Basic properties
| Modulus: | \(5390\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5390.dn
\(\chi_{5390}(61,\cdot)\) \(\chi_{5390}(101,\cdot)\) \(\chi_{5390}(171,\cdot)\) \(\chi_{5390}(271,\cdot)\) \(\chi_{5390}(381,\cdot)\) \(\chi_{5390}(481,\cdot)\) \(\chi_{5390}(591,\cdot)\) \(\chi_{5390}(761,\cdot)\) \(\chi_{5390}(831,\cdot)\) \(\chi_{5390}(871,\cdot)\) \(\chi_{5390}(941,\cdot)\) \(\chi_{5390}(1041,\cdot)\) \(\chi_{5390}(1151,\cdot)\) \(\chi_{5390}(1251,\cdot)\) \(\chi_{5390}(1361,\cdot)\) \(\chi_{5390}(1531,\cdot)\) \(\chi_{5390}(1601,\cdot)\) \(\chi_{5390}(1641,\cdot)\) \(\chi_{5390}(1711,\cdot)\) \(\chi_{5390}(1811,\cdot)\) \(\chi_{5390}(1921,\cdot)\) \(\chi_{5390}(2021,\cdot)\) \(\chi_{5390}(2131,\cdot)\) \(\chi_{5390}(2301,\cdot)\) \(\chi_{5390}(2411,\cdot)\) \(\chi_{5390}(2581,\cdot)\) \(\chi_{5390}(2691,\cdot)\) \(\chi_{5390}(2791,\cdot)\) \(\chi_{5390}(2901,\cdot)\) \(\chi_{5390}(3071,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((2157,4511,981)\) → \((1,e\left(\frac{11}{42}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 5390 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{210}\right)\) | \(e\left(\frac{97}{105}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{19}{105}\right)\) |