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.cp
\(\chi_{5577}(230,\cdot)\) \(\chi_{5577}(263,\cdot)\) \(\chi_{5577}(659,\cdot)\) \(\chi_{5577}(692,\cdot)\) \(\chi_{5577}(1088,\cdot)\) \(\chi_{5577}(1121,\cdot)\) \(\chi_{5577}(1517,\cdot)\) \(\chi_{5577}(1550,\cdot)\) \(\chi_{5577}(1946,\cdot)\) \(\chi_{5577}(1979,\cdot)\) \(\chi_{5577}(2375,\cdot)\) \(\chi_{5577}(2408,\cdot)\) \(\chi_{5577}(2804,\cdot)\) \(\chi_{5577}(2837,\cdot)\) \(\chi_{5577}(3266,\cdot)\) \(\chi_{5577}(3662,\cdot)\) \(\chi_{5577}(4091,\cdot)\) \(\chi_{5577}(4124,\cdot)\) \(\chi_{5577}(4520,\cdot)\) \(\chi_{5577}(4553,\cdot)\) \(\chi_{5577}(4949,\cdot)\) \(\chi_{5577}(4982,\cdot)\) \(\chi_{5577}(5378,\cdot)\) \(\chi_{5577}(5411,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((3719,508,1354)\) → \((-1,-1,e\left(\frac{35}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 5577 }(230, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) |