Basic properties
| Modulus: | \(4235\) | |
| Conductor: | \(4235\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4235.cz
\(\chi_{4235}(23,\cdot)\) \(\chi_{4235}(67,\cdot)\) \(\chi_{4235}(177,\cdot)\) \(\chi_{4235}(298,\cdot)\) \(\chi_{4235}(408,\cdot)\) \(\chi_{4235}(452,\cdot)\) \(\chi_{4235}(562,\cdot)\) \(\chi_{4235}(683,\cdot)\) \(\chi_{4235}(793,\cdot)\) \(\chi_{4235}(837,\cdot)\) \(\chi_{4235}(947,\cdot)\) \(\chi_{4235}(1068,\cdot)\) \(\chi_{4235}(1178,\cdot)\) \(\chi_{4235}(1222,\cdot)\) \(\chi_{4235}(1563,\cdot)\) \(\chi_{4235}(1607,\cdot)\) \(\chi_{4235}(1717,\cdot)\) \(\chi_{4235}(1838,\cdot)\) \(\chi_{4235}(1948,\cdot)\) \(\chi_{4235}(1992,\cdot)\) \(\chi_{4235}(2102,\cdot)\) \(\chi_{4235}(2223,\cdot)\) \(\chi_{4235}(2333,\cdot)\) \(\chi_{4235}(2377,\cdot)\) \(\chi_{4235}(2487,\cdot)\) \(\chi_{4235}(2608,\cdot)\) \(\chi_{4235}(2718,\cdot)\) \(\chi_{4235}(2762,\cdot)\) \(\chi_{4235}(2872,\cdot)\) \(\chi_{4235}(2993,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2542,1816,2906)\) → \((-i,e\left(\frac{2}{3}\right),e\left(\frac{4}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 4235 }(1068, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{132}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{31}{132}\right)\) |