Basic properties
Modulus: | \(8027\) | |
Conductor: | \(349\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(174\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{349}(330,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8027.bg
\(\chi_{8027}(70,\cdot)\) \(\chi_{8027}(93,\cdot)\) \(\chi_{8027}(323,\cdot)\) \(\chi_{8027}(553,\cdot)\) \(\chi_{8027}(1151,\cdot)\) \(\chi_{8027}(1381,\cdot)\) \(\chi_{8027}(1565,\cdot)\) \(\chi_{8027}(1634,\cdot)\) \(\chi_{8027}(1726,\cdot)\) \(\chi_{8027}(1749,\cdot)\) \(\chi_{8027}(1818,\cdot)\) \(\chi_{8027}(1887,\cdot)\) \(\chi_{8027}(2071,\cdot)\) \(\chi_{8027}(2485,\cdot)\) \(\chi_{8027}(2600,\cdot)\) \(\chi_{8027}(2715,\cdot)\) \(\chi_{8027}(2922,\cdot)\) \(\chi_{8027}(2945,\cdot)\) \(\chi_{8027}(3060,\cdot)\) \(\chi_{8027}(3129,\cdot)\) \(\chi_{8027}(3198,\cdot)\) \(\chi_{8027}(3382,\cdot)\) \(\chi_{8027}(3405,\cdot)\) \(\chi_{8027}(3474,\cdot)\) \(\chi_{8027}(3566,\cdot)\) \(\chi_{8027}(3681,\cdot)\) \(\chi_{8027}(3704,\cdot)\) \(\chi_{8027}(3819,\cdot)\) \(\chi_{8027}(3842,\cdot)\) \(\chi_{8027}(3888,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{87})$ |
Fixed field: | Number field defined by a degree 174 polynomial (not computed) |
Values on generators
\((350,5935)\) → \((1,e\left(\frac{7}{174}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8027 }(1726, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{174}\right)\) | \(e\left(\frac{4}{87}\right)\) | \(e\left(\frac{7}{87}\right)\) | \(e\left(\frac{55}{87}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{121}{174}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{8}{87}\right)\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{49}{58}\right)\) |