Basic properties
| Modulus: | \(4900\) | |
| Conductor: | \(4900\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4900.dj
\(\chi_{4900}(131,\cdot)\) \(\chi_{4900}(171,\cdot)\) \(\chi_{4900}(271,\cdot)\) \(\chi_{4900}(311,\cdot)\) \(\chi_{4900}(591,\cdot)\) \(\chi_{4900}(691,\cdot)\) \(\chi_{4900}(731,\cdot)\) \(\chi_{4900}(831,\cdot)\) \(\chi_{4900}(871,\cdot)\) \(\chi_{4900}(971,\cdot)\) \(\chi_{4900}(1111,\cdot)\) \(\chi_{4900}(1291,\cdot)\) \(\chi_{4900}(1431,\cdot)\) \(\chi_{4900}(1531,\cdot)\) \(\chi_{4900}(1571,\cdot)\) \(\chi_{4900}(1671,\cdot)\) \(\chi_{4900}(1711,\cdot)\) \(\chi_{4900}(1811,\cdot)\) \(\chi_{4900}(2091,\cdot)\) \(\chi_{4900}(2131,\cdot)\) \(\chi_{4900}(2231,\cdot)\) \(\chi_{4900}(2271,\cdot)\) \(\chi_{4900}(2411,\cdot)\) \(\chi_{4900}(2511,\cdot)\) \(\chi_{4900}(2691,\cdot)\) \(\chi_{4900}(2791,\cdot)\) \(\chi_{4900}(2831,\cdot)\) \(\chi_{4900}(2931,\cdot)\) \(\chi_{4900}(3071,\cdot)\) \(\chi_{4900}(3111,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((2451,1177,101)\) → \((-1,e\left(\frac{2}{5}\right),e\left(\frac{41}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 4900 }(131, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{199}{210}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{127}{210}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{209}{210}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{8}{15}\right)\) |