LMFDB - Dirichlet character orbit 1000.bh

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1000, base_ring=CyclotomicField(100)) M = H._module chi = DirichletCharacter(H, M([50,50,7])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(3,1000)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1000$
Conductor:	$1000$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$100$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{100})$
Fixed field:	Number field defined by a degree 100 polynomial

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{1000}(3,\cdot)$	$1$	$1$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{47}{100}\right)$
$\chi_{1000}(27,\cdot)$	$1$	$1$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{41}{100}\right)$
$\chi_{1000}(67,\cdot)$	$1$	$1$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{73}{100}\right)$
$\chi_{1000}(83,\cdot)$	$1$	$1$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{3}{100}\right)$
$\chi_{1000}(123,\cdot)$	$1$	$1$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{71}{100}\right)$
$\chi_{1000}(147,\cdot)$	$1$	$1$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{17}{100}\right)$
$\chi_{1000}(163,\cdot)$	$1$	$1$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{99}{100}\right)$
$\chi_{1000}(187,\cdot)$	$1$	$1$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{29}{100}\right)$
$\chi_{1000}(203,\cdot)$	$1$	$1$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{87}{100}\right)$
$\chi_{1000}(227,\cdot)$	$1$	$1$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{1}{100}\right)$
$\chi_{1000}(267,\cdot)$	$1$	$1$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{33}{100}\right)$
$\chi_{1000}(283,\cdot)$	$1$	$1$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{43}{100}\right)$
$\chi_{1000}(323,\cdot)$	$1$	$1$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{11}{100}\right)$
$\chi_{1000}(347,\cdot)$	$1$	$1$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{77}{100}\right)$
$\chi_{1000}(363,\cdot)$	$1$	$1$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{39}{100}\right)$
$\chi_{1000}(387,\cdot)$	$1$	$1$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{89}{100}\right)$
$\chi_{1000}(403,\cdot)$	$1$	$1$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{27}{100}\right)$
$\chi_{1000}(427,\cdot)$	$1$	$1$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{61}{100}\right)$
$\chi_{1000}(467,\cdot)$	$1$	$1$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{93}{100}\right)$
$\chi_{1000}(483,\cdot)$	$1$	$1$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{83}{100}\right)$
$\chi_{1000}(523,\cdot)$	$1$	$1$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{51}{100}\right)$
$\chi_{1000}(547,\cdot)$	$1$	$1$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{37}{100}\right)$
$\chi_{1000}(563,\cdot)$	$1$	$1$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{79}{100}\right)$
$\chi_{1000}(587,\cdot)$	$1$	$1$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{49}{100}\right)$
$\chi_{1000}(603,\cdot)$	$1$	$1$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{67}{100}\right)$
$\chi_{1000}(627,\cdot)$	$1$	$1$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{21}{100}\right)$
$\chi_{1000}(667,\cdot)$	$1$	$1$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{53}{100}\right)$
$\chi_{1000}(683,\cdot)$	$1$	$1$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{23}{100}\right)$
$\chi_{1000}(723,\cdot)$	$1$	$1$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{91}{100}\right)$
$\chi_{1000}(747,\cdot)$	$1$	$1$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{97}{100}\right)$
$\chi_{1000}(763,\cdot)$	$1$	$1$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{19}{100}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{1000}(3,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{47}{100}\right)\)
\(\chi_{1000}(27,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{41}{100}\right)\)
\(\chi_{1000}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{73}{100}\right)\)
\(\chi_{1000}(83,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{3}{100}\right)\)
\(\chi_{1000}(123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{71}{100}\right)\)
\(\chi_{1000}(147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{17}{100}\right)\)
\(\chi_{1000}(163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{99}{100}\right)\)
\(\chi_{1000}(187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{29}{100}\right)\)
\(\chi_{1000}(203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{87}{100}\right)\)
\(\chi_{1000}(227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{1}{100}\right)\)
\(\chi_{1000}(267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{33}{100}\right)\)
\(\chi_{1000}(283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{43}{100}\right)\)
\(\chi_{1000}(323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{11}{100}\right)\)
\(\chi_{1000}(347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{77}{100}\right)\)
\(\chi_{1000}(363,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{39}{100}\right)\)
\(\chi_{1000}(387,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{89}{100}\right)\)
\(\chi_{1000}(403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{27}{100}\right)\)
\(\chi_{1000}(427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{61}{100}\right)\)
\(\chi_{1000}(467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{93}{100}\right)\)
\(\chi_{1000}(483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{83}{100}\right)\)
\(\chi_{1000}(523,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{51}{100}\right)\)
\(\chi_{1000}(547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{37}{100}\right)\)
\(\chi_{1000}(563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{79}{100}\right)\)
\(\chi_{1000}(587,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{49}{100}\right)\)
\(\chi_{1000}(603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{67}{100}\right)\)
\(\chi_{1000}(627,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{21}{100}\right)\)
\(\chi_{1000}(667,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{53}{100}\right)\)
\(\chi_{1000}(683,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{23}{100}\right)\)
\(\chi_{1000}(723,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{91}{100}\right)\)
\(\chi_{1000}(747,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{97}{100}\right)\)
\(\chi_{1000}(763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{19}{100}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 40 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	1000.bh
Modulus	$1000$
Conductor	$1000$
Order	$100$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(1000\)
Conductor:	\(1000\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(100\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)