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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8027.bm
\(\chi_{8027}(27,\cdot)\) \(\chi_{8027}(36,\cdot)\) \(\chi_{8027}(48,\cdot)\) \(\chi_{8027}(64,\cdot)\) \(\chi_{8027}(75,\cdot)\) \(\chi_{8027}(100,\cdot)\) \(\chi_{8027}(121,\cdot)\) \(\chi_{8027}(223,\cdot)\) \(\chi_{8027}(239,\cdot)\) \(\chi_{8027}(261,\cdot)\) \(\chi_{8027}(282,\cdot)\) \(\chi_{8027}(308,\cdot)\) \(\chi_{8027}(376,\cdot)\) \(\chi_{8027}(386,\cdot)\) \(\chi_{8027}(394,\cdot)\) \(\chi_{8027}(397,\cdot)\) \(\chi_{8027}(409,\cdot)\) \(\chi_{8027}(418,\cdot)\) \(\chi_{8027}(441,\cdot)\) \(\chi_{8027}(449,\cdot)\) \(\chi_{8027}(464,\cdot)\) \(\chi_{8027}(588,\cdot)\) \(\chi_{8027}(610,\cdot)\) \(\chi_{8027}(657,\cdot)\) \(\chi_{8027}(715,\cdot)\) \(\chi_{8027}(725,\cdot)\) \(\chi_{8027}(762,\cdot)\) \(\chi_{8027}(767,\cdot)\) \(\chi_{8027}(784,\cdot)\) \(\chi_{8027}(790,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{319})$ |
Fixed field: | Number field defined by a degree 638 polynomial (not computed) |
Values on generators
\((350,5935)\) → \((e\left(\frac{9}{11}\right),e\left(\frac{51}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8027 }(75, a) \) | \(1\) | \(1\) | \(e\left(\frac{329}{638}\right)\) | \(e\left(\frac{304}{319}\right)\) | \(e\left(\frac{10}{319}\right)\) | \(e\left(\frac{294}{319}\right)\) | \(e\left(\frac{299}{638}\right)\) | \(e\left(\frac{293}{638}\right)\) | \(e\left(\frac{349}{638}\right)\) | \(e\left(\frac{289}{319}\right)\) | \(e\left(\frac{279}{638}\right)\) | \(e\left(\frac{529}{638}\right)\) |