Properties

Label 4016.bq
Modulus $4016$
Conductor $2008$
Order $250$
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4016, base_ring=CyclotomicField(250))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,125,32]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(9,4016))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(4016\)
Conductor: \(2008\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(250\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 2008.be
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: $\Q(\zeta_{125})$
Fixed field: Number field defined by a degree 250 polynomial (not computed)

First 31 of 100 characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(21\)
\(\chi_{4016}(9,\cdot)\) \(1\) \(1\) \(e\left(\frac{137}{250}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{93}{125}\right)\) \(e\left(\frac{12}{125}\right)\) \(e\left(\frac{127}{250}\right)\) \(e\left(\frac{199}{250}\right)\) \(e\left(\frac{86}{125}\right)\) \(e\left(\frac{59}{125}\right)\) \(e\left(\frac{91}{250}\right)\) \(e\left(\frac{73}{250}\right)\)
\(\chi_{4016}(41,\cdot)\) \(1\) \(1\) \(e\left(\frac{189}{250}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{121}{125}\right)\) \(e\left(\frac{64}{125}\right)\) \(e\left(\frac{219}{250}\right)\) \(e\left(\frac{103}{250}\right)\) \(e\left(\frac{42}{125}\right)\) \(e\left(\frac{23}{125}\right)\) \(e\left(\frac{27}{250}\right)\) \(e\left(\frac{181}{250}\right)\)
\(\chi_{4016}(73,\cdot)\) \(1\) \(1\) \(e\left(\frac{169}{250}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{91}{125}\right)\) \(e\left(\frac{44}{125}\right)\) \(e\left(\frac{49}{250}\right)\) \(e\left(\frac{63}{250}\right)\) \(e\left(\frac{107}{125}\right)\) \(e\left(\frac{8}{125}\right)\) \(e\left(\frac{167}{250}\right)\) \(e\left(\frac{101}{250}\right)\)
\(\chi_{4016}(89,\cdot)\) \(1\) \(1\) \(e\left(\frac{159}{250}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{76}{125}\right)\) \(e\left(\frac{34}{125}\right)\) \(e\left(\frac{89}{250}\right)\) \(e\left(\frac{43}{250}\right)\) \(e\left(\frac{77}{125}\right)\) \(e\left(\frac{63}{125}\right)\) \(e\left(\frac{237}{250}\right)\) \(e\left(\frac{61}{250}\right)\)
\(\chi_{4016}(105,\cdot)\) \(1\) \(1\) \(e\left(\frac{179}{250}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{106}{125}\right)\) \(e\left(\frac{54}{125}\right)\) \(e\left(\frac{9}{250}\right)\) \(e\left(\frac{83}{250}\right)\) \(e\left(\frac{12}{125}\right)\) \(e\left(\frac{78}{125}\right)\) \(e\left(\frac{97}{250}\right)\) \(e\left(\frac{141}{250}\right)\)
\(\chi_{4016}(121,\cdot)\) \(1\) \(1\) \(e\left(\frac{127}{250}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{78}{125}\right)\) \(e\left(\frac{2}{125}\right)\) \(e\left(\frac{167}{250}\right)\) \(e\left(\frac{179}{250}\right)\) \(e\left(\frac{56}{125}\right)\) \(e\left(\frac{114}{125}\right)\) \(e\left(\frac{161}{250}\right)\) \(e\left(\frac{33}{250}\right)\)
\(\chi_{4016}(153,\cdot)\) \(1\) \(1\) \(e\left(\frac{71}{250}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{19}{125}\right)\) \(e\left(\frac{71}{125}\right)\) \(e\left(\frac{241}{250}\right)\) \(e\left(\frac{167}{250}\right)\) \(e\left(\frac{113}{125}\right)\) \(e\left(\frac{47}{125}\right)\) \(e\left(\frac{153}{250}\right)\) \(e\left(\frac{109}{250}\right)\)
\(\chi_{4016}(169,\cdot)\) \(1\) \(1\) \(e\left(\frac{199}{250}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{11}{125}\right)\) \(e\left(\frac{74}{125}\right)\) \(e\left(\frac{179}{250}\right)\) \(e\left(\frac{123}{250}\right)\) \(e\left(\frac{72}{125}\right)\) \(e\left(\frac{93}{125}\right)\) \(e\left(\frac{207}{250}\right)\) \(e\left(\frac{221}{250}\right)\)
\(\chi_{4016}(217,\cdot)\) \(1\) \(1\) \(e\left(\frac{69}{250}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{66}{125}\right)\) \(e\left(\frac{69}{125}\right)\) \(e\left(\frac{199}{250}\right)\) \(e\left(\frac{113}{250}\right)\) \(e\left(\frac{57}{125}\right)\) \(e\left(\frac{58}{125}\right)\) \(e\left(\frac{117}{250}\right)\) \(e\left(\frac{201}{250}\right)\)
\(\chi_{4016}(233,\cdot)\) \(1\) \(1\) \(e\left(\frac{147}{250}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{108}{125}\right)\) \(e\left(\frac{22}{125}\right)\) \(e\left(\frac{87}{250}\right)\) \(e\left(\frac{219}{250}\right)\) \(e\left(\frac{116}{125}\right)\) \(e\left(\frac{4}{125}\right)\) \(e\left(\frac{21}{250}\right)\) \(e\left(\frac{113}{250}\right)\)
\(\chi_{4016}(361,\cdot)\) \(1\) \(1\) \(e\left(\frac{91}{250}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{49}{125}\right)\) \(e\left(\frac{91}{125}\right)\) \(e\left(\frac{161}{250}\right)\) \(e\left(\frac{207}{250}\right)\) \(e\left(\frac{48}{125}\right)\) \(e\left(\frac{62}{125}\right)\) \(e\left(\frac{13}{250}\right)\) \(e\left(\frac{189}{250}\right)\)
\(\chi_{4016}(393,\cdot)\) \(1\) \(1\) \(e\left(\frac{247}{250}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{8}{125}\right)\) \(e\left(\frac{122}{125}\right)\) \(e\left(\frac{187}{250}\right)\) \(e\left(\frac{169}{250}\right)\) \(e\left(\frac{41}{125}\right)\) \(e\left(\frac{79}{125}\right)\) \(e\left(\frac{71}{250}\right)\) \(e\left(\frac{13}{250}\right)\)
\(\chi_{4016}(425,\cdot)\) \(1\) \(1\) \(e\left(\frac{219}{250}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{41}{125}\right)\) \(e\left(\frac{94}{125}\right)\) \(e\left(\frac{99}{250}\right)\) \(e\left(\frac{163}{250}\right)\) \(e\left(\frac{7}{125}\right)\) \(e\left(\frac{108}{125}\right)\) \(e\left(\frac{67}{250}\right)\) \(e\left(\frac{51}{250}\right)\)
\(\chi_{4016}(441,\cdot)\) \(1\) \(1\) \(e\left(\frac{73}{250}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{97}{125}\right)\) \(e\left(\frac{73}{125}\right)\) \(e\left(\frac{33}{250}\right)\) \(e\left(\frac{221}{250}\right)\) \(e\left(\frac{44}{125}\right)\) \(e\left(\frac{36}{125}\right)\) \(e\left(\frac{189}{250}\right)\) \(e\left(\frac{17}{250}\right)\)
\(\chi_{4016}(473,\cdot)\) \(1\) \(1\) \(e\left(\frac{203}{250}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{42}{125}\right)\) \(e\left(\frac{78}{125}\right)\) \(e\left(\frac{13}{250}\right)\) \(e\left(\frac{231}{250}\right)\) \(e\left(\frac{59}{125}\right)\) \(e\left(\frac{71}{125}\right)\) \(e\left(\frac{29}{250}\right)\) \(e\left(\frac{37}{250}\right)\)
\(\chi_{4016}(505,\cdot)\) \(1\) \(1\) \(e\left(\frac{131}{250}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{109}{125}\right)\) \(e\left(\frac{6}{125}\right)\) \(e\left(\frac{1}{250}\right)\) \(e\left(\frac{37}{250}\right)\) \(e\left(\frac{43}{125}\right)\) \(e\left(\frac{92}{125}\right)\) \(e\left(\frac{233}{250}\right)\) \(e\left(\frac{99}{250}\right)\)
\(\chi_{4016}(537,\cdot)\) \(1\) \(1\) \(e\left(\frac{173}{250}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{122}{125}\right)\) \(e\left(\frac{48}{125}\right)\) \(e\left(\frac{133}{250}\right)\) \(e\left(\frac{171}{250}\right)\) \(e\left(\frac{94}{125}\right)\) \(e\left(\frac{111}{125}\right)\) \(e\left(\frac{239}{250}\right)\) \(e\left(\frac{167}{250}\right)\)
\(\chi_{4016}(569,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{250}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{21}{125}\right)\) \(e\left(\frac{39}{125}\right)\) \(e\left(\frac{69}{250}\right)\) \(e\left(\frac{53}{250}\right)\) \(e\left(\frac{92}{125}\right)\) \(e\left(\frac{98}{125}\right)\) \(e\left(\frac{77}{250}\right)\) \(e\left(\frac{81}{250}\right)\)
\(\chi_{4016}(585,\cdot)\) \(1\) \(1\) \(e\left(\frac{129}{250}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{31}{125}\right)\) \(e\left(\frac{4}{125}\right)\) \(e\left(\frac{209}{250}\right)\) \(e\left(\frac{233}{250}\right)\) \(e\left(\frac{112}{125}\right)\) \(e\left(\frac{103}{125}\right)\) \(e\left(\frac{197}{250}\right)\) \(e\left(\frac{191}{250}\right)\)
\(\chi_{4016}(617,\cdot)\) \(1\) \(1\) \(e\left(\frac{89}{250}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{96}{125}\right)\) \(e\left(\frac{89}{125}\right)\) \(e\left(\frac{119}{250}\right)\) \(e\left(\frac{153}{250}\right)\) \(e\left(\frac{117}{125}\right)\) \(e\left(\frac{73}{125}\right)\) \(e\left(\frac{227}{250}\right)\) \(e\left(\frac{31}{250}\right)\)
\(\chi_{4016}(633,\cdot)\) \(1\) \(1\) \(e\left(\frac{241}{250}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{24}{125}\right)\) \(e\left(\frac{116}{125}\right)\) \(e\left(\frac{61}{250}\right)\) \(e\left(\frac{7}{250}\right)\) \(e\left(\frac{123}{125}\right)\) \(e\left(\frac{112}{125}\right)\) \(e\left(\frac{213}{250}\right)\) \(e\left(\frac{39}{250}\right)\)
\(\chi_{4016}(649,\cdot)\) \(1\) \(1\) \(e\left(\frac{67}{250}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{113}{125}\right)\) \(e\left(\frac{67}{125}\right)\) \(e\left(\frac{157}{250}\right)\) \(e\left(\frac{59}{250}\right)\) \(e\left(\frac{1}{125}\right)\) \(e\left(\frac{69}{125}\right)\) \(e\left(\frac{81}{250}\right)\) \(e\left(\frac{43}{250}\right)\)
\(\chi_{4016}(681,\cdot)\) \(1\) \(1\) \(e\left(\frac{167}{250}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{13}{125}\right)\) \(e\left(\frac{42}{125}\right)\) \(e\left(\frac{7}{250}\right)\) \(e\left(\frac{9}{250}\right)\) \(e\left(\frac{51}{125}\right)\) \(e\left(\frac{19}{125}\right)\) \(e\left(\frac{131}{250}\right)\) \(e\left(\frac{193}{250}\right)\)
\(\chi_{4016}(697,\cdot)\) \(1\) \(1\) \(e\left(\frac{123}{250}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{47}{125}\right)\) \(e\left(\frac{123}{125}\right)\) \(e\left(\frac{83}{250}\right)\) \(e\left(\frac{71}{250}\right)\) \(e\left(\frac{69}{125}\right)\) \(e\left(\frac{11}{125}\right)\) \(e\left(\frac{89}{250}\right)\) \(e\left(\frac{217}{250}\right)\)
\(\chi_{4016}(729,\cdot)\) \(1\) \(1\) \(e\left(\frac{161}{250}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{29}{125}\right)\) \(e\left(\frac{36}{125}\right)\) \(e\left(\frac{131}{250}\right)\) \(e\left(\frac{97}{250}\right)\) \(e\left(\frac{8}{125}\right)\) \(e\left(\frac{52}{125}\right)\) \(e\left(\frac{23}{250}\right)\) \(e\left(\frac{219}{250}\right)\)
\(\chi_{4016}(841,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{250}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{84}{125}\right)\) \(e\left(\frac{31}{125}\right)\) \(e\left(\frac{151}{250}\right)\) \(e\left(\frac{87}{250}\right)\) \(e\left(\frac{118}{125}\right)\) \(e\left(\frac{17}{125}\right)\) \(e\left(\frac{183}{250}\right)\) \(e\left(\frac{199}{250}\right)\)
\(\chi_{4016}(905,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{250}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{7}{125}\right)\) \(e\left(\frac{13}{125}\right)\) \(e\left(\frac{23}{250}\right)\) \(e\left(\frac{101}{250}\right)\) \(e\left(\frac{114}{125}\right)\) \(e\left(\frac{116}{125}\right)\) \(e\left(\frac{109}{250}\right)\) \(e\left(\frac{27}{250}\right)\)
\(\chi_{4016}(985,\cdot)\) \(1\) \(1\) \(e\left(\frac{233}{250}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{87}{125}\right)\) \(e\left(\frac{108}{125}\right)\) \(e\left(\frac{143}{250}\right)\) \(e\left(\frac{41}{250}\right)\) \(e\left(\frac{24}{125}\right)\) \(e\left(\frac{31}{125}\right)\) \(e\left(\frac{69}{250}\right)\) \(e\left(\frac{157}{250}\right)\)
\(\chi_{4016}(1017,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{250}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{68}{125}\right)\) \(e\left(\frac{37}{125}\right)\) \(e\left(\frac{27}{250}\right)\) \(e\left(\frac{249}{250}\right)\) \(e\left(\frac{36}{125}\right)\) \(e\left(\frac{109}{125}\right)\) \(e\left(\frac{41}{250}\right)\) \(e\left(\frac{173}{250}\right)\)
\(\chi_{4016}(1049,\cdot)\) \(1\) \(1\) \(e\left(\frac{217}{250}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{88}{125}\right)\) \(e\left(\frac{92}{125}\right)\) \(e\left(\frac{57}{250}\right)\) \(e\left(\frac{109}{250}\right)\) \(e\left(\frac{76}{125}\right)\) \(e\left(\frac{119}{125}\right)\) \(e\left(\frac{31}{250}\right)\) \(e\left(\frac{143}{250}\right)\)
\(\chi_{4016}(1097,\cdot)\) \(1\) \(1\) \(e\left(\frac{107}{250}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{48}{125}\right)\) \(e\left(\frac{107}{125}\right)\) \(e\left(\frac{247}{250}\right)\) \(e\left(\frac{139}{250}\right)\) \(e\left(\frac{121}{125}\right)\) \(e\left(\frac{99}{125}\right)\) \(e\left(\frac{51}{250}\right)\) \(e\left(\frac{203}{250}\right)\)