LMFDB - Dirichlet character orbit 4000.db

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4000, base_ring=CyclotomicField(200)) M = H._module chi = DirichletCharacter(H, M([100,125,152])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(11,4000)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$4000$
Conductor:	$4000$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$200$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{200})$
Fixed field:	Number field defined by a degree 200 polynomial (not computed)

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{4000}(11,\cdot)$	$-1$	$1$	$e\left(\frac{139}{200}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{77}{200}\right)$	$e\left(\frac{3}{200}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{111}{200}\right)$	$e\left(\frac{9}{200}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{17}{200}\right)$
$\chi_{4000}(91,\cdot)$	$-1$	$1$	$e\left(\frac{111}{200}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{73}{200}\right)$	$e\left(\frac{47}{200}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{139}{200}\right)$	$e\left(\frac{141}{200}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{133}{200}\right)$
$\chi_{4000}(131,\cdot)$	$-1$	$1$	$e\left(\frac{37}{200}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{91}{200}\right)$	$e\left(\frac{149}{200}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{113}{200}\right)$	$e\left(\frac{47}{200}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{111}{200}\right)$
$\chi_{4000}(171,\cdot)$	$-1$	$1$	$e\left(\frac{123}{200}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{189}{200}\right)$	$e\left(\frac{171}{200}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{127}{200}\right)$	$e\left(\frac{113}{200}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{169}{200}\right)$
$\chi_{4000}(211,\cdot)$	$-1$	$1$	$e\left(\frac{169}{200}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{167}{200}\right)$	$e\left(\frac{113}{200}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{181}{200}\right)$	$e\left(\frac{139}{200}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{107}{200}\right)$
$\chi_{4000}(291,\cdot)$	$-1$	$1$	$e\left(\frac{141}{200}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{163}{200}\right)$	$e\left(\frac{157}{200}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{9}{200}\right)$	$e\left(\frac{71}{200}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{23}{200}\right)$
$\chi_{4000}(331,\cdot)$	$-1$	$1$	$e\left(\frac{67}{200}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{181}{200}\right)$	$e\left(\frac{59}{200}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{183}{200}\right)$	$e\left(\frac{177}{200}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{1}{200}\right)$
$\chi_{4000}(371,\cdot)$	$-1$	$1$	$e\left(\frac{153}{200}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{79}{200}\right)$	$e\left(\frac{81}{200}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{197}{200}\right)$	$e\left(\frac{43}{200}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{59}{200}\right)$
$\chi_{4000}(411,\cdot)$	$-1$	$1$	$e\left(\frac{199}{200}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{57}{200}\right)$	$e\left(\frac{23}{200}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{51}{200}\right)$	$e\left(\frac{69}{200}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{197}{200}\right)$
$\chi_{4000}(491,\cdot)$	$-1$	$1$	$e\left(\frac{171}{200}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{53}{200}\right)$	$e\left(\frac{67}{200}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{79}{200}\right)$	$e\left(\frac{1}{200}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{113}{200}\right)$
$\chi_{4000}(531,\cdot)$	$-1$	$1$	$e\left(\frac{97}{200}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{71}{200}\right)$	$e\left(\frac{169}{200}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{53}{200}\right)$	$e\left(\frac{107}{200}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{91}{200}\right)$
$\chi_{4000}(571,\cdot)$	$-1$	$1$	$e\left(\frac{183}{200}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{169}{200}\right)$	$e\left(\frac{191}{200}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{67}{200}\right)$	$e\left(\frac{173}{200}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{149}{200}\right)$
$\chi_{4000}(611,\cdot)$	$-1$	$1$	$e\left(\frac{29}{200}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{147}{200}\right)$	$e\left(\frac{133}{200}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{121}{200}\right)$	$e\left(\frac{199}{200}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{87}{200}\right)$
$\chi_{4000}(691,\cdot)$	$-1$	$1$	$e\left(\frac{1}{200}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{143}{200}\right)$	$e\left(\frac{177}{200}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{149}{200}\right)$	$e\left(\frac{131}{200}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{3}{200}\right)$
$\chi_{4000}(731,\cdot)$	$-1$	$1$	$e\left(\frac{127}{200}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{161}{200}\right)$	$e\left(\frac{79}{200}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{123}{200}\right)$	$e\left(\frac{37}{200}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{181}{200}\right)$
$\chi_{4000}(771,\cdot)$	$-1$	$1$	$e\left(\frac{13}{200}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{59}{200}\right)$	$e\left(\frac{101}{200}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{137}{200}\right)$	$e\left(\frac{103}{200}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{39}{200}\right)$
$\chi_{4000}(811,\cdot)$	$-1$	$1$	$e\left(\frac{59}{200}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{37}{200}\right)$	$e\left(\frac{43}{200}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{191}{200}\right)$	$e\left(\frac{129}{200}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{177}{200}\right)$
$\chi_{4000}(891,\cdot)$	$-1$	$1$	$e\left(\frac{31}{200}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{33}{200}\right)$	$e\left(\frac{87}{200}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{19}{200}\right)$	$e\left(\frac{61}{200}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{93}{200}\right)$
$\chi_{4000}(931,\cdot)$	$-1$	$1$	$e\left(\frac{157}{200}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{51}{200}\right)$	$e\left(\frac{189}{200}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{193}{200}\right)$	$e\left(\frac{167}{200}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{71}{200}\right)$
$\chi_{4000}(971,\cdot)$	$-1$	$1$	$e\left(\frac{43}{200}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{149}{200}\right)$	$e\left(\frac{11}{200}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{7}{200}\right)$	$e\left(\frac{33}{200}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{129}{200}\right)$
$\chi_{4000}(1011,\cdot)$	$-1$	$1$	$e\left(\frac{89}{200}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{127}{200}\right)$	$e\left(\frac{153}{200}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{61}{200}\right)$	$e\left(\frac{59}{200}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{67}{200}\right)$
$\chi_{4000}(1091,\cdot)$	$-1$	$1$	$e\left(\frac{61}{200}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{123}{200}\right)$	$e\left(\frac{197}{200}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{89}{200}\right)$	$e\left(\frac{191}{200}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{183}{200}\right)$
$\chi_{4000}(1131,\cdot)$	$-1$	$1$	$e\left(\frac{187}{200}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{141}{200}\right)$	$e\left(\frac{99}{200}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{63}{200}\right)$	$e\left(\frac{97}{200}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{161}{200}\right)$
$\chi_{4000}(1171,\cdot)$	$-1$	$1$	$e\left(\frac{73}{200}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{39}{200}\right)$	$e\left(\frac{121}{200}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{77}{200}\right)$	$e\left(\frac{163}{200}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{19}{200}\right)$
$\chi_{4000}(1211,\cdot)$	$-1$	$1$	$e\left(\frac{119}{200}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{17}{200}\right)$	$e\left(\frac{63}{200}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{131}{200}\right)$	$e\left(\frac{189}{200}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{157}{200}\right)$
$\chi_{4000}(1291,\cdot)$	$-1$	$1$	$e\left(\frac{91}{200}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{13}{200}\right)$	$e\left(\frac{107}{200}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{159}{200}\right)$	$e\left(\frac{121}{200}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{73}{200}\right)$
$\chi_{4000}(1331,\cdot)$	$-1$	$1$	$e\left(\frac{17}{200}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{31}{200}\right)$	$e\left(\frac{9}{200}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{133}{200}\right)$	$e\left(\frac{27}{200}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{51}{200}\right)$
$\chi_{4000}(1371,\cdot)$	$-1$	$1$	$e\left(\frac{103}{200}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{129}{200}\right)$	$e\left(\frac{31}{200}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{147}{200}\right)$	$e\left(\frac{93}{200}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{109}{200}\right)$
$\chi_{4000}(1411,\cdot)$	$-1$	$1$	$e\left(\frac{149}{200}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{107}{200}\right)$	$e\left(\frac{173}{200}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{1}{200}\right)$	$e\left(\frac{119}{200}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{47}{200}\right)$
$\chi_{4000}(1491,\cdot)$	$-1$	$1$	$e\left(\frac{121}{200}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{103}{200}\right)$	$e\left(\frac{17}{200}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{29}{200}\right)$	$e\left(\frac{51}{200}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{163}{200}\right)$
$\chi_{4000}(1531,\cdot)$	$-1$	$1$	$e\left(\frac{47}{200}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{121}{200}\right)$	$e\left(\frac{119}{200}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{3}{200}\right)$	$e\left(\frac{157}{200}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{141}{200}\right)$

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 $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{4000}(11,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{200}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{77}{200}\right)\)	\(e\left(\frac{3}{200}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{111}{200}\right)\)	\(e\left(\frac{9}{200}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{17}{200}\right)\)
\(\chi_{4000}(91,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{111}{200}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{73}{200}\right)\)	\(e\left(\frac{47}{200}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{139}{200}\right)\)	\(e\left(\frac{141}{200}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{133}{200}\right)\)
\(\chi_{4000}(131,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{200}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{91}{200}\right)\)	\(e\left(\frac{149}{200}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{113}{200}\right)\)	\(e\left(\frac{47}{200}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{111}{200}\right)\)
\(\chi_{4000}(171,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{123}{200}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{189}{200}\right)\)	\(e\left(\frac{171}{200}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{127}{200}\right)\)	\(e\left(\frac{113}{200}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{169}{200}\right)\)
\(\chi_{4000}(211,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{169}{200}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{167}{200}\right)\)	\(e\left(\frac{113}{200}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{181}{200}\right)\)	\(e\left(\frac{139}{200}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{107}{200}\right)\)
\(\chi_{4000}(291,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{141}{200}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{163}{200}\right)\)	\(e\left(\frac{157}{200}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{9}{200}\right)\)	\(e\left(\frac{71}{200}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{23}{200}\right)\)
\(\chi_{4000}(331,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{200}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{181}{200}\right)\)	\(e\left(\frac{59}{200}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{183}{200}\right)\)	\(e\left(\frac{177}{200}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{1}{200}\right)\)
\(\chi_{4000}(371,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{153}{200}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{79}{200}\right)\)	\(e\left(\frac{81}{200}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{197}{200}\right)\)	\(e\left(\frac{43}{200}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{59}{200}\right)\)
\(\chi_{4000}(411,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{199}{200}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{57}{200}\right)\)	\(e\left(\frac{23}{200}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{51}{200}\right)\)	\(e\left(\frac{69}{200}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{197}{200}\right)\)
\(\chi_{4000}(491,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{171}{200}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{53}{200}\right)\)	\(e\left(\frac{67}{200}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{79}{200}\right)\)	\(e\left(\frac{1}{200}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{113}{200}\right)\)
\(\chi_{4000}(531,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{200}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{71}{200}\right)\)	\(e\left(\frac{169}{200}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{53}{200}\right)\)	\(e\left(\frac{107}{200}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{91}{200}\right)\)
\(\chi_{4000}(571,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{183}{200}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{169}{200}\right)\)	\(e\left(\frac{191}{200}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{67}{200}\right)\)	\(e\left(\frac{173}{200}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{149}{200}\right)\)
\(\chi_{4000}(611,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{200}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{147}{200}\right)\)	\(e\left(\frac{133}{200}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{121}{200}\right)\)	\(e\left(\frac{199}{200}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{87}{200}\right)\)
\(\chi_{4000}(691,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{200}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{143}{200}\right)\)	\(e\left(\frac{177}{200}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{149}{200}\right)\)	\(e\left(\frac{131}{200}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{3}{200}\right)\)
\(\chi_{4000}(731,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{200}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{161}{200}\right)\)	\(e\left(\frac{79}{200}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{123}{200}\right)\)	\(e\left(\frac{37}{200}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{181}{200}\right)\)
\(\chi_{4000}(771,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{200}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{59}{200}\right)\)	\(e\left(\frac{101}{200}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{137}{200}\right)\)	\(e\left(\frac{103}{200}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{39}{200}\right)\)
\(\chi_{4000}(811,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{200}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{37}{200}\right)\)	\(e\left(\frac{43}{200}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{191}{200}\right)\)	\(e\left(\frac{129}{200}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{177}{200}\right)\)
\(\chi_{4000}(891,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{200}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{33}{200}\right)\)	\(e\left(\frac{87}{200}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{19}{200}\right)\)	\(e\left(\frac{61}{200}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{93}{200}\right)\)
\(\chi_{4000}(931,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{157}{200}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{51}{200}\right)\)	\(e\left(\frac{189}{200}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{193}{200}\right)\)	\(e\left(\frac{167}{200}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{71}{200}\right)\)
\(\chi_{4000}(971,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{200}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{149}{200}\right)\)	\(e\left(\frac{11}{200}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{7}{200}\right)\)	\(e\left(\frac{33}{200}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{129}{200}\right)\)
\(\chi_{4000}(1011,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{200}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{127}{200}\right)\)	\(e\left(\frac{153}{200}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{61}{200}\right)\)	\(e\left(\frac{59}{200}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{67}{200}\right)\)
\(\chi_{4000}(1091,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{200}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{123}{200}\right)\)	\(e\left(\frac{197}{200}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{89}{200}\right)\)	\(e\left(\frac{191}{200}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{183}{200}\right)\)
\(\chi_{4000}(1131,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{187}{200}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{141}{200}\right)\)	\(e\left(\frac{99}{200}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{63}{200}\right)\)	\(e\left(\frac{97}{200}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{161}{200}\right)\)
\(\chi_{4000}(1171,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{200}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{39}{200}\right)\)	\(e\left(\frac{121}{200}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{77}{200}\right)\)	\(e\left(\frac{163}{200}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{19}{200}\right)\)
\(\chi_{4000}(1211,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{200}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{17}{200}\right)\)	\(e\left(\frac{63}{200}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{131}{200}\right)\)	\(e\left(\frac{189}{200}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{157}{200}\right)\)
\(\chi_{4000}(1291,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{200}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{13}{200}\right)\)	\(e\left(\frac{107}{200}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{159}{200}\right)\)	\(e\left(\frac{121}{200}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{73}{200}\right)\)
\(\chi_{4000}(1331,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{200}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{31}{200}\right)\)	\(e\left(\frac{9}{200}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{133}{200}\right)\)	\(e\left(\frac{27}{200}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{51}{200}\right)\)
\(\chi_{4000}(1371,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{200}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{129}{200}\right)\)	\(e\left(\frac{31}{200}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{147}{200}\right)\)	\(e\left(\frac{93}{200}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{109}{200}\right)\)
\(\chi_{4000}(1411,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{200}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{107}{200}\right)\)	\(e\left(\frac{173}{200}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{1}{200}\right)\)	\(e\left(\frac{119}{200}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{47}{200}\right)\)
\(\chi_{4000}(1491,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{200}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{103}{200}\right)\)	\(e\left(\frac{17}{200}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{29}{200}\right)\)	\(e\left(\frac{51}{200}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{163}{200}\right)\)
\(\chi_{4000}(1531,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{200}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{121}{200}\right)\)	\(e\left(\frac{119}{200}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{3}{200}\right)\)	\(e\left(\frac{157}{200}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{141}{200}\right)\)

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First 31 of 80 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	4000.db
Modulus	$4000$
Conductor	$4000$
Order	$200$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(4000\)
Conductor:	\(4000\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(200\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)