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.da
\(\chi_{6815}(2,\cdot)\) \(\chi_{6815}(8,\cdot)\) \(\chi_{6815}(18,\cdot)\) \(\chi_{6815}(32,\cdot)\) \(\chi_{6815}(68,\cdot)\) \(\chi_{6815}(72,\cdot)\) \(\chi_{6815}(143,\cdot)\) \(\chi_{6815}(147,\cdot)\) \(\chi_{6815}(153,\cdot)\) \(\chi_{6815}(177,\cdot)\) \(\chi_{6815}(213,\cdot)\) \(\chi_{6815}(222,\cdot)\) \(\chi_{6815}(272,\cdot)\) \(\chi_{6815}(288,\cdot)\) \(\chi_{6815}(298,\cdot)\) \(\chi_{6815}(363,\cdot)\) \(\chi_{6815}(403,\cdot)\) \(\chi_{6815}(427,\cdot)\) \(\chi_{6815}(437,\cdot)\) \(\chi_{6815}(507,\cdot)\) \(\chi_{6815}(512,\cdot)\) \(\chi_{6815}(572,\cdot)\) \(\chi_{6815}(578,\cdot)\) \(\chi_{6815}(582,\cdot)\) \(\chi_{6815}(588,\cdot)\) \(\chi_{6815}(598,\cdot)\) \(\chi_{6815}(648,\cdot)\) \(\chi_{6815}(653,\cdot)\) \(\chi_{6815}(707,\cdot)\) \(\chi_{6815}(717,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{644})$ |
| Fixed field: | Number field defined by a degree 644 polynomial (not computed) |
Values on generators
\((2727,2351,146)\) → \((-i,e\left(\frac{11}{28}\right),e\left(\frac{6}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6815 }(18, a) \) | \(1\) | \(1\) | \(e\left(\frac{135}{161}\right)\) | \(e\left(\frac{139}{322}\right)\) | \(e\left(\frac{109}{161}\right)\) | \(e\left(\frac{87}{322}\right)\) | \(e\left(\frac{523}{644}\right)\) | \(e\left(\frac{83}{161}\right)\) | \(e\left(\frac{139}{161}\right)\) | \(e\left(\frac{417}{644}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{123}{644}\right)\) |