Basic properties
| Modulus: | \(6026\) | |
| Conductor: | \(3013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3013}(201,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6026.t
\(\chi_{6026}(201,\cdot)\) \(\chi_{6026}(435,\cdot)\) \(\chi_{6026}(471,\cdot)\) \(\chi_{6026}(697,\cdot)\) \(\chi_{6026}(733,\cdot)\) \(\chi_{6026}(987,\cdot)\) \(\chi_{6026}(1121,\cdot)\) \(\chi_{6026}(1249,\cdot)\) \(\chi_{6026}(1257,\cdot)\) \(\chi_{6026}(1483,\cdot)\) \(\chi_{6026}(1745,\cdot)\) \(\chi_{6026}(1781,\cdot)\) \(\chi_{6026}(1907,\cdot)\) \(\chi_{6026}(2035,\cdot)\) \(\chi_{6026}(2043,\cdot)\) \(\chi_{6026}(2169,\cdot)\) \(\chi_{6026}(2269,\cdot)\) \(\chi_{6026}(2297,\cdot)\) \(\chi_{6026}(2305,\cdot)\) \(\chi_{6026}(2567,\cdot)\) \(\chi_{6026}(2793,\cdot)\) \(\chi_{6026}(2821,\cdot)\) \(\chi_{6026}(2955,\cdot)\) \(\chi_{6026}(3055,\cdot)\) \(\chi_{6026}(3217,\cdot)\) \(\chi_{6026}(3317,\cdot)\) \(\chi_{6026}(3345,\cdot)\) \(\chi_{6026}(3579,\cdot)\) \(\chi_{6026}(3607,\cdot)\) \(\chi_{6026}(3741,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((787,4325)\) → \((e\left(\frac{7}{22}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6026 }(201, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{103}{110}\right)\) |