Basic properties
| Modulus: | \(6019\) | |
| Conductor: | \(463\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(77\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{463}(66,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6019.cw
\(\chi_{6019}(66,\cdot)\) \(\chi_{6019}(144,\cdot)\) \(\chi_{6019}(209,\cdot)\) \(\chi_{6019}(313,\cdot)\) \(\chi_{6019}(456,\cdot)\) \(\chi_{6019}(521,\cdot)\) \(\chi_{6019}(547,\cdot)\) \(\chi_{6019}(560,\cdot)\) \(\chi_{6019}(586,\cdot)\) \(\chi_{6019}(612,\cdot)\) \(\chi_{6019}(729,\cdot)\) \(\chi_{6019}(742,\cdot)\) \(\chi_{6019}(820,\cdot)\) \(\chi_{6019}(846,\cdot)\) \(\chi_{6019}(1366,\cdot)\) \(\chi_{6019}(1379,\cdot)\) \(\chi_{6019}(1509,\cdot)\) \(\chi_{6019}(1535,\cdot)\) \(\chi_{6019}(1548,\cdot)\) \(\chi_{6019}(1665,\cdot)\) \(\chi_{6019}(1756,\cdot)\) \(\chi_{6019}(1769,\cdot)\) \(\chi_{6019}(1808,\cdot)\) \(\chi_{6019}(1860,\cdot)\) \(\chi_{6019}(1899,\cdot)\) \(\chi_{6019}(1938,\cdot)\) \(\chi_{6019}(2094,\cdot)\) \(\chi_{6019}(2198,\cdot)\) \(\chi_{6019}(2263,\cdot)\) \(\chi_{6019}(2380,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 77 polynomial |
Values on generators
\((2316,1392)\) → \((1,e\left(\frac{13}{77}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6019 }(66, a) \) | \(1\) | \(1\) | \(e\left(\frac{57}{77}\right)\) | \(e\left(\frac{13}{77}\right)\) | \(e\left(\frac{37}{77}\right)\) | \(e\left(\frac{8}{77}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{64}{77}\right)\) | \(e\left(\frac{17}{77}\right)\) | \(e\left(\frac{26}{77}\right)\) | \(e\left(\frac{65}{77}\right)\) | \(e\left(\frac{20}{77}\right)\) |