Basic properties
| Modulus: | \(5577\) | |
| Conductor: | \(5577\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | 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.cl
\(\chi_{5577}(296,\cdot)\) \(\chi_{5577}(329,\cdot)\) \(\chi_{5577}(725,\cdot)\) \(\chi_{5577}(758,\cdot)\) \(\chi_{5577}(1154,\cdot)\) \(\chi_{5577}(1187,\cdot)\) \(\chi_{5577}(1583,\cdot)\) \(\chi_{5577}(1616,\cdot)\) \(\chi_{5577}(2012,\cdot)\) \(\chi_{5577}(2045,\cdot)\) \(\chi_{5577}(2441,\cdot)\) \(\chi_{5577}(2474,\cdot)\) \(\chi_{5577}(2870,\cdot)\) \(\chi_{5577}(2903,\cdot)\) \(\chi_{5577}(3299,\cdot)\) \(\chi_{5577}(3332,\cdot)\) \(\chi_{5577}(3728,\cdot)\) \(\chi_{5577}(3761,\cdot)\) \(\chi_{5577}(4157,\cdot)\) \(\chi_{5577}(4190,\cdot)\) \(\chi_{5577}(4619,\cdot)\) \(\chi_{5577}(5015,\cdot)\) \(\chi_{5577}(5444,\cdot)\) \(\chi_{5577}(5477,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((3719,508,1354)\) → \((-1,-1,e\left(\frac{77}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 5577 }(296, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{2}{3}\right)\) |