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.ib
\(\chi_{7056}(85,\cdot)\) \(\chi_{7056}(421,\cdot)\) \(\chi_{7056}(925,\cdot)\) \(\chi_{7056}(1093,\cdot)\) \(\chi_{7056}(1429,\cdot)\) \(\chi_{7056}(1597,\cdot)\) \(\chi_{7056}(1933,\cdot)\) \(\chi_{7056}(2101,\cdot)\) \(\chi_{7056}(2437,\cdot)\) \(\chi_{7056}(2605,\cdot)\) \(\chi_{7056}(3109,\cdot)\) \(\chi_{7056}(3445,\cdot)\) \(\chi_{7056}(3613,\cdot)\) \(\chi_{7056}(3949,\cdot)\) \(\chi_{7056}(4453,\cdot)\) \(\chi_{7056}(4621,\cdot)\) \(\chi_{7056}(4957,\cdot)\) \(\chi_{7056}(5125,\cdot)\) \(\chi_{7056}(5461,\cdot)\) \(\chi_{7056}(5629,\cdot)\) \(\chi_{7056}(5965,\cdot)\) \(\chi_{7056}(6133,\cdot)\) \(\chi_{7056}(6637,\cdot)\) \(\chi_{7056}(6973,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6175,1765,785,4609)\) → \((1,i,e\left(\frac{2}{3}\right),e\left(\frac{1}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 7056 }(4453, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(-i\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{23}{28}\right)\) |