Basic properties
| Modulus: | \(4334\) | |
| Conductor: | \(197\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(196\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{197}(46,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4334.bd
\(\chi_{4334}(45,\cdot)\) \(\chi_{4334}(67,\cdot)\) \(\chi_{4334}(89,\cdot)\) \(\chi_{4334}(111,\cdot)\) \(\chi_{4334}(199,\cdot)\) \(\chi_{4334}(243,\cdot)\) \(\chi_{4334}(397,\cdot)\) \(\chi_{4334}(485,\cdot)\) \(\chi_{4334}(573,\cdot)\) \(\chi_{4334}(639,\cdot)\) \(\chi_{4334}(771,\cdot)\) \(\chi_{4334}(793,\cdot)\) \(\chi_{4334}(815,\cdot)\) \(\chi_{4334}(859,\cdot)\) \(\chi_{4334}(903,\cdot)\) \(\chi_{4334}(947,\cdot)\) \(\chi_{4334}(1035,\cdot)\) \(\chi_{4334}(1057,\cdot)\) \(\chi_{4334}(1079,\cdot)\) \(\chi_{4334}(1255,\cdot)\) \(\chi_{4334}(1277,\cdot)\) \(\chi_{4334}(1299,\cdot)\) \(\chi_{4334}(1321,\cdot)\) \(\chi_{4334}(1387,\cdot)\) \(\chi_{4334}(1409,\cdot)\) \(\chi_{4334}(1431,\cdot)\) \(\chi_{4334}(1453,\cdot)\) \(\chi_{4334}(1497,\cdot)\) \(\chi_{4334}(1519,\cdot)\) \(\chi_{4334}(1541,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{196})$ |
| Fixed field: | Number field defined by a degree 196 polynomial (not computed) |
Values on generators
\((1971,199)\) → \((1,e\left(\frac{121}{196}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 4334 }(243, a) \) | \(-1\) | \(1\) | \(e\left(\frac{145}{196}\right)\) | \(e\left(\frac{185}{196}\right)\) | \(e\left(\frac{13}{98}\right)\) | \(e\left(\frac{47}{98}\right)\) | \(e\left(\frac{85}{196}\right)\) | \(e\left(\frac{67}{98}\right)\) | \(e\left(\frac{31}{196}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{171}{196}\right)\) | \(e\left(\frac{4}{49}\right)\) |