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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 195657.gz
\(\chi_{195657}(8,\cdot)\) \(\chi_{195657}(29,\cdot)\) \(\chi_{195657}(134,\cdot)\) \(\chi_{195657}(260,\cdot)\) \(\chi_{195657}(281,\cdot)\) \(\chi_{195657}(365,\cdot)\) \(\chi_{195657}(470,\cdot)\) \(\chi_{195657}(512,\cdot)\) \(\chi_{195657}(701,\cdot)\) \(\chi_{195657}(722,\cdot)\) \(\chi_{195657}(743,\cdot)\) \(\chi_{195657}(827,\cdot)\) \(\chi_{195657}(953,\cdot)\) \(\chi_{195657}(974,\cdot)\) \(\chi_{195657}(1058,\cdot)\) \(\chi_{195657}(1163,\cdot)\) \(\chi_{195657}(1184,\cdot)\) \(\chi_{195657}(1205,\cdot)\) \(\chi_{195657}(1289,\cdot)\) \(\chi_{195657}(1394,\cdot)\) \(\chi_{195657}(1415,\cdot)\) \(\chi_{195657}(1436,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{4235})$ |
| Fixed field: | Number field defined by a degree 8470 polynomial (not computed) |
Values on generators
\((130439,179686,73207)\) → \((-1,e\left(\frac{6}{7}\right),e\left(\frac{3}{1210}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 195657 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{3338}{4235}\right)\) | \(e\left(\frac{2441}{4235}\right)\) | \(e\left(\frac{6889}{8470}\right)\) | \(e\left(\frac{1544}{4235}\right)\) | \(e\left(\frac{1019}{1694}\right)\) | \(e\left(\frac{2231}{8470}\right)\) | \(e\left(\frac{647}{4235}\right)\) | \(e\left(\frac{1367}{4235}\right)\) | \(e\left(\frac{799}{1210}\right)\) | \(e\left(\frac{3301}{8470}\right)\) |