Properties

Label 4235.dh
Modulus $4235$
Conductor $847$
Order $330$
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4235, base_ring=CyclotomicField(330))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,275,306]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(26,4235))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(4235\)
Conductor: \(847\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(330\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 847.bd
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: $\Q(\zeta_{165})$
Fixed field: Number field defined by a degree 330 polynomial (not computed)

First 31 of 80 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(8\) \(9\) \(12\) \(13\) \(16\) \(17\)
\(\chi_{4235}(26,\cdot)\) \(-1\) \(1\) \(e\left(\frac{98}{165}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{31}{165}\right)\) \(e\left(\frac{3}{110}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{62}{165}\right)\) \(e\left(\frac{89}{330}\right)\)
\(\chi_{4235}(31,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{165}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{38}{165}\right)\) \(e\left(\frac{9}{110}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{76}{165}\right)\) \(e\left(\frac{157}{330}\right)\)
\(\chi_{4235}(136,\cdot)\) \(-1\) \(1\) \(e\left(\frac{133}{165}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{101}{165}\right)\) \(e\left(\frac{63}{110}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{27}{110}\right)\) \(e\left(\frac{37}{165}\right)\) \(e\left(\frac{109}{330}\right)\)
\(\chi_{4235}(201,\cdot)\) \(-1\) \(1\) \(e\left(\frac{62}{165}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{124}{165}\right)\) \(e\left(\frac{67}{110}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{13}{110}\right)\) \(e\left(\frac{83}{165}\right)\) \(e\left(\frac{191}{330}\right)\)
\(\chi_{4235}(236,\cdot)\) \(-1\) \(1\) \(e\left(\frac{161}{165}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{157}{165}\right)\) \(e\left(\frac{1}{110}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{79}{110}\right)\) \(e\left(\frac{149}{165}\right)\) \(e\left(\frac{323}{330}\right)\)
\(\chi_{4235}(306,\cdot)\) \(-1\) \(1\) \(e\left(\frac{119}{165}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{73}{165}\right)\) \(e\left(\frac{39}{110}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{1}{110}\right)\) \(e\left(\frac{146}{165}\right)\) \(e\left(\frac{167}{330}\right)\)
\(\chi_{4235}(311,\cdot)\) \(-1\) \(1\) \(e\left(\frac{127}{165}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{89}{165}\right)\) \(e\left(\frac{37}{110}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{63}{110}\right)\) \(e\left(\frac{13}{165}\right)\) \(e\left(\frac{181}{330}\right)\)
\(\chi_{4235}(346,\cdot)\) \(-1\) \(1\) \(e\left(\frac{46}{165}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{92}{165}\right)\) \(e\left(\frac{71}{110}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{109}{110}\right)\) \(e\left(\frac{19}{165}\right)\) \(e\left(\frac{163}{330}\right)\)
\(\chi_{4235}(411,\cdot)\) \(-1\) \(1\) \(e\left(\frac{83}{165}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{165}\right)\) \(e\left(\frac{103}{110}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{107}{110}\right)\) \(e\left(\frac{2}{165}\right)\) \(e\left(\frac{269}{330}\right)\)
\(\chi_{4235}(416,\cdot)\) \(-1\) \(1\) \(e\left(\frac{49}{165}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{98}{165}\right)\) \(e\left(\frac{29}{110}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{91}{110}\right)\) \(e\left(\frac{31}{165}\right)\) \(e\left(\frac{127}{330}\right)\)
\(\chi_{4235}(521,\cdot)\) \(-1\) \(1\) \(e\left(\frac{118}{165}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{71}{165}\right)\) \(e\left(\frac{53}{110}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{7}{110}\right)\) \(e\left(\frac{142}{165}\right)\) \(e\left(\frac{289}{330}\right)\)
\(\chi_{4235}(586,\cdot)\) \(-1\) \(1\) \(e\left(\frac{152}{165}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{139}{165}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{113}{165}\right)\) \(e\left(\frac{101}{330}\right)\)
\(\chi_{4235}(621,\cdot)\) \(-1\) \(1\) \(e\left(\frac{116}{165}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{67}{165}\right)\) \(e\left(\frac{81}{110}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{19}{110}\right)\) \(e\left(\frac{134}{165}\right)\) \(e\left(\frac{203}{330}\right)\)
\(\chi_{4235}(691,\cdot)\) \(-1\) \(1\) \(e\left(\frac{149}{165}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{133}{165}\right)\) \(e\left(\frac{59}{110}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{41}{110}\right)\) \(e\left(\frac{101}{165}\right)\) \(e\left(\frac{137}{330}\right)\)
\(\chi_{4235}(696,\cdot)\) \(-1\) \(1\) \(e\left(\frac{52}{165}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{104}{165}\right)\) \(e\left(\frac{97}{110}\right)\) \(e\left(\frac{52}{55}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{43}{165}\right)\) \(e\left(\frac{91}{330}\right)\)
\(\chi_{4235}(731,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{165}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{2}{165}\right)\) \(e\left(\frac{41}{110}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{49}{110}\right)\) \(e\left(\frac{4}{165}\right)\) \(e\left(\frac{43}{330}\right)\)
\(\chi_{4235}(796,\cdot)\) \(-1\) \(1\) \(e\left(\frac{68}{165}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{136}{165}\right)\) \(e\left(\frac{93}{110}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{87}{110}\right)\) \(e\left(\frac{107}{165}\right)\) \(e\left(\frac{119}{330}\right)\)
\(\chi_{4235}(801,\cdot)\) \(-1\) \(1\) \(e\left(\frac{79}{165}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{158}{165}\right)\) \(e\left(\frac{49}{110}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{21}{110}\right)\) \(e\left(\frac{151}{165}\right)\) \(e\left(\frac{97}{330}\right)\)
\(\chi_{4235}(906,\cdot)\) \(-1\) \(1\) \(e\left(\frac{103}{165}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{41}{165}\right)\) \(e\left(\frac{43}{110}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{97}{110}\right)\) \(e\left(\frac{82}{165}\right)\) \(e\left(\frac{139}{330}\right)\)
\(\chi_{4235}(1006,\cdot)\) \(-1\) \(1\) \(e\left(\frac{71}{165}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{142}{165}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{69}{110}\right)\) \(e\left(\frac{119}{165}\right)\) \(e\left(\frac{83}{330}\right)\)
\(\chi_{4235}(1076,\cdot)\) \(-1\) \(1\) \(e\left(\frac{14}{165}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{28}{165}\right)\) \(e\left(\frac{79}{110}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{81}{110}\right)\) \(e\left(\frac{56}{165}\right)\) \(e\left(\frac{107}{330}\right)\)
\(\chi_{4235}(1081,\cdot)\) \(-1\) \(1\) \(e\left(\frac{142}{165}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{119}{165}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{83}{110}\right)\) \(e\left(\frac{73}{165}\right)\) \(e\left(\frac{1}{330}\right)\)
\(\chi_{4235}(1181,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{165}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{106}{165}\right)\) \(e\left(\frac{83}{110}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{67}{110}\right)\) \(e\left(\frac{47}{165}\right)\) \(e\left(\frac{299}{330}\right)\)
\(\chi_{4235}(1186,\cdot)\) \(-1\) \(1\) \(e\left(\frac{109}{165}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{53}{165}\right)\) \(e\left(\frac{69}{110}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{106}{165}\right)\) \(e\left(\frac{67}{330}\right)\)
\(\chi_{4235}(1356,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{165}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{165}\right)\) \(e\left(\frac{27}{110}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{43}{110}\right)\) \(e\left(\frac{8}{165}\right)\) \(e\left(\frac{251}{330}\right)\)
\(\chi_{4235}(1391,\cdot)\) \(-1\) \(1\) \(e\left(\frac{26}{165}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{52}{165}\right)\) \(e\left(\frac{21}{110}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{9}{110}\right)\) \(e\left(\frac{104}{165}\right)\) \(e\left(\frac{293}{330}\right)\)
\(\chi_{4235}(1466,\cdot)\) \(-1\) \(1\) \(e\left(\frac{67}{165}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{134}{165}\right)\) \(e\left(\frac{107}{110}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{93}{110}\right)\) \(e\left(\frac{103}{165}\right)\) \(e\left(\frac{241}{330}\right)\)
\(\chi_{4235}(1501,\cdot)\) \(-1\) \(1\) \(e\left(\frac{76}{165}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{152}{165}\right)\) \(e\left(\frac{91}{110}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{39}{110}\right)\) \(e\left(\frac{139}{165}\right)\) \(e\left(\frac{133}{330}\right)\)
\(\chi_{4235}(1566,\cdot)\) \(-1\) \(1\) \(e\left(\frac{38}{165}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{76}{165}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{152}{165}\right)\) \(e\left(\frac{149}{330}\right)\)
\(\chi_{4235}(1571,\cdot)\) \(-1\) \(1\) \(e\left(\frac{139}{165}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{113}{165}\right)\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{101}{110}\right)\) \(e\left(\frac{61}{165}\right)\) \(e\left(\frac{37}{330}\right)\)
\(\chi_{4235}(1676,\cdot)\) \(-1\) \(1\) \(e\left(\frac{73}{165}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{146}{165}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{57}{110}\right)\) \(e\left(\frac{127}{165}\right)\) \(e\left(\frac{169}{330}\right)\)