Properties

Label 1980.dm
Modulus 19801980
Conductor 19801980
Order 6060
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1980, base_ring=CyclotomicField(60)) M = H._module chi = DirichletCharacter(H, M([30,10,15,48])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(47,1980)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 19801980
Conductor: 19801980
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 6060
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content 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 1313 1717 1919 2323 2929 3131 3737 4141 4343
χ1980(47,)\chi_{1980}(47,\cdot) 1-1 11 e(160)e\left(\frac{1}{60}\right) e(5360)e\left(\frac{53}{60}\right) e(1920)e\left(\frac{19}{20}\right) e(25)e\left(\frac{2}{5}\right) e(112)e\left(\frac{1}{12}\right) e(415)e\left(\frac{4}{15}\right) e(1930)e\left(\frac{19}{30}\right) e(1720)e\left(\frac{17}{20}\right) e(730)e\left(\frac{7}{30}\right) e(1112)e\left(\frac{11}{12}\right)
χ1980(203,)\chi_{1980}(203,\cdot) 1-1 11 e(2360)e\left(\frac{23}{60}\right) e(1960)e\left(\frac{19}{60}\right) e(1720)e\left(\frac{17}{20}\right) e(15)e\left(\frac{1}{5}\right) e(1112)e\left(\frac{11}{12}\right) e(215)e\left(\frac{2}{15}\right) e(1730)e\left(\frac{17}{30}\right) e(1120)e\left(\frac{11}{20}\right) e(1130)e\left(\frac{11}{30}\right) e(112)e\left(\frac{1}{12}\right)
χ1980(383,)\chi_{1980}(383,\cdot) 1-1 11 e(4760)e\left(\frac{47}{60}\right) e(3160)e\left(\frac{31}{60}\right) e(1320)e\left(\frac{13}{20}\right) e(45)e\left(\frac{4}{5}\right) e(1112)e\left(\frac{11}{12}\right) e(815)e\left(\frac{8}{15}\right) e(2330)e\left(\frac{23}{30}\right) e(1920)e\left(\frac{19}{20}\right) e(2930)e\left(\frac{29}{30}\right) e(112)e\left(\frac{1}{12}\right)
χ1980(443,)\chi_{1980}(443,\cdot) 1-1 11 e(3160)e\left(\frac{31}{60}\right) e(2360)e\left(\frac{23}{60}\right) e(920)e\left(\frac{9}{20}\right) e(25)e\left(\frac{2}{5}\right) e(712)e\left(\frac{7}{12}\right) e(415)e\left(\frac{4}{15}\right) e(1930)e\left(\frac{19}{30}\right) e(720)e\left(\frac{7}{20}\right) e(730)e\left(\frac{7}{30}\right) e(512)e\left(\frac{5}{12}\right)
χ1980(587,)\chi_{1980}(587,\cdot) 1-1 11 e(4960)e\left(\frac{49}{60}\right) e(1760)e\left(\frac{17}{60}\right) e(1120)e\left(\frac{11}{20}\right) e(35)e\left(\frac{3}{5}\right) e(112)e\left(\frac{1}{12}\right) e(115)e\left(\frac{1}{15}\right) e(130)e\left(\frac{1}{30}\right) e(1320)e\left(\frac{13}{20}\right) e(1330)e\left(\frac{13}{30}\right) e(1112)e\left(\frac{11}{12}\right)
χ1980(707,)\chi_{1980}(707,\cdot) 1-1 11 e(4160)e\left(\frac{41}{60}\right) e(1360)e\left(\frac{13}{60}\right) e(1920)e\left(\frac{19}{20}\right) e(25)e\left(\frac{2}{5}\right) e(512)e\left(\frac{5}{12}\right) e(1415)e\left(\frac{14}{15}\right) e(2930)e\left(\frac{29}{30}\right) e(1720)e\left(\frac{17}{20}\right) e(1730)e\left(\frac{17}{30}\right) e(712)e\left(\frac{7}{12}\right)
χ1980(983,)\chi_{1980}(983,\cdot) 1-1 11 e(1960)e\left(\frac{19}{60}\right) e(4760)e\left(\frac{47}{60}\right) e(120)e\left(\frac{1}{20}\right) e(35)e\left(\frac{3}{5}\right) e(712)e\left(\frac{7}{12}\right) e(115)e\left(\frac{1}{15}\right) e(130)e\left(\frac{1}{30}\right) e(320)e\left(\frac{3}{20}\right) e(1330)e\left(\frac{13}{30}\right) e(512)e\left(\frac{5}{12}\right)
χ1980(1103,)\chi_{1980}(1103,\cdot) 1-1 11 e(1160)e\left(\frac{11}{60}\right) e(4360)e\left(\frac{43}{60}\right) e(920)e\left(\frac{9}{20}\right) e(25)e\left(\frac{2}{5}\right) e(1112)e\left(\frac{11}{12}\right) e(1415)e\left(\frac{14}{15}\right) e(2930)e\left(\frac{29}{30}\right) e(720)e\left(\frac{7}{20}\right) e(1730)e\left(\frac{17}{30}\right) e(112)e\left(\frac{1}{12}\right)
χ1980(1127,)\chi_{1980}(1127,\cdot) 1-1 11 e(1360)e\left(\frac{13}{60}\right) e(2960)e\left(\frac{29}{60}\right) e(720)e\left(\frac{7}{20}\right) e(15)e\left(\frac{1}{5}\right) e(112)e\left(\frac{1}{12}\right) e(715)e\left(\frac{7}{15}\right) e(730)e\left(\frac{7}{30}\right) e(120)e\left(\frac{1}{20}\right) e(130)e\left(\frac{1}{30}\right) e(1112)e\left(\frac{11}{12}\right)
χ1980(1247,)\chi_{1980}(1247,\cdot) 1-1 11 e(2960)e\left(\frac{29}{60}\right) e(3760)e\left(\frac{37}{60}\right) e(1120)e\left(\frac{11}{20}\right) e(35)e\left(\frac{3}{5}\right) e(512)e\left(\frac{5}{12}\right) e(1115)e\left(\frac{11}{15}\right) e(1130)e\left(\frac{11}{30}\right) e(1320)e\left(\frac{13}{20}\right) e(2330)e\left(\frac{23}{30}\right) e(712)e\left(\frac{7}{12}\right)
χ1980(1307,)\chi_{1980}(1307,\cdot) 1-1 11 e(3760)e\left(\frac{37}{60}\right) e(4160)e\left(\frac{41}{60}\right) e(320)e\left(\frac{3}{20}\right) e(45)e\left(\frac{4}{5}\right) e(112)e\left(\frac{1}{12}\right) e(1315)e\left(\frac{13}{15}\right) e(1330)e\left(\frac{13}{30}\right) e(920)e\left(\frac{9}{20}\right) e(1930)e\left(\frac{19}{30}\right) e(1112)e\left(\frac{11}{12}\right)
χ1980(1523,)\chi_{1980}(1523,\cdot) 1-1 11 e(4360)e\left(\frac{43}{60}\right) e(5960)e\left(\frac{59}{60}\right) e(1720)e\left(\frac{17}{20}\right) e(15)e\left(\frac{1}{5}\right) e(712)e\left(\frac{7}{12}\right) e(715)e\left(\frac{7}{15}\right) e(730)e\left(\frac{7}{30}\right) e(1120)e\left(\frac{11}{20}\right) e(130)e\left(\frac{1}{30}\right) e(512)e\left(\frac{5}{12}\right)
χ1980(1643,)\chi_{1980}(1643,\cdot) 1-1 11 e(5960)e\left(\frac{59}{60}\right) e(760)e\left(\frac{7}{60}\right) e(120)e\left(\frac{1}{20}\right) e(35)e\left(\frac{3}{5}\right) e(1112)e\left(\frac{11}{12}\right) e(1115)e\left(\frac{11}{15}\right) e(1130)e\left(\frac{11}{30}\right) e(320)e\left(\frac{3}{20}\right) e(2330)e\left(\frac{23}{30}\right) e(112)e\left(\frac{1}{12}\right)
χ1980(1703,)\chi_{1980}(1703,\cdot) 1-1 11 e(760)e\left(\frac{7}{60}\right) e(1160)e\left(\frac{11}{60}\right) e(1320)e\left(\frac{13}{20}\right) e(45)e\left(\frac{4}{5}\right) e(712)e\left(\frac{7}{12}\right) e(1315)e\left(\frac{13}{15}\right) e(1330)e\left(\frac{13}{30}\right) e(1920)e\left(\frac{19}{20}\right) e(1930)e\left(\frac{19}{30}\right) e(512)e\left(\frac{5}{12}\right)
χ1980(1787,)\chi_{1980}(1787,\cdot) 1-1 11 e(5360)e\left(\frac{53}{60}\right) e(4960)e\left(\frac{49}{60}\right) e(720)e\left(\frac{7}{20}\right) e(15)e\left(\frac{1}{5}\right) e(512)e\left(\frac{5}{12}\right) e(215)e\left(\frac{2}{15}\right) e(1730)e\left(\frac{17}{30}\right) e(120)e\left(\frac{1}{20}\right) e(1130)e\left(\frac{11}{30}\right) e(712)e\left(\frac{7}{12}\right)
χ1980(1967,)\chi_{1980}(1967,\cdot) 1-1 11 e(1760)e\left(\frac{17}{60}\right) e(160)e\left(\frac{1}{60}\right) e(320)e\left(\frac{3}{20}\right) e(45)e\left(\frac{4}{5}\right) e(512)e\left(\frac{5}{12}\right) e(815)e\left(\frac{8}{15}\right) e(2330)e\left(\frac{23}{30}\right) e(920)e\left(\frac{9}{20}\right) e(2930)e\left(\frac{29}{30}\right) e(712)e\left(\frac{7}{12}\right)