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.cw
\(\chi_{6815}(23,\cdot)\) \(\chi_{6815}(52,\cdot)\) \(\chi_{6815}(78,\cdot)\) \(\chi_{6815}(82,\cdot)\) \(\chi_{6815}(107,\cdot)\) \(\chi_{6815}(123,\cdot)\) \(\chi_{6815}(132,\cdot)\) \(\chi_{6815}(152,\cdot)\) \(\chi_{6815}(198,\cdot)\) \(\chi_{6815}(223,\cdot)\) \(\chi_{6815}(227,\cdot)\) \(\chi_{6815}(228,\cdot)\) \(\chi_{6815}(248,\cdot)\) \(\chi_{6815}(257,\cdot)\) \(\chi_{6815}(268,\cdot)\) \(\chi_{6815}(297,\cdot)\) \(\chi_{6815}(313,\cdot)\) \(\chi_{6815}(342,\cdot)\) \(\chi_{6815}(368,\cdot)\) \(\chi_{6815}(372,\cdot)\) \(\chi_{6815}(373,\cdot)\) \(\chi_{6815}(402,\cdot)\) \(\chi_{6815}(442,\cdot)\) \(\chi_{6815}(458,\cdot)\) \(\chi_{6815}(513,\cdot)\) \(\chi_{6815}(547,\cdot)\) \(\chi_{6815}(558,\cdot)\) \(\chi_{6815}(587,\cdot)\) \(\chi_{6815}(603,\cdot)\) \(\chi_{6815}(633,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{644})$ |
| Fixed field: | Number field defined by a degree 644 polynomial (not computed) |
Values on generators
\((2727,2351,146)\) → \((-i,e\left(\frac{6}{7}\right),e\left(\frac{3}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6815 }(78, a) \) | \(1\) | \(1\) | \(e\left(\frac{503}{644}\right)\) | \(e\left(\frac{541}{644}\right)\) | \(e\left(\frac{181}{322}\right)\) | \(e\left(\frac{100}{161}\right)\) | \(e\left(\frac{79}{644}\right)\) | \(e\left(\frac{221}{644}\right)\) | \(e\left(\frac{219}{322}\right)\) | \(e\left(\frac{285}{322}\right)\) | \(e\left(\frac{37}{92}\right)\) | \(e\left(\frac{255}{644}\right)\) |