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Properties

Label 4650.ft
Modulus 46504650
Conductor 23252325
Order 6060
Real no
Primitive no
Minimal yes
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4650, base_ring=CyclotomicField(60))
 
M = H._module
 
chi = DirichletCharacter(H, M([30,3,40]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(377,4650))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 46504650
Conductor: 23252325
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 6060
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 2325.fz
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 77 1111 1313 1717 1919 2323 2929 3737 4141 4343
χ4650(377,⋅)\chi_{4650}(377,\cdot) 11 11 e(1112)e\left(\frac{11}{12}\right) e(1930)e\left(\frac{19}{30}\right) e(1760)e\left(\frac{17}{60}\right) e(4960)e\left(\frac{49}{60}\right) e(1730)e\left(\frac{17}{30}\right) e(120)e\left(\frac{1}{20}\right) e(35)e\left(\frac{3}{5}\right) e(760)e\left(\frac{7}{60}\right) e(130)e\left(\frac{1}{30}\right) e(512)e\left(\frac{5}{12}\right)
χ4650(563,⋅)\chi_{4650}(563,\cdot) 11 11 e(512)e\left(\frac{5}{12}\right) e(130)e\left(\frac{1}{30}\right) e(2360)e\left(\frac{23}{60}\right) e(3160)e\left(\frac{31}{60}\right) e(2330)e\left(\frac{23}{30}\right) e(1920)e\left(\frac{19}{20}\right) e(25)e\left(\frac{2}{5}\right) e(1360)e\left(\frac{13}{60}\right) e(1930)e\left(\frac{19}{30}\right) e(1112)e\left(\frac{11}{12}\right)
χ4650(1637,⋅)\chi_{4650}(1637,\cdot) 11 11 e(712)e\left(\frac{7}{12}\right) e(1130)e\left(\frac{11}{30}\right) e(1360)e\left(\frac{13}{60}\right) e(4160)e\left(\frac{41}{60}\right) e(1330)e\left(\frac{13}{30}\right) e(920)e\left(\frac{9}{20}\right) e(25)e\left(\frac{2}{5}\right) e(2360)e\left(\frac{23}{60}\right) e(2930)e\left(\frac{29}{30}\right) e(112)e\left(\frac{1}{12}\right)
χ4650(1823,⋅)\chi_{4650}(1823,\cdot) 11 11 e(112)e\left(\frac{1}{12}\right) e(2930)e\left(\frac{29}{30}\right) e(760)e\left(\frac{7}{60}\right) e(5960)e\left(\frac{59}{60}\right) e(730)e\left(\frac{7}{30}\right) e(1120)e\left(\frac{11}{20}\right) e(35)e\left(\frac{3}{5}\right) e(1760)e\left(\frac{17}{60}\right) e(1130)e\left(\frac{11}{30}\right) e(712)e\left(\frac{7}{12}\right)
χ4650(2237,⋅)\chi_{4650}(2237,\cdot) 11 11 e(1112)e\left(\frac{11}{12}\right) e(130)e\left(\frac{1}{30}\right) e(5360)e\left(\frac{53}{60}\right) e(160)e\left(\frac{1}{60}\right) e(2330)e\left(\frac{23}{30}\right) e(920)e\left(\frac{9}{20}\right) e(25)e\left(\frac{2}{5}\right) e(4360)e\left(\frac{43}{60}\right) e(1930)e\left(\frac{19}{30}\right) e(512)e\left(\frac{5}{12}\right)
χ4650(2423,⋅)\chi_{4650}(2423,\cdot) 11 11 e(512)e\left(\frac{5}{12}\right) e(1930)e\left(\frac{19}{30}\right) e(4760)e\left(\frac{47}{60}\right) e(1960)e\left(\frac{19}{60}\right) e(1730)e\left(\frac{17}{30}\right) e(1120)e\left(\frac{11}{20}\right) e(35)e\left(\frac{3}{5}\right) e(3760)e\left(\frac{37}{60}\right) e(130)e\left(\frac{1}{30}\right) e(1112)e\left(\frac{11}{12}\right)
χ4650(2567,⋅)\chi_{4650}(2567,\cdot) 11 11 e(712)e\left(\frac{7}{12}\right) e(1730)e\left(\frac{17}{30}\right) e(160)e\left(\frac{1}{60}\right) e(1760)e\left(\frac{17}{60}\right) e(130)e\left(\frac{1}{30}\right) e(1320)e\left(\frac{13}{20}\right) e(45)e\left(\frac{4}{5}\right) e(1160)e\left(\frac{11}{60}\right) e(2330)e\left(\frac{23}{30}\right) e(112)e\left(\frac{1}{12}\right)
χ4650(2753,⋅)\chi_{4650}(2753,\cdot) 11 11 e(112)e\left(\frac{1}{12}\right) e(2330)e\left(\frac{23}{30}\right) e(1960)e\left(\frac{19}{60}\right) e(2360)e\left(\frac{23}{60}\right) e(1930)e\left(\frac{19}{30}\right) e(720)e\left(\frac{7}{20}\right) e(15)e\left(\frac{1}{5}\right) e(2960)e\left(\frac{29}{60}\right) e(1730)e\left(\frac{17}{30}\right) e(712)e\left(\frac{7}{12}\right)
χ4650(3167,⋅)\chi_{4650}(3167,\cdot) 11 11 e(1112)e\left(\frac{11}{12}\right) e(730)e\left(\frac{7}{30}\right) e(4160)e\left(\frac{41}{60}\right) e(3760)e\left(\frac{37}{60}\right) e(1130)e\left(\frac{11}{30}\right) e(1320)e\left(\frac{13}{20}\right) e(45)e\left(\frac{4}{5}\right) e(3160)e\left(\frac{31}{60}\right) e(1330)e\left(\frac{13}{30}\right) e(512)e\left(\frac{5}{12}\right)
χ4650(3353,⋅)\chi_{4650}(3353,\cdot) 11 11 e(512)e\left(\frac{5}{12}\right) e(1330)e\left(\frac{13}{30}\right) e(5960)e\left(\frac{59}{60}\right) e(4360)e\left(\frac{43}{60}\right) e(2930)e\left(\frac{29}{30}\right) e(720)e\left(\frac{7}{20}\right) e(15)e\left(\frac{1}{5}\right) e(4960)e\left(\frac{49}{60}\right) e(730)e\left(\frac{7}{30}\right) e(1112)e\left(\frac{11}{12}\right)
χ4650(3497,⋅)\chi_{4650}(3497,\cdot) 11 11 e(712)e\left(\frac{7}{12}\right) e(2330)e\left(\frac{23}{30}\right) e(4960)e\left(\frac{49}{60}\right) e(5360)e\left(\frac{53}{60}\right) e(1930)e\left(\frac{19}{30}\right) e(1720)e\left(\frac{17}{20}\right) e(15)e\left(\frac{1}{5}\right) e(5960)e\left(\frac{59}{60}\right) e(1730)e\left(\frac{17}{30}\right) e(112)e\left(\frac{1}{12}\right)
χ4650(3683,⋅)\chi_{4650}(3683,\cdot) 11 11 e(112)e\left(\frac{1}{12}\right) e(1730)e\left(\frac{17}{30}\right) e(3160)e\left(\frac{31}{60}\right) e(4760)e\left(\frac{47}{60}\right) e(130)e\left(\frac{1}{30}\right) e(320)e\left(\frac{3}{20}\right) e(45)e\left(\frac{4}{5}\right) e(4160)e\left(\frac{41}{60}\right) e(2330)e\left(\frac{23}{30}\right) e(712)e\left(\frac{7}{12}\right)
χ4650(4097,⋅)\chi_{4650}(4097,\cdot) 11 11 e(1112)e\left(\frac{11}{12}\right) e(1330)e\left(\frac{13}{30}\right) e(2960)e\left(\frac{29}{60}\right) e(1360)e\left(\frac{13}{60}\right) e(2930)e\left(\frac{29}{30}\right) e(1720)e\left(\frac{17}{20}\right) e(15)e\left(\frac{1}{5}\right) e(1960)e\left(\frac{19}{60}\right) e(730)e\left(\frac{7}{30}\right) e(512)e\left(\frac{5}{12}\right)
χ4650(4283,⋅)\chi_{4650}(4283,\cdot) 11 11 e(512)e\left(\frac{5}{12}\right) e(730)e\left(\frac{7}{30}\right) e(1160)e\left(\frac{11}{60}\right) e(760)e\left(\frac{7}{60}\right) e(1130)e\left(\frac{11}{30}\right) e(320)e\left(\frac{3}{20}\right) e(45)e\left(\frac{4}{5}\right) e(160)e\left(\frac{1}{60}\right) e(1330)e\left(\frac{13}{30}\right) e(1112)e\left(\frac{11}{12}\right)
χ4650(4427,⋅)\chi_{4650}(4427,\cdot) 11 11 e(712)e\left(\frac{7}{12}\right) e(2930)e\left(\frac{29}{30}\right) e(3760)e\left(\frac{37}{60}\right) e(2960)e\left(\frac{29}{60}\right) e(730)e\left(\frac{7}{30}\right) e(120)e\left(\frac{1}{20}\right) e(35)e\left(\frac{3}{5}\right) e(4760)e\left(\frac{47}{60}\right) e(1130)e\left(\frac{11}{30}\right) e(112)e\left(\frac{1}{12}\right)
χ4650(4613,⋅)\chi_{4650}(4613,\cdot) 11 11 e(112)e\left(\frac{1}{12}\right) e(1130)e\left(\frac{11}{30}\right) e(4360)e\left(\frac{43}{60}\right) e(1160)e\left(\frac{11}{60}\right) e(1330)e\left(\frac{13}{30}\right) e(1920)e\left(\frac{19}{20}\right) e(25)e\left(\frac{2}{5}\right) e(5360)e\left(\frac{53}{60}\right) e(2930)e\left(\frac{29}{30}\right) e(712)e\left(\frac{7}{12}\right)