Basic properties
| Modulus: | \(6010\) | |
| Conductor: | \(601\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(300\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{601}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6010.db
\(\chi_{6010}(61,\cdot)\) \(\chi_{6010}(121,\cdot)\) \(\chi_{6010}(131,\cdot)\) \(\chi_{6010}(281,\cdot)\) \(\chi_{6010}(331,\cdot)\) \(\chi_{6010}(361,\cdot)\) \(\chi_{6010}(521,\cdot)\) \(\chi_{6010}(541,\cdot)\) \(\chi_{6010}(561,\cdot)\) \(\chi_{6010}(571,\cdot)\) \(\chi_{6010}(581,\cdot)\) \(\chi_{6010}(591,\cdot)\) \(\chi_{6010}(611,\cdot)\) \(\chi_{6010}(621,\cdot)\) \(\chi_{6010}(631,\cdot)\) \(\chi_{6010}(641,\cdot)\) \(\chi_{6010}(661,\cdot)\) \(\chi_{6010}(681,\cdot)\) \(\chi_{6010}(841,\cdot)\) \(\chi_{6010}(871,\cdot)\) \(\chi_{6010}(921,\cdot)\) \(\chi_{6010}(1071,\cdot)\) \(\chi_{6010}(1081,\cdot)\) \(\chi_{6010}(1141,\cdot)\) \(\chi_{6010}(1241,\cdot)\) \(\chi_{6010}(1251,\cdot)\) \(\chi_{6010}(1271,\cdot)\) \(\chi_{6010}(1351,\cdot)\) \(\chi_{6010}(1411,\cdot)\) \(\chi_{6010}(1541,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{300})$ |
| Fixed field: | Number field defined by a degree 300 polynomial (not computed) |
Values on generators
\((3607,2411)\) → \((1,e\left(\frac{113}{300}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6010 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{38}{75}\right)\) | \(e\left(\frac{113}{300}\right)\) | \(e\left(\frac{1}{75}\right)\) | \(e\left(\frac{41}{300}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{233}{300}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{13}{150}\right)\) | \(e\left(\frac{13}{25}\right)\) |