Basic properties
| Modulus: | \(5577\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(100,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5577.ca
\(\chi_{5577}(100,\cdot)\) \(\chi_{5577}(133,\cdot)\) \(\chi_{5577}(562,\cdot)\) \(\chi_{5577}(958,\cdot)\) \(\chi_{5577}(1387,\cdot)\) \(\chi_{5577}(1420,\cdot)\) \(\chi_{5577}(1816,\cdot)\) \(\chi_{5577}(1849,\cdot)\) \(\chi_{5577}(2245,\cdot)\) \(\chi_{5577}(2278,\cdot)\) \(\chi_{5577}(2674,\cdot)\) \(\chi_{5577}(2707,\cdot)\) \(\chi_{5577}(3103,\cdot)\) \(\chi_{5577}(3136,\cdot)\) \(\chi_{5577}(3532,\cdot)\) \(\chi_{5577}(3565,\cdot)\) \(\chi_{5577}(3961,\cdot)\) \(\chi_{5577}(3994,\cdot)\) \(\chi_{5577}(4390,\cdot)\) \(\chi_{5577}(4423,\cdot)\) \(\chi_{5577}(4819,\cdot)\) \(\chi_{5577}(4852,\cdot)\) \(\chi_{5577}(5248,\cdot)\) \(\chi_{5577}(5281,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((3719,508,1354)\) → \((1,1,e\left(\frac{5}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 5577 }(100, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) |