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.cs
\(\chi_{6815}(19,\cdot)\) \(\chi_{6815}(39,\cdot)\) \(\chi_{6815}(44,\cdot)\) \(\chi_{6815}(69,\cdot)\) \(\chi_{6815}(114,\cdot)\) \(\chi_{6815}(124,\cdot)\) \(\chi_{6815}(134,\cdot)\) \(\chi_{6815}(164,\cdot)\) \(\chi_{6815}(184,\cdot)\) \(\chi_{6815}(214,\cdot)\) \(\chi_{6815}(229,\cdot)\) \(\chi_{6815}(264,\cdot)\) \(\chi_{6815}(279,\cdot)\) \(\chi_{6815}(304,\cdot)\) \(\chi_{6815}(334,\cdot)\) \(\chi_{6815}(359,\cdot)\) \(\chi_{6815}(369,\cdot)\) \(\chi_{6815}(374,\cdot)\) \(\chi_{6815}(409,\cdot)\) \(\chi_{6815}(414,\cdot)\) \(\chi_{6815}(449,\cdot)\) \(\chi_{6815}(454,\cdot)\) \(\chi_{6815}(514,\cdot)\) \(\chi_{6815}(569,\cdot)\) \(\chi_{6815}(594,\cdot)\) \(\chi_{6815}(599,\cdot)\) \(\chi_{6815}(624,\cdot)\) \(\chi_{6815}(649,\cdot)\) \(\chi_{6815}(669,\cdot)\) \(\chi_{6815}(699,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{644})$ |
| Fixed field: | Number field defined by a degree 644 polynomial (not computed) |
Values on generators
\((2727,2351,146)\) → \((-1,e\left(\frac{9}{28}\right),e\left(\frac{45}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6815 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{277}{644}\right)\) | \(e\left(\frac{433}{644}\right)\) | \(e\left(\frac{277}{322}\right)\) | \(e\left(\frac{33}{322}\right)\) | \(e\left(\frac{213}{322}\right)\) | \(e\left(\frac{187}{644}\right)\) | \(e\left(\frac{111}{322}\right)\) | \(e\left(\frac{569}{644}\right)\) | \(e\left(\frac{49}{92}\right)\) | \(e\left(\frac{15}{322}\right)\) |