	yes	$1$	$1$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{13}{43}\right)$	$e\left(\frac{2}{43}\right)$	$e\left(\frac{84}{215}\right)$	$e\left(\frac{14}{43}\right)$	$e\left(\frac{87}{215}\right)$	$e\left(\frac{3}{43}\right)$	$e\left(\frac{26}{43}\right)$	$e\left(\frac{89}{215}\right)$	$e\left(\frac{31}{215}\right)$
$\chi_{431}(20,\cdot)$	431.g	215	yes	$1$	$1$	$e\left(\frac{4}{43}\right)$	$e\left(\frac{9}{43}\right)$	$e\left(\frac{8}{43}\right)$	$e\left(\frac{207}{215}\right)$	$e\left(\frac{13}{43}\right)$	$e\left(\frac{176}{215}\right)$	$e\left(\frac{12}{43}\right)$	$e\left(\frac{18}{43}\right)$	$e\left(\frac{12}{215}\right)$	$e\left(\frac{38}{215}\right)$
$\chi_{431}(21,\cdot)$	431.h	430	yes	$-1$	$1$	$e\left(\frac{33}{43}\right)$	$e\left(\frac{42}{43}\right)$	$e\left(\frac{23}{43}\right)$	$e\left(\frac{106}{215}\right)$	$e\left(\frac{32}{43}\right)$	$e\left(\frac{281}{430}\right)$	$e\left(\frac{13}{43}\right)$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{56}{215}\right)$	$e\left(\frac{34}{215}\right)$
$\chi_{431}(22,\cdot)$	431.g	215	yes	$1$	$1$	$e\left(\frac{18}{43}\right)$	$e\left(\frac{19}{43}\right)$	$e\left(\frac{36}{43}\right)$	$e\left(\frac{93}{215}\right)$	$e\left(\frac{37}{43}\right)$	$e\left(\frac{104}{215}\right)$	$e\left(\frac{11}{43}\right)$	$e\left(\frac{38}{43}\right)$	$e\left(\frac{183}{215}\right)$	$e\left(\frac{42}{215}\right)$
$\chi_{431}(23,\cdot)$	431.g	215	yes	$1$	$1$	$e\left(\frac{34}{43}\right)$	$e\left(\frac{12}{43}\right)$	$e\left(\frac{25}{43}\right)$	$e\left(\frac{61}{215}\right)$	$e\left(\frac{3}{43}\right)$	$e\left(\frac{163}{215}\right)$	$e\left(\frac{16}{43}\right)$	$e\left(\frac{24}{43}\right)$	$e\left(\frac{16}{215}\right)$	$e\left(\frac{194}{215}\right)$
$\chi_{431}(24,\cdot)$	431.e	43	yes	$1$	$1$	$e\left(\frac{40}{43}\right)$	$e\left(\frac{4}{43}\right)$	$e\left(\frac{37}{43}\right)$	$e\left(\frac{27}{43}\right)$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{8}{43}\right)$	$e\left(\frac{34}{43}\right)$	$e\left(\frac{8}{43}\right)$	$e\left(\frac{24}{43}\right)$	$e\left(\frac{33}{43}\right)$
$\chi_{431}(25,\cdot)$	431.g	215	yes	$1$	$1$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{17}{43}\right)$	$e\left(\frac{39}{43}\right)$	$e\left(\frac{4}{215}\right)$	$e\left(\frac{15}{43}\right)$	$e\left(\frac{127}{215}\right)$	$e\left(\frac{37}{43}\right)$	$e\left(\frac{34}{43}\right)$	$e\left(\frac{209}{215}\right)$	$e\left(\frac{196}{215}\right)$
$\chi_{431}(26,\cdot)$	431.d	10	yes	$-1$	$1$	$1$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{431}(27,\cdot)$	431.e	43	yes	$1$	$1$	$e\left(\frac{33}{43}\right)$	$e\left(\frac{42}{43}\right)$	$e\left(\frac{23}{43}\right)$	$e\left(\frac{4}{43}\right)$	$e\left(\frac{32}{43}\right)$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{13}{43}\right)$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{37}{43}\right)$	$e\left(\frac{24}{43}\right)$
$\chi_{431}(28,\cdot)$	431.h	430	yes	$-1$	$1$	$e\left(\frac{27}{43}\right)$	$e\left(\frac{7}{43}\right)$	$e\left(\frac{11}{43}\right)$	$e\left(\frac{161}{215}\right)$	$e\left(\frac{34}{43}\right)$	$e\left(\frac{11}{430}\right)$	$e\left(\frac{38}{43}\right)$	$e\left(\frac{14}{43}\right)$	$e\left(\frac{81}{215}\right)$	$e\left(\frac{149}{215}\right)$
$\chi_{431}(29,\cdot)$	431.g	215	yes	$1$	$1$	$e\left(\frac{38}{43}\right)$	$e\left(\frac{21}{43}\right)$	$e\left(\frac{33}{43}\right)$	$e\left(\frac{53}{215}\right)$	$e\left(\frac{16}{43}\right)$	$e\left(\frac{124}{215}\right)$	$e\left(\frac{28}{43}\right)$	$e\left(\frac{42}{43}\right)$	$e\left(\frac{28}{215}\right)$	$e\left(\frac{17}{215}\right)$
$\chi_{431}(30,\cdot)$	431.g	215	yes	$1$	$1$	$e\left(\frac{34}{43}\right)$	$e\left(\frac{12}{43}\right)$	$e\left(\frac{25}{43}\right)$	$e\left(\frac{147}{215}\right)$	$e\left(\frac{3}{43}\right)$	$e\left(\frac{206}{215}\right)$	$e\left(\frac{16}{43}\right)$	$e\left(\frac{24}{43}\right)$	$e\left(\frac{102}{215}\right)$	$e\left(\frac{108}{215}\right)$
$\chi_{431}(31,\cdot)$	431.h	430	yes	$-1$	$1$	$e\left(\frac{8}{43}\right)$	$e\left(\frac{18}{43}\right)$	$e\left(\frac{16}{43}\right)$	$e\left(\frac{199}{215}\right)$	$e\left(\frac{26}{43}\right)$	$e\left(\frac{59}{430}\right)$	$e\left(\frac{24}{43}\right)$	$e\left(\frac{36}{43}\right)$	$e\left(\frac{24}{215}\right)$	$e\left(\frac{76}{215}\right)$
$\chi_{431}(32,\cdot)$	431.e	43	yes	$1$	$1$	$e\left(\frac{34}{43}\right)$	$e\left(\frac{12}{43}\right)$	$e\left(\frac{25}{43}\right)$	$e\left(\frac{38}{43}\right)$	$e\left(\frac{3}{43}\right)$	$e\left(\frac{24}{43}\right)$	$e\left(\frac{16}{43}\right)$	$e\left(\frac{24}{43}\right)$	$e\left(\frac{29}{43}\right)$	$e\left(\frac{13}{43}\right)$

Click here to search among the remaining 398 characters.

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	$431$
Structure	\(C_{430}\)
Order	$430$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{431}(1,\cdot)\)	431.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{431}(2,\cdot)\)	431.e	43	yes	\(1\)	\(1\)	\(e\left(\frac{24}{43}\right)\)	\(e\left(\frac{11}{43}\right)\)	\(e\left(\frac{5}{43}\right)\)	\(e\left(\frac{42}{43}\right)\)	\(e\left(\frac{35}{43}\right)\)	\(e\left(\frac{22}{43}\right)\)	\(e\left(\frac{29}{43}\right)\)	\(e\left(\frac{22}{43}\right)\)	\(e\left(\frac{23}{43}\right)\)	\(e\left(\frac{37}{43}\right)\)
\(\chi_{431}(3,\cdot)\)	431.e	43	yes	\(1\)	\(1\)	\(e\left(\frac{11}{43}\right)\)	\(e\left(\frac{14}{43}\right)\)	\(e\left(\frac{22}{43}\right)\)	\(e\left(\frac{30}{43}\right)\)	\(e\left(\frac{25}{43}\right)\)	\(e\left(\frac{28}{43}\right)\)	\(e\left(\frac{33}{43}\right)\)	\(e\left(\frac{28}{43}\right)\)	\(e\left(\frac{41}{43}\right)\)	\(e\left(\frac{8}{43}\right)\)
\(\chi_{431}(4,\cdot)\)	431.e	43	yes	\(1\)	\(1\)	\(e\left(\frac{5}{43}\right)\)	\(e\left(\frac{22}{43}\right)\)	\(e\left(\frac{10}{43}\right)\)	\(e\left(\frac{41}{43}\right)\)	\(e\left(\frac{27}{43}\right)\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{15}{43}\right)\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{3}{43}\right)\)	\(e\left(\frac{31}{43}\right)\)
\(\chi_{431}(5,\cdot)\)	431.g	215	yes	\(1\)	\(1\)	\(e\left(\frac{42}{43}\right)\)	\(e\left(\frac{30}{43}\right)\)	\(e\left(\frac{41}{43}\right)\)	\(e\left(\frac{2}{215}\right)\)	\(e\left(\frac{29}{43}\right)\)	\(e\left(\frac{171}{215}\right)\)	\(e\left(\frac{40}{43}\right)\)	\(e\left(\frac{17}{43}\right)\)	\(e\left(\frac{212}{215}\right)\)	\(e\left(\frac{98}{215}\right)\)
\(\chi_{431}(6,\cdot)\)	431.e	43	yes	\(1\)	\(1\)	\(e\left(\frac{35}{43}\right)\)	\(e\left(\frac{25}{43}\right)\)	\(e\left(\frac{27}{43}\right)\)	\(e\left(\frac{29}{43}\right)\)	\(e\left(\frac{17}{43}\right)\)	\(e\left(\frac{7}{43}\right)\)	\(e\left(\frac{19}{43}\right)\)	\(e\left(\frac{7}{43}\right)\)	\(e\left(\frac{21}{43}\right)\)	\(e\left(\frac{2}{43}\right)\)
\(\chi_{431}(7,\cdot)\)	431.h	430	yes	\(-1\)	\(1\)	\(e\left(\frac{22}{43}\right)\)	\(e\left(\frac{28}{43}\right)\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{171}{215}\right)\)	\(e\left(\frac{7}{43}\right)\)	\(e\left(\frac{1}{430}\right)\)	\(e\left(\frac{23}{43}\right)\)	\(e\left(\frac{13}{43}\right)\)	\(e\left(\frac{66}{215}\right)\)	\(e\left(\frac{209}{215}\right)\)
\(\chi_{431}(8,\cdot)\)	431.e	43	yes	\(1\)	\(1\)	\(e\left(\frac{29}{43}\right)\)	\(e\left(\frac{33}{43}\right)\)	\(e\left(\frac{15}{43}\right)\)	\(e\left(\frac{40}{43}\right)\)	\(e\left(\frac{19}{43}\right)\)	\(e\left(\frac{23}{43}\right)\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{23}{43}\right)\)	\(e\left(\frac{26}{43}\right)\)	\(e\left(\frac{25}{43}\right)\)
\(\chi_{431}(9,\cdot)\)	431.e	43	yes	\(1\)	\(1\)	\(e\left(\frac{22}{43}\right)\)	\(e\left(\frac{28}{43}\right)\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{17}{43}\right)\)	\(e\left(\frac{7}{43}\right)\)	\(e\left(\frac{13}{43}\right)\)	\(e\left(\frac{23}{43}\right)\)	\(e\left(\frac{13}{43}\right)\)	\(e\left(\frac{39}{43}\right)\)	\(e\left(\frac{16}{43}\right)\)
\(\chi_{431}(10,\cdot)\)	431.g	215	yes	\(1\)	\(1\)	\(e\left(\frac{23}{43}\right)\)	\(e\left(\frac{41}{43}\right)\)	\(e\left(\frac{3}{43}\right)\)	\(e\left(\frac{212}{215}\right)\)	\(e\left(\frac{21}{43}\right)\)	\(e\left(\frac{66}{215}\right)\)	\(e\left(\frac{26}{43}\right)\)	\(e\left(\frac{39}{43}\right)\)	\(e\left(\frac{112}{215}\right)\)	\(e\left(\frac{68}{215}\right)\)
\(\chi_{431}(11,\cdot)\)	431.g	215	yes	\(1\)	\(1\)	\(e\left(\frac{37}{43}\right)\)	\(e\left(\frac{8}{43}\right)\)	\(e\left(\frac{31}{43}\right)\)	\(e\left(\frac{98}{215}\right)\)	\(e\left(\frac{2}{43}\right)\)	\(e\left(\frac{209}{215}\right)\)	\(e\left(\frac{25}{43}\right)\)	\(e\left(\frac{16}{43}\right)\)	\(e\left(\frac{68}{215}\right)\)	\(e\left(\frac{72}{215}\right)\)
\(\chi_{431}(12,\cdot)\)	431.e	43	yes	\(1\)	\(1\)	\(e\left(\frac{16}{43}\right)\)	\(e\left(\frac{36}{43}\right)\)	\(e\left(\frac{32}{43}\right)\)	\(e\left(\frac{28}{43}\right)\)	\(e\left(\frac{9}{43}\right)\)	\(e\left(\frac{29}{43}\right)\)	\(e\left(\frac{5}{43}\right)\)	\(e\left(\frac{29}{43}\right)\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{39}{43}\right)\)
\(\chi_{431}(13,\cdot)\)	431.h	430	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{43}\right)\)	\(e\left(\frac{32}{43}\right)\)	\(e\left(\frac{38}{43}\right)\)	\(e\left(\frac{177}{215}\right)\)	\(e\left(\frac{8}{43}\right)\)	\(e\left(\frac{167}{430}\right)\)	\(e\left(\frac{14}{43}\right)\)	\(e\left(\frac{21}{43}\right)\)	\(e\left(\frac{57}{215}\right)\)	\(e\left(\frac{73}{215}\right)\)
\(\chi_{431}(14,\cdot)\)	431.h	430	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{43}\right)\)	\(e\left(\frac{39}{43}\right)\)	\(e\left(\frac{6}{43}\right)\)	\(e\left(\frac{166}{215}\right)\)	\(e\left(\frac{42}{43}\right)\)	\(e\left(\frac{221}{430}\right)\)	\(e\left(\frac{9}{43}\right)\)	\(e\left(\frac{35}{43}\right)\)	\(e\left(\frac{181}{215}\right)\)	\(e\left(\frac{179}{215}\right)\)
\(\chi_{431}(15,\cdot)\)	431.g	215	yes	\(1\)	\(1\)	\(e\left(\frac{10}{43}\right)\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{20}{43}\right)\)	\(e\left(\frac{152}{215}\right)\)	\(e\left(\frac{11}{43}\right)\)	\(e\left(\frac{96}{215}\right)\)	\(e\left(\frac{30}{43}\right)\)	\(e\left(\frac{2}{43}\right)\)	\(e\left(\frac{202}{215}\right)\)	\(e\left(\frac{138}{215}\right)\)
\(\chi_{431}(16,\cdot)\)	431.e	43	yes	\(1\)	\(1\)	\(e\left(\frac{10}{43}\right)\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{20}{43}\right)\)	\(e\left(\frac{39}{43}\right)\)	\(e\left(\frac{11}{43}\right)\)	\(e\left(\frac{2}{43}\right)\)	\(e\left(\frac{30}{43}\right)\)	\(e\left(\frac{2}{43}\right)\)	\(e\left(\frac{6}{43}\right)\)	\(e\left(\frac{19}{43}\right)\)
\(\chi_{431}(17,\cdot)\)	431.h	430	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{43}\right)\)	\(e\left(\frac{8}{43}\right)\)	\(e\left(\frac{31}{43}\right)\)	\(e\left(\frac{141}{215}\right)\)	\(e\left(\frac{2}{43}\right)\)	\(e\left(\frac{31}{430}\right)\)	\(e\left(\frac{25}{43}\right)\)	\(e\left(\frac{16}{43}\right)\)	\(e\left(\frac{111}{215}\right)\)	\(e\left(\frac{29}{215}\right)\)
\(\chi_{431}(18,\cdot)\)	431.e	43	yes	\(1\)	\(1\)	\(e\left(\frac{3}{43}\right)\)	\(e\left(\frac{39}{43}\right)\)	\(e\left(\frac{6}{43}\right)\)	\(e\left(\frac{16}{43}\right)\)	\(e\left(\frac{42}{43}\right)\)	\(e\left(\frac{35}{43}\right)\)	\(e\left(\frac{9}{43}\right)\)	\(e\left(\frac{35}{43}\right)\)	\(e\left(\frac{19}{43}\right)\)	\(e\left(\frac{10}{43}\right)\)
\(\chi_{431}(19,\cdot)\)	431.g	215	yes	\(1\)	\(1\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{13}{43}\right)\)	\(e\left(\frac{2}{43}\right)\)	\(e\left(\frac{84}{215}\right)\)	\(e\left(\frac{14}{43}\right)\)	\(e\left(\frac{87}{215}\right)\)	\(e\left(\frac{3}{43}\right)\)	\(e\left(\frac{26}{43}\right)\)	\(e\left(\frac{89}{215}\right)\)	\(e\left(\frac{31}{215}\right)\)
\(\chi_{431}(20,\cdot)\)	431.g	215	yes	\(1\)	\(1\)	\(e\left(\frac{4}{43}\right)\)	\(e\left(\frac{9}{43}\right)\)	\(e\left(\frac{8}{43}\right)\)	\(e\left(\frac{207}{215}\right)\)	\(e\left(\frac{13}{43}\right)\)	\(e\left(\frac{176}{215}\right)\)	\(e\left(\frac{12}{43}\right)\)	\(e\left(\frac{18}{43}\right)\)	\(e\left(\frac{12}{215}\right)\)	\(e\left(\frac{38}{215}\right)\)
\(\chi_{431}(21,\cdot)\)	431.h	430	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{43}\right)\)	\(e\left(\frac{42}{43}\right)\)	\(e\left(\frac{23}{43}\right)\)	\(e\left(\frac{106}{215}\right)\)	\(e\left(\frac{32}{43}\right)\)	\(e\left(\frac{281}{430}\right)\)	\(e\left(\frac{13}{43}\right)\)	\(e\left(\frac{41}{43}\right)\)	\(e\left(\frac{56}{215}\right)\)	\(e\left(\frac{34}{215}\right)\)
\(\chi_{431}(22,\cdot)\)	431.g	215	yes	\(1\)	\(1\)	\(e\left(\frac{18}{43}\right)\)	\(e\left(\frac{19}{43}\right)\)	\(e\left(\frac{36}{43}\right)\)	\(e\left(\frac{93}{215}\right)\)	\(e\left(\frac{37}{43}\right)\)	\(e\left(\frac{104}{215}\right)\)	\(e\left(\frac{11}{43}\right)\)	\(e\left(\frac{38}{43}\right)\)	\(e\left(\frac{183}{215}\right)\)	\(e\left(\frac{42}{215}\right)\)
\(\chi_{431}(23,\cdot)\)	431.g	215	yes	\(1\)	\(1\)	\(e\left(\frac{34}{43}\right)\)	\(e\left(\frac{12}{43}\right)\)	\(e\left(\frac{25}{43}\right)\)	\(e\left(\frac{61}{215}\right)\)	\(e\left(\frac{3}{43}\right)\)	\(e\left(\frac{163}{215}\right)\)	\(e\left(\frac{16}{43}\right)\)	\(e\left(\frac{24}{43}\right)\)	\(e\left(\frac{16}{215}\right)\)	\(e\left(\frac{194}{215}\right)\)
\(\chi_{431}(24,\cdot)\)	431.e	43	yes	\(1\)	\(1\)	\(e\left(\frac{40}{43}\right)\)	\(e\left(\frac{4}{43}\right)\)	\(e\left(\frac{37}{43}\right)\)	\(e\left(\frac{27}{43}\right)\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{8}{43}\right)\)	\(e\left(\frac{34}{43}\right)\)	\(e\left(\frac{8}{43}\right)\)	\(e\left(\frac{24}{43}\right)\)	\(e\left(\frac{33}{43}\right)\)
\(\chi_{431}(25,\cdot)\)	431.g	215	yes	\(1\)	\(1\)	\(e\left(\frac{41}{43}\right)\)	\(e\left(\frac{17}{43}\right)\)	\(e\left(\frac{39}{43}\right)\)	\(e\left(\frac{4}{215}\right)\)	\(e\left(\frac{15}{43}\right)\)	\(e\left(\frac{127}{215}\right)\)	\(e\left(\frac{37}{43}\right)\)	\(e\left(\frac{34}{43}\right)\)	\(e\left(\frac{209}{215}\right)\)	\(e\left(\frac{196}{215}\right)\)
\(\chi_{431}(26,\cdot)\)	431.d	10	yes	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{431}(27,\cdot)\)	431.e	43	yes	\(1\)	\(1\)	\(e\left(\frac{33}{43}\right)\)	\(e\left(\frac{42}{43}\right)\)	\(e\left(\frac{23}{43}\right)\)	\(e\left(\frac{4}{43}\right)\)	\(e\left(\frac{32}{43}\right)\)	\(e\left(\frac{41}{43}\right)\)	\(e\left(\frac{13}{43}\right)\)	\(e\left(\frac{41}{43}\right)\)	\(e\left(\frac{37}{43}\right)\)	\(e\left(\frac{24}{43}\right)\)
\(\chi_{431}(28,\cdot)\)	431.h	430	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{43}\right)\)	\(e\left(\frac{7}{43}\right)\)	\(e\left(\frac{11}{43}\right)\)	\(e\left(\frac{161}{215}\right)\)	\(e\left(\frac{34}{43}\right)\)	\(e\left(\frac{11}{430}\right)\)	\(e\left(\frac{38}{43}\right)\)	\(e\left(\frac{14}{43}\right)\)	\(e\left(\frac{81}{215}\right)\)	\(e\left(\frac{149}{215}\right)\)
\(\chi_{431}(29,\cdot)\)	431.g	215	yes	\(1\)	\(1\)	\(e\left(\frac{38}{43}\right)\)	\(e\left(\frac{21}{43}\right)\)	\(e\left(\frac{33}{43}\right)\)	\(e\left(\frac{53}{215}\right)\)	\(e\left(\frac{16}{43}\right)\)	\(e\left(\frac{124}{215}\right)\)	\(e\left(\frac{28}{43}\right)\)	\(e\left(\frac{42}{43}\right)\)	\(e\left(\frac{28}{215}\right)\)	\(e\left(\frac{17}{215}\right)\)
\(\chi_{431}(30,\cdot)\)	431.g	215	yes	\(1\)	\(1\)	\(e\left(\frac{34}{43}\right)\)	\(e\left(\frac{12}{43}\right)\)	\(e\left(\frac{25}{43}\right)\)	\(e\left(\frac{147}{215}\right)\)	\(e\left(\frac{3}{43}\right)\)	\(e\left(\frac{206}{215}\right)\)	\(e\left(\frac{16}{43}\right)\)	\(e\left(\frac{24}{43}\right)\)	\(e\left(\frac{102}{215}\right)\)	\(e\left(\frac{108}{215}\right)\)
\(\chi_{431}(31,\cdot)\)	431.h	430	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{43}\right)\)	\(e\left(\frac{18}{43}\right)\)	\(e\left(\frac{16}{43}\right)\)	\(e\left(\frac{199}{215}\right)\)	\(e\left(\frac{26}{43}\right)\)	\(e\left(\frac{59}{430}\right)\)	\(e\left(\frac{24}{43}\right)\)	\(e\left(\frac{36}{43}\right)\)	\(e\left(\frac{24}{215}\right)\)	\(e\left(\frac{76}{215}\right)\)
\(\chi_{431}(32,\cdot)\)	431.e	43	yes	\(1\)	\(1\)	\(e\left(\frac{34}{43}\right)\)	\(e\left(\frac{12}{43}\right)\)	\(e\left(\frac{25}{43}\right)\)	\(e\left(\frac{38}{43}\right)\)	\(e\left(\frac{3}{43}\right)\)	\(e\left(\frac{24}{43}\right)\)	\(e\left(\frac{16}{43}\right)\)	\(e\left(\frac{24}{43}\right)\)	\(e\left(\frac{29}{43}\right)\)	\(e\left(\frac{13}{43}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 430 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.