Basic properties
Modulus: | \(8027\) | |
Conductor: | \(8027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(319\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.bi
\(\chi_{8027}(31,\cdot)\) \(\chi_{8027}(41,\cdot)\) \(\chi_{8027}(110,\cdot)\) \(\chi_{8027}(118,\cdot)\) \(\chi_{8027}(210,\cdot)\) \(\chi_{8027}(234,\cdot)\) \(\chi_{8027}(257,\cdot)\) \(\chi_{8027}(269,\cdot)\) \(\chi_{8027}(280,\cdot)\) \(\chi_{8027}(285,\cdot)\) \(\chi_{8027}(289,\cdot)\) \(\chi_{8027}(301,\cdot)\) \(\chi_{8027}(312,\cdot)\) \(\chi_{8027}(380,\cdot)\) \(\chi_{8027}(416,\cdot)\) \(\chi_{8027}(577,\cdot)\) \(\chi_{8027}(583,\cdot)\) \(\chi_{8027}(606,\cdot)\) \(\chi_{8027}(623,\cdot)\) \(\chi_{8027}(629,\cdot)\) \(\chi_{8027}(634,\cdot)\) \(\chi_{8027}(650,\cdot)\) \(\chi_{8027}(653,\cdot)\) \(\chi_{8027}(662,\cdot)\) \(\chi_{8027}(671,\cdot)\) \(\chi_{8027}(729,\cdot)\) \(\chi_{8027}(739,\cdot)\) \(\chi_{8027}(765,\cdot)\) \(\chi_{8027}(786,\cdot)\) \(\chi_{8027}(808,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{319})$ |
Fixed field: | Number field defined by a degree 319 polynomial (not computed) |
Values on generators
\((350,5935)\) → \((e\left(\frac{3}{11}\right),e\left(\frac{3}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8027 }(629, a) \) | \(1\) | \(1\) | \(e\left(\frac{207}{319}\right)\) | \(e\left(\frac{17}{319}\right)\) | \(e\left(\frac{95}{319}\right)\) | \(e\left(\frac{241}{319}\right)\) | \(e\left(\frac{224}{319}\right)\) | \(e\left(\frac{36}{319}\right)\) | \(e\left(\frac{302}{319}\right)\) | \(e\left(\frac{34}{319}\right)\) | \(e\left(\frac{129}{319}\right)\) | \(e\left(\frac{200}{319}\right)\) |