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Properties

Label 2600.fk
Modulus 26002600
Conductor 325325
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(2600, base_ring=CyclotomicField(60))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,27,55]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(137,2600))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 26002600
Conductor: 325325
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 6060
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 325.bi
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 33 77 99 1111 1717 1919 2121 2323 2727 2929
χ2600(137,⋅)\chi_{2600}(137,\cdot) 11 11 e(4960)e\left(\frac{49}{60}\right) e(13)e\left(\frac{1}{3}\right) e(1930)e\left(\frac{19}{30}\right) e(3760)e\left(\frac{37}{60}\right) e(4160)e\left(\frac{41}{60}\right) e(4160)e\left(\frac{41}{60}\right) e(320)e\left(\frac{3}{20}\right) e(760)e\left(\frac{7}{60}\right) e(920)e\left(\frac{9}{20}\right) e(1730)e\left(\frac{17}{30}\right)
χ2600(297,⋅)\chi_{2600}(297,\cdot) 11 11 e(1760)e\left(\frac{17}{60}\right) e(23)e\left(\frac{2}{3}\right) e(1730)e\left(\frac{17}{30}\right) e(4160)e\left(\frac{41}{60}\right) e(1360)e\left(\frac{13}{60}\right) e(1360)e\left(\frac{13}{60}\right) e(1920)e\left(\frac{19}{20}\right) e(1160)e\left(\frac{11}{60}\right) e(1720)e\left(\frac{17}{20}\right) e(130)e\left(\frac{1}{30}\right)
χ2600(353,⋅)\chi_{2600}(353,\cdot) 11 11 e(4760)e\left(\frac{47}{60}\right) e(23)e\left(\frac{2}{3}\right) e(1730)e\left(\frac{17}{30}\right) e(1160)e\left(\frac{11}{60}\right) e(4360)e\left(\frac{43}{60}\right) e(4360)e\left(\frac{43}{60}\right) e(920)e\left(\frac{9}{20}\right) e(4160)e\left(\frac{41}{60}\right) e(720)e\left(\frac{7}{20}\right) e(130)e\left(\frac{1}{30}\right)
χ2600(513,⋅)\chi_{2600}(513,\cdot) 11 11 e(1960)e\left(\frac{19}{60}\right) e(13)e\left(\frac{1}{3}\right) e(1930)e\left(\frac{19}{30}\right) e(760)e\left(\frac{7}{60}\right) e(1160)e\left(\frac{11}{60}\right) e(1160)e\left(\frac{11}{60}\right) e(1320)e\left(\frac{13}{20}\right) e(3760)e\left(\frac{37}{60}\right) e(1920)e\left(\frac{19}{20}\right) e(1730)e\left(\frac{17}{30}\right)
χ2600(817,⋅)\chi_{2600}(817,\cdot) 11 11 e(5360)e\left(\frac{53}{60}\right) e(23)e\left(\frac{2}{3}\right) e(2330)e\left(\frac{23}{30}\right) e(2960)e\left(\frac{29}{60}\right) e(3760)e\left(\frac{37}{60}\right) e(3760)e\left(\frac{37}{60}\right) e(1120)e\left(\frac{11}{20}\right) e(5960)e\left(\frac{59}{60}\right) e(1320)e\left(\frac{13}{20}\right) e(1930)e\left(\frac{19}{30}\right)
χ2600(873,⋅)\chi_{2600}(873,\cdot) 11 11 e(1160)e\left(\frac{11}{60}\right) e(23)e\left(\frac{2}{3}\right) e(1130)e\left(\frac{11}{30}\right) e(2360)e\left(\frac{23}{60}\right) e(1960)e\left(\frac{19}{60}\right) e(1960)e\left(\frac{19}{60}\right) e(1720)e\left(\frac{17}{20}\right) e(5360)e\left(\frac{53}{60}\right) e(1120)e\left(\frac{11}{20}\right) e(1330)e\left(\frac{13}{30}\right)
χ2600(1033,⋅)\chi_{2600}(1033,\cdot) 11 11 e(4360)e\left(\frac{43}{60}\right) e(13)e\left(\frac{1}{3}\right) e(1330)e\left(\frac{13}{30}\right) e(1960)e\left(\frac{19}{60}\right) e(4760)e\left(\frac{47}{60}\right) e(4760)e\left(\frac{47}{60}\right) e(120)e\left(\frac{1}{20}\right) e(4960)e\left(\frac{49}{60}\right) e(320)e\left(\frac{3}{20}\right) e(2930)e\left(\frac{29}{30}\right)
χ2600(1177,⋅)\chi_{2600}(1177,\cdot) 11 11 e(160)e\left(\frac{1}{60}\right) e(13)e\left(\frac{1}{3}\right) e(130)e\left(\frac{1}{30}\right) e(1360)e\left(\frac{13}{60}\right) e(2960)e\left(\frac{29}{60}\right) e(2960)e\left(\frac{29}{60}\right) e(720)e\left(\frac{7}{20}\right) e(4360)e\left(\frac{43}{60}\right) e(120)e\left(\frac{1}{20}\right) e(2330)e\left(\frac{23}{30}\right)
χ2600(1337,⋅)\chi_{2600}(1337,\cdot) 11 11 e(2960)e\left(\frac{29}{60}\right) e(23)e\left(\frac{2}{3}\right) e(2930)e\left(\frac{29}{30}\right) e(1760)e\left(\frac{17}{60}\right) e(160)e\left(\frac{1}{60}\right) e(160)e\left(\frac{1}{60}\right) e(320)e\left(\frac{3}{20}\right) e(4760)e\left(\frac{47}{60}\right) e(920)e\left(\frac{9}{20}\right) e(730)e\left(\frac{7}{30}\right)
χ2600(1553,⋅)\chi_{2600}(1553,\cdot) 11 11 e(760)e\left(\frac{7}{60}\right) e(13)e\left(\frac{1}{3}\right) e(730)e\left(\frac{7}{30}\right) e(3160)e\left(\frac{31}{60}\right) e(2360)e\left(\frac{23}{60}\right) e(2360)e\left(\frac{23}{60}\right) e(920)e\left(\frac{9}{20}\right) e(160)e\left(\frac{1}{60}\right) e(720)e\left(\frac{7}{20}\right) e(1130)e\left(\frac{11}{30}\right)
χ2600(1697,⋅)\chi_{2600}(1697,\cdot) 11 11 e(3760)e\left(\frac{37}{60}\right) e(13)e\left(\frac{1}{3}\right) e(730)e\left(\frac{7}{30}\right) e(160)e\left(\frac{1}{60}\right) e(5360)e\left(\frac{53}{60}\right) e(5360)e\left(\frac{53}{60}\right) e(1920)e\left(\frac{19}{20}\right) e(3160)e\left(\frac{31}{60}\right) e(1720)e\left(\frac{17}{20}\right) e(1130)e\left(\frac{11}{30}\right)
χ2600(1913,⋅)\chi_{2600}(1913,\cdot) 11 11 e(5960)e\left(\frac{59}{60}\right) e(23)e\left(\frac{2}{3}\right) e(2930)e\left(\frac{29}{30}\right) e(4760)e\left(\frac{47}{60}\right) e(3160)e\left(\frac{31}{60}\right) e(3160)e\left(\frac{31}{60}\right) e(1320)e\left(\frac{13}{20}\right) e(1760)e\left(\frac{17}{60}\right) e(1920)e\left(\frac{19}{20}\right) e(730)e\left(\frac{7}{30}\right)
χ2600(2073,⋅)\chi_{2600}(2073,\cdot) 11 11 e(3160)e\left(\frac{31}{60}\right) e(13)e\left(\frac{1}{3}\right) e(130)e\left(\frac{1}{30}\right) e(4360)e\left(\frac{43}{60}\right) e(5960)e\left(\frac{59}{60}\right) e(5960)e\left(\frac{59}{60}\right) e(1720)e\left(\frac{17}{20}\right) e(1360)e\left(\frac{13}{60}\right) e(1120)e\left(\frac{11}{20}\right) e(2330)e\left(\frac{23}{30}\right)
χ2600(2217,⋅)\chi_{2600}(2217,\cdot) 11 11 e(1360)e\left(\frac{13}{60}\right) e(13)e\left(\frac{1}{3}\right) e(1330)e\left(\frac{13}{30}\right) e(4960)e\left(\frac{49}{60}\right) e(1760)e\left(\frac{17}{60}\right) e(1760)e\left(\frac{17}{60}\right) e(1120)e\left(\frac{11}{20}\right) e(1960)e\left(\frac{19}{60}\right) e(1320)e\left(\frac{13}{20}\right) e(2930)e\left(\frac{29}{30}\right)
χ2600(2377,⋅)\chi_{2600}(2377,\cdot) 11 11 e(4160)e\left(\frac{41}{60}\right) e(23)e\left(\frac{2}{3}\right) e(1130)e\left(\frac{11}{30}\right) e(5360)e\left(\frac{53}{60}\right) e(4960)e\left(\frac{49}{60}\right) e(4960)e\left(\frac{49}{60}\right) e(720)e\left(\frac{7}{20}\right) e(2360)e\left(\frac{23}{60}\right) e(120)e\left(\frac{1}{20}\right) e(1330)e\left(\frac{13}{30}\right)
χ2600(2433,⋅)\chi_{2600}(2433,\cdot) 11 11 e(2360)e\left(\frac{23}{60}\right) e(23)e\left(\frac{2}{3}\right) e(2330)e\left(\frac{23}{30}\right) e(5960)e\left(\frac{59}{60}\right) e(760)e\left(\frac{7}{60}\right) e(760)e\left(\frac{7}{60}\right) e(120)e\left(\frac{1}{20}\right) e(2960)e\left(\frac{29}{60}\right) e(320)e\left(\frac{3}{20}\right) e(1930)e\left(\frac{19}{30}\right)