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Properties

Label 1800.dp
Modulus 18001800
Conductor 900900
Order 6060
Real no
Primitive no
Minimal no
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1800, base_ring=CyclotomicField(60)) M = H._module chi = DirichletCharacter(H, M([30,0,50,33])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(23,1800)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 18001800
Conductor: 900900
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: no, induced from 900.bu
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
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 1111 1313 1717 1919 2323 2929 3131 3737 4141
χ1800(23,⋅)\chi_{1800}(23,\cdot) −1-1 11 e(712)e\left(\frac{7}{12}\right) e(215)e\left(\frac{2}{15}\right) e(760)e\left(\frac{7}{60}\right) e(1320)e\left(\frac{13}{20}\right) e(25)e\left(\frac{2}{5}\right) e(4360)e\left(\frac{43}{60}\right) e(1415)e\left(\frac{14}{15}\right) e(1730)e\left(\frac{17}{30}\right) e(1920)e\left(\frac{19}{20}\right) e(1130)e\left(\frac{11}{30}\right)
χ1800(47,⋅)\chi_{1800}(47,\cdot) −1-1 11 e(512)e\left(\frac{5}{12}\right) e(415)e\left(\frac{4}{15}\right) e(2960)e\left(\frac{29}{60}\right) e(1120)e\left(\frac{11}{20}\right) e(45)e\left(\frac{4}{5}\right) e(4160)e\left(\frac{41}{60}\right) e(1315)e\left(\frac{13}{15}\right) e(1930)e\left(\frac{19}{30}\right) e(1320)e\left(\frac{13}{20}\right) e(730)e\left(\frac{7}{30}\right)
χ1800(167,⋅)\chi_{1800}(167,\cdot) −1-1 11 e(112)e\left(\frac{1}{12}\right) e(1115)e\left(\frac{11}{15}\right) e(160)e\left(\frac{1}{60}\right) e(1920)e\left(\frac{19}{20}\right) e(15)e\left(\frac{1}{5}\right) e(4960)e\left(\frac{49}{60}\right) e(215)e\left(\frac{2}{15}\right) e(1130)e\left(\frac{11}{30}\right) e(1720)e\left(\frac{17}{20}\right) e(2330)e\left(\frac{23}{30}\right)
χ1800(263,⋅)\chi_{1800}(263,\cdot) −1-1 11 e(1112)e\left(\frac{11}{12}\right) e(1315)e\left(\frac{13}{15}\right) e(2360)e\left(\frac{23}{60}\right) e(1720)e\left(\frac{17}{20}\right) e(35)e\left(\frac{3}{5}\right) e(4760)e\left(\frac{47}{60}\right) e(115)e\left(\frac{1}{15}\right) e(1330)e\left(\frac{13}{30}\right) e(1120)e\left(\frac{11}{20}\right) e(1930)e\left(\frac{19}{30}\right)
χ1800(383,⋅)\chi_{1800}(383,\cdot) −1-1 11 e(712)e\left(\frac{7}{12}\right) e(1115)e\left(\frac{11}{15}\right) e(3160)e\left(\frac{31}{60}\right) e(920)e\left(\frac{9}{20}\right) e(15)e\left(\frac{1}{5}\right) e(1960)e\left(\frac{19}{60}\right) e(215)e\left(\frac{2}{15}\right) e(1130)e\left(\frac{11}{30}\right) e(720)e\left(\frac{7}{20}\right) e(2330)e\left(\frac{23}{30}\right)
χ1800(527,⋅)\chi_{1800}(527,\cdot) −1-1 11 e(112)e\left(\frac{1}{12}\right) e(215)e\left(\frac{2}{15}\right) e(3760)e\left(\frac{37}{60}\right) e(320)e\left(\frac{3}{20}\right) e(25)e\left(\frac{2}{5}\right) e(1360)e\left(\frac{13}{60}\right) e(1415)e\left(\frac{14}{15}\right) e(1730)e\left(\frac{17}{30}\right) e(920)e\left(\frac{9}{20}\right) e(1130)e\left(\frac{11}{30}\right)
χ1800(623,⋅)\chi_{1800}(623,\cdot) −1-1 11 e(1112)e\left(\frac{11}{12}\right) e(715)e\left(\frac{7}{15}\right) e(4760)e\left(\frac{47}{60}\right) e(1320)e\left(\frac{13}{20}\right) e(25)e\left(\frac{2}{5}\right) e(2360)e\left(\frac{23}{60}\right) e(415)e\left(\frac{4}{15}\right) e(730)e\left(\frac{7}{30}\right) e(1920)e\left(\frac{19}{20}\right) e(130)e\left(\frac{1}{30}\right)
χ1800(767,⋅)\chi_{1800}(767,\cdot) −1-1 11 e(512)e\left(\frac{5}{12}\right) e(115)e\left(\frac{1}{15}\right) e(4160)e\left(\frac{41}{60}\right) e(1920)e\left(\frac{19}{20}\right) e(15)e\left(\frac{1}{5}\right) e(2960)e\left(\frac{29}{60}\right) e(715)e\left(\frac{7}{15}\right) e(130)e\left(\frac{1}{30}\right) e(1720)e\left(\frac{17}{20}\right) e(1330)e\left(\frac{13}{30}\right)
χ1800(887,⋅)\chi_{1800}(887,\cdot) −1-1 11 e(112)e\left(\frac{1}{12}\right) e(815)e\left(\frac{8}{15}\right) e(1360)e\left(\frac{13}{60}\right) e(720)e\left(\frac{7}{20}\right) e(35)e\left(\frac{3}{5}\right) e(3760)e\left(\frac{37}{60}\right) e(1115)e\left(\frac{11}{15}\right) e(2330)e\left(\frac{23}{30}\right) e(120)e\left(\frac{1}{20}\right) e(2930)e\left(\frac{29}{30}\right)
χ1800(983,⋅)\chi_{1800}(983,\cdot) −1-1 11 e(1112)e\left(\frac{11}{12}\right) e(115)e\left(\frac{1}{15}\right) e(1160)e\left(\frac{11}{60}\right) e(920)e\left(\frac{9}{20}\right) e(15)e\left(\frac{1}{5}\right) e(5960)e\left(\frac{59}{60}\right) e(715)e\left(\frac{7}{15}\right) e(130)e\left(\frac{1}{30}\right) e(720)e\left(\frac{7}{20}\right) e(1330)e\left(\frac{13}{30}\right)
χ1800(1103,⋅)\chi_{1800}(1103,\cdot) −1-1 11 e(712)e\left(\frac{7}{12}\right) e(1415)e\left(\frac{14}{15}\right) e(1960)e\left(\frac{19}{60}\right) e(120)e\left(\frac{1}{20}\right) e(45)e\left(\frac{4}{5}\right) e(3160)e\left(\frac{31}{60}\right) e(815)e\left(\frac{8}{15}\right) e(2930)e\left(\frac{29}{30}\right) e(320)e\left(\frac{3}{20}\right) e(1730)e\left(\frac{17}{30}\right)
χ1800(1127,⋅)\chi_{1800}(1127,\cdot) −1-1 11 e(512)e\left(\frac{5}{12}\right) e(715)e\left(\frac{7}{15}\right) e(1760)e\left(\frac{17}{60}\right) e(320)e\left(\frac{3}{20}\right) e(25)e\left(\frac{2}{5}\right) e(5360)e\left(\frac{53}{60}\right) e(415)e\left(\frac{4}{15}\right) e(730)e\left(\frac{7}{30}\right) e(920)e\left(\frac{9}{20}\right) e(130)e\left(\frac{1}{30}\right)
χ1800(1247,⋅)\chi_{1800}(1247,\cdot) −1-1 11 e(112)e\left(\frac{1}{12}\right) e(1415)e\left(\frac{14}{15}\right) e(4960)e\left(\frac{49}{60}\right) e(1120)e\left(\frac{11}{20}\right) e(45)e\left(\frac{4}{5}\right) e(160)e\left(\frac{1}{60}\right) e(815)e\left(\frac{8}{15}\right) e(2930)e\left(\frac{29}{30}\right) e(1320)e\left(\frac{13}{20}\right) e(1730)e\left(\frac{17}{30}\right)
χ1800(1463,⋅)\chi_{1800}(1463,\cdot) −1-1 11 e(712)e\left(\frac{7}{12}\right) e(815)e\left(\frac{8}{15}\right) e(4360)e\left(\frac{43}{60}\right) e(1720)e\left(\frac{17}{20}\right) e(35)e\left(\frac{3}{5}\right) e(760)e\left(\frac{7}{60}\right) e(1115)e\left(\frac{11}{15}\right) e(2330)e\left(\frac{23}{30}\right) e(1120)e\left(\frac{11}{20}\right) e(2930)e\left(\frac{29}{30}\right)
χ1800(1487,⋅)\chi_{1800}(1487,\cdot) −1-1 11 e(512)e\left(\frac{5}{12}\right) e(1315)e\left(\frac{13}{15}\right) e(5360)e\left(\frac{53}{60}\right) e(720)e\left(\frac{7}{20}\right) e(35)e\left(\frac{3}{5}\right) e(1760)e\left(\frac{17}{60}\right) e(115)e\left(\frac{1}{15}\right) e(1330)e\left(\frac{13}{30}\right) e(120)e\left(\frac{1}{20}\right) e(1930)e\left(\frac{19}{30}\right)
χ1800(1703,⋅)\chi_{1800}(1703,\cdot) −1-1 11 e(1112)e\left(\frac{11}{12}\right) e(415)e\left(\frac{4}{15}\right) e(5960)e\left(\frac{59}{60}\right) e(120)e\left(\frac{1}{20}\right) e(45)e\left(\frac{4}{5}\right) e(1160)e\left(\frac{11}{60}\right) e(1315)e\left(\frac{13}{15}\right) e(1930)e\left(\frac{19}{30}\right) e(320)e\left(\frac{3}{20}\right) e(730)e\left(\frac{7}{30}\right)