Basic properties
| Modulus: | \(4332\) | |
| Conductor: | \(4332\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | 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 4332.bk
\(\chi_{4332}(11,\cdot)\) \(\chi_{4332}(83,\cdot)\) \(\chi_{4332}(239,\cdot)\) \(\chi_{4332}(311,\cdot)\) \(\chi_{4332}(467,\cdot)\) \(\chi_{4332}(539,\cdot)\) \(\chi_{4332}(695,\cdot)\) \(\chi_{4332}(767,\cdot)\) \(\chi_{4332}(923,\cdot)\) \(\chi_{4332}(995,\cdot)\) \(\chi_{4332}(1223,\cdot)\) \(\chi_{4332}(1379,\cdot)\) \(\chi_{4332}(1451,\cdot)\) \(\chi_{4332}(1607,\cdot)\) \(\chi_{4332}(1679,\cdot)\) \(\chi_{4332}(1835,\cdot)\) \(\chi_{4332}(1907,\cdot)\) \(\chi_{4332}(2063,\cdot)\) \(\chi_{4332}(2135,\cdot)\) \(\chi_{4332}(2291,\cdot)\) \(\chi_{4332}(2363,\cdot)\) \(\chi_{4332}(2519,\cdot)\) \(\chi_{4332}(2591,\cdot)\) \(\chi_{4332}(2747,\cdot)\) \(\chi_{4332}(2975,\cdot)\) \(\chi_{4332}(3047,\cdot)\) \(\chi_{4332}(3203,\cdot)\) \(\chi_{4332}(3275,\cdot)\) \(\chi_{4332}(3431,\cdot)\) \(\chi_{4332}(3503,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2167,1445,3973)\) → \((-1,-1,e\left(\frac{17}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4332 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{114}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{65}{114}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{53}{57}\right)\) |