↑

Properties

Label 4598.z
Modulus 45984598
Conductor 209209
Order 4545
Real no
Primitive no
Minimal no
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4598, base_ring=CyclotomicField(90))
 
M = H._module
 
chi = DirichletCharacter(H, M([54,40]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(9,4598))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 45984598
Conductor: 209209
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 4545
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 209.u
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ45)\Q(\zeta_{45})
Fixed field: 45.45.43679806300610465846484971330073185012597520004657724600953543350870941304329239684756561.1

Characters in Galois orbit

Character −1-1 11 33 55 77 99 1313 1515 1717 2121 2323 2525
χ4598(9,⋅)\chi_{4598}(9,\cdot) 11 11 e(2645)e\left(\frac{26}{45}\right) e(2345)e\left(\frac{23}{45}\right) e(1315)e\left(\frac{13}{15}\right) e(745)e\left(\frac{7}{45}\right) e(3745)e\left(\frac{37}{45}\right) e(445)e\left(\frac{4}{45}\right) e(3845)e\left(\frac{38}{45}\right) e(49)e\left(\frac{4}{9}\right) e(89)e\left(\frac{8}{9}\right) e(145)e\left(\frac{1}{45}\right)
χ4598(81,⋅)\chi_{4598}(81,\cdot) 11 11 e(745)e\left(\frac{7}{45}\right) e(145)e\left(\frac{1}{45}\right) e(1115)e\left(\frac{11}{15}\right) e(1445)e\left(\frac{14}{45}\right) e(2945)e\left(\frac{29}{45}\right) e(845)e\left(\frac{8}{45}\right) e(3145)e\left(\frac{31}{45}\right) e(89)e\left(\frac{8}{9}\right) e(79)e\left(\frac{7}{9}\right) e(245)e\left(\frac{2}{45}\right)
χ4598(245,⋅)\chi_{4598}(245,\cdot) 11 11 e(2845)e\left(\frac{28}{45}\right) e(445)e\left(\frac{4}{45}\right) e(1415)e\left(\frac{14}{15}\right) e(1145)e\left(\frac{11}{45}\right) e(2645)e\left(\frac{26}{45}\right) e(3245)e\left(\frac{32}{45}\right) e(3445)e\left(\frac{34}{45}\right) e(59)e\left(\frac{5}{9}\right) e(19)e\left(\frac{1}{9}\right) e(845)e\left(\frac{8}{45}\right)
χ4598(251,⋅)\chi_{4598}(251,\cdot) 11 11 e(1145)e\left(\frac{11}{45}\right) e(845)e\left(\frac{8}{45}\right) e(1315)e\left(\frac{13}{15}\right) e(2245)e\left(\frac{22}{45}\right) e(745)e\left(\frac{7}{45}\right) e(1945)e\left(\frac{19}{45}\right) e(2345)e\left(\frac{23}{45}\right) e(19)e\left(\frac{1}{9}\right) e(29)e\left(\frac{2}{9}\right) e(1645)e\left(\frac{16}{45}\right)
χ4598(511,⋅)\chi_{4598}(511,\cdot) 11 11 e(1945)e\left(\frac{19}{45}\right) e(2245)e\left(\frac{22}{45}\right) e(215)e\left(\frac{2}{15}\right) e(3845)e\left(\frac{38}{45}\right) e(845)e\left(\frac{8}{45}\right) e(4145)e\left(\frac{41}{45}\right) e(745)e\left(\frac{7}{45}\right) e(59)e\left(\frac{5}{9}\right) e(19)e\left(\frac{1}{9}\right) e(4445)e\left(\frac{44}{45}\right)
χ4598(807,⋅)\chi_{4598}(807,\cdot) 11 11 e(1745)e\left(\frac{17}{45}\right) e(4145)e\left(\frac{41}{45}\right) e(115)e\left(\frac{1}{15}\right) e(3445)e\left(\frac{34}{45}\right) e(1945)e\left(\frac{19}{45}\right) e(1345)e\left(\frac{13}{45}\right) e(1145)e\left(\frac{11}{45}\right) e(49)e\left(\frac{4}{9}\right) e(89)e\left(\frac{8}{9}\right) e(3745)e\left(\frac{37}{45}\right)
χ4598(1049,⋅)\chi_{4598}(1049,\cdot) 11 11 e(245)e\left(\frac{2}{45}\right) e(2645)e\left(\frac{26}{45}\right) e(115)e\left(\frac{1}{15}\right) e(445)e\left(\frac{4}{45}\right) e(3445)e\left(\frac{34}{45}\right) e(2845)e\left(\frac{28}{45}\right) e(4145)e\left(\frac{41}{45}\right) e(19)e\left(\frac{1}{9}\right) e(29)e\left(\frac{2}{9}\right) e(745)e\left(\frac{7}{45}\right)
χ4598(1213,⋅)\chi_{4598}(1213,\cdot) 11 11 e(1345)e\left(\frac{13}{45}\right) e(3445)e\left(\frac{34}{45}\right) e(1415)e\left(\frac{14}{15}\right) e(2645)e\left(\frac{26}{45}\right) e(4145)e\left(\frac{41}{45}\right) e(245)e\left(\frac{2}{45}\right) e(1945)e\left(\frac{19}{45}\right) e(29)e\left(\frac{2}{9}\right) e(49)e\left(\frac{4}{9}\right) e(2345)e\left(\frac{23}{45}\right)
χ4598(1461,⋅)\chi_{4598}(1461,\cdot) 11 11 e(145)e\left(\frac{1}{45}\right) e(1345)e\left(\frac{13}{45}\right) e(815)e\left(\frac{8}{15}\right) e(245)e\left(\frac{2}{45}\right) e(1745)e\left(\frac{17}{45}\right) e(1445)e\left(\frac{14}{45}\right) e(4345)e\left(\frac{43}{45}\right) e(59)e\left(\frac{5}{9}\right) e(19)e\left(\frac{1}{9}\right) e(2645)e\left(\frac{26}{45}\right)
χ4598(1479,⋅)\chi_{4598}(1479,\cdot) 11 11 e(445)e\left(\frac{4}{45}\right) e(745)e\left(\frac{7}{45}\right) e(215)e\left(\frac{2}{15}\right) e(845)e\left(\frac{8}{45}\right) e(2345)e\left(\frac{23}{45}\right) e(1145)e\left(\frac{11}{45}\right) e(3745)e\left(\frac{37}{45}\right) e(29)e\left(\frac{2}{9}\right) e(49)e\left(\frac{4}{9}\right) e(1445)e\left(\frac{14}{45}\right)
χ4598(1697,⋅)\chi_{4598}(1697,\cdot) 11 11 e(2345)e\left(\frac{23}{45}\right) e(2945)e\left(\frac{29}{45}\right) e(415)e\left(\frac{4}{15}\right) e(145)e\left(\frac{1}{45}\right) e(3145)e\left(\frac{31}{45}\right) e(745)e\left(\frac{7}{45}\right) e(4445)e\left(\frac{44}{45}\right) e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\right) e(1345)e\left(\frac{13}{45}\right)
χ4598(1963,⋅)\chi_{4598}(1963,\cdot) 11 11 e(1445)e\left(\frac{14}{45}\right) e(245)e\left(\frac{2}{45}\right) e(715)e\left(\frac{7}{15}\right) e(2845)e\left(\frac{28}{45}\right) e(1345)e\left(\frac{13}{45}\right) e(1645)e\left(\frac{16}{45}\right) e(1745)e\left(\frac{17}{45}\right) e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\right) e(445)e\left(\frac{4}{45}\right)
χ4598(2259,⋅)\chi_{4598}(2259,\cdot) 11 11 e(3745)e\left(\frac{37}{45}\right) e(3145)e\left(\frac{31}{45}\right) e(1115)e\left(\frac{11}{15}\right) e(2945)e\left(\frac{29}{45}\right) e(4445)e\left(\frac{44}{45}\right) e(2345)e\left(\frac{23}{45}\right) e(1645)e\left(\frac{16}{45}\right) e(59)e\left(\frac{5}{9}\right) e(19)e\left(\frac{1}{9}\right) e(1745)e\left(\frac{17}{45}\right)
χ4598(2429,⋅)\chi_{4598}(2429,\cdot) 11 11 e(3145)e\left(\frac{31}{45}\right) e(4345)e\left(\frac{43}{45}\right) e(815)e\left(\frac{8}{15}\right) e(1745)e\left(\frac{17}{45}\right) e(3245)e\left(\frac{32}{45}\right) e(2945)e\left(\frac{29}{45}\right) e(2845)e\left(\frac{28}{45}\right) e(29)e\left(\frac{2}{9}\right) e(49)e\left(\frac{4}{9}\right) e(4145)e\left(\frac{41}{45}\right)
χ4598(2665,⋅)\chi_{4598}(2665,\cdot) 11 11 e(4345)e\left(\frac{43}{45}\right) e(1945)e\left(\frac{19}{45}\right) e(1415)e\left(\frac{14}{15}\right) e(4145)e\left(\frac{41}{45}\right) e(1145)e\left(\frac{11}{45}\right) e(1745)e\left(\frac{17}{45}\right) e(445)e\left(\frac{4}{45}\right) e(89)e\left(\frac{8}{9}\right) e(79)e\left(\frac{7}{9}\right) e(3845)e\left(\frac{38}{45}\right)
χ4598(2913,⋅)\chi_{4598}(2913,\cdot) 11 11 e(4145)e\left(\frac{41}{45}\right) e(3845)e\left(\frac{38}{45}\right) e(1315)e\left(\frac{13}{15}\right) e(3745)e\left(\frac{37}{45}\right) e(2245)e\left(\frac{22}{45}\right) e(3445)e\left(\frac{34}{45}\right) e(845)e\left(\frac{8}{45}\right) e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\right) e(3145)e\left(\frac{31}{45}\right)
χ4598(2931,⋅)\chi_{4598}(2931,\cdot) 11 11 e(3445)e\left(\frac{34}{45}\right) e(3745)e\left(\frac{37}{45}\right) e(215)e\left(\frac{2}{15}\right) e(2345)e\left(\frac{23}{45}\right) e(3845)e\left(\frac{38}{45}\right) e(2645)e\left(\frac{26}{45}\right) e(2245)e\left(\frac{22}{45}\right) e(89)e\left(\frac{8}{9}\right) e(79)e\left(\frac{7}{9}\right) e(2945)e\left(\frac{29}{45}\right)
χ4598(3227,⋅)\chi_{4598}(3227,\cdot) 11 11 e(2245)e\left(\frac{22}{45}\right) e(1645)e\left(\frac{16}{45}\right) e(1115)e\left(\frac{11}{15}\right) e(4445)e\left(\frac{44}{45}\right) e(1445)e\left(\frac{14}{45}\right) e(3845)e\left(\frac{38}{45}\right) e(145)e\left(\frac{1}{45}\right) e(29)e\left(\frac{2}{9}\right) e(49)e\left(\frac{4}{9}\right) e(3245)e\left(\frac{32}{45}\right)
χ4598(3391,⋅)\chi_{4598}(3391,\cdot) 11 11 e(845)e\left(\frac{8}{45}\right) e(1445)e\left(\frac{14}{45}\right) e(415)e\left(\frac{4}{15}\right) e(1645)e\left(\frac{16}{45}\right) e(145)e\left(\frac{1}{45}\right) e(2245)e\left(\frac{22}{45}\right) e(2945)e\left(\frac{29}{45}\right) e(49)e\left(\frac{4}{9}\right) e(89)e\left(\frac{8}{9}\right) e(2845)e\left(\frac{28}{45}\right)
χ4598(3633,⋅)\chi_{4598}(3633,\cdot) 11 11 e(3845)e\left(\frac{38}{45}\right) e(4445)e\left(\frac{44}{45}\right) e(415)e\left(\frac{4}{15}\right) e(3145)e\left(\frac{31}{45}\right) e(1645)e\left(\frac{16}{45}\right) e(3745)e\left(\frac{37}{45}\right) e(1445)e\left(\frac{14}{45}\right) e(19)e\left(\frac{1}{9}\right) e(29)e\left(\frac{2}{9}\right) e(4345)e\left(\frac{43}{45}\right)
χ4598(3657,⋅)\chi_{4598}(3657,\cdot) 11 11 e(4445)e\left(\frac{44}{45}\right) e(3245)e\left(\frac{32}{45}\right) e(715)e\left(\frac{7}{15}\right) e(4345)e\left(\frac{43}{45}\right) e(2845)e\left(\frac{28}{45}\right) e(3145)e\left(\frac{31}{45}\right) e(245)e\left(\frac{2}{45}\right) e(49)e\left(\frac{4}{9}\right) e(89)e\left(\frac{8}{9}\right) e(1945)e\left(\frac{19}{45}\right)
χ4598(3711,⋅)\chi_{4598}(3711,\cdot) 11 11 e(3245)e\left(\frac{32}{45}\right) e(1145)e\left(\frac{11}{45}\right) e(115)e\left(\frac{1}{15}\right) e(1945)e\left(\frac{19}{45}\right) e(445)e\left(\frac{4}{45}\right) e(4345)e\left(\frac{43}{45}\right) e(2645)e\left(\frac{26}{45}\right) e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\right) e(2245)e\left(\frac{22}{45}\right)
χ4598(3881,⋅)\chi_{4598}(3881,\cdot) 11 11 e(1645)e\left(\frac{16}{45}\right) e(2845)e\left(\frac{28}{45}\right) e(815)e\left(\frac{8}{15}\right) e(3245)e\left(\frac{32}{45}\right) e(245)e\left(\frac{2}{45}\right) e(4445)e\left(\frac{44}{45}\right) e(1345)e\left(\frac{13}{45}\right) e(89)e\left(\frac{8}{9}\right) e(79)e\left(\frac{7}{9}\right) e(1145)e\left(\frac{11}{45}\right)
χ4598(3899,⋅)\chi_{4598}(3899,\cdot) 11 11 e(2945)e\left(\frac{29}{45}\right) e(1745)e\left(\frac{17}{45}\right) e(715)e\left(\frac{7}{15}\right) e(1345)e\left(\frac{13}{45}\right) e(4345)e\left(\frac{43}{45}\right) e(145)e\left(\frac{1}{45}\right) e(3245)e\left(\frac{32}{45}\right) e(19)e\left(\frac{1}{9}\right) e(29)e\left(\frac{2}{9}\right) e(3445)e\left(\frac{34}{45}\right)