Basic properties
| Modulus: | \(8027\) | |
| Conductor: | \(8027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(638\) | 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 8027.bl
\(\chi_{8027}(17,\cdot)\) \(\chi_{8027}(37,\cdot)\) \(\chi_{8027}(60,\cdot)\) \(\chi_{8027}(80,\cdot)\) \(\chi_{8027}(86,\cdot)\) \(\chi_{8027}(125,\cdot)\) \(\chi_{8027}(178,\cdot)\) \(\chi_{8027}(181,\cdot)\) \(\chi_{8027}(283,\cdot)\) \(\chi_{8027}(318,\cdot)\) \(\chi_{8027}(366,\cdot)\) \(\chi_{8027}(385,\cdot)\) \(\chi_{8027}(424,\cdot)\) \(\chi_{8027}(429,\cdot)\) \(\chi_{8027}(435,\cdot)\) \(\chi_{8027}(470,\cdot)\) \(\chi_{8027}(474,\cdot)\) \(\chi_{8027}(488,\cdot)\) \(\chi_{8027}(527,\cdot)\) \(\chi_{8027}(572,\cdot)\) \(\chi_{8027}(580,\cdot)\) \(\chi_{8027}(631,\cdot)\) \(\chi_{8027}(632,\cdot)\) \(\chi_{8027}(734,\cdot)\) \(\chi_{8027}(743,\cdot)\) \(\chi_{8027}(746,\cdot)\) \(\chi_{8027}(773,\cdot)\) \(\chi_{8027}(778,\cdot)\) \(\chi_{8027}(819,\cdot)\) \(\chi_{8027}(879,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{319})$ |
| Fixed field: | Number field defined by a degree 638 polynomial (not computed) |
Values on generators
\((350,5935)\) → \((e\left(\frac{21}{22}\right),e\left(\frac{51}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8027 }(773, a) \) | \(-1\) | \(1\) | \(e\left(\frac{503}{638}\right)\) | \(e\left(\frac{43}{319}\right)\) | \(e\left(\frac{184}{319}\right)\) | \(e\left(\frac{37}{638}\right)\) | \(e\left(\frac{589}{638}\right)\) | \(e\left(\frac{16}{319}\right)\) | \(e\left(\frac{233}{638}\right)\) | \(e\left(\frac{86}{319}\right)\) | \(e\left(\frac{270}{319}\right)\) | \(e\left(\frac{18}{319}\right)\) |