Properties

Label 4334.485
Modulus 43344334
Conductor 197197
Order 196196
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4334, base_ring=CyclotomicField(196))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,171]))
 
pari: [g,chi] = znchar(Mod(485,4334))
 

Basic properties

Modulus: 43344334
Conductor: 197197
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 196196
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from χ197(91,)\chi_{197}(91,\cdot)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4334.bd

χ4334(45,)\chi_{4334}(45,\cdot) χ4334(67,)\chi_{4334}(67,\cdot) χ4334(89,)\chi_{4334}(89,\cdot) χ4334(111,)\chi_{4334}(111,\cdot) χ4334(199,)\chi_{4334}(199,\cdot) χ4334(243,)\chi_{4334}(243,\cdot) χ4334(397,)\chi_{4334}(397,\cdot) χ4334(485,)\chi_{4334}(485,\cdot) χ4334(573,)\chi_{4334}(573,\cdot) χ4334(639,)\chi_{4334}(639,\cdot) χ4334(771,)\chi_{4334}(771,\cdot) χ4334(793,)\chi_{4334}(793,\cdot) χ4334(815,)\chi_{4334}(815,\cdot) χ4334(859,)\chi_{4334}(859,\cdot) χ4334(903,)\chi_{4334}(903,\cdot) χ4334(947,)\chi_{4334}(947,\cdot) χ4334(1035,)\chi_{4334}(1035,\cdot) χ4334(1057,)\chi_{4334}(1057,\cdot) χ4334(1079,)\chi_{4334}(1079,\cdot) χ4334(1255,)\chi_{4334}(1255,\cdot) χ4334(1277,)\chi_{4334}(1277,\cdot) χ4334(1299,)\chi_{4334}(1299,\cdot) χ4334(1321,)\chi_{4334}(1321,\cdot) χ4334(1387,)\chi_{4334}(1387,\cdot) χ4334(1409,)\chi_{4334}(1409,\cdot) χ4334(1431,)\chi_{4334}(1431,\cdot) χ4334(1453,)\chi_{4334}(1453,\cdot) χ4334(1497,)\chi_{4334}(1497,\cdot) χ4334(1519,)\chi_{4334}(1519,\cdot) χ4334(1541,)\chi_{4334}(1541,\cdot) ...

sage: chi.galois_orbit()
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: Q(ζ196)\Q(\zeta_{196})
Fixed field: Number field defined by a degree 196 polynomial (not computed)

Values on generators

(1971,199)(1971,199)(1,e(171196))(1,e\left(\frac{171}{196}\right))

First values

aa 1-11133557799131315151717191921212323
χ4334(485,a) \chi_{ 4334 }(485, a) 1-111e(179196)e\left(\frac{179}{196}\right)e(127196)e\left(\frac{127}{196}\right)e(3798)e\left(\frac{37}{98}\right)e(8198)e\left(\frac{81}{98}\right)e(159196)e\left(\frac{159}{196}\right)e(5598)e\left(\frac{55}{98}\right)e(141196)e\left(\frac{141}{196}\right)e(514)e\left(\frac{5}{14}\right)e(57196)e\left(\frac{57}{196}\right)e(3449)e\left(\frac{34}{49}\right)
sage: chi.jacobi_sum(n)
 
χ4334(485,a)   \chi_{ 4334 }(485,a) \; at   a=\;a = e.g. 2