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Properties

Label 2925.gh
Modulus 29252925
Conductor 29252925
Order 6060
Real no
Primitive yes
Minimal yes
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2925, base_ring=CyclotomicField(60))
 
M = H._module
 
chi = DirichletCharacter(H, M([50,3,20]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(302,2925))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 29252925
Conductor: 29252925
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 6060
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(ζ60)\Q(\zeta_{60})
Fixed field: Number field defined by a degree 60 polynomial

Characters in Galois orbit

Character −1-1 11 22 44 77 88 1111 1414 1616 1717 1919 2222
χ2925(302,⋅)\chi_{2925}(302,\cdot) 11 11 e(1360)e\left(\frac{13}{60}\right) e(1330)e\left(\frac{13}{30}\right) ii e(1320)e\left(\frac{13}{20}\right) e(2930)e\left(\frac{29}{30}\right) e(715)e\left(\frac{7}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(4960)e\left(\frac{49}{60}\right) e(1730)e\left(\frac{17}{30}\right) e(1160)e\left(\frac{11}{60}\right)
χ2925(308,⋅)\chi_{2925}(308,\cdot) 11 11 e(5960)e\left(\frac{59}{60}\right) e(2930)e\left(\frac{29}{30}\right) −i-i e(1920)e\left(\frac{19}{20}\right) e(730)e\left(\frac{7}{30}\right) e(1115)e\left(\frac{11}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(4760)e\left(\frac{47}{60}\right) e(130)e\left(\frac{1}{30}\right) e(1360)e\left(\frac{13}{60}\right)
χ2925(542,⋅)\chi_{2925}(542,\cdot) 11 11 e(2960)e\left(\frac{29}{60}\right) e(2930)e\left(\frac{29}{30}\right) ii e(920)e\left(\frac{9}{20}\right) e(730)e\left(\frac{7}{30}\right) e(1115)e\left(\frac{11}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(1760)e\left(\frac{17}{60}\right) e(130)e\left(\frac{1}{30}\right) e(4360)e\left(\frac{43}{60}\right)
χ2925(653,⋅)\chi_{2925}(653,\cdot) 11 11 e(3160)e\left(\frac{31}{60}\right) e(130)e\left(\frac{1}{30}\right) −i-i e(1120)e\left(\frac{11}{20}\right) e(2330)e\left(\frac{23}{30}\right) e(415)e\left(\frac{4}{15}\right) e(115)e\left(\frac{1}{15}\right) e(4360)e\left(\frac{43}{60}\right) e(2930)e\left(\frac{29}{30}\right) e(1760)e\left(\frac{17}{60}\right)
χ2925(887,⋅)\chi_{2925}(887,\cdot) 11 11 e(3760)e\left(\frac{37}{60}\right) e(730)e\left(\frac{7}{30}\right) ii e(1720)e\left(\frac{17}{20}\right) e(1130)e\left(\frac{11}{30}\right) e(1315)e\left(\frac{13}{15}\right) e(715)e\left(\frac{7}{15}\right) e(160)e\left(\frac{1}{60}\right) e(2330)e\left(\frac{23}{30}\right) e(5960)e\left(\frac{59}{60}\right)
χ2925(1127,⋅)\chi_{2925}(1127,\cdot) 11 11 e(5360)e\left(\frac{53}{60}\right) e(2330)e\left(\frac{23}{30}\right) ii e(1320)e\left(\frac{13}{20}\right) e(1930)e\left(\frac{19}{30}\right) e(215)e\left(\frac{2}{15}\right) e(815)e\left(\frac{8}{15}\right) e(2960)e\left(\frac{29}{60}\right) e(730)e\left(\frac{7}{30}\right) e(3160)e\left(\frac{31}{60}\right)
χ2925(1238,⋅)\chi_{2925}(1238,\cdot) 11 11 e(760)e\left(\frac{7}{60}\right) e(730)e\left(\frac{7}{30}\right) −i-i e(720)e\left(\frac{7}{20}\right) e(1130)e\left(\frac{11}{30}\right) e(1315)e\left(\frac{13}{15}\right) e(715)e\left(\frac{7}{15}\right) e(3160)e\left(\frac{31}{60}\right) e(2330)e\left(\frac{23}{30}\right) e(2960)e\left(\frac{29}{60}\right)
χ2925(1472,⋅)\chi_{2925}(1472,\cdot) 11 11 e(160)e\left(\frac{1}{60}\right) e(130)e\left(\frac{1}{30}\right) ii e(120)e\left(\frac{1}{20}\right) e(2330)e\left(\frac{23}{30}\right) e(415)e\left(\frac{4}{15}\right) e(115)e\left(\frac{1}{15}\right) e(1360)e\left(\frac{13}{60}\right) e(2930)e\left(\frac{29}{30}\right) e(4760)e\left(\frac{47}{60}\right)
χ2925(1478,⋅)\chi_{2925}(1478,\cdot) 11 11 e(1160)e\left(\frac{11}{60}\right) e(1130)e\left(\frac{11}{30}\right) −i-i e(1120)e\left(\frac{11}{20}\right) e(1330)e\left(\frac{13}{30}\right) e(1415)e\left(\frac{14}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(2360)e\left(\frac{23}{60}\right) e(1930)e\left(\frac{19}{30}\right) e(3760)e\left(\frac{37}{60}\right)
χ2925(1712,⋅)\chi_{2925}(1712,\cdot) 11 11 e(1760)e\left(\frac{17}{60}\right) e(1730)e\left(\frac{17}{30}\right) ii e(1720)e\left(\frac{17}{20}\right) e(130)e\left(\frac{1}{30}\right) e(815)e\left(\frac{8}{15}\right) e(215)e\left(\frac{2}{15}\right) e(4160)e\left(\frac{41}{60}\right) e(1330)e\left(\frac{13}{30}\right) e(1960)e\left(\frac{19}{60}\right)
χ2925(1823,⋅)\chi_{2925}(1823,\cdot) 11 11 e(4360)e\left(\frac{43}{60}\right) e(1330)e\left(\frac{13}{30}\right) −i-i e(320)e\left(\frac{3}{20}\right) e(2930)e\left(\frac{29}{30}\right) e(715)e\left(\frac{7}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(1960)e\left(\frac{19}{60}\right) e(1730)e\left(\frac{17}{30}\right) e(4160)e\left(\frac{41}{60}\right)
χ2925(2063,⋅)\chi_{2925}(2063,\cdot) 11 11 e(4760)e\left(\frac{47}{60}\right) e(1730)e\left(\frac{17}{30}\right) −i-i e(720)e\left(\frac{7}{20}\right) e(130)e\left(\frac{1}{30}\right) e(815)e\left(\frac{8}{15}\right) e(215)e\left(\frac{2}{15}\right) e(1160)e\left(\frac{11}{60}\right) e(1330)e\left(\frac{13}{30}\right) e(4960)e\left(\frac{49}{60}\right)
χ2925(2297,⋅)\chi_{2925}(2297,\cdot) 11 11 e(4160)e\left(\frac{41}{60}\right) e(1130)e\left(\frac{11}{30}\right) ii e(120)e\left(\frac{1}{20}\right) e(1330)e\left(\frac{13}{30}\right) e(1415)e\left(\frac{14}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(5360)e\left(\frac{53}{60}\right) e(1930)e\left(\frac{19}{30}\right) e(760)e\left(\frac{7}{60}\right)
χ2925(2408,⋅)\chi_{2925}(2408,\cdot) 11 11 e(1960)e\left(\frac{19}{60}\right) e(1930)e\left(\frac{19}{30}\right) −i-i e(1920)e\left(\frac{19}{20}\right) e(1730)e\left(\frac{17}{30}\right) e(115)e\left(\frac{1}{15}\right) e(415)e\left(\frac{4}{15}\right) e(760)e\left(\frac{7}{60}\right) e(1130)e\left(\frac{11}{30}\right) e(5360)e\left(\frac{53}{60}\right)
χ2925(2642,⋅)\chi_{2925}(2642,\cdot) 11 11 e(4960)e\left(\frac{49}{60}\right) e(1930)e\left(\frac{19}{30}\right) ii e(920)e\left(\frac{9}{20}\right) e(1730)e\left(\frac{17}{30}\right) e(115)e\left(\frac{1}{15}\right) e(415)e\left(\frac{4}{15}\right) e(3760)e\left(\frac{37}{60}\right) e(1130)e\left(\frac{11}{30}\right) e(2360)e\left(\frac{23}{60}\right)
χ2925(2648,⋅)\chi_{2925}(2648,\cdot) 11 11 e(2360)e\left(\frac{23}{60}\right) e(2330)e\left(\frac{23}{30}\right) −i-i e(320)e\left(\frac{3}{20}\right) e(1930)e\left(\frac{19}{30}\right) e(215)e\left(\frac{2}{15}\right) e(815)e\left(\frac{8}{15}\right) e(5960)e\left(\frac{59}{60}\right) e(730)e\left(\frac{7}{30}\right) e(160)e\left(\frac{1}{60}\right)