Basic properties
Modulus: | \(8027\) | |
Conductor: | \(8027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(957\) | 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.bo
\(\chi_{8027}(9,\cdot)\) \(\chi_{8027}(12,\cdot)\) \(\chi_{8027}(16,\cdot)\) \(\chi_{8027}(25,\cdot)\) \(\chi_{8027}(26,\cdot)\) \(\chi_{8027}(77,\cdot)\) \(\chi_{8027}(81,\cdot)\) \(\chi_{8027}(85,\cdot)\) \(\chi_{8027}(87,\cdot)\) \(\chi_{8027}(94,\cdot)\) \(\chi_{8027}(108,\cdot)\) \(\chi_{8027}(144,\cdot)\) \(\chi_{8027}(147,\cdot)\) \(\chi_{8027}(151,\cdot)\) \(\chi_{8027}(192,\cdot)\) \(\chi_{8027}(196,\cdot)\) \(\chi_{8027}(219,\cdot)\) \(\chi_{8027}(225,\cdot)\) \(\chi_{8027}(256,\cdot)\) \(\chi_{8027}(266,\cdot)\) \(\chi_{8027}(271,\cdot)\) \(\chi_{8027}(279,\cdot)\) \(\chi_{8027}(292,\cdot)\) \(\chi_{8027}(307,\cdot)\) \(\chi_{8027}(358,\cdot)\) \(\chi_{8027}(361,\cdot)\) \(\chi_{8027}(363,\cdot)\) \(\chi_{8027}(372,\cdot)\) \(\chi_{8027}(374,\cdot)\) \(\chi_{8027}(400,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{957})$ |
Fixed field: | Number field defined by a degree 957 polynomial (not computed) |
Values on generators
\((350,5935)\) → \((e\left(\frac{6}{11}\right),e\left(\frac{43}{87}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8027 }(87, a) \) | \(1\) | \(1\) | \(e\left(\frac{560}{957}\right)\) | \(e\left(\frac{553}{957}\right)\) | \(e\left(\frac{163}{957}\right)\) | \(e\left(\frac{709}{957}\right)\) | \(e\left(\frac{52}{319}\right)\) | \(e\left(\frac{458}{957}\right)\) | \(e\left(\frac{241}{319}\right)\) | \(e\left(\frac{149}{957}\right)\) | \(e\left(\frac{104}{319}\right)\) | \(e\left(\frac{92}{319}\right)\) |