Basic properties
| Modulus: | \(6019\) | |
| Conductor: | \(6019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | 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.do
\(\chi_{6019}(64,\cdot)\) \(\chi_{6019}(272,\cdot)\) \(\chi_{6019}(324,\cdot)\) \(\chi_{6019}(376,\cdot)\) \(\chi_{6019}(389,\cdot)\) \(\chi_{6019}(740,\cdot)\) \(\chi_{6019}(844,\cdot)\) \(\chi_{6019}(870,\cdot)\) \(\chi_{6019}(1026,\cdot)\) \(\chi_{6019}(1260,\cdot)\) \(\chi_{6019}(1377,\cdot)\) \(\chi_{6019}(1455,\cdot)\) \(\chi_{6019}(1533,\cdot)\) \(\chi_{6019}(1598,\cdot)\) \(\chi_{6019}(1702,\cdot)\) \(\chi_{6019}(1845,\cdot)\) \(\chi_{6019}(1910,\cdot)\) \(\chi_{6019}(1936,\cdot)\) \(\chi_{6019}(1949,\cdot)\) \(\chi_{6019}(1975,\cdot)\) \(\chi_{6019}(2001,\cdot)\) \(\chi_{6019}(2118,\cdot)\) \(\chi_{6019}(2131,\cdot)\) \(\chi_{6019}(2209,\cdot)\) \(\chi_{6019}(2235,\cdot)\) \(\chi_{6019}(2755,\cdot)\) \(\chi_{6019}(2768,\cdot)\) \(\chi_{6019}(2898,\cdot)\) \(\chi_{6019}(2924,\cdot)\) \(\chi_{6019}(2937,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((2316,1392)\) → \((-1,e\left(\frac{34}{77}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6019 }(64, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{154}\right)\) | \(e\left(\frac{34}{77}\right)\) | \(e\left(\frac{2}{77}\right)\) | \(e\left(\frac{107}{154}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{9}{154}\right)\) | \(e\left(\frac{83}{154}\right)\) | \(e\left(\frac{68}{77}\right)\) | \(e\left(\frac{16}{77}\right)\) | \(e\left(\frac{75}{154}\right)\) |