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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6815.cy
\(\chi_{6815}(7,\cdot)\) \(\chi_{6815}(53,\cdot)\) \(\chi_{6815}(83,\cdot)\) \(\chi_{6815}(103,\cdot)\) \(\chi_{6815}(112,\cdot)\) \(\chi_{6815}(168,\cdot)\) \(\chi_{6815}(197,\cdot)\) \(\chi_{6815}(252,\cdot)\) \(\chi_{6815}(277,\cdot)\) \(\chi_{6815}(343,\cdot)\) \(\chi_{6815}(393,\cdot)\) \(\chi_{6815}(397,\cdot)\) \(\chi_{6815}(413,\cdot)\) \(\chi_{6815}(487,\cdot)\) \(\chi_{6815}(488,\cdot)\) \(\chi_{6815}(538,\cdot)\) \(\chi_{6815}(542,\cdot)\) \(\chi_{6815}(567,\cdot)\) \(\chi_{6815}(632,\cdot)\) \(\chi_{6815}(662,\cdot)\) \(\chi_{6815}(683,\cdot)\) \(\chi_{6815}(692,\cdot)\) \(\chi_{6815}(712,\cdot)\) \(\chi_{6815}(732,\cdot)\) \(\chi_{6815}(777,\cdot)\) \(\chi_{6815}(803,\cdot)\) \(\chi_{6815}(807,\cdot)\) \(\chi_{6815}(808,\cdot)\) \(\chi_{6815}(848,\cdot)\) \(\chi_{6815}(948,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{644})$ |
Fixed field: | Number field defined by a degree 644 polynomial (not computed) |
Values on generators
\((2727,2351,146)\) → \((i,e\left(\frac{3}{7}\right),e\left(\frac{16}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 6815 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{129}{644}\right)\) | \(e\left(\frac{519}{644}\right)\) | \(e\left(\frac{129}{322}\right)\) | \(e\left(\frac{1}{161}\right)\) | \(e\left(\frac{421}{644}\right)\) | \(e\left(\frac{387}{644}\right)\) | \(e\left(\frac{197}{322}\right)\) | \(e\left(\frac{94}{161}\right)\) | \(e\left(\frac{19}{92}\right)\) | \(e\left(\frac{75}{644}\right)\) |