Properties

Label 287.bf
Modulus $287$
Conductor $287$
Order $120$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(287, base_ring=CyclotomicField(120))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([80,9]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(11,287))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(287\)
Conductor: \(287\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(120\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
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: $\Q(\zeta_{120})$
Fixed field: Number field defined by a degree 120 polynomial (not computed)

First 31 of 32 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(8\) \(9\) \(10\) \(11\) \(12\)
\(\chi_{287}(11,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{107}{120}\right)\) \(e\left(\frac{43}{120}\right)\)
\(\chi_{287}(30,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{120}\right)\) \(e\left(\frac{23}{120}\right)\)
\(\chi_{287}(53,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{83}{120}\right)\) \(e\left(\frac{67}{120}\right)\)
\(\chi_{287}(58,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{97}{120}\right)\) \(e\left(\frac{113}{120}\right)\)
\(\chi_{287}(60,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{41}{120}\right)\) \(e\left(\frac{49}{120}\right)\)
\(\chi_{287}(65,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{37}{120}\right)\) \(e\left(\frac{53}{120}\right)\)
\(\chi_{287}(67,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{113}{120}\right)\) \(e\left(\frac{97}{120}\right)\)
\(\chi_{287}(88,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{89}{120}\right)\) \(e\left(\frac{1}{120}\right)\)
\(\chi_{287}(93,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{67}{120}\right)\) \(e\left(\frac{83}{120}\right)\)
\(\chi_{287}(95,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{119}{120}\right)\) \(e\left(\frac{31}{120}\right)\)
\(\chi_{287}(116,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{120}\right)\) \(e\left(\frac{19}{120}\right)\)
\(\chi_{287}(130,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{71}{120}\right)\) \(e\left(\frac{79}{120}\right)\)
\(\chi_{287}(135,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{43}{120}\right)\) \(e\left(\frac{107}{120}\right)\)
\(\chi_{287}(142,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{120}\right)\) \(e\left(\frac{89}{120}\right)\)
\(\chi_{287}(149,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{73}{120}\right)\) \(e\left(\frac{17}{120}\right)\)
\(\chi_{287}(151,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{59}{120}\right)\) \(e\left(\frac{91}{120}\right)\)
\(\chi_{287}(158,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{29}{120}\right)\) \(e\left(\frac{61}{120}\right)\)
\(\chi_{287}(170,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{49}{120}\right)\) \(e\left(\frac{41}{120}\right)\)
\(\chi_{287}(177,\cdot)\) \(-1\) \(1\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{79}{120}\right)\) \(e\left(\frac{71}{120}\right)\)
\(\chi_{287}(179,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{53}{120}\right)\) \(e\left(\frac{37}{120}\right)\)
\(\chi_{287}(186,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{101}{120}\right)\) \(e\left(\frac{109}{120}\right)\)
\(\chi_{287}(193,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{23}{120}\right)\) \(e\left(\frac{7}{120}\right)\)
\(\chi_{287}(198,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{91}{120}\right)\) \(e\left(\frac{59}{120}\right)\)
\(\chi_{287}(212,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{31}{120}\right)\) \(e\left(\frac{119}{120}\right)\)
\(\chi_{287}(233,\cdot)\) \(-1\) \(1\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{19}{120}\right)\) \(e\left(\frac{11}{120}\right)\)
\(\chi_{287}(235,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{47}{120}\right)\) \(e\left(\frac{103}{120}\right)\)
\(\chi_{287}(240,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{109}{120}\right)\) \(e\left(\frac{101}{120}\right)\)
\(\chi_{287}(261,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{120}\right)\) \(e\left(\frac{77}{120}\right)\)
\(\chi_{287}(263,\cdot)\) \(-1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{17}{120}\right)\) \(e\left(\frac{73}{120}\right)\)
\(\chi_{287}(268,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{61}{120}\right)\) \(e\left(\frac{29}{120}\right)\)
\(\chi_{287}(270,\cdot)\) \(-1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{77}{120}\right)\) \(e\left(\frac{13}{120}\right)\)