Basic properties
| Modulus: | \(6815\) | |
| Conductor: | \(6815\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(644\) | 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.cr
\(\chi_{6815}(3,\cdot)\) \(\chi_{6815}(27,\cdot)\) \(\chi_{6815}(37,\cdot)\) \(\chi_{6815}(97,\cdot)\) \(\chi_{6815}(98,\cdot)\) \(\chi_{6815}(102,\cdot)\) \(\chi_{6815}(108,\cdot)\) \(\chi_{6815}(118,\cdot)\) \(\chi_{6815}(148,\cdot)\) \(\chi_{6815}(192,\cdot)\) \(\chi_{6815}(242,\cdot)\) \(\chi_{6815}(243,\cdot)\) \(\chi_{6815}(247,\cdot)\) \(\chi_{6815}(253,\cdot)\) \(\chi_{6815}(263,\cdot)\) \(\chi_{6815}(333,\cdot)\) \(\chi_{6815}(337,\cdot)\) \(\chi_{6815}(338,\cdot)\) \(\chi_{6815}(388,\cdot)\) \(\chi_{6815}(392,\cdot)\) \(\chi_{6815}(408,\cdot)\) \(\chi_{6815}(432,\cdot)\) \(\chi_{6815}(472,\cdot)\) \(\chi_{6815}(478,\cdot)\) \(\chi_{6815}(482,\cdot)\) \(\chi_{6815}(533,\cdot)\) \(\chi_{6815}(553,\cdot)\) \(\chi_{6815}(617,\cdot)\) \(\chi_{6815}(623,\cdot)\) \(\chi_{6815}(627,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{644})$ |
| Fixed field: | Number field defined by a degree 644 polynomial (not computed) |
Values on generators
\((2727,2351,146)\) → \((i,e\left(\frac{3}{28}\right),e\left(\frac{21}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6815 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{255}{322}\right)\) | \(e\left(\frac{88}{161}\right)\) | \(e\left(\frac{94}{161}\right)\) | \(e\left(\frac{109}{322}\right)\) | \(e\left(\frac{485}{644}\right)\) | \(e\left(\frac{121}{322}\right)\) | \(e\left(\frac{15}{161}\right)\) | \(e\left(\frac{45}{644}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{465}{644}\right)\) |