LMFDB - Group of Dirichlet characters of modulus 1601

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1601)

pari: g = idealstar(,1601,2)

Character group

sage: G.order() pari: g.no
Order	=	1600
sage: H.invariants() pari: g.cyc
Structure	=	$C_{1600}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1601}(3,\cdot)$

First 32 of 1600 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{1601}(1,\cdot)$	1601.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1601}(2,\cdot)$	1601.s	400	yes	$1$	$1$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{13}{400}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{289}{400}\right)$	$e\left(\frac{31}{400}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{13}{200}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{229}{400}\right)$
$\chi_{1601}(3,\cdot)$	1601.u	1600	yes	$-1$	$1$	$e\left(\frac{13}{400}\right)$	$e\left(\frac{1}{1600}\right)$	$e\left(\frac{13}{200}\right)$	$e\left(\frac{261}{400}\right)$	$e\left(\frac{53}{1600}\right)$	$e\left(\frac{587}{1600}\right)$	$e\left(\frac{39}{400}\right)$	$e\left(\frac{1}{800}\right)$	$e\left(\frac{137}{200}\right)$	$e\left(\frac{633}{1600}\right)$
$\chi_{1601}(4,\cdot)$	1601.q	200	yes	$1$	$1$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{13}{200}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{89}{200}\right)$	$e\left(\frac{31}{200}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{29}{200}\right)$
$\chi_{1601}(5,\cdot)$	1601.s	400	yes	$1$	$1$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{261}{400}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{233}{400}\right)$	$e\left(\frac{7}{400}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{61}{200}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{13}{400}\right)$
$\chi_{1601}(6,\cdot)$	1601.u	1600	yes	$-1$	$1$	$e\left(\frac{289}{400}\right)$	$e\left(\frac{53}{1600}\right)$	$e\left(\frac{89}{200}\right)$	$e\left(\frac{233}{400}\right)$	$e\left(\frac{1209}{1600}\right)$	$e\left(\frac{711}{1600}\right)$	$e\left(\frac{67}{400}\right)$	$e\left(\frac{53}{800}\right)$	$e\left(\frac{61}{200}\right)$	$e\left(\frac{1549}{1600}\right)$
$\chi_{1601}(7,\cdot)$	1601.u	1600	yes	$-1$	$1$	$e\left(\frac{31}{400}\right)$	$e\left(\frac{587}{1600}\right)$	$e\left(\frac{31}{200}\right)$	$e\left(\frac{7}{400}\right)$	$e\left(\frac{711}{1600}\right)$	$e\left(\frac{569}{1600}\right)$	$e\left(\frac{93}{400}\right)$	$e\left(\frac{587}{800}\right)$	$e\left(\frac{19}{200}\right)$	$e\left(\frac{371}{1600}\right)$
$\chi_{1601}(8,\cdot)$	1601.s	400	yes	$1$	$1$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{39}{400}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{67}{400}\right)$	$e\left(\frac{93}{400}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{39}{200}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{287}{400}\right)$
$\chi_{1601}(9,\cdot)$	1601.t	800	yes	$1$	$1$	$e\left(\frac{13}{200}\right)$	$e\left(\frac{1}{800}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{61}{200}\right)$	$e\left(\frac{53}{800}\right)$	$e\left(\frac{587}{800}\right)$	$e\left(\frac{39}{200}\right)$	$e\left(\frac{1}{400}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{633}{800}\right)$
$\chi_{1601}(10,\cdot)$	1601.q	200	yes	$1$	$1$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{137}{200}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{61}{200}\right)$	$e\left(\frac{19}{200}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{121}{200}\right)$
$\chi_{1601}(11,\cdot)$	1601.u	1600	yes	$-1$	$1$	$e\left(\frac{229}{400}\right)$	$e\left(\frac{633}{1600}\right)$	$e\left(\frac{29}{200}\right)$	$e\left(\frac{13}{400}\right)$	$e\left(\frac{1549}{1600}\right)$	$e\left(\frac{371}{1600}\right)$	$e\left(\frac{287}{400}\right)$	$e\left(\frac{633}{800}\right)$	$e\left(\frac{121}{200}\right)$	$e\left(\frac{689}{1600}\right)$
$\chi_{1601}(12,\cdot)$	1601.r	320	yes	$-1$	$1$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{21}{320}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{153}{320}\right)$	$e\left(\frac{167}{320}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{21}{160}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{173}{320}\right)$
$\chi_{1601}(13,\cdot)$	1601.m	64	yes	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{64}\right)$
$\chi_{1601}(14,\cdot)$	1601.u	1600	yes	$-1$	$1$	$e\left(\frac{307}{400}\right)$	$e\left(\frac{639}{1600}\right)$	$e\left(\frac{107}{200}\right)$	$e\left(\frac{379}{400}\right)$	$e\left(\frac{267}{1600}\right)$	$e\left(\frac{693}{1600}\right)$	$e\left(\frac{121}{400}\right)$	$e\left(\frac{639}{800}\right)$	$e\left(\frac{143}{200}\right)$	$e\left(\frac{1287}{1600}\right)$
$\chi_{1601}(15,\cdot)$	1601.r	320	yes	$-1$	$1$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{209}{320}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{197}{320}\right)$	$e\left(\frac{123}{320}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{49}{160}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{137}{320}\right)$
$\chi_{1601}(16,\cdot)$	1601.o	100	yes	$1$	$1$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{29}{100}\right)$
$\chi_{1601}(17,\cdot)$	1601.u	1600	yes	$-1$	$1$	$e\left(\frac{159}{400}\right)$	$e\left(\frac{43}{1600}\right)$	$e\left(\frac{159}{200}\right)$	$e\left(\frac{23}{400}\right)$	$e\left(\frac{679}{1600}\right)$	$e\left(\frac{1241}{1600}\right)$	$e\left(\frac{77}{400}\right)$	$e\left(\frac{43}{800}\right)$	$e\left(\frac{91}{200}\right)$	$e\left(\frac{19}{1600}\right)$
$\chi_{1601}(18,\cdot)$	1601.t	800	yes	$1$	$1$	$e\left(\frac{151}{200}\right)$	$e\left(\frac{27}{800}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{47}{200}\right)$	$e\left(\frac{631}{800}\right)$	$e\left(\frac{649}{800}\right)$	$e\left(\frac{53}{200}\right)$	$e\left(\frac{27}{400}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{291}{800}\right)$
$\chi_{1601}(19,\cdot)$	1601.i	25	yes	$1$	$1$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{19}{25}\right)$
$\chi_{1601}(20,\cdot)$	1601.s	400	yes	$1$	$1$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{287}{400}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{11}{400}\right)$	$e\left(\frac{69}{400}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{87}{200}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{71}{400}\right)$
$\chi_{1601}(21,\cdot)$	1601.s	400	yes	$1$	$1$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{147}{400}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{191}{400}\right)$	$e\left(\frac{289}{400}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{147}{200}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{251}{400}\right)$
$\chi_{1601}(22,\cdot)$	1601.r	320	yes	$-1$	$1$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{137}{320}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{221}{320}\right)$	$e\left(\frac{99}{320}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{137}{160}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{1}{320}\right)$
$\chi_{1601}(23,\cdot)$	1601.u	1600	yes	$-1$	$1$	$e\left(\frac{147}{400}\right)$	$e\left(\frac{1519}{1600}\right)$	$e\left(\frac{147}{200}\right)$	$e\left(\frac{59}{400}\right)$	$e\left(\frac{507}{1600}\right)$	$e\left(\frac{453}{1600}\right)$	$e\left(\frac{41}{400}\right)$	$e\left(\frac{719}{800}\right)$	$e\left(\frac{103}{200}\right)$	$e\left(\frac{1527}{1600}\right)$
$\chi_{1601}(24,\cdot)$	1601.u	1600	yes	$-1$	$1$	$e\left(\frac{41}{400}\right)$	$e\left(\frac{157}{1600}\right)$	$e\left(\frac{41}{200}\right)$	$e\left(\frac{177}{400}\right)$	$e\left(\frac{321}{1600}\right)$	$e\left(\frac{959}{1600}\right)$	$e\left(\frac{123}{400}\right)$	$e\left(\frac{157}{800}\right)$	$e\left(\frac{109}{200}\right)$	$e\left(\frac{181}{1600}\right)$
$\chi_{1601}(25,\cdot)$	1601.q	200	yes	$1$	$1$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{61}{200}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{33}{200}\right)$	$e\left(\frac{7}{200}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{13}{200}\right)$
$\chi_{1601}(26,\cdot)$	1601.u	1600	yes	$-1$	$1$	$e\left(\frac{1}{400}\right)$	$e\left(\frac{277}{1600}\right)$	$e\left(\frac{1}{200}\right)$	$e\left(\frac{297}{400}\right)$	$e\left(\frac{281}{1600}\right)$	$e\left(\frac{999}{1600}\right)$	$e\left(\frac{3}{400}\right)$	$e\left(\frac{277}{800}\right)$	$e\left(\frac{149}{200}\right)$	$e\left(\frac{941}{1600}\right)$
$\chi_{1601}(27,\cdot)$	1601.u	1600	yes	$-1$	$1$	$e\left(\frac{39}{400}\right)$	$e\left(\frac{3}{1600}\right)$	$e\left(\frac{39}{200}\right)$	$e\left(\frac{383}{400}\right)$	$e\left(\frac{159}{1600}\right)$	$e\left(\frac{161}{1600}\right)$	$e\left(\frac{117}{400}\right)$	$e\left(\frac{3}{800}\right)$	$e\left(\frac{11}{200}\right)$	$e\left(\frac{299}{1600}\right)$
$\chi_{1601}(28,\cdot)$	1601.u	1600	yes	$-1$	$1$	$e\left(\frac{183}{400}\right)$	$e\left(\frac{691}{1600}\right)$	$e\left(\frac{183}{200}\right)$	$e\left(\frac{351}{400}\right)$	$e\left(\frac{1423}{1600}\right)$	$e\left(\frac{817}{1600}\right)$	$e\left(\frac{149}{400}\right)$	$e\left(\frac{691}{800}\right)$	$e\left(\frac{67}{200}\right)$	$e\left(\frac{603}{1600}\right)$
$\chi_{1601}(29,\cdot)$	1601.q	200	yes	$1$	$1$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{97}{200}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{141}{200}\right)$	$e\left(\frac{139}{200}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{1}{200}\right)$
$\chi_{1601}(30,\cdot)$	1601.u	1600	yes	$-1$	$1$	$e\left(\frac{261}{400}\right)$	$e\left(\frac{1097}{1600}\right)$	$e\left(\frac{61}{200}\right)$	$e\left(\frac{317}{400}\right)$	$e\left(\frac{541}{1600}\right)$	$e\left(\frac{739}{1600}\right)$	$e\left(\frac{383}{400}\right)$	$e\left(\frac{297}{800}\right)$	$e\left(\frac{89}{200}\right)$	$e\left(\frac{1}{1600}\right)$
$\chi_{1601}(31,\cdot)$	1601.o	100	yes	$1$	$1$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{27}{100}\right)$
$\chi_{1601}(32,\cdot)$	1601.n	80	yes	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{69}{80}\right)$

Click here to search among the remaining 1568 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	$1601$
Structure	\(C_{1600}\)
Order	$1600$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{1601}(1,\cdot)\)	1601.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1601}(2,\cdot)\)	1601.s	400	yes	\(1\)	\(1\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{13}{400}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{289}{400}\right)\)	\(e\left(\frac{31}{400}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{13}{200}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{229}{400}\right)\)
\(\chi_{1601}(3,\cdot)\)	1601.u	1600	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{400}\right)\)	\(e\left(\frac{1}{1600}\right)\)	\(e\left(\frac{13}{200}\right)\)	\(e\left(\frac{261}{400}\right)\)	\(e\left(\frac{53}{1600}\right)\)	\(e\left(\frac{587}{1600}\right)\)	\(e\left(\frac{39}{400}\right)\)	\(e\left(\frac{1}{800}\right)\)	\(e\left(\frac{137}{200}\right)\)	\(e\left(\frac{633}{1600}\right)\)
\(\chi_{1601}(4,\cdot)\)	1601.q	200	yes	\(1\)	\(1\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{13}{200}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{89}{200}\right)\)	\(e\left(\frac{31}{200}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{29}{200}\right)\)
\(\chi_{1601}(5,\cdot)\)	1601.s	400	yes	\(1\)	\(1\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{261}{400}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{233}{400}\right)\)	\(e\left(\frac{7}{400}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{61}{200}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{13}{400}\right)\)
\(\chi_{1601}(6,\cdot)\)	1601.u	1600	yes	\(-1\)	\(1\)	\(e\left(\frac{289}{400}\right)\)	\(e\left(\frac{53}{1600}\right)\)	\(e\left(\frac{89}{200}\right)\)	\(e\left(\frac{233}{400}\right)\)	\(e\left(\frac{1209}{1600}\right)\)	\(e\left(\frac{711}{1600}\right)\)	\(e\left(\frac{67}{400}\right)\)	\(e\left(\frac{53}{800}\right)\)	\(e\left(\frac{61}{200}\right)\)	\(e\left(\frac{1549}{1600}\right)\)
\(\chi_{1601}(7,\cdot)\)	1601.u	1600	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{400}\right)\)	\(e\left(\frac{587}{1600}\right)\)	\(e\left(\frac{31}{200}\right)\)	\(e\left(\frac{7}{400}\right)\)	\(e\left(\frac{711}{1600}\right)\)	\(e\left(\frac{569}{1600}\right)\)	\(e\left(\frac{93}{400}\right)\)	\(e\left(\frac{587}{800}\right)\)	\(e\left(\frac{19}{200}\right)\)	\(e\left(\frac{371}{1600}\right)\)
\(\chi_{1601}(8,\cdot)\)	1601.s	400	yes	\(1\)	\(1\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{39}{400}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{67}{400}\right)\)	\(e\left(\frac{93}{400}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{39}{200}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{287}{400}\right)\)
\(\chi_{1601}(9,\cdot)\)	1601.t	800	yes	\(1\)	\(1\)	\(e\left(\frac{13}{200}\right)\)	\(e\left(\frac{1}{800}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{61}{200}\right)\)	\(e\left(\frac{53}{800}\right)\)	\(e\left(\frac{587}{800}\right)\)	\(e\left(\frac{39}{200}\right)\)	\(e\left(\frac{1}{400}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{633}{800}\right)\)
\(\chi_{1601}(10,\cdot)\)	1601.q	200	yes	\(1\)	\(1\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{137}{200}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{61}{200}\right)\)	\(e\left(\frac{19}{200}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{121}{200}\right)\)
\(\chi_{1601}(11,\cdot)\)	1601.u	1600	yes	\(-1\)	\(1\)	\(e\left(\frac{229}{400}\right)\)	\(e\left(\frac{633}{1600}\right)\)	\(e\left(\frac{29}{200}\right)\)	\(e\left(\frac{13}{400}\right)\)	\(e\left(\frac{1549}{1600}\right)\)	\(e\left(\frac{371}{1600}\right)\)	\(e\left(\frac{287}{400}\right)\)	\(e\left(\frac{633}{800}\right)\)	\(e\left(\frac{121}{200}\right)\)	\(e\left(\frac{689}{1600}\right)\)
\(\chi_{1601}(12,\cdot)\)	1601.r	320	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{21}{320}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{153}{320}\right)\)	\(e\left(\frac{167}{320}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{21}{160}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{173}{320}\right)\)
\(\chi_{1601}(13,\cdot)\)	1601.m	64	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{64}\right)\)
\(\chi_{1601}(14,\cdot)\)	1601.u	1600	yes	\(-1\)	\(1\)	\(e\left(\frac{307}{400}\right)\)	\(e\left(\frac{639}{1600}\right)\)	\(e\left(\frac{107}{200}\right)\)	\(e\left(\frac{379}{400}\right)\)	\(e\left(\frac{267}{1600}\right)\)	\(e\left(\frac{693}{1600}\right)\)	\(e\left(\frac{121}{400}\right)\)	\(e\left(\frac{639}{800}\right)\)	\(e\left(\frac{143}{200}\right)\)	\(e\left(\frac{1287}{1600}\right)\)
\(\chi_{1601}(15,\cdot)\)	1601.r	320	yes	\(-1\)	\(1\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{209}{320}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{197}{320}\right)\)	\(e\left(\frac{123}{320}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{49}{160}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{137}{320}\right)\)
\(\chi_{1601}(16,\cdot)\)	1601.o	100	yes	\(1\)	\(1\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{29}{100}\right)\)
\(\chi_{1601}(17,\cdot)\)	1601.u	1600	yes	\(-1\)	\(1\)	\(e\left(\frac{159}{400}\right)\)	\(e\left(\frac{43}{1600}\right)\)	\(e\left(\frac{159}{200}\right)\)	\(e\left(\frac{23}{400}\right)\)	\(e\left(\frac{679}{1600}\right)\)	\(e\left(\frac{1241}{1600}\right)\)	\(e\left(\frac{77}{400}\right)\)	\(e\left(\frac{43}{800}\right)\)	\(e\left(\frac{91}{200}\right)\)	\(e\left(\frac{19}{1600}\right)\)
\(\chi_{1601}(18,\cdot)\)	1601.t	800	yes	\(1\)	\(1\)	\(e\left(\frac{151}{200}\right)\)	\(e\left(\frac{27}{800}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{47}{200}\right)\)	\(e\left(\frac{631}{800}\right)\)	\(e\left(\frac{649}{800}\right)\)	\(e\left(\frac{53}{200}\right)\)	\(e\left(\frac{27}{400}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{291}{800}\right)\)
\(\chi_{1601}(19,\cdot)\)	1601.i	25	yes	\(1\)	\(1\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)
\(\chi_{1601}(20,\cdot)\)	1601.s	400	yes	\(1\)	\(1\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{287}{400}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{11}{400}\right)\)	\(e\left(\frac{69}{400}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{87}{200}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{71}{400}\right)\)
\(\chi_{1601}(21,\cdot)\)	1601.s	400	yes	\(1\)	\(1\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{147}{400}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{191}{400}\right)\)	\(e\left(\frac{289}{400}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{147}{200}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{251}{400}\right)\)
\(\chi_{1601}(22,\cdot)\)	1601.r	320	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{137}{320}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{221}{320}\right)\)	\(e\left(\frac{99}{320}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{137}{160}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{1}{320}\right)\)
\(\chi_{1601}(23,\cdot)\)	1601.u	1600	yes	\(-1\)	\(1\)	\(e\left(\frac{147}{400}\right)\)	\(e\left(\frac{1519}{1600}\right)\)	\(e\left(\frac{147}{200}\right)\)	\(e\left(\frac{59}{400}\right)\)	\(e\left(\frac{507}{1600}\right)\)	\(e\left(\frac{453}{1600}\right)\)	\(e\left(\frac{41}{400}\right)\)	\(e\left(\frac{719}{800}\right)\)	\(e\left(\frac{103}{200}\right)\)	\(e\left(\frac{1527}{1600}\right)\)
\(\chi_{1601}(24,\cdot)\)	1601.u	1600	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{400}\right)\)	\(e\left(\frac{157}{1600}\right)\)	\(e\left(\frac{41}{200}\right)\)	\(e\left(\frac{177}{400}\right)\)	\(e\left(\frac{321}{1600}\right)\)	\(e\left(\frac{959}{1600}\right)\)	\(e\left(\frac{123}{400}\right)\)	\(e\left(\frac{157}{800}\right)\)	\(e\left(\frac{109}{200}\right)\)	\(e\left(\frac{181}{1600}\right)\)
\(\chi_{1601}(25,\cdot)\)	1601.q	200	yes	\(1\)	\(1\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{61}{200}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{33}{200}\right)\)	\(e\left(\frac{7}{200}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{13}{200}\right)\)
\(\chi_{1601}(26,\cdot)\)	1601.u	1600	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{400}\right)\)	\(e\left(\frac{277}{1600}\right)\)	\(e\left(\frac{1}{200}\right)\)	\(e\left(\frac{297}{400}\right)\)	\(e\left(\frac{281}{1600}\right)\)	\(e\left(\frac{999}{1600}\right)\)	\(e\left(\frac{3}{400}\right)\)	\(e\left(\frac{277}{800}\right)\)	\(e\left(\frac{149}{200}\right)\)	\(e\left(\frac{941}{1600}\right)\)
\(\chi_{1601}(27,\cdot)\)	1601.u	1600	yes	\(-1\)	\(1\)	\(e\left(\frac{39}{400}\right)\)	\(e\left(\frac{3}{1600}\right)\)	\(e\left(\frac{39}{200}\right)\)	\(e\left(\frac{383}{400}\right)\)	\(e\left(\frac{159}{1600}\right)\)	\(e\left(\frac{161}{1600}\right)\)	\(e\left(\frac{117}{400}\right)\)	\(e\left(\frac{3}{800}\right)\)	\(e\left(\frac{11}{200}\right)\)	\(e\left(\frac{299}{1600}\right)\)
\(\chi_{1601}(28,\cdot)\)	1601.u	1600	yes	\(-1\)	\(1\)	\(e\left(\frac{183}{400}\right)\)	\(e\left(\frac{691}{1600}\right)\)	\(e\left(\frac{183}{200}\right)\)	\(e\left(\frac{351}{400}\right)\)	\(e\left(\frac{1423}{1600}\right)\)	\(e\left(\frac{817}{1600}\right)\)	\(e\left(\frac{149}{400}\right)\)	\(e\left(\frac{691}{800}\right)\)	\(e\left(\frac{67}{200}\right)\)	\(e\left(\frac{603}{1600}\right)\)
\(\chi_{1601}(29,\cdot)\)	1601.q	200	yes	\(1\)	\(1\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{97}{200}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{141}{200}\right)\)	\(e\left(\frac{139}{200}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{1}{200}\right)\)
\(\chi_{1601}(30,\cdot)\)	1601.u	1600	yes	\(-1\)	\(1\)	\(e\left(\frac{261}{400}\right)\)	\(e\left(\frac{1097}{1600}\right)\)	\(e\left(\frac{61}{200}\right)\)	\(e\left(\frac{317}{400}\right)\)	\(e\left(\frac{541}{1600}\right)\)	\(e\left(\frac{739}{1600}\right)\)	\(e\left(\frac{383}{400}\right)\)	\(e\left(\frac{297}{800}\right)\)	\(e\left(\frac{89}{200}\right)\)	\(e\left(\frac{1}{1600}\right)\)
\(\chi_{1601}(31,\cdot)\)	1601.o	100	yes	\(1\)	\(1\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{27}{100}\right)\)
\(\chi_{1601}(32,\cdot)\)	1601.n	80	yes	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{69}{80}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 1600 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.