Basic properties
Modulus: | \(7056\) | |
Conductor: | \(7056\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | 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 7056.jf
\(\chi_{7056}(139,\cdot)\) \(\chi_{7056}(475,\cdot)\) \(\chi_{7056}(643,\cdot)\) \(\chi_{7056}(1147,\cdot)\) \(\chi_{7056}(1483,\cdot)\) \(\chi_{7056}(1651,\cdot)\) \(\chi_{7056}(1987,\cdot)\) \(\chi_{7056}(2491,\cdot)\) \(\chi_{7056}(2659,\cdot)\) \(\chi_{7056}(2995,\cdot)\) \(\chi_{7056}(3163,\cdot)\) \(\chi_{7056}(3499,\cdot)\) \(\chi_{7056}(3667,\cdot)\) \(\chi_{7056}(4003,\cdot)\) \(\chi_{7056}(4171,\cdot)\) \(\chi_{7056}(4675,\cdot)\) \(\chi_{7056}(5011,\cdot)\) \(\chi_{7056}(5179,\cdot)\) \(\chi_{7056}(5515,\cdot)\) \(\chi_{7056}(6019,\cdot)\) \(\chi_{7056}(6187,\cdot)\) \(\chi_{7056}(6523,\cdot)\) \(\chi_{7056}(6691,\cdot)\) \(\chi_{7056}(7027,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6175,1765,785,4609)\) → \((-1,i,e\left(\frac{1}{3}\right),e\left(\frac{5}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 7056 }(139, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(-i\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{19}{28}\right)\) |