Basic properties
| Modulus: | \(4025\) | |
| Conductor: | \(805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{805}(108,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4025.db
\(\chi_{4025}(82,\cdot)\) \(\chi_{4025}(243,\cdot)\) \(\chi_{4025}(257,\cdot)\) \(\chi_{4025}(418,\cdot)\) \(\chi_{4025}(432,\cdot)\) \(\chi_{4025}(593,\cdot)\) \(\chi_{4025}(607,\cdot)\) \(\chi_{4025}(768,\cdot)\) \(\chi_{4025}(857,\cdot)\) \(\chi_{4025}(1018,\cdot)\) \(\chi_{4025}(1382,\cdot)\) \(\chi_{4025}(1543,\cdot)\) \(\chi_{4025}(1557,\cdot)\) \(\chi_{4025}(1718,\cdot)\) \(\chi_{4025}(2007,\cdot)\) \(\chi_{4025}(2082,\cdot)\) \(\chi_{4025}(2168,\cdot)\) \(\chi_{4025}(2243,\cdot)\) \(\chi_{4025}(2257,\cdot)\) \(\chi_{4025}(2418,\cdot)\) \(\chi_{4025}(2532,\cdot)\) \(\chi_{4025}(2607,\cdot)\) \(\chi_{4025}(2693,\cdot)\) \(\chi_{4025}(2707,\cdot)\) \(\chi_{4025}(2768,\cdot)\) \(\chi_{4025}(2868,\cdot)\) \(\chi_{4025}(2957,\cdot)\) \(\chi_{4025}(3118,\cdot)\) \(\chi_{4025}(3132,\cdot)\) \(\chi_{4025}(3232,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((-i,e\left(\frac{1}{6}\right),e\left(\frac{4}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 4025 }(1718, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{31}{132}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{113}{132}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{8}{33}\right)\) |