Basic properties
| Modulus: | \(4334\) | |
| Conductor: | \(2167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(98\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2167}(175,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4334.y
\(\chi_{4334}(175,\cdot)\) \(\chi_{4334}(285,\cdot)\) \(\chi_{4334}(329,\cdot)\) \(\chi_{4334}(351,\cdot)\) \(\chi_{4334}(417,\cdot)\) \(\chi_{4334}(527,\cdot)\) \(\chi_{4334}(615,\cdot)\) \(\chi_{4334}(681,\cdot)\) \(\chi_{4334}(747,\cdot)\) \(\chi_{4334}(923,\cdot)\) \(\chi_{4334}(1055,\cdot)\) \(\chi_{4334}(1143,\cdot)\) \(\chi_{4334}(1231,\cdot)\) \(\chi_{4334}(1407,\cdot)\) \(\chi_{4334}(1561,\cdot)\) \(\chi_{4334}(1605,\cdot)\) \(\chi_{4334}(1627,\cdot)\) \(\chi_{4334}(2023,\cdot)\) \(\chi_{4334}(2221,\cdot)\) \(\chi_{4334}(2243,\cdot)\) \(\chi_{4334}(2309,\cdot)\) \(\chi_{4334}(2551,\cdot)\) \(\chi_{4334}(2595,\cdot)\) \(\chi_{4334}(2661,\cdot)\) \(\chi_{4334}(2749,\cdot)\) \(\chi_{4334}(2859,\cdot)\) \(\chi_{4334}(3145,\cdot)\) \(\chi_{4334}(3189,\cdot)\) \(\chi_{4334}(3211,\cdot)\) \(\chi_{4334}(3233,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{49})$ |
| Fixed field: | Number field defined by a degree 98 polynomial |
Values on generators
\((1971,199)\) → \((-1,e\left(\frac{32}{49}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 4334 }(175, a) \) | \(-1\) | \(1\) | \(e\left(\frac{10}{49}\right)\) | \(e\left(\frac{6}{49}\right)\) | \(e\left(\frac{83}{98}\right)\) | \(e\left(\frac{20}{49}\right)\) | \(e\left(\frac{81}{98}\right)\) | \(e\left(\frac{16}{49}\right)\) | \(e\left(\frac{33}{98}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{5}{98}\right)\) | \(e\left(\frac{18}{49}\right)\) |