Basic properties
| Modulus: | \(4256\) | |
| Conductor: | \(4256\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | 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 4256.jv
\(\chi_{4256}(541,\cdot)\) \(\chi_{4256}(613,\cdot)\) \(\chi_{4256}(709,\cdot)\) \(\chi_{4256}(821,\cdot)\) \(\chi_{4256}(1005,\cdot)\) \(\chi_{4256}(1061,\cdot)\) \(\chi_{4256}(1605,\cdot)\) \(\chi_{4256}(1677,\cdot)\) \(\chi_{4256}(1773,\cdot)\) \(\chi_{4256}(1885,\cdot)\) \(\chi_{4256}(2069,\cdot)\) \(\chi_{4256}(2125,\cdot)\) \(\chi_{4256}(2669,\cdot)\) \(\chi_{4256}(2741,\cdot)\) \(\chi_{4256}(2837,\cdot)\) \(\chi_{4256}(2949,\cdot)\) \(\chi_{4256}(3133,\cdot)\) \(\chi_{4256}(3189,\cdot)\) \(\chi_{4256}(3733,\cdot)\) \(\chi_{4256}(3805,\cdot)\) \(\chi_{4256}(3901,\cdot)\) \(\chi_{4256}(4013,\cdot)\) \(\chi_{4256}(4197,\cdot)\) \(\chi_{4256}(4253,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((799,2661,3041,3137)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{1}{3}\right),e\left(\frac{7}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 4256 }(709, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{72}\right)\) | \(e\left(\frac{17}{72}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{55}{72}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{11}{24}\right)\) |