Basic properties
| Modulus: | \(6019\) | |
| Conductor: | \(6019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | 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 6019.dg
\(\chi_{6019}(148,\cdot)\) \(\chi_{6019}(320,\cdot)\) \(\chi_{6019}(330,\cdot)\) \(\chi_{6019}(369,\cdot)\) \(\chi_{6019}(395,\cdot)\) \(\chi_{6019}(424,\cdot)\) \(\chi_{6019}(697,\cdot)\) \(\chi_{6019}(798,\cdot)\) \(\chi_{6019}(1019,\cdot)\) \(\chi_{6019}(1074,\cdot)\) \(\chi_{6019}(1256,\cdot)\) \(\chi_{6019}(1295,\cdot)\) \(\chi_{6019}(1321,\cdot)\) \(\chi_{6019}(1724,\cdot)\) \(\chi_{6019}(1942,\cdot)\) \(\chi_{6019}(1945,\cdot)\) \(\chi_{6019}(2683,\cdot)\) \(\chi_{6019}(2868,\cdot)\) \(\chi_{6019}(3047,\cdot)\) \(\chi_{6019}(3164,\cdot)\) \(\chi_{6019}(3411,\cdot)\) \(\chi_{6019}(3476,\cdot)\) \(\chi_{6019}(3609,\cdot)\) \(\chi_{6019}(3710,\cdot)\) \(\chi_{6019}(3973,\cdot)\) \(\chi_{6019}(4035,\cdot)\) \(\chi_{6019}(4090,\cdot)\) \(\chi_{6019}(4337,\cdot)\) \(\chi_{6019}(4402,\cdot)\) \(\chi_{6019}(4451,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2316,1392)\) → \((-i,e\left(\frac{7}{66}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6019 }(148, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{132}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{1}{132}\right)\) | \(e\left(\frac{61}{132}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{107}{132}\right)\) |