Properties

Label 4235.dp
Modulus $4235$
Conductor $4235$
Order $660$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4235, base_ring=CyclotomicField(660))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([495,110,504]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(38,4235))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(4235\)
Conductor: \(4235\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(660\)
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: $\Q(\zeta_{660})$
Fixed field: Number field defined by a degree 660 polynomial (not computed)

First 31 of 160 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(8\) \(9\) \(12\) \(13\) \(16\) \(17\)
\(\chi_{4235}(38,\cdot)\) \(1\) \(1\) \(e\left(\frac{559}{660}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{229}{330}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{119}{220}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{41}{132}\right)\) \(e\left(\frac{193}{220}\right)\) \(e\left(\frac{64}{165}\right)\) \(e\left(\frac{221}{660}\right)\)
\(\chi_{4235}(47,\cdot)\) \(1\) \(1\) \(e\left(\frac{533}{660}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{203}{330}\right)\) \(e\left(\frac{87}{110}\right)\) \(e\left(\frac{93}{220}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{79}{132}\right)\) \(e\left(\frac{51}{220}\right)\) \(e\left(\frac{38}{165}\right)\) \(e\left(\frac{487}{660}\right)\)
\(\chi_{4235}(82,\cdot)\) \(1\) \(1\) \(e\left(\frac{89}{660}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{89}{330}\right)\) \(e\left(\frac{101}{110}\right)\) \(e\left(\frac{89}{220}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{132}\right)\) \(e\left(\frac{63}{220}\right)\) \(e\left(\frac{89}{165}\right)\) \(e\left(\frac{511}{660}\right)\)
\(\chi_{4235}(103,\cdot)\) \(1\) \(1\) \(e\left(\frac{347}{660}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{17}{330}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{127}{220}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{97}{132}\right)\) \(e\left(\frac{169}{220}\right)\) \(e\left(\frac{17}{165}\right)\) \(e\left(\frac{613}{660}\right)\)
\(\chi_{4235}(108,\cdot)\) \(1\) \(1\) \(e\left(\frac{331}{660}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{1}{330}\right)\) \(e\left(\frac{79}{110}\right)\) \(e\left(\frac{111}{220}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{29}{132}\right)\) \(e\left(\frac{217}{220}\right)\) \(e\left(\frac{1}{165}\right)\) \(e\left(\frac{269}{660}\right)\)
\(\chi_{4235}(152,\cdot)\) \(1\) \(1\) \(e\left(\frac{461}{660}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{131}{330}\right)\) \(e\left(\frac{9}{110}\right)\) \(e\left(\frac{21}{220}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{103}{132}\right)\) \(e\left(\frac{47}{220}\right)\) \(e\left(\frac{131}{165}\right)\) \(e\left(\frac{259}{660}\right)\)
\(\chi_{4235}(157,\cdot)\) \(1\) \(1\) \(e\left(\frac{133}{660}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{133}{330}\right)\) \(e\left(\frac{57}{110}\right)\) \(e\left(\frac{133}{220}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{95}{132}\right)\) \(e\left(\frac{151}{220}\right)\) \(e\left(\frac{133}{165}\right)\) \(e\left(\frac{467}{660}\right)\)
\(\chi_{4235}(192,\cdot)\) \(1\) \(1\) \(e\left(\frac{289}{660}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{289}{330}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{69}{220}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{131}{132}\right)\) \(e\left(\frac{123}{220}\right)\) \(e\left(\frac{124}{165}\right)\) \(e\left(\frac{191}{660}\right)\)
\(\chi_{4235}(213,\cdot)\) \(1\) \(1\) \(e\left(\frac{487}{660}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{157}{330}\right)\) \(e\left(\frac{83}{110}\right)\) \(e\left(\frac{47}{220}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{65}{132}\right)\) \(e\left(\frac{189}{220}\right)\) \(e\left(\frac{157}{165}\right)\) \(e\left(\frac{653}{660}\right)\)
\(\chi_{4235}(257,\cdot)\) \(1\) \(1\) \(e\left(\frac{257}{660}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{257}{330}\right)\) \(e\left(\frac{63}{110}\right)\) \(e\left(\frac{37}{220}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{127}{132}\right)\) \(e\left(\frac{219}{220}\right)\) \(e\left(\frac{92}{165}\right)\) \(e\left(\frac{163}{660}\right)\)
\(\chi_{4235}(262,\cdot)\) \(1\) \(1\) \(e\left(\frac{181}{660}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{181}{330}\right)\) \(e\left(\frac{109}{110}\right)\) \(e\left(\frac{181}{220}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{35}{132}\right)\) \(e\left(\frac{7}{220}\right)\) \(e\left(\frac{16}{165}\right)\) \(e\left(\frac{179}{660}\right)\)
\(\chi_{4235}(278,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{660}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{23}{330}\right)\) \(e\left(\frac{57}{110}\right)\) \(e\left(\frac{23}{220}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{73}{132}\right)\) \(e\left(\frac{41}{220}\right)\) \(e\left(\frac{23}{165}\right)\) \(e\left(\frac{577}{660}\right)\)
\(\chi_{4235}(313,\cdot)\) \(1\) \(1\) \(e\left(\frac{179}{660}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{179}{330}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{179}{220}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{109}{132}\right)\) \(e\left(\frac{13}{220}\right)\) \(e\left(\frac{14}{165}\right)\) \(e\left(\frac{301}{660}\right)\)
\(\chi_{4235}(367,\cdot)\) \(1\) \(1\) \(e\left(\frac{397}{660}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{67}{330}\right)\) \(e\left(\frac{13}{110}\right)\) \(e\left(\frac{177}{220}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{95}{132}\right)\) \(e\left(\frac{19}{220}\right)\) \(e\left(\frac{67}{165}\right)\) \(e\left(\frac{203}{660}\right)\)
\(\chi_{4235}(383,\cdot)\) \(1\) \(1\) \(e\left(\frac{71}{660}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{71}{330}\right)\) \(e\left(\frac{109}{110}\right)\) \(e\left(\frac{71}{220}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{13}{132}\right)\) \(e\left(\frac{117}{220}\right)\) \(e\left(\frac{71}{165}\right)\) \(e\left(\frac{289}{660}\right)\)
\(\chi_{4235}(388,\cdot)\) \(1\) \(1\) \(e\left(\frac{283}{660}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{283}{330}\right)\) \(e\left(\frac{27}{110}\right)\) \(e\left(\frac{63}{220}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{89}{132}\right)\) \(e\left(\frac{141}{220}\right)\) \(e\left(\frac{118}{165}\right)\) \(e\left(\frac{557}{660}\right)\)
\(\chi_{4235}(423,\cdot)\) \(1\) \(1\) \(e\left(\frac{379}{660}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{49}{330}\right)\) \(e\left(\frac{21}{110}\right)\) \(e\left(\frac{159}{220}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{101}{132}\right)\) \(e\left(\frac{73}{220}\right)\) \(e\left(\frac{49}{165}\right)\) \(e\left(\frac{641}{660}\right)\)
\(\chi_{4235}(432,\cdot)\) \(1\) \(1\) \(e\left(\frac{233}{660}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{233}{330}\right)\) \(e\left(\frac{37}{110}\right)\) \(e\left(\frac{13}{220}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{91}{132}\right)\) \(e\left(\frac{71}{220}\right)\) \(e\left(\frac{68}{165}\right)\) \(e\left(\frac{307}{660}\right)\)
\(\chi_{4235}(467,\cdot)\) \(1\) \(1\) \(e\left(\frac{569}{660}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{239}{330}\right)\) \(e\left(\frac{71}{110}\right)\) \(e\left(\frac{129}{220}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{67}{132}\right)\) \(e\left(\frac{163}{220}\right)\) \(e\left(\frac{74}{165}\right)\) \(e\left(\frac{271}{660}\right)\)
\(\chi_{4235}(488,\cdot)\) \(1\) \(1\) \(e\left(\frac{287}{660}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{287}{330}\right)\) \(e\left(\frac{13}{110}\right)\) \(e\left(\frac{67}{220}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{73}{132}\right)\) \(e\left(\frac{129}{220}\right)\) \(e\left(\frac{122}{165}\right)\) \(e\left(\frac{313}{660}\right)\)
\(\chi_{4235}(537,\cdot)\) \(1\) \(1\) \(e\left(\frac{581}{660}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{251}{330}\right)\) \(e\left(\frac{29}{110}\right)\) \(e\left(\frac{141}{220}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{19}{132}\right)\) \(e\left(\frac{127}{220}\right)\) \(e\left(\frac{86}{165}\right)\) \(e\left(\frac{199}{660}\right)\)
\(\chi_{4235}(542,\cdot)\) \(1\) \(1\) \(e\left(\frac{493}{660}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{163}{330}\right)\) \(e\left(\frac{7}{110}\right)\) \(e\left(\frac{53}{220}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{107}{132}\right)\) \(e\left(\frac{171}{220}\right)\) \(e\left(\frac{163}{165}\right)\) \(e\left(\frac{287}{660}\right)\)
\(\chi_{4235}(577,\cdot)\) \(1\) \(1\) \(e\left(\frac{109}{660}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{109}{330}\right)\) \(e\left(\frac{31}{110}\right)\) \(e\left(\frac{109}{220}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{59}{132}\right)\) \(e\left(\frac{3}{220}\right)\) \(e\left(\frac{109}{165}\right)\) \(e\left(\frac{611}{660}\right)\)
\(\chi_{4235}(598,\cdot)\) \(1\) \(1\) \(e\left(\frac{427}{660}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{97}{330}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{207}{220}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{41}{132}\right)\) \(e\left(\frac{149}{220}\right)\) \(e\left(\frac{97}{165}\right)\) \(e\left(\frac{353}{660}\right)\)
\(\chi_{4235}(642,\cdot)\) \(1\) \(1\) \(e\left(\frac{197}{660}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{197}{330}\right)\) \(e\left(\frac{53}{110}\right)\) \(e\left(\frac{197}{220}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{103}{132}\right)\) \(e\left(\frac{179}{220}\right)\) \(e\left(\frac{32}{165}\right)\) \(e\left(\frac{523}{660}\right)\)
\(\chi_{4235}(647,\cdot)\) \(1\) \(1\) \(e\left(\frac{301}{660}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{301}{330}\right)\) \(e\left(\frac{19}{110}\right)\) \(e\left(\frac{81}{220}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{83}{132}\right)\) \(e\left(\frac{87}{220}\right)\) \(e\left(\frac{136}{165}\right)\) \(e\left(\frac{119}{660}\right)\)
\(\chi_{4235}(663,\cdot)\) \(1\) \(1\) \(e\left(\frac{383}{660}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{53}{330}\right)\) \(e\left(\frac{7}{110}\right)\) \(e\left(\frac{163}{220}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{85}{132}\right)\) \(e\left(\frac{61}{220}\right)\) \(e\left(\frac{53}{165}\right)\) \(e\left(\frac{397}{660}\right)\)
\(\chi_{4235}(698,\cdot)\) \(1\) \(1\) \(e\left(\frac{659}{660}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{329}{330}\right)\) \(e\left(\frac{31}{110}\right)\) \(e\left(\frac{219}{220}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{37}{132}\right)\) \(e\left(\frac{113}{220}\right)\) \(e\left(\frac{164}{165}\right)\) \(e\left(\frac{61}{660}\right)\)
\(\chi_{4235}(752,\cdot)\) \(1\) \(1\) \(e\left(\frac{337}{660}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{7}{330}\right)\) \(e\left(\frac{3}{110}\right)\) \(e\left(\frac{117}{220}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{71}{132}\right)\) \(e\left(\frac{199}{220}\right)\) \(e\left(\frac{7}{165}\right)\) \(e\left(\frac{563}{660}\right)\)
\(\chi_{4235}(768,\cdot)\) \(1\) \(1\) \(e\left(\frac{191}{660}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{191}{330}\right)\) \(e\left(\frac{19}{110}\right)\) \(e\left(\frac{191}{220}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{61}{132}\right)\) \(e\left(\frac{197}{220}\right)\) \(e\left(\frac{26}{165}\right)\) \(e\left(\frac{229}{660}\right)\)
\(\chi_{4235}(773,\cdot)\) \(1\) \(1\) \(e\left(\frac{643}{660}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{313}{330}\right)\) \(e\left(\frac{87}{110}\right)\) \(e\left(\frac{203}{220}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{101}{132}\right)\) \(e\left(\frac{161}{220}\right)\) \(e\left(\frac{148}{165}\right)\) \(e\left(\frac{377}{660}\right)\)