Basic properties
| Modulus: | \(5577\) | |
| Conductor: | \(5577\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(130\) | 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.cu
\(\chi_{5577}(116,\cdot)\) \(\chi_{5577}(194,\cdot)\) \(\chi_{5577}(233,\cdot)\) \(\chi_{5577}(272,\cdot)\) \(\chi_{5577}(545,\cdot)\) \(\chi_{5577}(623,\cdot)\) \(\chi_{5577}(662,\cdot)\) \(\chi_{5577}(701,\cdot)\) \(\chi_{5577}(974,\cdot)\) \(\chi_{5577}(1052,\cdot)\) \(\chi_{5577}(1091,\cdot)\) \(\chi_{5577}(1130,\cdot)\) \(\chi_{5577}(1403,\cdot)\) \(\chi_{5577}(1481,\cdot)\) \(\chi_{5577}(1559,\cdot)\) \(\chi_{5577}(1832,\cdot)\) \(\chi_{5577}(1910,\cdot)\) \(\chi_{5577}(1949,\cdot)\) \(\chi_{5577}(1988,\cdot)\) \(\chi_{5577}(2261,\cdot)\) \(\chi_{5577}(2339,\cdot)\) \(\chi_{5577}(2378,\cdot)\) \(\chi_{5577}(2417,\cdot)\) \(\chi_{5577}(2690,\cdot)\) \(\chi_{5577}(2768,\cdot)\) \(\chi_{5577}(2807,\cdot)\) \(\chi_{5577}(2846,\cdot)\) \(\chi_{5577}(3119,\cdot)\) \(\chi_{5577}(3197,\cdot)\) \(\chi_{5577}(3236,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((3719,508,1354)\) → \((-1,e\left(\frac{9}{10}\right),e\left(\frac{7}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 5577 }(116, a) \) | \(1\) | \(1\) | \(e\left(\frac{87}{130}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{1}{130}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{101}{130}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{1}{5}\right)\) |