Basic properties
| Modulus: | \(195657\) | |
| Conductor: | \(195657\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(8470\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 195657.gx
\(\chi_{195657}(41,\cdot)\) \(\chi_{195657}(62,\cdot)\) \(\chi_{195657}(83,\cdot)\) \(\chi_{195657}(167,\cdot)\) \(\chi_{195657}(272,\cdot)\) \(\chi_{195657}(314,\cdot)\) \(\chi_{195657}(398,\cdot)\) \(\chi_{195657}(503,\cdot)\) \(\chi_{195657}(545,\cdot)\) \(\chi_{195657}(629,\cdot)\) \(\chi_{195657}(755,\cdot)\) \(\chi_{195657}(776,\cdot)\) \(\chi_{195657}(860,\cdot)\) \(\chi_{195657}(986,\cdot)\) \(\chi_{195657}(1007,\cdot)\) \(\chi_{195657}(1091,\cdot)\) \(\chi_{195657}(1196,\cdot)\) \(\chi_{195657}(1217,\cdot)\) \(\chi_{195657}(1238,\cdot)\) \(\chi_{195657}(1427,\cdot)\) \(\chi_{195657}(1448,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{4235})$ |
| Fixed field: | Number field defined by a degree 8470 polynomial (not computed) |
Values on generators
\((130439,179686,73207)\) → \((-1,e\left(\frac{11}{14}\right),e\left(\frac{967}{1210}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 195657 }(62, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3082}{4235}\right)\) | \(e\left(\frac{1929}{4235}\right)\) | \(e\left(\frac{1413}{4235}\right)\) | \(e\left(\frac{776}{4235}\right)\) | \(e\left(\frac{52}{847}\right)\) | \(e\left(\frac{3117}{4235}\right)\) | \(e\left(\frac{3858}{4235}\right)\) | \(e\left(\frac{1791}{8470}\right)\) | \(e\left(\frac{8}{605}\right)\) | \(e\left(\frac{3342}{4235}\right)\) |