Basic properties
| Modulus: | \(2997\) | |
| Conductor: | \(2997\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2997.fn
\(\chi_{2997}(22,\cdot)\) \(\chi_{2997}(61,\cdot)\) \(\chi_{2997}(241,\cdot)\) \(\chi_{2997}(553,\cdot)\) \(\chi_{2997}(742,\cdot)\) \(\chi_{2997}(745,\cdot)\) \(\chi_{2997}(760,\cdot)\) \(\chi_{2997}(772,\cdot)\) \(\chi_{2997}(790,\cdot)\) \(\chi_{2997}(868,\cdot)\) \(\chi_{2997}(940,\cdot)\) \(\chi_{2997}(943,\cdot)\) \(\chi_{2997}(1021,\cdot)\) \(\chi_{2997}(1060,\cdot)\) \(\chi_{2997}(1240,\cdot)\) \(\chi_{2997}(1552,\cdot)\) \(\chi_{2997}(1741,\cdot)\) \(\chi_{2997}(1744,\cdot)\) \(\chi_{2997}(1759,\cdot)\) \(\chi_{2997}(1771,\cdot)\) \(\chi_{2997}(1789,\cdot)\) \(\chi_{2997}(1867,\cdot)\) \(\chi_{2997}(1939,\cdot)\) \(\chi_{2997}(1942,\cdot)\) \(\chi_{2997}(2020,\cdot)\) \(\chi_{2997}(2059,\cdot)\) \(\chi_{2997}(2239,\cdot)\) \(\chi_{2997}(2551,\cdot)\) \(\chi_{2997}(2740,\cdot)\) \(\chi_{2997}(2743,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1703,1297)\) → \((e\left(\frac{19}{27}\right),e\left(\frac{7}{36}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2997 }(868, a) \) | \(-1\) | \(1\) | \(e\left(\frac{97}{108}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{71}{108}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{83}{108}\right)\) | \(e\left(\frac{41}{108}\right)\) | \(e\left(\frac{16}{27}\right)\) |