Basic properties
| Modulus: | \(6815\) | |
| Conductor: | \(6815\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(322\) | 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 6815.cn
\(\chi_{6815}(4,\cdot)\) \(\chi_{6815}(9,\cdot)\) \(\chi_{6815}(34,\cdot)\) \(\chi_{6815}(64,\cdot)\) \(\chi_{6815}(149,\cdot)\) \(\chi_{6815}(209,\cdot)\) \(\chi_{6815}(294,\cdot)\) \(\chi_{6815}(299,\cdot)\) \(\chi_{6815}(324,\cdot)\) \(\chi_{6815}(354,\cdot)\) \(\chi_{6815}(439,\cdot)\) \(\chi_{6815}(444,\cdot)\) \(\chi_{6815}(544,\cdot)\) \(\chi_{6815}(589,\cdot)\) \(\chi_{6815}(614,\cdot)\) \(\chi_{6815}(709,\cdot)\) \(\chi_{6815}(729,\cdot)\) \(\chi_{6815}(759,\cdot)\) \(\chi_{6815}(789,\cdot)\) \(\chi_{6815}(854,\cdot)\) \(\chi_{6815}(874,\cdot)\) \(\chi_{6815}(999,\cdot)\) \(\chi_{6815}(1019,\cdot)\) \(\chi_{6815}(1024,\cdot)\) \(\chi_{6815}(1144,\cdot)\) \(\chi_{6815}(1164,\cdot)\) \(\chi_{6815}(1224,\cdot)\) \(\chi_{6815}(1369,\cdot)\) \(\chi_{6815}(1414,\cdot)\) \(\chi_{6815}(1434,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{161})$ |
| Fixed field: | Number field defined by a degree 322 polynomial (not computed) |
Values on generators
\((2727,2351,146)\) → \((-1,e\left(\frac{1}{14}\right),e\left(\frac{18}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6815 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{106}{161}\right)\) | \(e\left(\frac{82}{161}\right)\) | \(e\left(\frac{51}{161}\right)\) | \(e\left(\frac{27}{161}\right)\) | \(e\left(\frac{129}{322}\right)\) | \(e\left(\frac{157}{161}\right)\) | \(e\left(\frac{3}{161}\right)\) | \(e\left(\frac{85}{322}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{127}{322}\right)\) |