Basic properties
| Modulus: | \(4018\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(420\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2009}(39,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4018.cj
\(\chi_{4018}(39,\cdot)\) \(\chi_{4018}(121,\cdot)\) \(\chi_{4018}(207,\cdot)\) \(\chi_{4018}(289,\cdot)\) \(\chi_{4018}(333,\cdot)\) \(\chi_{4018}(389,\cdot)\) \(\chi_{4018}(415,\cdot)\) \(\chi_{4018}(431,\cdot)\) \(\chi_{4018}(443,\cdot)\) \(\chi_{4018}(487,\cdot)\) \(\chi_{4018}(513,\cdot)\) \(\chi_{4018}(541,\cdot)\) \(\chi_{4018}(613,\cdot)\) \(\chi_{4018}(695,\cdot)\) \(\chi_{4018}(781,\cdot)\) \(\chi_{4018}(907,\cdot)\) \(\chi_{4018}(935,\cdot)\) \(\chi_{4018}(963,\cdot)\) \(\chi_{4018}(989,\cdot)\) \(\chi_{4018}(1005,\cdot)\) \(\chi_{4018}(1017,\cdot)\) \(\chi_{4018}(1033,\cdot)\) \(\chi_{4018}(1045,\cdot)\) \(\chi_{4018}(1061,\cdot)\) \(\chi_{4018}(1087,\cdot)\) \(\chi_{4018}(1115,\cdot)\) \(\chi_{4018}(1143,\cdot)\) \(\chi_{4018}(1187,\cdot)\) \(\chi_{4018}(1269,\cdot)\) \(\chi_{4018}(1355,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{17}{21}\right),e\left(\frac{3}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 4018 }(39, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{163}{210}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{349}{420}\right)\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{79}{420}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{58}{105}\right)\) |