Basic properties
Modulus: | \(8027\) | |
Conductor: | \(8027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(116\) | 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.bb
\(\chi_{8027}(321,\cdot)\) \(\chi_{8027}(482,\cdot)\) \(\chi_{8027}(528,\cdot)\) \(\chi_{8027}(597,\cdot)\) \(\chi_{8027}(1057,\cdot)\) \(\chi_{8027}(1126,\cdot)\) \(\chi_{8027}(1149,\cdot)\) \(\chi_{8027}(1402,\cdot)\) \(\chi_{8027}(1448,\cdot)\) \(\chi_{8027}(1494,\cdot)\) \(\chi_{8027}(1563,\cdot)\) \(\chi_{8027}(1724,\cdot)\) \(\chi_{8027}(1908,\cdot)\) \(\chi_{8027}(1931,\cdot)\) \(\chi_{8027}(2115,\cdot)\) \(\chi_{8027}(2276,\cdot)\) \(\chi_{8027}(2345,\cdot)\) \(\chi_{8027}(2391,\cdot)\) \(\chi_{8027}(2437,\cdot)\) \(\chi_{8027}(2690,\cdot)\) \(\chi_{8027}(2713,\cdot)\) \(\chi_{8027}(2782,\cdot)\) \(\chi_{8027}(3242,\cdot)\) \(\chi_{8027}(3311,\cdot)\) \(\chi_{8027}(3357,\cdot)\) \(\chi_{8027}(3518,\cdot)\) \(\chi_{8027}(3886,\cdot)\) \(\chi_{8027}(4001,\cdot)\) \(\chi_{8027}(4484,\cdot)\) \(\chi_{8027}(4576,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{116})$ |
Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((350,5935)\) → \((-1,e\left(\frac{81}{116}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8027 }(321, a) \) | \(1\) | \(1\) | \(e\left(\frac{81}{116}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{99}{116}\right)\) | \(e\left(\frac{33}{116}\right)\) | \(e\left(\frac{11}{116}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{53}{116}\right)\) | \(e\left(\frac{19}{116}\right)\) |