Basic properties
| Modulus: | \(4225\) | |
| Conductor: | \(4225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(195\) | 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 4225.cm
\(\chi_{4225}(16,\cdot)\) \(\chi_{4225}(61,\cdot)\) \(\chi_{4225}(81,\cdot)\) \(\chi_{4225}(211,\cdot)\) \(\chi_{4225}(256,\cdot)\) \(\chi_{4225}(321,\cdot)\) \(\chi_{4225}(341,\cdot)\) \(\chi_{4225}(386,\cdot)\) \(\chi_{4225}(406,\cdot)\) \(\chi_{4225}(471,\cdot)\) \(\chi_{4225}(516,\cdot)\) \(\chi_{4225}(536,\cdot)\) \(\chi_{4225}(581,\cdot)\) \(\chi_{4225}(646,\cdot)\) \(\chi_{4225}(666,\cdot)\) \(\chi_{4225}(711,\cdot)\) \(\chi_{4225}(731,\cdot)\) \(\chi_{4225}(796,\cdot)\) \(\chi_{4225}(841,\cdot)\) \(\chi_{4225}(861,\cdot)\) \(\chi_{4225}(906,\cdot)\) \(\chi_{4225}(971,\cdot)\) \(\chi_{4225}(1056,\cdot)\) \(\chi_{4225}(1121,\cdot)\) \(\chi_{4225}(1166,\cdot)\) \(\chi_{4225}(1186,\cdot)\) \(\chi_{4225}(1231,\cdot)\) \(\chi_{4225}(1296,\cdot)\) \(\chi_{4225}(1316,\cdot)\) \(\chi_{4225}(1361,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{195})$ |
| Fixed field: | Number field defined by a degree 195 polynomial (not computed) |
Values on generators
\((677,3551)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{1}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 4225 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{44}{195}\right)\) | \(e\left(\frac{113}{195}\right)\) | \(e\left(\frac{88}{195}\right)\) | \(e\left(\frac{157}{195}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{31}{195}\right)\) | \(e\left(\frac{164}{195}\right)\) | \(e\left(\frac{2}{65}\right)\) | \(e\left(\frac{63}{65}\right)\) |