Properties

Label 8016.bp
Modulus $8016$
Conductor $2672$
Order $332$
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8016, base_ring=CyclotomicField(332))
 
M = H._module
 
chi = DirichletCharacter(H, M([166,249,0,116]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(19,8016))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(8016\)
Conductor: \(2672\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(332\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 2672.v
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: $\Q(\zeta_{332})$
Fixed field: Number field defined by a degree 332 polynomial (not computed)

First 31 of 164 characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\)
\(\chi_{8016}(19,\cdot)\) \(-1\) \(1\) \(e\left(\frac{33}{332}\right)\) \(e\left(\frac{19}{83}\right)\) \(e\left(\frac{11}{332}\right)\) \(e\left(\frac{79}{332}\right)\) \(e\left(\frac{43}{83}\right)\) \(e\left(\frac{5}{332}\right)\) \(e\left(\frac{49}{83}\right)\) \(e\left(\frac{33}{166}\right)\) \(e\left(\frac{219}{332}\right)\) \(e\left(\frac{157}{166}\right)\)
\(\chi_{8016}(115,\cdot)\) \(-1\) \(1\) \(e\left(\frac{117}{332}\right)\) \(e\left(\frac{7}{83}\right)\) \(e\left(\frac{39}{332}\right)\) \(e\left(\frac{99}{332}\right)\) \(e\left(\frac{77}{83}\right)\) \(e\left(\frac{229}{332}\right)\) \(e\left(\frac{53}{83}\right)\) \(e\left(\frac{117}{166}\right)\) \(e\left(\frac{203}{332}\right)\) \(e\left(\frac{119}{166}\right)\)
\(\chi_{8016}(211,\cdot)\) \(-1\) \(1\) \(e\left(\frac{133}{332}\right)\) \(e\left(\frac{64}{83}\right)\) \(e\left(\frac{155}{332}\right)\) \(e\left(\frac{87}{332}\right)\) \(e\left(\frac{40}{83}\right)\) \(e\left(\frac{161}{332}\right)\) \(e\left(\frac{34}{83}\right)\) \(e\left(\frac{133}{166}\right)\) \(e\left(\frac{279}{332}\right)\) \(e\left(\frac{9}{166}\right)\)
\(\chi_{8016}(283,\cdot)\) \(-1\) \(1\) \(e\left(\frac{211}{332}\right)\) \(e\left(\frac{41}{83}\right)\) \(e\left(\frac{181}{332}\right)\) \(e\left(\frac{153}{332}\right)\) \(e\left(\frac{36}{83}\right)\) \(e\left(\frac{203}{332}\right)\) \(e\left(\frac{14}{83}\right)\) \(e\left(\frac{45}{166}\right)\) \(e\left(\frac{193}{332}\right)\) \(e\left(\frac{33}{166}\right)\)
\(\chi_{8016}(355,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{332}\right)\) \(e\left(\frac{58}{83}\right)\) \(e\left(\frac{3}{332}\right)\) \(e\left(\frac{263}{332}\right)\) \(e\left(\frac{57}{83}\right)\) \(e\left(\frac{273}{332}\right)\) \(e\left(\frac{36}{83}\right)\) \(e\left(\frac{9}{166}\right)\) \(e\left(\frac{271}{332}\right)\) \(e\left(\frac{73}{166}\right)\)
\(\chi_{8016}(427,\cdot)\) \(-1\) \(1\) \(e\left(\frac{119}{332}\right)\) \(e\left(\frac{66}{83}\right)\) \(e\left(\frac{261}{332}\right)\) \(e\left(\frac{305}{332}\right)\) \(e\left(\frac{62}{83}\right)\) \(e\left(\frac{179}{332}\right)\) \(e\left(\frac{61}{83}\right)\) \(e\left(\frac{119}{166}\right)\) \(e\left(\frac{5}{332}\right)\) \(e\left(\frac{43}{166}\right)\)
\(\chi_{8016}(475,\cdot)\) \(-1\) \(1\) \(e\left(\frac{203}{332}\right)\) \(e\left(\frac{54}{83}\right)\) \(e\left(\frac{289}{332}\right)\) \(e\left(\frac{325}{332}\right)\) \(e\left(\frac{13}{83}\right)\) \(e\left(\frac{71}{332}\right)\) \(e\left(\frac{65}{83}\right)\) \(e\left(\frac{37}{166}\right)\) \(e\left(\frac{321}{332}\right)\) \(e\left(\frac{5}{166}\right)\)
\(\chi_{8016}(523,\cdot)\) \(-1\) \(1\) \(e\left(\frac{219}{332}\right)\) \(e\left(\frac{28}{83}\right)\) \(e\left(\frac{73}{332}\right)\) \(e\left(\frac{313}{332}\right)\) \(e\left(\frac{59}{83}\right)\) \(e\left(\frac{3}{332}\right)\) \(e\left(\frac{46}{83}\right)\) \(e\left(\frac{53}{166}\right)\) \(e\left(\frac{65}{332}\right)\) \(e\left(\frac{61}{166}\right)\)
\(\chi_{8016}(595,\cdot)\) \(-1\) \(1\) \(e\left(\frac{261}{332}\right)\) \(e\left(\frac{22}{83}\right)\) \(e\left(\frac{87}{332}\right)\) \(e\left(\frac{323}{332}\right)\) \(e\left(\frac{76}{83}\right)\) \(e\left(\frac{281}{332}\right)\) \(e\left(\frac{48}{83}\right)\) \(e\left(\frac{95}{166}\right)\) \(e\left(\frac{223}{332}\right)\) \(e\left(\frac{125}{166}\right)\)
\(\chi_{8016}(715,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{332}\right)\) \(e\left(\frac{69}{83}\right)\) \(e\left(\frac{5}{332}\right)\) \(e\left(\frac{217}{332}\right)\) \(e\left(\frac{12}{83}\right)\) \(e\left(\frac{123}{332}\right)\) \(e\left(\frac{60}{83}\right)\) \(e\left(\frac{15}{166}\right)\) \(e\left(\frac{9}{332}\right)\) \(e\left(\frac{11}{166}\right)\)
\(\chi_{8016}(859,\cdot)\) \(-1\) \(1\) \(e\left(\frac{179}{332}\right)\) \(e\left(\frac{10}{83}\right)\) \(e\left(\frac{281}{332}\right)\) \(e\left(\frac{177}{332}\right)\) \(e\left(\frac{27}{83}\right)\) \(e\left(\frac{7}{332}\right)\) \(e\left(\frac{52}{83}\right)\) \(e\left(\frac{13}{166}\right)\) \(e\left(\frac{41}{332}\right)\) \(e\left(\frac{87}{166}\right)\)
\(\chi_{8016}(883,\cdot)\) \(-1\) \(1\) \(e\left(\frac{93}{332}\right)\) \(e\left(\frac{46}{83}\right)\) \(e\left(\frac{31}{332}\right)\) \(e\left(\frac{283}{332}\right)\) \(e\left(\frac{8}{83}\right)\) \(e\left(\frac{165}{332}\right)\) \(e\left(\frac{40}{83}\right)\) \(e\left(\frac{93}{166}\right)\) \(e\left(\frac{255}{332}\right)\) \(e\left(\frac{35}{166}\right)\)
\(\chi_{8016}(907,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{332}\right)\) \(e\left(\frac{78}{83}\right)\) \(e\left(\frac{233}{332}\right)\) \(e\left(\frac{285}{332}\right)\) \(e\left(\frac{28}{83}\right)\) \(e\left(\frac{287}{332}\right)\) \(e\left(\frac{57}{83}\right)\) \(e\left(\frac{35}{166}\right)\) \(e\left(\frac{21}{332}\right)\) \(e\left(\frac{81}{166}\right)\)
\(\chi_{8016}(931,\cdot)\) \(-1\) \(1\) \(e\left(\frac{173}{332}\right)\) \(e\left(\frac{82}{83}\right)\) \(e\left(\frac{279}{332}\right)\) \(e\left(\frac{223}{332}\right)\) \(e\left(\frac{72}{83}\right)\) \(e\left(\frac{157}{332}\right)\) \(e\left(\frac{28}{83}\right)\) \(e\left(\frac{7}{166}\right)\) \(e\left(\frac{303}{332}\right)\) \(e\left(\frac{149}{166}\right)\)
\(\chi_{8016}(979,\cdot)\) \(-1\) \(1\) \(e\left(\frac{281}{332}\right)\) \(e\left(\frac{31}{83}\right)\) \(e\left(\frac{315}{332}\right)\) \(e\left(\frac{59}{332}\right)\) \(e\left(\frac{9}{83}\right)\) \(e\left(\frac{113}{332}\right)\) \(e\left(\frac{45}{83}\right)\) \(e\left(\frac{115}{166}\right)\) \(e\left(\frac{235}{332}\right)\) \(e\left(\frac{29}{166}\right)\)
\(\chi_{8016}(1027,\cdot)\) \(-1\) \(1\) \(e\left(\frac{253}{332}\right)\) \(e\left(\frac{35}{83}\right)\) \(e\left(\frac{195}{332}\right)\) \(e\left(\frac{163}{332}\right)\) \(e\left(\frac{53}{83}\right)\) \(e\left(\frac{149}{332}\right)\) \(e\left(\frac{16}{83}\right)\) \(e\left(\frac{87}{166}\right)\) \(e\left(\frac{19}{332}\right)\) \(e\left(\frac{97}{166}\right)\)
\(\chi_{8016}(1051,\cdot)\) \(-1\) \(1\) \(e\left(\frac{223}{332}\right)\) \(e\left(\frac{63}{83}\right)\) \(e\left(\frac{185}{332}\right)\) \(e\left(\frac{61}{332}\right)\) \(e\left(\frac{29}{83}\right)\) \(e\left(\frac{235}{332}\right)\) \(e\left(\frac{62}{83}\right)\) \(e\left(\frac{57}{166}\right)\) \(e\left(\frac{1}{332}\right)\) \(e\left(\frac{75}{166}\right)\)
\(\chi_{8016}(1099,\cdot)\) \(-1\) \(1\) \(e\left(\frac{235}{332}\right)\) \(e\left(\frac{2}{83}\right)\) \(e\left(\frac{189}{332}\right)\) \(e\left(\frac{301}{332}\right)\) \(e\left(\frac{22}{83}\right)\) \(e\left(\frac{267}{332}\right)\) \(e\left(\frac{27}{83}\right)\) \(e\left(\frac{69}{166}\right)\) \(e\left(\frac{141}{332}\right)\) \(e\left(\frac{117}{166}\right)\)
\(\chi_{8016}(1123,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{332}\right)\) \(e\left(\frac{67}{83}\right)\) \(e\left(\frac{231}{332}\right)\) \(e\left(\frac{331}{332}\right)\) \(e\left(\frac{73}{83}\right)\) \(e\left(\frac{105}{332}\right)\) \(e\left(\frac{33}{83}\right)\) \(e\left(\frac{29}{166}\right)\) \(e\left(\frac{283}{332}\right)\) \(e\left(\frac{143}{166}\right)\)
\(\chi_{8016}(1171,\cdot)\) \(-1\) \(1\) \(e\left(\frac{329}{332}\right)\) \(e\left(\frac{36}{83}\right)\) \(e\left(\frac{331}{332}\right)\) \(e\left(\frac{23}{332}\right)\) \(e\left(\frac{64}{83}\right)\) \(e\left(\frac{241}{332}\right)\) \(e\left(\frac{71}{83}\right)\) \(e\left(\frac{163}{166}\right)\) \(e\left(\frac{131}{332}\right)\) \(e\left(\frac{31}{166}\right)\)
\(\chi_{8016}(1219,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{332}\right)\) \(e\left(\frac{71}{83}\right)\) \(e\left(\frac{111}{332}\right)\) \(e\left(\frac{103}{332}\right)\) \(e\left(\frac{34}{83}\right)\) \(e\left(\frac{141}{332}\right)\) \(e\left(\frac{4}{83}\right)\) \(e\left(\frac{1}{166}\right)\) \(e\left(\frac{67}{332}\right)\) \(e\left(\frac{45}{166}\right)\)
\(\chi_{8016}(1267,\cdot)\) \(-1\) \(1\) \(e\left(\frac{137}{332}\right)\) \(e\left(\frac{16}{83}\right)\) \(e\left(\frac{267}{332}\right)\) \(e\left(\frac{167}{332}\right)\) \(e\left(\frac{10}{83}\right)\) \(e\left(\frac{61}{332}\right)\) \(e\left(\frac{50}{83}\right)\) \(e\left(\frac{137}{166}\right)\) \(e\left(\frac{215}{332}\right)\) \(e\left(\frac{23}{166}\right)\)
\(\chi_{8016}(1291,\cdot)\) \(-1\) \(1\) \(e\left(\frac{295}{332}\right)\) \(e\left(\frac{29}{83}\right)\) \(e\left(\frac{209}{332}\right)\) \(e\left(\frac{173}{332}\right)\) \(e\left(\frac{70}{83}\right)\) \(e\left(\frac{95}{332}\right)\) \(e\left(\frac{18}{83}\right)\) \(e\left(\frac{129}{166}\right)\) \(e\left(\frac{177}{332}\right)\) \(e\left(\frac{161}{166}\right)\)
\(\chi_{8016}(1339,\cdot)\) \(-1\) \(1\) \(e\left(\frac{271}{332}\right)\) \(e\left(\frac{68}{83}\right)\) \(e\left(\frac{201}{332}\right)\) \(e\left(\frac{25}{332}\right)\) \(e\left(\frac{1}{83}\right)\) \(e\left(\frac{31}{332}\right)\) \(e\left(\frac{5}{83}\right)\) \(e\left(\frac{105}{166}\right)\) \(e\left(\frac{229}{332}\right)\) \(e\left(\frac{77}{166}\right)\)
\(\chi_{8016}(1363,\cdot)\) \(-1\) \(1\) \(e\left(\frac{149}{332}\right)\) \(e\left(\frac{38}{83}\right)\) \(e\left(\frac{271}{332}\right)\) \(e\left(\frac{75}{332}\right)\) \(e\left(\frac{3}{83}\right)\) \(e\left(\frac{93}{332}\right)\) \(e\left(\frac{15}{83}\right)\) \(e\left(\frac{149}{166}\right)\) \(e\left(\frac{23}{332}\right)\) \(e\left(\frac{65}{166}\right)\)
\(\chi_{8016}(1411,\cdot)\) \(-1\) \(1\) \(e\left(\frac{109}{332}\right)\) \(e\left(\frac{20}{83}\right)\) \(e\left(\frac{147}{332}\right)\) \(e\left(\frac{271}{332}\right)\) \(e\left(\frac{54}{83}\right)\) \(e\left(\frac{97}{332}\right)\) \(e\left(\frac{21}{83}\right)\) \(e\left(\frac{109}{166}\right)\) \(e\left(\frac{331}{332}\right)\) \(e\left(\frac{91}{166}\right)\)
\(\chi_{8016}(1435,\cdot)\) \(-1\) \(1\) \(e\left(\frac{183}{332}\right)\) \(e\left(\frac{45}{83}\right)\) \(e\left(\frac{61}{332}\right)\) \(e\left(\frac{257}{332}\right)\) \(e\left(\frac{80}{83}\right)\) \(e\left(\frac{239}{332}\right)\) \(e\left(\frac{68}{83}\right)\) \(e\left(\frac{17}{166}\right)\) \(e\left(\frac{309}{332}\right)\) \(e\left(\frac{101}{166}\right)\)
\(\chi_{8016}(1483,\cdot)\) \(-1\) \(1\) \(e\left(\frac{79}{332}\right)\) \(e\left(\frac{48}{83}\right)\) \(e\left(\frac{137}{332}\right)\) \(e\left(\frac{169}{332}\right)\) \(e\left(\frac{30}{83}\right)\) \(e\left(\frac{183}{332}\right)\) \(e\left(\frac{67}{83}\right)\) \(e\left(\frac{79}{166}\right)\) \(e\left(\frac{313}{332}\right)\) \(e\left(\frac{69}{166}\right)\)
\(\chi_{8016}(1507,\cdot)\) \(-1\) \(1\) \(e\left(\frac{77}{332}\right)\) \(e\left(\frac{72}{83}\right)\) \(e\left(\frac{247}{332}\right)\) \(e\left(\frac{295}{332}\right)\) \(e\left(\frac{45}{83}\right)\) \(e\left(\frac{233}{332}\right)\) \(e\left(\frac{59}{83}\right)\) \(e\left(\frac{77}{166}\right)\) \(e\left(\frac{179}{332}\right)\) \(e\left(\frac{145}{166}\right)\)
\(\chi_{8016}(1531,\cdot)\) \(-1\) \(1\) \(e\left(\frac{147}{332}\right)\) \(e\left(\frac{62}{83}\right)\) \(e\left(\frac{49}{332}\right)\) \(e\left(\frac{201}{332}\right)\) \(e\left(\frac{18}{83}\right)\) \(e\left(\frac{143}{332}\right)\) \(e\left(\frac{7}{83}\right)\) \(e\left(\frac{147}{166}\right)\) \(e\left(\frac{221}{332}\right)\) \(e\left(\frac{141}{166}\right)\)
\(\chi_{8016}(1579,\cdot)\) \(-1\) \(1\) \(e\left(\frac{27}{332}\right)\) \(e\left(\frac{8}{83}\right)\) \(e\left(\frac{9}{332}\right)\) \(e\left(\frac{125}{332}\right)\) \(e\left(\frac{5}{83}\right)\) \(e\left(\frac{155}{332}\right)\) \(e\left(\frac{25}{83}\right)\) \(e\left(\frac{27}{166}\right)\) \(e\left(\frac{149}{332}\right)\) \(e\left(\frac{53}{166}\right)\)