Basic properties
| Modulus: | \(5577\) | |
| Conductor: | \(5577\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(390\) | 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 5577.di
\(\chi_{5577}(29,\cdot)\) \(\chi_{5577}(35,\cdot)\) \(\chi_{5577}(68,\cdot)\) \(\chi_{5577}(74,\cdot)\) \(\chi_{5577}(107,\cdot)\) \(\chi_{5577}(347,\cdot)\) \(\chi_{5577}(380,\cdot)\) \(\chi_{5577}(425,\cdot)\) \(\chi_{5577}(458,\cdot)\) \(\chi_{5577}(464,\cdot)\) \(\chi_{5577}(497,\cdot)\) \(\chi_{5577}(503,\cdot)\) \(\chi_{5577}(536,\cdot)\) \(\chi_{5577}(776,\cdot)\) \(\chi_{5577}(809,\cdot)\) \(\chi_{5577}(854,\cdot)\) \(\chi_{5577}(887,\cdot)\) \(\chi_{5577}(893,\cdot)\) \(\chi_{5577}(926,\cdot)\) \(\chi_{5577}(932,\cdot)\) \(\chi_{5577}(965,\cdot)\) \(\chi_{5577}(1238,\cdot)\) \(\chi_{5577}(1283,\cdot)\) \(\chi_{5577}(1316,\cdot)\) \(\chi_{5577}(1322,\cdot)\) \(\chi_{5577}(1355,\cdot)\) \(\chi_{5577}(1361,\cdot)\) \(\chi_{5577}(1394,\cdot)\) \(\chi_{5577}(1634,\cdot)\) \(\chi_{5577}(1745,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{195})$ |
| Fixed field: | Number field defined by a degree 390 polynomial (not computed) |
Values on generators
\((3719,508,1354)\) → \((-1,e\left(\frac{7}{10}\right),e\left(\frac{10}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 5577 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{195}\right)\) | \(e\left(\frac{178}{195}\right)\) | \(e\left(\frac{79}{130}\right)\) | \(e\left(\frac{131}{390}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{103}{130}\right)\) | \(e\left(\frac{161}{195}\right)\) | \(e\left(\frac{46}{195}\right)\) | \(e\left(\frac{23}{30}\right)\) |