LMFDB - Dirichlet character orbit 4000.cm

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4000, base_ring=CyclotomicField(100)) M = H._module chi = DirichletCharacter(H, M([50,25,72])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(71,4000)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$4000$
Conductor:	$2000$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$100$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2000.bw	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{4000}(71,\cdot)$	$-1$	$1$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{87}{100}\right)$
$\chi_{4000}(231,\cdot)$	$-1$	$1$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{3}{100}\right)$
$\chi_{4000}(311,\cdot)$	$-1$	$1$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{1}{100}\right)$
$\chi_{4000}(391,\cdot)$	$-1$	$1$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{59}{100}\right)$
$\chi_{4000}(471,\cdot)$	$-1$	$1$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{77}{100}\right)$
$\chi_{4000}(631,\cdot)$	$-1$	$1$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{93}{100}\right)$
$\chi_{4000}(711,\cdot)$	$-1$	$1$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{91}{100}\right)$
$\chi_{4000}(791,\cdot)$	$-1$	$1$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{49}{100}\right)$
$\chi_{4000}(871,\cdot)$	$-1$	$1$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{67}{100}\right)$
$\chi_{4000}(1031,\cdot)$	$-1$	$1$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{83}{100}\right)$
$\chi_{4000}(1111,\cdot)$	$-1$	$1$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{81}{100}\right)$
$\chi_{4000}(1191,\cdot)$	$-1$	$1$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{39}{100}\right)$
$\chi_{4000}(1271,\cdot)$	$-1$	$1$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{57}{100}\right)$
$\chi_{4000}(1431,\cdot)$	$-1$	$1$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{73}{100}\right)$
$\chi_{4000}(1511,\cdot)$	$-1$	$1$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{71}{100}\right)$
$\chi_{4000}(1591,\cdot)$	$-1$	$1$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{29}{100}\right)$
$\chi_{4000}(1671,\cdot)$	$-1$	$1$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{47}{100}\right)$
$\chi_{4000}(1831,\cdot)$	$-1$	$1$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{63}{100}\right)$
$\chi_{4000}(1911,\cdot)$	$-1$	$1$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{61}{100}\right)$
$\chi_{4000}(1991,\cdot)$	$-1$	$1$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{19}{100}\right)$
$\chi_{4000}(2071,\cdot)$	$-1$	$1$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{37}{100}\right)$
$\chi_{4000}(2231,\cdot)$	$-1$	$1$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{53}{100}\right)$
$\chi_{4000}(2311,\cdot)$	$-1$	$1$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{51}{100}\right)$
$\chi_{4000}(2391,\cdot)$	$-1$	$1$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{9}{100}\right)$
$\chi_{4000}(2471,\cdot)$	$-1$	$1$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{27}{100}\right)$
$\chi_{4000}(2631,\cdot)$	$-1$	$1$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{43}{100}\right)$
$\chi_{4000}(2711,\cdot)$	$-1$	$1$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{41}{100}\right)$
$\chi_{4000}(2791,\cdot)$	$-1$	$1$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{99}{100}\right)$
$\chi_{4000}(2871,\cdot)$	$-1$	$1$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{17}{100}\right)$
$\chi_{4000}(3031,\cdot)$	$-1$	$1$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{33}{100}\right)$
$\chi_{4000}(3111,\cdot)$	$-1$	$1$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{31}{100}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{4000}(71,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{87}{100}\right)\)
\(\chi_{4000}(231,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{3}{100}\right)\)
\(\chi_{4000}(311,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{1}{100}\right)\)
\(\chi_{4000}(391,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{59}{100}\right)\)
\(\chi_{4000}(471,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{77}{100}\right)\)
\(\chi_{4000}(631,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{93}{100}\right)\)
\(\chi_{4000}(711,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{91}{100}\right)\)
\(\chi_{4000}(791,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{49}{100}\right)\)
\(\chi_{4000}(871,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{67}{100}\right)\)
\(\chi_{4000}(1031,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{83}{100}\right)\)
\(\chi_{4000}(1111,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{81}{100}\right)\)
\(\chi_{4000}(1191,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{39}{100}\right)\)
\(\chi_{4000}(1271,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{57}{100}\right)\)
\(\chi_{4000}(1431,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{73}{100}\right)\)
\(\chi_{4000}(1511,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{71}{100}\right)\)
\(\chi_{4000}(1591,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{29}{100}\right)\)
\(\chi_{4000}(1671,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{47}{100}\right)\)
\(\chi_{4000}(1831,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{63}{100}\right)\)
\(\chi_{4000}(1911,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{61}{100}\right)\)
\(\chi_{4000}(1991,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{19}{100}\right)\)
\(\chi_{4000}(2071,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{37}{100}\right)\)
\(\chi_{4000}(2231,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{53}{100}\right)\)
\(\chi_{4000}(2311,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{51}{100}\right)\)
\(\chi_{4000}(2391,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{9}{100}\right)\)
\(\chi_{4000}(2471,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{27}{100}\right)\)
\(\chi_{4000}(2631,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{43}{100}\right)\)
\(\chi_{4000}(2711,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{41}{100}\right)\)
\(\chi_{4000}(2791,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{99}{100}\right)\)
\(\chi_{4000}(2871,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{17}{100}\right)\)
\(\chi_{4000}(3031,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{33}{100}\right)\)
\(\chi_{4000}(3111,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{31}{100}\right)\)

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	4000.cm
Modulus	$4000$
Conductor	$2000$
Order	$100$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(4000\)
Conductor:	\(2000\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(100\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2000.bw	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)